STDWORK PRESENTATION ENG REV3-20040414-220704 CN

頁 次制定部門制定日期1.目的：運用統計方法對本公司的生產制程中相關的量測系統進行重復性(Repeatability)與再現性(Reproducibility)分析，將相關測量工作的變異性能控制在適當範圍，以保証量測結果的準確性和有效性。

2.範圍：本程序適用於進行量測的材料、半成品及最終產品的量測系統和儀器的統計變異分析。

3.權責：3.1品保課負責量測變異性分析管理的規劃及制定。

3.2品保課負責進行儀器的R&R分析(適用於材料驗收與制程管制的所有量測系統。

4.定義：4.1量測系統(Measurement System)：量測人員依據一定的操作程序，利用適當(特定)的量測儀器、軟体、設備等，取得被量測對象的量測特性結果的過程所構成的整個系統。

(用來對被測量之值的操作程序、量具、設備、軟体、人員等共同組成，亦可取得量測結果的整個過程)。

4.2量具(Gauge)：任何用於獲得量測結果之設施、裝備，通常用來指製造現場的設施(包括不合格的設施)。

4.3重復性(Repeatability)：同一作業者採用同一種量測儀器，經過多次測量同一制品的同一特性時，所量測值間的變異。

4.4再現性(Reproducibility)：不同的作業者，採用相同的量測儀器，經過多次測量同一制品的同一核 准修 訂 內 容修 訂 日 期符號1234修改號1/4李道俊品保課2004-03-12版本號A 文件名稱程序文件量測系統分析作業程序版 本審 查擬 案2/4頁 次特性，所量測的平均值間的變異。

5. 作業內容：5.1根據管制計劃表，在生產制程中、進料檢驗時和出貨檢驗時選擇合適的量測儀器作為量測變異分析的對象，並保証選用的儀器所量測的結果能夠反映出產品的品質特性。

5.2選擇生產線合適制程，保証對該制程的量測分析具有有效性。

5.3選擇合適之量測人員，保証其操作方法依據相同的操作規範，避免操作的不一致性。

5.4量測變異分析時機：5.4.1C.P中有規定時5.4.1.1量測修理再使用時5.4.2量具變動時5.4.3產品變更時5.5量測分析變異方法：5.5.1選擇三名量測人員分別測量10個相同的樣品，每人分別測量2次。

新视野大学英语第三版第四册第四单元教案XXX EnglishUnit 4: Achieving Sustainable EnvironmentalismXXX of this unit is to help students understand the main idea and structure of the text。

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IEEE Std 1028-1997IEEE Std 1028-1997 IEEE Standard for Software ReviewsIEEE Computer SocietySponsored by theSoftware Engineering Standards Committee4 March 1998SH94592IEEE Std 1028-1997 IEEE Standard for Software ReviewsSponsorSoftware Engineering Standards Committeeof theIEEE Computer SocietyApproved 9 December 1997IEEE Standards BoardAbstract:This standard defines five types of software reviews, together with procedures required for the execution of each review type. This standard is concerned only with the reviews; it does not define proce-dures for determining the necessity of a review, nor does it specify the disposition of the results of the review. Review types include management reviews, technical reviews, inspections, walk-throughs, and audits.Keywords: audit, inspection, review, walk-throughIEEE Standards documents are developed within the IEEE Societies and the Standards Coordinat-ing Committees of the IEEE Standards Board. Members of the committees serve voluntarily and without compensation. They are not necessarily members of the Institute. The standards developed within IEEE represent a consensus of the broad expertise on the subject within the Institute as well as those activities outside of IEEE that have expressed an interest in participating in the develop-ment of the standard.Use of an IEEE Standard is wholly voluntary. The existence of an IEEE Standard does not imply that there are no other ways to produce, test, measure, purchase, market, or provide other goods and services related to the scope of the IEEE Standard. Furthermore, the viewpoint expressed at the time a standard is approved and issued is subject to change brought about through developments in the state of the art and comments received from users of the standard. Every IEEE Standard is sub-jected to review at least every five years for revision or reaffirmation. When a document is more than five years old and has not been reaffirmed, it is reasonable to conclude that its contents, although still of some value, do not wholly reflect the present state of the art. Users are cautioned to check to determine that they have the latest edition of any IEEE Standard.Comments for revision of IEEE Standards are welcome from any interested party, regardless of membership affiliation with IEEE. Suggestions for changes in documents should be in the form of a proposed change of text, together with appropriate supporting comments.Interpretations: Occasionally questions may arise regarding the meaning of portions of standards as they relate to specific applications. When the need for interpretations is brought to the attention of IEEE, the Institute will initiate action to prepare appropriate responses. Since IEEE Standards rep-resent a consensus of all concerned interests, it is important to ensure that any interpretation has also received the concurrence of a balance of interests. For this reason, IEEE and the members of its societies and Standards Coordinating Committees are not able to provide an instant response to interpretation requests except in those cases where the matter has previously received formal consideration.Comments on standards and requests for interpretations should be addressed to:Secretary, IEEE Standards Board445 Hoes LaneP.O. Box 1331Piscataway, NJ 08855-1331USAAuthorization to photocopy portions of any individual standard for internal or personal use is granted by the Institute of Electrical and Electronics Engineers, Inc., provided that the appropriate fee is paid to Copyright Clearance Center. To arrange for payment of licensing fee, please contact Copyright Clearance Center, Customer Service, 222 Rosewood Drive, Danvers, MA 01923 USA; (508) 750-8400. Permission to photocopy portions of any individual standard for educational class-room use can also be obtained through the Copyright Clearance Center.Introduction(This introduction is not part of IEEE Std 1028-1997, IEEE Standard for Software Reviews.)This Introduction provides the user with the rationale and background of the reviews outlined in this stan-dard and their relationships to other IEEE standards.PurposeThis standard defines five types of software reviews, together with procedures required for the execution of each review type. This standard is concerned only with the reviews; it does not define procedures for deter-mining the necessity of a review, nor does it specify the disposition of the results of the review. Review types include management reviews, technical reviews, inspections, walk-throughs, and audits.This standard is meant to be used either in conjunction with other IEEE software engineering standards or as a stand-alone definition of software review procedures. In the latter case, local management must determine the events that precede and follow the actual software reviews.The need for reviews is described in several other IEEE standards, as well as standards prepared by other standards-writing organizations. IEEE Std 1028-1997 is meant to support these other standards. In particu-lar, reviews required by the following standards can be executed using the procedures described herein:—IEEE Std 730-1989 [B1]a—IEEE Std 828-1990 [B2]—IEEE Std 1012-1986 [B5]—IEEE Std 1058.1-1987 [B8]—IEEE Std 1074-1995 [B10]—IEEE Std 1219-1992 [B11]—IEEE Std 1220-1994 [B12]—IEEE Std 1228-1994 B13]—IEEE Std 1298-1992 (AS 3563.1-1991) [B14]—ISO/IEC 12207:1995 [B15]The use of IEEE Std 1044-1993 [B7] is encouraged as part of the reporting procedures for this standard. General application intentThis standard applies throughout the scope of any selected software life-cycle model and provides a standard against which software review plans can be prepared and assessed. Maximum benefit can be derived from this standard by planning for its application early in the project life cycle.This standard for software reviews was written in consideration of both the software and its system operating environment. It can be used where software is the total system entity or where it is part of a larger system. Care should be taken to integrate software review activities into any total system life-cycle planning; soft-ware reviews should exist in concert with hardware and computer system reviews to the benefit of the entire system.Reviews carried out in conformance with this standard may include both personnel internal to the project and customers or acquirers of the product, according to local procedures. Subcontractors may also be included if appropriate.a The numbers in brackets correspond to those of the bibliography in Annex C.The information obtained during software reviews (particularly inspections) may be of benefit for improving the user’s software acquisition, supply, development, operation, and maintenance processes. The use of review data for process improvement is not required by this standard, but their use is strongly encouraged. ConformanceConformance to this standard for a specific review type can be claimed when all mandatory actions (indi-cated by “shall”) are carried out as defined in this standard for the review type used. Claims for conformance should be phrased to indicate the review types used; for example, “conforming to IEEE Std 1028-1997 for inspections.”Development procedureThis standard was developed by the Software Engineering Review Working Group. The entire standards writing procedure was carried out via electronic mail. ParticipantsAt the time this standard was completed, the Software Engineering Review Working Group had the follow-ing membership:J. Dennis Lawrence, Chair Patricia A. Trellue, Technical Editor* Principal writers † Ballot resolutionFrank Ackerman Leo Beltracchi Ron BerlackAntonio Bertolino Richard J. Blauw Audrey Brewer James E. Cardow Hu Cheng Pat Daggett Ronald Dean†Janet Deeney*†Claude G. Diderich Leo G. Egan Martin Elliot Jon Fairclough*Karol Fruehauf Andrew Gabb Tom Gilb Jon Hagar John HarauzHans-Ludwig Hausen Michael Haux Herb Hecht Chuck Howell Laura Ippolito Rikkila JuhaGeorge X. Kambic Myron S. Karasik Stanley H. Levinson Michael S. Lines Jordan MatejceckArchibald McKinlay Warren L. Persons†Peter T. Poon Christian Reiser Helmut Sandmayr Hans Schaefer*Katsu Shintani Mel E. Smyre Julia Stesney Gina To†André Villas-Boas Dolores Wallace David A. Wheeler Ron YunTony ZawilskiThe following persons were on the balloting committee:Leo Beltracchi Mordechai Ben-Menachem H. Ronald Berlack Audrey C. BrewerAlan L. Bridges Kathleen L. BriggsDavid W. Burnett Edward R. Byrne Thomas G. Callaghan Stuart Ross Campbell James E. CardowJaya R. CarlLeslie ChambersKeith ChanJohn P. ChihorekS. V. ChiyyarathAntonio M. CicuTheo ClarkeSylvain Clermont Rosemary Coleman Darrell CookseyGeoff CozensThomas Crowley Gregory T. DaichHillary Davidson Bostjan K. Derganc Sanjay DewalMichael P. Dewalt Charles DrozRobert G. Ebenau Chrisof EbertWilliam Eventoff Jonathan H. Fairclough John W. FendrichJay ForsterKirby FortenberryBarry L. GarnerAdel N. Ghannam Hiranmay GhoshMarilyn Ginsberg-Finner M. Joel GittlemanJohn Garth Glynn Julio Gonzalez-SanzLewis GrayLawrence M. GuntherJon HagarJohn HarauzRob HarkerHerbert HechtWilliam HefleyManfred HeinMark HenleyUmesh P. HiriyannaiahJohn W. HorchFabrizio ImelioGeorge JackelenFrank V. JorgensenVladan V. JovanovicWilliam S. JunkGeorge X. KambicDavid W. KaneMyron S. KarasikRon S. KenettJudy KernerRobert J. KierzykMotti Y. KleinDwayne L. KnirkShaye KoenigJoan KundigThomas M. KuriharaJ. Dennis LawrenceRandal LeavittStanley H. LevinsonMichael LinesWilliam M. LivelyDieter LookDavid MaiborPhilip P. MakTomoo MatsubaraScott D. MatthewsPatrick McCraySue McGrathBret MichaelAlan MillerMillard Allen MobleyJames W. MooreMike OttewillMark PaulkDavid E. PeercyWarren L. PersonsJohn G. PhippenPeter T. PoonMargaretha W. PriceLawrence S. PrzybylskiKenneth R. PtackTerence P. RoutAndrew P. SageHelmut SandmayrStephen R. SchachHans SchaeferDavid J. SchultzGregory D. SchumacherRobert W. ShillatoKatsutoshi ShintaniCarl A. SingerJames M. SivakAlfred R. SorkowitzDonald W. SovaFred J. StraussMichael SurrattDouglas H. ThieleBooker ThomasCarmen J. TrammellPatricia A. TrellueRichard D. TuckerMargaret C. UpdikeTheodore J. UrbanowiczGlenn D. VenablesDolores WallaceDavid A. WheelerCamille S. White-PartainCharles D. WilsonPaul R. WorkWeider D. YuPeter F. ZollWhen the IEEE Standards Board approved this standard on 9 December 1997, it had the following membership:Donald C. Loughry, ChairRichard J. Holleman, Vice ChairAndrew G. Salem, Secretary*Member EmeritusAlso included are the following nonvoting IEEE Standards Board liaisons:Satish K. Aggarwal Alan H. Cookson Paula M. KeltyIEEE Standards Project EditorClyde R. CampStephen L. Diamond Harold E. EpsteinDonald C. Fleckenstein Jay Forster*Thomas F. Garrity Donald N. Heirman Jim IsaakBen C. Johnson Lowell Johnson Robert Kennelly E. G. "Al" Kiener Joseph L. Koepfinger*Stephen R. Lambert Lawrence V . McCall L. Bruce McClung Marco W. MigliaroLouis-François Pau Gerald H. Peterson John W. Pope Jose R. Ramos Ronald H. Reimer Ingo Rüsch John S. Ryan Chee Kiow TanHoward L. WolfmanContents1.Overview (1)1.1Purpose (1)1.2Scope (1)1.3Conformance (2)1.4Organization of standard (2)1.5Application of standard (3)2.References (4)3.Definitions (4)4.Management reviews (5)4.1Introduction (5)4.2Responsibilities (6)4.3Input (7)4.4Entry criteria (7)4.5Procedures (7)4.6Exit criteria (9)4.7Output (9)5.Technical reviews (9)5.1Introduction (9)5.2Responsibilities (10)5.3Input (10)5.4Entry criteria (11)5.5Procedures (11)5.6Exit criteria (13)5.7Output (13)6.Inspections (13)6.1Introduction (13)6.2Responsibilities (14)6.3Input (15)6.4Entry criteria (15)6.5Procedures (16)6.6Exit criteria (18)6.7Output (18)6.8Data collection recommendations (19)6.9Improvement (20)7.Walk-throughs (20)7.1Introduction (20)7.2Responsibilities (20)7.3Input (21)7.4Entry criteria (21)7.5Procedures (22)7.6Exit criteria (23)7.7Output (23)7.8Data collection recommendations (24)7.9Improvement (24)8.Audits (25)8.1Introduction (25)8.2Responsibilities (26)8.3Input (27)8.4Entry criteria (27)8.5Procedures (28)8.6Exit criteria (30)8.7Output (30)Annex A (informative) Relationship of this standard to the life cycle processes of other standards (32)Annex B (informative) Comparison of review types (35)Annex C (informative) Bibliography (37)IEEE Standard for Software Reviews1. Overview1.1 PurposeThe purpose of this standard is to define systematic reviews applicable to software acquisition, supply, devel-opment, operation, and maintenance. This standard describes how to carry out a review. Other standards or local management define the context within which a review is performed, and the use made of the results of the review. Software reviews can be used in support of the objectives of project management, system engi-neering (for example, functional allocation between hardware and software), verification and validation, configuration management, and quality assurance. Different types of reviews reflect differences in the goals of each review type. Systematic reviews are described by their defined procedures, scope, and objectives. 1.2 ScopeThis standard provides minimum acceptable requirements for systematic software reviews, where “system-atic” includes the following attributes:a)Team participationb)Documented results of the reviewc)Documented procedures for conducting the reviewReviews that do not meet the requirements of this standard are considered to be nonsystematic reviews. This standard is not intended to discourage or prohibit the use of nonsystematic reviews.The definitions, requirements, and procedures for the following five types of reviews are included within this standard:a)Management reviewsb)Technical reviewsc)Inspectionsd)Walk-throughse)AuditsThis standard does not establish the need to conduct specific reviews; that need is defined by other software engineering standards or by local procedures. This standard provides definitions, requirements, and proce-dures that are applicable to the reviews of software development products throughout the software life cycle.IEEEStd 1028-1997IEEE ST ANDARD FOR Users of this standard shall specify where and when this standard applies and any intended deviations from this standard.It is intended that this standard be used with other software engineering standards that determine the prod-ucts to be reviewed, the timing of reviews, and the necessity for reviews. This standard is closely aligned with IEEE Std 1012-1986 [B5],1 but can also be used with IEEE Std 1074-1995 [B10], IEEE Std 730-1989 [B1], ISO/IEC 12207:1995 [B15], and other standards. Use with other standards is described in Annex A. A useful model is to consider IEEE Std 1028-1997 as a subroutine to the other standards. Thus, if IEEE Std 1012-1986 were used to carry out the verification and validation process, the procedure in IEEE Std 1012-1986 could be followed until such time as instructions to carry out a specific review are encountered. At that point, IEEE Std 1028-1997 would be “called” to carry out the review, using the specific review type described herein. Once the review has been completed, IEEE Std 1012-1986 would be returned to for dispo-sition of the results of the review and any additional action required by IEEE Std 1012-1986.In this model, requirements and quality attributes for the software product are “parameter inputs” to the review and are imposed by the “caller.” When the review is finished, the review outputs are “returned” to the “caller” for action. Review outputs typically include anomaly lists and action item lists; the resolution of the anomalies and action items are the responsibility of the “caller.”1.3 ConformanceConformance to this standard for a specific review type can be claimed when all mandatory actions (indi-cated by “shall”) are carried out as defined in this standard for the review type used. Claims for conformance should be phrased to indicate the review types used; for example, “conforming to IEEE Std 1028-1997 for inspections.” The word “shall” is used to express a requirement, “should,” to express a recommendation, and “may,” to express alternative or optional methods of satisfying a requirement.1.4 Organization of standardClauses 4–8 of this standard provide guidance and descriptions for the five types of systematic reviews addressed by this standard. Each of these clauses contains the following information:a)Introduction. Describes the objectives of the systematic review and provides an overview of the sys-tematic review procedures.b)Responsibilities. Defines the roles and responsibilities needed for the systematic review.c)Input. Describes the requirements for input needed by the systematic review.d)Entry criteria. Describes the criteria to be met before the systematic review can begin, including1)Authorization2)Initiating evente)Procedures. Details the procedures for the systematic review, including1)Planning the review2)Overview of procedures3)Preparation4)Examination/evaluation/recording of results5)Rework/follow-upf)Exit criteria. Describes the criteria to be met before the systematic review can be considered com-plete.g)Output. Describes the minimum set of deliverables to be produced by the systematic review.1The numbers in brackets correspond to those of the bibliography in Annex C.IEEE SOFTWARE REVIEWS Std 1028-1997 1.5 Application of standardThe procedures and terminology defined in this standard apply to software acquisition, supply, development, operation, and maintenance processes requiring systematic reviews. Systematic reviews are performed on a software product as required by other standards or local procedures.The term “software product” is used in this standard in a very broad sense. Examples of software products include, but are not limited to, the following:a)Anomaly reportsb)Audit reportsc)Back up and recovery plansd)Build procedurese)Contingency plansf)Contractsg)Customer or user representative complaintsh)Disaster plansi)Hardware performance plansj)Inspection reportsk)Installation plansl)Installation proceduresm)Maintenance manualsn)Maintenance planso)Management review reportsp)Operations and user manualsq)Procurement and contracting methodsr)Progress reportss)Release notest)Reports and data (for example, review, audit, project status, anomaly reports, test data)u)Request for proposalv)Risk management plansw)Software configuration management plans (see IEEE Std 828-1990 [B2])x)Software design descriptions (see IEEE Std 1016-1987 [B6])y)Software project management plans (see IEEE Std 1058-1987 [B8])z)Software quality assurance plans (see IEEE Std 730-1989 [B1])aa)Software requirements specifications (see IEEE Std 830-1993 [B4])ab)Software safety plans (see IEEE 1228-1994 [B13])ac)Software test documentation (see IEEE Std 829-1983 [B3])ad)Software user documentation (see IEEE Std 1063-1987 [B9])ae)Software verification and validation plans (see IEEE Std 1012-1986 [B5])af)Source codeag)Standards, regulations, guidelines, and proceduresah)System build proceduresai)Technical review reportsaj)Vendor documentsak)Walk-through reportsThis standard permits reviews that are held by means other than physically meeting in a single location. Examples include telephone conferences, video conferences, and other means of group electronic communi-cation. In such cases the communication means should be defined in addition to the meeting places, and all other review requirements remain applicable.IEEEStd 1028-1997IEEE ST ANDARD FOR In order to make use of this standard to carry out a software review, first decide the objective of the review. Next, select an appropriate review type using the guidance in Annex B or a local procedure. Then follow the procedure described in the appropriate clause (4–8) of this standard.2. ReferencesThis standard shall be used in conjunction with the following publications. If the following publications are superseded by an approved revision, the revision shall apply. (Additional standards that may be used to pre-pare software products that are the subject of reviews are cited in a bibliography in Annex C.)IEEE Std 100-1996, The IEEE Standard Dictionary of Electrical and Electronics Terms, Sixth Edition. IEEE Std 610.12-1990, IEEE Standard Glossary of Software Engineering Terminology.3. DefinitionsFor purposes of this standard, the following terms and definitions apply. IEEE Std 610.12-19902 and IEEE Std 100-1996 should be consulted for terms not defined in this clause.Six of the terms given here are defined in other IEEE software engineering standards. The definition of the term “anomaly” is identical to that given in IEEE Std 1044-1993 [B7]. The terms “audit,” “inspection,”“review,” “software product,” and “walk-through” are all defined in IEEE Std 610.12-1990; however, some minor modifications have been made to those definitions to more closely match the content of this standard, as explained in the succeeding paragraph.IEEE Std 610.12-1990 uses different terms for the object of a review: audits and reviews are defined therein in terms of “work products,” inspections are defined in terms of “development products,” and walk-throughs are defined in terms of “segment of documentation or code.” “Work products” are not defined in IEEE Std 610.12-1990. Since “software product” is defined therein, and it is desirable to use a single term in this stan-dard, a change in terminology was made. Since software products being reviewed are not limited to those “designated for delivery to a user,” that phrase was dropped from the definition of “software product.” The definition of “inspection” has been changed considerably. No other changes to the definitions from IEEE Std 610.12-1990 were made.3.1 anomaly: Any condition that deviates from expectations based on requirements specifications, design documents, user documents, standards, etc., or from someone’s perceptions or experiences. Anomalies may be found during, but not limited to, the review, test, analysis, compilation, or use of software products or applicable documentation.3.2 audit: An independent examination of a software product, software process, or set of software processes to assess compliance with specifications, standards, contractual agreements, or other criteria.3.3 inspection: A visual examination of a software product to detect and identify software anomalies, including errors and deviations from standards and specifications. Inspections are peer examinations led by impartial facilitators who are trained in inspection techniques. Determination of remedial or investigative action for an anomaly is a mandatory element of a software inspection, although the solution should not be determined in the inspection meeting.2Information on references can be found in Clause 2.IEEE SOFTWARE REVIEWS Std 1028-1997 3.4 management review: A systematic evaluation of a software acquisition, supply, development, operation, or maintenance process performed by or on behalf of management that monitors progress, determines the status of plans and schedules, confirms requirements and their system allocation, or evaluates the effective-ness of management approaches used to achieve fitness for purpose.3.5 review: A process or meeting during which a software product is presented to project personnel, manag-ers, users, customers, user representatives, or other interested parties for comment or approval.3.6 software product: (A) A complete set of computer programs, procedures, and associated documentation and data. (B) One or more of the individual items in (A).3.7 technical review: A systematic evaluation of a software product by a team of qualified personnel that examines the suitability of the software product for its intended use and identifies discrepancies from speci-fications and standards. Technical reviews may also provide recommendations of alternatives and examina-tion of various alternatives.3.8 walk-through: A static analysis technique in which a designer or programmer leads members of the development team and other interested parties through a software product, and the participants ask questions and make comments about possible errors, violation of development standards, and other problems.4. Management reviews4.1 IntroductionThe purpose of a management review is to monitor progress, determine the status of plans and schedules, confirm requirements and their system allocation, or evaluate the effectiveness of management approaches used to achieve fitness for purpose. Management reviews support decisions about corrective actions, changes in the allocation of resources, or changes to the scope of the project.Management reviews are carried out by, or on behalf of, the management personnel having direct responsi-bility for the system. Management reviews identify consistency with and deviations from plans, or adequa-cies and inadequacies of management procedures. This examination may require more than one meeting. The examination need not address all aspects of the product.Examples of software products subject to management review include, but are not limited toa)Anomaly reportsb)Audit reportsc)Back-up and recovery plansd)Contingency planse)Customer or user representative complaintsf)Disaster plansg)Hardware performance plansh)Installation plansi)Maintenance plansj)Procurement and contracting methodsk)Progress reportsl)Risk management plansm)Software configuration management plansn)Software project management planso)Software quality assurance plansp)Software safety plansIEEEStd 1028-1997IEEE ST ANDARD FOR q)Software verification and validation plansr)Technical review reportss)Software product analysest)Verification and validation reports4.2 ResponsibilitiesManagement reviews are carried out by, or on behalf of, the management personnel having direct responsi-bility for the system. Technical knowledge may be necessary to conduct a successful management review. Management reviews shall be performed by the available personnel who are best qualified to evaluate the software product.The following roles shall be established for the management review:a)Decision makerb)Review leaderc)Recorderd)Management staffe)Technical staffThe following roles may also be established for the management review:f)Other team membersg)Customer or user representativeh)Individual participants may act in more than one role4.2.1 Decision makerThe decision maker is the person for whom the management review is conducted. The decision maker shall determine if the review objectives have been met.4.2.2 Review leaderThe review leader shall be responsible for administrative tasks pertaining to the review, shall be responsible for planning and preparation as described in 4.5.2 and 4.5.4, shall ensure that the review is conducted in an orderly manner and meets its objectives, and shall issue the review outputs as described in 4.7.4.2.3 RecorderThe recorder shall document anomalies, action items, decisions, and recommendations made by the review team.4.2.4 Management staffManagement staff assigned to carry out management reviews are responsible for active participation in the review. Managers responsible for the system as a whole have additional responsibilities as defined in 4.5.1.4.2.5 Technical staffThe technical staff shall provide the information necessary for the management staff to fulfill its responsibil-ities.。

Framework for the Preparation and Presentation of Financial StatementsThe IASB Framework was approved by the IASC Board in April 1989 for publication in July 1989, and adopted by the IASB in April 2001.© IASCF29Framework30© IASCF C ONTENTSparagraphs PREFACEINTRODUCTION1–11Purpose and status1–4Scope5–8Users and their information needs9–11THE OBJECTIVE OF FINANCIAL STATEMENTS12–21Financial position, performance and changes in financial position15–21Notes and supplementary schedules21UNDERLYING ASSUMPTIONS22–23Accrual basis22Going concern23QUALITATIVE CHARACTERISTICS OF FINANCIAL STATEMENTS24–46Understandability25Relevance26–30Materiality29–30Reliability31–38Faithful representation33–34Substance over form35Neutrality36Prudence37Completeness38Comparability39–42Constraints on relevant and reliable information43–45Timeliness43Balance between benefit and cost44Balance between qualitative characteristics45True and fair view/fair presentation46THE ELEMENTS OF FINANCIAL STATEMENTS47–81Financial position49–52Assets53–59Liabilities60–64Equity65–68Performance69–73Income74–77Expenses78–80Capital maintenance adjustments81FrameworkRECOGNITION OF THE ELEMENTS OF FINANCIAL STATEMENTS82–98 The probability of future economic benefit85 Reliability of measurement86–88 Recognition of assets89–90 Recognition of liabilities91 Recognition of income92–93 Recognition of expenses94–98 MEASUREMENT OF THE ELEMENTS OF FINANCIAL STATEMENTS99–101 CONCEPTS OF CAPITAL AND CAPITAL MAINTENANCE102–110 Concepts of capital102–103 Concepts of capital maintenance and the determination of profit104–110© IASCF31FrameworkPrefaceFinancial statements are prepared and presented for external users by many entities around the world. Although such financial statements may appear similar from country to country, there are differences which have probably been caused by a variety of social, economic and legal circumstances and by different countries having in mind the needs of different users of financial statements when setting national requirements.These different circumstances have led to the use of a variety of definitions of the elements of financial statements; that is, for example, assets, liabilities, equity, income and expenses. They have also resulted in the use of different criteria for the recognition of items in the financial statements and in a preference for different bases of measurement. The scope of the financial statements and the disclosures made in them have also been affected.The International Accounting Standards Committee (IASC) is committed to narrowing these differences by seeking to harmonise regulations, accounting standards and procedures relating to the preparation and presentation of financial statements. It believes that further harmonisation can best be pursued by focusing on financial statements that are prepared for the purpose of providing information that is useful in making economic decisions.The Board of IASC believes that financial statements prepared for this purpose meet the common needs of most users. This is because nearly all users are making economic decisions, for example, to:(a)decide when to buy, hold or sell an equity investment;(b)assess the stewardship or accountability of management;(c)assess the ability of the entity to pay and provide other benefits to its employees;(d)assess the security for amounts lent to the entity;(e)determine taxation policies;(f)determine distributable profits and dividends;(g)prepare and use national income statistics; or(h)regulate the activities of entities.The Board recognises, however, that governments, in particular, may specify different or additional requirements for their own purposes. These requirements should not, however, affect financial statements published for the benefit of other users unless they also meet the needs of those other users.Financial statements are most commonly prepared in accordance with an accounting model based on recoverable historical cost and the nominal financial capital maintenance concept. O ther models and concepts may be more appropriate in order to meet the objective of providing information that is useful for making economic decisions although there is presently no consensus for change. This Framework has been developed so that it is applicable to a range of accounting models and concepts of capital and capital maintenance.32© IASCFFramework IntroductionPurpose and status1This Framework sets out the concepts that underlie the preparation and presentation of financial statements for external users. The purpose of the Framework is to:(a)assist the Board of IASC in the development of future InternationalAccounting Standards and in its review of existing InternationalAccounting Standards;(b)assist the Board of IASC in promoting harmonisation of regulations,accounting standards and procedures relating to the presentation offinancial statements by providing a basis for reducing the number ofalternative accounting treatments permitted by International AccountingStandards;(c)assist national standard-setting bodies in developing national standards;(d)assist preparers of financial statements in applying InternationalAccounting Standards and in dealing with topics that have yet to form thesubject of an International Accounting Standard;(e)assist auditors in forming an opinion as to whether financial statementsconform with International Accounting Standards;(f)assist users of financial statements in interpreting the informationcontained in financial statements prepared in conformity withInternational Accounting Standards; and(g)provide those who are interested in the work of IASC with informationabout its approach to the formulation of International AccountingStandards.2This Framework is not an International Accounting Standard and hence does not define standards for any particular measurement or disclosure issue. Nothing in this Framework overrides any specific International Accounting Standard.3The Board of IASC recognises that in a limited number of cases there may be a conflict between the Framework and an International Accounting Standard.In those cases where there is a conflict, the requirements of the International Accounting Standard prevail over those of the Framework. As, however, the Board of IASC will be guided by the Framework in the development of future Standards and in its review of existing Standards, the number of cases of conflict between the Framework and International Accounting Standards will diminish through time.4The Framework will be revised from time to time on the basis of the Board’s experience of working with it.© IASCF33FrameworkScope5The Framework deals with:(a)the objective of financial statements;(b)the qualitative characteristics that determine the usefulness ofinformation in financial statements;(c)the definition, recognition and measurement of the elements from whichfinancial statements are constructed; and(d)concepts of capital and capital maintenance.6The Framework is concerned with general purpose financial statements (hereafter referred to as ‘financial statements’) including consolidated financial statements.Such financial statements are prepared and presented at least annually and are directed toward the common information needs of a wide range of users. Some of these users may require, and have the power to obtain, information in addition to that contained in the financial statements. Many users, however, have to rely on the financial statements as their major source of financial information and such financial statements should, therefore, be prepared and presented with their needs in view. Special purpose financial reports, for example, prospectuses and computations prepared for taxation purposes, are outside the scope of this Framework. Nevertheless, the Framework may be applied in the preparation of such special purpose reports where their requirements permit.7Financial statements form part of the process of financial reporting. A complete set of financial statements normally includes a balance sheet, an income statement, a statement of changes in financial position (which may be presented in a variety of ways, for example, as a statement of cash flows or a statement of funds flow), and those notes and other statements and explanatory material that are an integral part of the financial statements. They may also include supplementary schedules and information based on or derived from, and expected to be read with, such statements. Such schedules and supplementary information may deal, for example, with financial information about industrial and geographical segments and disclosures about the effects of changing prices.Financial statements do not, however, include such items as reports by directors, statements by the chairman, discussion and analysis by management and similar items that may be included in a financial or annual report.8The Framework applies to the financial statements of all commercial, industrial and business reporting entities, whether in the public or the private sectors.A reporting entity is an entity for which there are users who rely on the financialstatements as their major source of financial information about the entity.Users and their information needs9The users of financial statements include present and potential investors, employees, lenders, suppliers and other trade creditors, customers, governments and their agencies and the public. They use financial statements in order to 34© IASCFFramework satisfy some of their different needs for information. These needs include the following:(a)Investors. The providers of risk capital and their advisers are concerned withthe risk inherent in, and return provided by, their investments. They needinformation to help them determine whether they should buy, hold or sell.Shareholders are also interested in information which enables them toassess the ability of the entity to pay dividends.(b)Employees. Employees and their representative groups are interested ininformation about the stability and profitability of their employers.They are also interested in information which enables them to assess theability of the entity to provide remuneration, retirement benefits andemployment opportunities.(c)Lenders. Lenders are interested in information that enables them todetermine whether their loans, and the interest attaching to them, will bepaid when due.(d)Suppliers and other trade creditors. Suppliers and other creditors are interestedin information that enables them to determine whether amounts owing tothem will be paid when due. Trade creditors are likely to be interested inan entity over a shorter period than lenders unless they are dependentupon the continuation of the entity as a major customer.(e)Customers. Customers have an interest in information about thecontinuance of an entity, especially when they have a long-terminvolvement with, or are dependent on, the entity.(f)Governments and th eir agencies. Governments and their agencies areinterested in the allocation of resources and, therefore, the activities ofentities. They also require information in order to regulate the activities ofentities, determine taxation policies and as the basis for national incomeand similar statistics.(g)Public. Entities affect members of the public in a variety of ways.For example, entities may make a substantial contribution to the localeconomy in many ways including the number of people they employ andtheir patronage of local suppliers. Financial statements may assist thepublic by providing information about the trends and recent developmentsin the prosperity of the entity and the range of its activities.10While all of the information needs of these users cannot be met by financial statements, there are needs which are common to all users. As investors are providers of risk capital to the entity, the provision of financial statements that meet their needs will also meet most of the needs of other users that financial statements can satisfy.11The management of an entity has the primary responsibility for the preparation and presentation of the financial statements of the entity. Management is also interested in the information contained in the financial statements even though it has access to additional management and financial information that helps it carry out its planning, decision-making and control responsibilities.Management has the ability to determine the form and content of such additional© IASCF35Frameworkinformation in order to meet its own needs. The reporting of such information, however, is beyond the scope of this Framework. Nevertheless, published financial statements are based on the information used by management about the financial position, performance and changes in financial position of the entity. The objective of financial statements12The objective of financial statements is to provide information about the financial position, performance and changes in financial position of an entity that is useful to a wide range of users in making economic decisions.13Financial statements prepared for this purpose meet the common needs of most users. However, financial statements do not provide all the information that users may need to make economic decisions since they largely portray the financial effects of past events and do not necessarily provide non-financial information.14Financial statements also show the results of the stewardship of management, or the accountability of management for the resources entrusted to it. Those users who wish to assess the stewardship or accountability of management do so in order that they may make economic decisions; these decisions may include, for example, whether to hold or sell their investment in the entity or whether to reappoint or replace the management.Financial position, performance and changes infinancial position15The economic decisions that are taken by users of financial statements require an evaluation of the ability of an entity to generate cash and cash equivalents and of the timing and certainty of their generation. This ability ultimately determines, for example, the capacity of an entity to pay its employees and suppliers, meet interest payments, repay loans and make distributions to its owners. Users are better able to evaluate this ability to generate cash and cash equivalents if they are provided with information that focuses on the financial position, performance and changes in financial position of an entity.16The financial position of an entity is affected by the economic resources it controls, its financial structure, its liquidity and solvency, and its capacity to adapt to changes in the environment in which it operates. Information about the economic resources controlled by the entity and its capacity in the past to modify these resources is useful in predicting the ability of the entity to generate cash and cash equivalents in the future. Information about financial structure is useful in predicting future borrowing needs and how future profits and cash flows will be distributed among those with an interest in the entity; it is also useful in predicting how successful the entity is likely to be in raising further finance. Information about liquidity and solvency is useful in predicting the ability of the entity to meet its financial commitments as they fall due. Liquidity refers to the availability of cash in the near future after taking account of financial commitments over this period. Solvency refers to the availability of cash over the longer term to meet financial commitments as they fall due.36© IASCFFramework 17Information about the performance of an entity, in particular its profitability, is required in order to assess potential changes in the economic resources that it is likely to control in the future. Information about variability of performance is important in this respect. Information about performance is useful in predicting the capacity of the entity to generate cash flows from its existing resource base.It is also useful in forming judgements about the effectiveness with which the entity might employ additional resources.18Information concerning changes in the financial position of an entity is useful in order to assess its investing, financing and operating activities during the reporting period. This information is useful in providing the user with a basis to assess the ability of the entity to generate cash and cash equivalents and the needs of the entity to utilise those cash flows. In constructing a statement of changes in financial position, funds can be defined in various ways, such as all financial resources, working capital, liquid assets or cash. No attempt is made in this Framework to specify a definition of funds.19Information about financial position is primarily provided in a balance rmation about performance is primarily provided in an income statement. Information about changes in financial position is provided in the financial statements by means of a separate statement.20The component parts of the financial statements interrelate because they reflect different aspects of the same transactions or other events. Although each statement provides information that is different from the others, none is likely to serve only a single purpose or provide all the information necessary for particular needs of users. For example, an income statement provides an incomplete picture of performance unless it is used in conjunction with the balance sheet and the statement of changes in financial position.Notes and supplementary schedules21The financial statements also contain notes and supplementary schedules and other information. For example, they may contain additional information that is relevant to the needs of users about the items in the balance sheet and income statement. They may include disclosures about the risks and uncertainties affecting the entity and any resources and obligations not recognised in the balance sheet (such as mineral reserves). Information about geographical and industry segments and the effect on the entity of changing prices may also be provided in the form of supplementary information.Underlying assumptionsAccrual basis22In order to meet their objectives, financial statements are prepared on the accrual basis of accounting. Under this basis, the effects of transactions and other events are recognised when they occur (and not as cash or its equivalent is received or paid) and they are recorded in the accounting records and reported in the financial statements of the periods to which they relate. Financial statements prepared on the accrual basis inform users not only of past transactions involving© IASCF37Frameworkthe payment and receipt of cash but also of obligations to pay cash in the future and of resources that represent cash to be received in the future. Hence, they provide the type of information about past transactions and other events that is most useful to users in making economic decisions.Going concern23The financial statements are normally prepared on the assumption that an entity is a going concern and will continue in operation for the foreseeable future.Hence, it is assumed that the entity has neither the intention nor the need to liquidate or curtail materially the scale of its operations; if such an intention or need exists, the financial statements may have to be prepared on a different basis and, if so, the basis used is disclosed.Qualitative characteristics of financial statements24Qualitative characteristics are the attributes that make the information provided in financial statements useful to users. The four principal qualitative characteristics are understandability, relevance, reliability and comparability.Understandability25An essential quality of the information provided in financial statements is that it is readily understandable by users. For this purpose, users are assumed to have a reasonable knowledge of business and economic activities and accounting and a willingness to study the information with reasonable diligence. However, information about complex matters that should be included in the financial statements because of its relevance to the economic decision-making needs of users should not be excluded merely on the grounds that it may be too difficult for certain users to understand.Relevance26To be useful, information must be relevant to the decision-making needs of users.Information has the quality of relevance when it influences the economic decisions of users by helping them evaluate past, present or future events or confirming, or correcting, their past evaluations.27The predictive and confirmatory roles of information are interrelated.For example, information about the current level and structure of asset holdings has value to users when they endeavour to predict the ability of the entity to take advantage of opportunities and its ability to react to adverse situations. The same information plays a confirmatory role in respect of past predictions about, for example, the way in which the entity would be structured or the outcome of planned operations.28Information about financial position and past performance is frequently used as the basis for predicting future financial position and performance and other matters in which users are directly interested, such as dividend and wage payments, security price movements and the ability of the entity to meet its commitments as they fall due. To have predictive value, information need not be in the form of an explicit forecast. The ability to make predictions from financial 38© IASCFFramework statements is enhanced, however, by the manner in which information on past transactions and events is displayed. For example, the predictive value of the income statement is enhanced if unusual, abnormal and infrequent items of income or expense are separately disclosed.Materiality29The relevance of information is affected by its nature and materiality. In some cases, the nature of information alone is sufficient to determine its relevance.For example, the reporting of a new segment may affect the assessment of the risks and opportunities facing the entity irrespective of the materiality of the results achieved by the new segment in the reporting period. In other cases, both the nature and materiality are important, for example, the amounts of inventories held in each of the main categories that are appropriate to the business.30Information is material if its omission or misstatement could influence the economic decisions of users taken on the basis of the financial statements.Materiality depends on the size of the item or error judged in the particular circumstances of its omission or misstatement. Thus, materiality provides a threshold or cut-off point rather than being a primary qualitative characteristic which information must have if it is to be useful.Reliability31To be useful, information must also be reliable. Information has the quality of reliability when it is free from material error and bias and can be depended upon by users to represent faithfully that which it either purports to represent or could reasonably be expected to represent.32Information may be relevant but so unreliable in nature or representation that its recognition may be potentially misleading. For example, if the validity and amount of a claim for damages under a legal action are disputed, it may be inappropriate for the entity to recognise the full amount of the claim in the balance sheet, although it may be appropriate to disclose the amount and circumstances of the claim.Faithful representation33To be reliable, information must represent faithfully the transactions and other events it either purports to represent or could reasonably be expected to represent. Thus, for example, a balance sheet should represent faithfully the transactions and other events that result in assets, liabilities and equity of the entity at the reporting date which meet the recognition criteria.34Most financial information is subject to some risk of being less than a faithful representation of that which it purports to portray. This is not due to bias, but rather to inherent difficulties either in identifying the transactions and other events to be measured or in devising and applying measurement and presentation techniques that can convey messages that correspond with those transactions and events. In certain cases, the measurement of the financial effects of items could be so uncertain that entities generally would not recognise© IASCF39Frameworkthem in the financial statements; for example, although most entities generate goodwill internally over time, it is usually difficult to identify or measure that goodwill reliably. In other cases, however, it may be relevant to recognise items and to disclose the risk of error surrounding their recognition and measurement.Substance over form35If information is to represent faithfully the transactions and other events that it purports to represent, it is necessary that they are accounted for and presented in accordance with their substance and economic reality and not merely their legal form. The substance of transactions or other events is not always consistent with that which is apparent from their legal or contrived form. For example, an entity may dispose of an asset to another party in such a way that the documentation purports to pass legal ownership to that party; nevertheless, agreements may exist that ensure that the entity continues to enjoy the future economic benefits embodied in the asset. In such circumstances, the reporting of a sale would not represent faithfully the transaction entered into (if indeed there was a transaction).Neutrality36To be reliable, the information contained in financial statements must be neutral, that is, free from bias. Financial statements are not neutral if, by the selection or presentation of information, they influence the making of a decision or judgement in order to achieve a predetermined result or outcome.Prudence37The preparers of financial statements do, however, have to contend with the uncertainties that inevitably surround many events and circumstances, such as the collectability of doubtful receivables, the probable useful life of plant and equipment and the number of warranty claims that may occur. Such uncertainties are recognised by the disclosure of their nature and extent and by the exercise of prudence in the preparation of the financial statements. Prudence is the inclusion of a degree of caution in the exercise of the judgements needed in making the estimates required under conditions of uncertainty, such that assets or income are not overstated and liabilities or expenses are not understated.However, the exercise of prudence does not allow, for example, the creation of hidden reserves or excessive provisions, the deliberate understatement of assets or income, or the deliberate overstatement of liabilities or expenses, because the financial statements would not be neutral and, therefore, not have the quality of reliability.Completeness38To be reliable, the information in financial statements must be complete within the bounds of materiality and cost. An omission can cause information to be false or misleading and thus unreliable and deficient in terms of its relevance.40© IASCF。

STUDENT GUIDE BROADENING HORIZONSCORPORATE LEARNING COURSE“TEAMBUILDING” BLOCKSEMINAR 3.1SEMINAR OVERVIEWSCOPECAP is an organization wherein each person has an individual tasking that is paramount in achieving the corporate missions for America. Each person in interconnected with another person or group. This seminar provides students with an understanding of personal goals as a member of CAP, as well as the structure and functions of each corporate entity, and how each person plays a part in the team concept. This seminar is designed to be an open, yet guided, discussion to gain a clearer overview of the total organizational structure and the corporate responsibility of each member.COURSE OBJECTIVETo develop an effective contributor in a team environment.BLOCK OBJECTIVETo develop a knowledgeable corporate citizen who can effectively contribute in a team environment.LESSON OBJECTIVES1.To comprehend how local perspectives can be impacted by corporate responsibilities and authority.2.To define “personal interest” in a Civil Air Patrol context.3.To define “corporate responsibility” in a Civil Air Patrol context.INTRODUCTION and OVERVIEWThis lesson introduces the second block of instruction for the course. The focus will be on the need for team building skills and their use in the corporate environment of CAP.DURATIONMAIN POINT #1— As a leader in CAP, personal interest needs to transition to corporate responsibility. DESIRED LEARNING OUTCOME #1Define “personal interest”1. “Personal interest” is the motivations, needs, and goals that the individual desires for Civil AirPatrol to meet in their lives.2. What personal interests do you wish to fulfill as a member of CAP?a. Reasons for joining CAP?_________________________________________________________________________________b.Needs you wish to meet?________________________________________________________________________________c.Goals you hope to attain?_________________________________________________________________________________d.Other personal interests you wish to fulfill?_________________________________________________________________________________ DESIRED LEARNING OUTCOME #2Define “corporate responsibility”1. “Corporate responsibility” is the acceptance of the roles in CAP that maintain the organizational standards, goals, missions and values. This is experienced from the squadron level through the national level of service.2. Examples of how the needs and goals of individuals can be fulfilled in CAP:a.______________________________________________________________________________b.______________________________________________________________________________c.______________________________________________________________________________d.______________________________________________________________________________3. Identify elements of the corporate responsibility.a________________________________________________________________________________ b________________________________________________________________________________ c________________________________________________________________________________MAIN POINT #2Unit and Wing perspectives align and contrast on routine functions and clarityt.DESIRED LEARNING OUTCOME #1Understand, via a panel discussion, the various perspectives and functions of units and wings in order to work well within both entities.1. List the structure and functions of each area below as gleaned from the panel discussion.a. Finance_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________b. Logistics_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________c. Aerospace Education_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ d. Safety_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ e. Operations_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ f. Command_________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________g. Other: _________________________________________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________h. Other: _________________________________________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________DESIRED LEARNING OUTCOME #2List questions and answers of pertinence to you.1.____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2.____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3.____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________CONCLUSIONSUMMARY1.Each person has personal obligations to fulfill in becoming a member of the organization and these needto be recognized and acted upon during membership performance and activity.2.Each person has the right to be informed of various corporate responsibilities available to become abeneficial part of a team. After selection of personal corporate responsibilities for ownership, each person has the obligation to fulfill these to the best of his/her ability.3.Each person has the right to be informed of the unit, wing, region, and national structure and functions tobe able to perform at a level of excellence while a member of CAP working within all of these entities. REMOTIVATION & CLOSEAs a volunteer organization, CAP needs each member to set personal goals for self-fulfillment within the organization. Just as important, each member needs to be given the opportunity to explore and locate the area(s) in which he/she can be most productive to the team. Each member has the responsibility, then, to learn his/her role and do his/her personal best to fulfill that responsibility with the best interest of the organization always at the forefront.。

(Revision ofIEEE Std 344-1987)---` , , ` , ` , , ` , , ` -` -, ` , ` , , ` --IEEE Std 344™-2004(Revision ofIEEE Std 344-1987) --`,,`,`,-`-`,,`,,`,`,,`---IEEE Recommended Practice for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating StationsSponsorNuclear Power Engineering Committeeof theIEEE Power Engineering SocietyApproved 8 December 2004IEEE-SA Standards BoardAbstract: Recommended practices are provided for establishing procedures that will yield data to demonstrate that the Class 1E equipment can meet its performance requirements during and/or fol-lowing one safe shutdown earthquake event preceded by a number of operating basis earthquake events. This recommended practice may be used to establish tests, analyses, or experienced-based evaluations that will yield data to demonstrate Class 1E equipment performance claims or to evaluate and verify performance of devices and assemblies as part of an overall qualification effort. Common methods currently in use for seismic qualification by test are presented. Two approaches to seismic analysis are described, one based on dynamic analysis and the other on static coefficient analysis. Two approaches to experienced-based seismic evaluation are described, one based on earthquake experience and the other based on test experience.Keywords: Class 1E, earthquake, earthquake experience, equipment qualification, inclusion rules, nuclear, operating basis earthquake, prohibited features, qualification methods, required response spectrum, response spectra, safe shutdown earthquake, safety function, seismic, seismic analysis, test response spectrum, test experience, type testingIEEE Standards documents are developed within the IEEE Societies and the Standards Coordinating Commit-tees of the IEEE Standards Association (IEEE-SA) Standards Board. The IEEE develops its standards through a consensus development process, approved by the American National Standards Institute, which brings together volunteers representing varied viewpoints and interests to achieve the final product. Volunteers are not necessar-ily members of the Institute and serve without compensation. While the IEEE administers the process and estab-lishes rules to promote fairness in the consensus development process, the IEEE does not independently evaluate, test, or verify the accuracy of any of the information contained in its standards.Use of an IEEE Standard is wholly voluntary. The IEEE disclaims liability for any personal injury, property or other damage, of any nature whatsoever, whether special, indirect, consequential, or compensatory, directly or indirectly resulting from the publication, use of, or reliance upon this, or any other IEEE Standard document. The IEEE does not warrant or represent the accuracy or content of the material contained herein, and expressly disclaims any express or implied warranty, including any implied warranty of merchantability or fitness for a spe-cific purpose, or that the use of the material contained herein is free from patent infringement. IEEE Standards documents are supplied “AS IS.”The existence of an IEEE Standard does not imply that there are no other ways to produce, test, measure, pur-chase, market, or provide other goods and services related to the scope of the IEEE Standard. Furthermore, the viewpoint expressed at the time a standard is approved and issued is subject to change brought about through developments in the state of the art and comments received from users of the standard. Every IEEE Standard is subjected to review at least every five years for revision or reaffirmation. When a document is more than five years old and has not been reaffirmed, it is reasonable to conclude that its contents, although still of some value, do not wholly reflect the present state of the art. Users are cautioned to check to determine that they have the lat-est edition of any IEEE Standard.In publishing and making this document available, the IEEE is not suggesting or rendering professional or other services for, or on behalf of, any person or entity. Nor is the IEEE undertaking to perform any duty owed by any other person or entity to another. Any person utilizing this, and any other IEEE Standards document, should rely upon the advice of a competent professional in determining the exercise of reasonable care in any given circumstances.I nterpretations: Occasionally questions may arise regarding the meaning of portions of standards as they relate to specific applications. When the need for interpretations is brought to the attention of IEEE, the Institute will initiate action to prepare appropriate responses. Since IEEE Standards represent a consensus of concerned interests, it is important to ensure that any interpretation has also received the concurrence of a balance of interests. For this reason, IEEE and the members of its societies and Standards Coordinating Committees are not able to provide an instant response to interpretation requests except in those cases where the matter has previously received formal consideration. At lectures, symposia, seminars, or educational courses, an individual presenting information on IEEE standards shall make it clear that his or her views should be considered the personal views of that individual rather than the formal position, explanation, or interpretation of the IEEE.Comments for revision of IEEE Standards are welcome from any interested party, regardless of membership affiliation with IEEE. Suggestions for changes in documents should be in the form of a proposed change of text, together with appropriate supporting comments. Comments on standards and requests for interpretations should be addressed to:Secretary, IEEE-SA Standards Board445 Hoes LanePiscataway, NJ 08854Authorization to photocopy portions of any individual standard for internal or personal use is granted by the Insti-tute of Electrical and Electronics Engineers, Inc., provided that the appropriate fee is paid to Copyright Clearance Center. To arrange for payment of licensing fee, please contact Copyright Clearance Center, Customer Service, 222 Rosewood Drive, Danvers, MA 01923 USA; +1 978 750 8400. Permission to photocopy portions of any individual standard for educational classroom use can also be obtained through the Copyright Clearance Center.IntroductionThis revision of IEEE Std 344-1987 was developed to expand and clarify guidance for developing programs to seismically qualify Class 1E equipment for nuclear power generating stations. Specific areas of amplification included are based on experience gained since 1987.The Class 1E equipment to be qualified by procedures or standards based upon this revised recommended practice can be of many forms; therefore, this recommended practice presents the guidelines for many acceptable seismic qualification methods with the intent of permitting the user to make a judicious selection from the options offered. This revised recommended practice attempts to define more fully the procedures by which Class 1E equipment can be seismically qualified. It presents the methods that are known by the working group to be practices that are acceptable to the nuclear power generation industry, its equipment suppliers, and the industrial test and analysis facilities utilized by the industry. The clarification and update of methods in this recommended practice reflect an effort to recommend state-of-the-art techniques at the time of publication.The methods and definitions presented in this revision are not intended to limit other seismic qualification techniques. Exceptions to these recommended practices may be made at any time where it can be shown that the substituted procedure verifies that the equipment can perform its safety function with justifiable methodology. The basis for a technical justification may be, but is not limited to, partial analysis, tests on similar equipment, experience data, or a combination thereof. Engineering judgment may be used in conjunction with these methods. Exceptions to these guidelines, which are founded on a broad base of actual test, analysis, and earthquake experience, supplemented by engineering judgment, may be used to meet the intent of this standard, provided the methods are justified.The Foreword of the 1987 revision of this standard noted that experience-based methods for seismic qualification of equipment were under development, and Clause 9 of the 1987 revision contained interim guidance for the use of experience data for this purpose. Since then, development of the experience-based approach has been furthered by the Seismic Qualification Utility Group (SQUG). The SQUG approach was used at many nuclear power plants to resolve USI A-46. It has also been adopted, in part, and used by other governmental and industrial organizations. Accordingly, Clause 10 and relevant parts of Clause 11 of this revision of the standard have been rewritten to incorporate the results of this development. Use of the experience-based approach in this recommended practice is acceptable for use in nuclear plants if it is consistent with the plant’s licensing/regulatory design basis.Issues related to use of median-centered in-structure response spectra for the earthquake experience-based method, operating basis earthquake (OBE) requirements associated with the test experience method, and generation of a test-experience spectrum were considered at length by the working group in the preparation of this document.Further guidance for qualification of replacement components and devices within an existing, previously qualified larger equipment assembly by the earthquake experience-based method is deferred to the next revision of the standard. Special consideration could be added to determine how to extend earthquake experience data to replacement of components and devices in a previously qualified equipment assembly so that there is sufficient detail and traceability in the areas of equipment performance (physical configuration,operational, and dynamic), installation, excitation, and demonstration of safety function.Adherence to this recommended practice to obtain equipment seismic qualification alone will not suffice for assurance of public health and safety since it is the integrated performance of structures, fluid systems,This introduction is not part of IEEE Std 344-2004, IEEE Recommended Practice for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations.instrumentation systems, electrical systems, and man/machine interface systems of a nuclear power generating station that establishes totally safe operating conditions.This standard was prepared by Subcommittee 2 Working Group 2.5 (Seismic) of the Nuclear Power Engineering Committee of the IEEE Power Engineering Society.Notice to usersErrataErrata, if any, for this and all other standards can be accessed at the following URL: /reading/ieee/updates/errata/index.html. Users are encouraged to check this URL for errata periodically.InterpretationsCurrent interpretations can be accessed at the following URL: /reading/ieee/interp/index.html.PatentsAttention is called to the possibility that implementation of this standard may require use of subject matter covered by patent rights. By publication of this standard, no position is taken with respect to the existence or validity of any patent rights in connection therewith. The IEEE shall not be responsible for identifying patents or patent applications for which a license may be required to implement an IEEE standard or for conducting inquiries into the legal validity or scope of those patents that are brought to its attention. ParticipantsAt the time this standard was balloted, Working Group SC 2.5 (Seismic) of Subcommittee 2 (Qualification)of the Nuclear Power Engineering Committee had the following membership:James Parello, a ChairaMember of the Writing Group bPast Chair of the Working GroupMostafa A. Ahmed a Paul D. Baughman a Suresh Channarasappa a Garry V. Chapman a Pei-Ying Chen a Walter Djordjevic a Robert Enis Gregory Ferguson Gregory Hardy Paul Ibanez Johnny Jenkins Robert Kassawara Mohsin Khan Bruce M. Lory a William LaPay b Darren Martin Donald P. Moore aKarur S. Parthasarathy Daniel J. Pomerening John M. Richards aWilliam Schmidt aK. M. Skreiner bDonald Smith Richard G. Starck a --`,,`,`,-`-`,,`,,`,`,,`---At the time this standard was balloted, Subcommittee 2 (Qualification) under the Nuclear Power Engineering Committee had the following membership:Satish K. Aggarwal, ChairRobert Lofaro, SecretaryAt the time this standard was balloted, the Nuclear Power Engineering Committee had the following membership:John P. Carter, ChairJohn J. Disosway, Vice ChairDavid A. Horvath,SecretaryBohumil Bartonicek Paul D. Baughman Anup K. Behera Brij M. Bharteey Thomas Brewington Nissen M. Burstein Craig R. Butcher Steve Casadevall Suresh Channarasappa Garry V. Chapman Javier Alonso Chicote Marty Chipkin Jeff Chivers Sun Yeong Choi James M. Dean Liviu Nicolae Delcea Dennis E. Dellinger Philip DiBenedetto Quang H. Duong Frank Drumm Wells D. Fargo Artur J. FayaRobert Francis James F. Gleason Patrick Gove William L. Hadovski Peter Helander Thomas R. Hencey III Jerrell C. Henley David A. Horvath Craig S. Irish Serena A. Jagtiani-Krause Sushant Kapur Mohsin Khan Henry Leung Bruce M. Lory Darin R. Martin P. G. McQuillan Daniel R. Mikow Todd Mitton Asif Mohiuddin Edward Mohtashemi Carole Monchy-LeroyBill Newell James Parello Janez Pavsek Daniel J. Pomerening Robert Queenan John M. Richards Fredrick Roy Steve Sandberg Glen E Schinzel Roderick Simms Kjell Spang Richard G. Starck Marek Tengler Marco Van Uffelen Laszlo Varga Carl Weber John Wheless John White Toni Wittamore Richard T. Wood Toshio Yamamoto Satish K. Aggarwal Ijaz Ahmad George Attarian Farouk D. Baxter Brij M. Bharteey Wesley W. Bowers Daniel F. Brosnan Nissen M. Burstein Robert C. Carruth Surin K. Dureja Stephen A. Fleger Robert Fletcher Robert B. Fuld James F. Gleason Dale Goodney Britton P. Grim Paul R. Johnson Harvey C. Leake John D. MacDonald J. Scott Malcolm Alexander Marion Michael H. Miller Gerald L. NicelyRoger D. Parker Glen E. Schinzel Neil P. Smith James E. Stoner John Taylor James E. Thomas Terence J. Voss John Waclo John White Paul L. Yanosy, Sr. David J. Zaprazny --`,,`,`,-`-`,,`,,`,`,,`---The following members of the individual balloting committee voted on this standard. Balloters may have voted for approval, disapproval, or abstention.When the IEEE-SA Standards Board approved this standard on 8 December 2004, it had the following membership:Don Wright, ChairSteve M. Mills, Vice ChairJudith Gorman, Secretary*Member Emeritus Also included are the following nonvoting IEEE-SA Standards Board liaisons:Satish K. Aggarwal, NRC RepresentativeRichard DeBlasio, DOE RepresentativeAlan Cookson, NIST RepresentativeDon MessinaIEEE Standards Project EditorSatish K. Aggarwal Faropuk D. Baxter Wesley W. Bowers Thomas Brewington Daniel F. Brosnan Nissen M. Burstein Salvatore Carfagno John P. Carter Suresh Channarasappa Garry V. Chapman Dr. Guru Dutt Dhingra Philip DiBenedetto John J. Disosway Surin Dureja Amir El-Sheikh Jay Forster James F. Gleason Lawrence Gradin Britton P. Grim Randall Groves Ajit Gwal Paul R. Johnson Harvey C. Leake John D. MacDonald G. Michel William Mindick James Parello Roger D. Parker Fredrick Roy James Ruggieri Neil P. Smith Richard G. Starck James E. Stoner James E. Thomas John Ullo Terence J. Voss John White Paul L. Yanosy, Sr. Li ZhangChuck Adams Stephen Berger Mark D. Bowman Joseph A. Bruder Bob Davis Roberto de Marca Boisson Julian Forster*Arnold M. Greenspan Mark S. HalpinRaymond Hapeman Richard J. Holleman Richard H. Hulett Lowell G. Johnson Joseph L. Koepfinger*Hermann Koch Thomas J. McGean Daleep C. Mohla Paul Nikolich T. W. Olsen Ronald C. Petersen Gary S. Robinson Frank Stone Malcolm V. Thaden Doug Topping Joe D. WatsonContents1.Overview (1)1.1Scope (1)1.2Purpose (2)2.Normative references (2)3.Definitions (2)4.General discussion of earthquake environment and equipment response (5)4.1Earthquake environment (5)4.2Equipment on foundations (5)4.3Equipment on structures (5)4.4Simulating the earthquake (6)4.5Support structure and interactions (7)5.Seismic qualification approach (7)6.Damping (8)6.1Introduction (8)6.2Measurement of damping (8)6.3Application of damping (9)7.Analysis (10)7.1Introduction (10)7.2Dynamic analysis (10)7.3Static coefficient analysis (12)7.4Nonlinear equipment response (12)7.5Other dynamic loads (13)7.6OBE and SSE analysis (13)7.7Documentation of analysis (13)8.Testing (13)8.1Introduction (13)8.2Proof and generic testing (17)8.3Fragility testing (18)8.4Device testing (18)8.5Assembly testing (18)8.6Test methods (19)8.7Test documentation....................................................................................................................29--` , , ` , ` , -` -` , , ` , , ` , ` , , ` ---bined analysis and testing (29)9.1Introduction (29)9.2Modal testing (29)9.3Extrapolation for similar equipment (31)9.4Shock testing (32)9.5Extrapolation for multicabinet assemblies (33)9.6Other test/analysis (33)10.Experience (33)10.1Introduction (33)10.2Earthquake experience data (33)10.3Test experience data (37)10.4Special considerations (39)11.Documentation (40)11.1General (40)11.2Qualification specification requirements (41)11.3Seismic qualification report (41)Annex A (informative) Measurement of ZPA (45)Annex B (informative) Frequency content and stationarity (46)Annex C (informative) Fragility testing (47)Annex D (informative) Test duration and number of cycles (49)Annex E (informative) Statistically independent motions (52)Annex F (informative) Bibliography.............................................................................................................53--`,,`,`,-`-`,,`,,`,`,,`---IEEE Recommended Practice for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations1. OverviewThis recommended practice is divided into 11 clauses. Clause 1 provides the scope of this recommended practice. Clause 2 lists normative references to other standards that are useful in applying this recommended practice. Clause 3 provides definitions that are either not found in other standards or have been modified for use with this recommended practice. Clause 4 provides background information on earthquake behavior andon the performance of equipment during simulated seismic events. Clause 5 defines the most commonly used methods for seismic qualification of equipment contained in this recommended practice. Clause 6 provides guidance on the measurement and application of damping in the seismic qualification of equipment. Clause 7 provides procedures for two approaches most commonly used to seismically qualify equipment by analysis. Clause 8 provides procedures for the commonly used methods for seismic qualification of equipment by test. Clause 9 provides guidelines for seismic qualification of equipment that cannot be practically qualified by analysis or testing alone. Clause 10 provides guidelines for two approaches to seismically qualify equipment using experience data for a reference equipment class. Clause 11 provides documentation guidelines for the seismic qualification of equipment.This recommended practice also contains six annexes. Annex A explains how to measure the zero period acceleration (ZPA) from seismic test data. Annex B explains frequency content and stationarity of the input waveform. Annex C provides guidance on fragility testing. Annex D explains the use of test duration and response cycles in ensuring adequate equipment response relative to low-cycle fatigue capability. Annex E provides guidance in establishing statistically independent simulated simultaneous multiaxis motions for seismic testing and analysis. Annex F provides bibliographic references.1.1 ScopeThis document describes recommended practices for establishing seismic qualification procedures that will yield quantitative data to demonstrate that the Class 1E equipment can meet its performance requirements during and/or following one safe shutdown earthquake (SSE) event preceded by a number of operating basis earthquake (OBE) events. The test, analysis, or experienced-based evaluation methods described herein may be used to yield data to demonstrate Class 1E equipment performance claims or to evaluate and verify performance of devices and assemblies as part of an overall qualification effort.--` , , ` , ` , -` -` , , ` , , ` , ` , , ` ---IEEEStd 344-2004IEEE RECOMMENDED PRACTICE FOR SEISMIC QUALIFICATION1.2 PurposeThe purpose of this document is to provide recommended practices and documentation requirements for seismic qualification of Class 1E equipment to verify the equipment’s ability to perform its safety function during and/or after the specified seismic motions.2. Normative referencesThis recommended practice shall be used in conjunction with the following publications. When the following standards are superseded by an approved revision, the revision shall apply.IEEE Std 323™-2003, IEEE Standard for Qualifying Class 1E Equipment for Nuclear Power Generating Stations.1,2IEEE Std 382™-1996, IEEE Standard for Qualification of Actuators for Power-Operated Valve Assemblies with Safety-Related Functions for Nuclear Power Plants.MIL-S-901C-1963, Requirements for Shock Tests, H. I. (High Impact); Shipboard Machinery, Equipment and Systems.310 CFR, Energy—Chapter 1, Nuclear Regulatory Commission.43. DefinitionsFor the purpose of this recommended practice, the following terms and conditions apply. IEEE 100, The Authoritative Dictionary of IEEE Standards Terms, Seventh Edition [B1],5 should be referenced for terms not defined in this clause.--`,,`,`,-`-`,,`,,`,`,,`---3.1 broadband response spectrum:A response spectrum that describes motion in which amplifiedresponse occurs over a wide (broad) range of frequencies.3.2 coherence function: A comparative relationship between two time histories. It provides a statistical esti-mate of how much two motions are related, as a function of frequency. The numerical range is from zero for unrelated, to +1.0 for related motions.3.3 correlation coefficient function: A comparative relationship between two time histories. It provides astatistical estimate of how much two motions are related, as a function of time delay. The numerical range is from zero for unrelated, to +1.0 for related motions.3.4 critical seismic characteristics: Those design, material, and performance characteristics of an equip-ment item that provide assurance that the item will perform its required function under seismic loads.1IEEE publications are available from the Institute of Electrical and Electronics Engineers, Inc., 445 Hoes Lane, Piscataway, NJ 08854, USA (/).2The IEEE standards or products referred to in this clause are trademarks of the Institute of Electrical and Electronics Engineers, Inc.3MIL publications are available from Customer Service, Defense Printing Service, 700 Robbins Ave., Bldg. 4D, Philadelphia, PA 19111-5094.4CFR publications are available from the Superintendent of Documents, U.S. Government Printing Office, P.O. Box 37082, Washing-ton, DC 20013-7082, USA (/).5The numbers in brackets correspond to those of the bibliography in Annex F.IEEEOF CLASS 1E EQUIPMENT FOR NUCLEAR POWER GENERATING STATIONS Std 344-20043.5 cutoff frequency: The frequency in the response spectrum where the ZPA asymptote begins. This is the frequency beyond which the single-degree-of-freedom (SDOF) oscillators exhibit no amplification of motion and indicate the upper limit of the frequency content of the waveform being analyzed.3.6 damping: An energy dissipation mechanism that reduces the amplification and broadens the vibratory response in the region of resonance. It is usually expressed as a percentage of critical damping. Critical damping is defined as the least amount of viscous damping that causes a SDOF system to return to its origi-nal position without oscillation after initial disturbance.3.7 earthquake experience spectrum (EES): The response spectrum that defines the seismic capacity of a reference equipment class based on earthquake experience data.3.8 flexible equipment: Equipment, structures, and components whose lowest resonant frequency is less than the cutoff frequency on the response spectrum.3.9 floor acceleration: The acceleration of a particular building floor (or equipment mounting) resulting from the motion of a given earthquake. The maximum floor acceleration is the ZPA of the floor response spectrum.3.10 Fourier spectrum: A complex valued function that provides amplitude and phase information as a function of frequency for a time domain waveform.3.11 ground acceleration: The acceleration of the ground resulting from the motion of a given earthquake.The maximum ground acceleration is the ZPA of the ground response spectrum.3.12 inclusion rules: The rules that define the bounds of equipment included in a reference equipment class based on an acceptable range of equipment physical characteristics, dynamic characteristics, and functions for which seismic ruggedness has been demonstrated by experience data.NOTE—See 10.2.3.1 and 10.3.3.1. 63.13 independent items: Components and equipment that (a) have different physical characteristics or (b)experienced different seismic motion characteristics, e.g., different earthquakes, different sites, different buildings, or different orientations/locations in the same building.3.14 median-centered in-structure response spectrum: In-structure response spectrum developed using realistic damping and best estimate modeling parameters to obtain the most probable structural amplification that could realistically occur for the level of the specified earthquake ground motion.3.15 narrowband response spectrum: A response spectrum that describes the motion in which amplified response occurs over a limited (narrow) range of frequencies.3.16 natural frequency: The frequency(s) at which a body vibrates due to its own physical characteristics (mass and stiffness) when the body is distorted in a specific direction and then released.3.17 operating basis earthquake (OBE): An earthquake that could reasonably be expected to occur at the plant site during the operating life of the plant considering the regional and local geology and seismology and specific characteristics of local subsurface material. It is that earthquake that produces the vibratory ground motion for which those features of the nuclear power plant, necessary for continued operation with-out undue risk to the health and safety of the public, are designed to remain functional.6Notes in text, tables, and figures are given for information only, and do not contain requirements needed to implement the standard.--`,,`,`,-`-`,,`,,`,`,,`---IEEEStd 344-2004IEEE RECOMMENDED PRACTICE FOR SEISMIC QUALIFICATION 3.18 power spectral density (PSD): The mean squared amplitude per unit frequency of a waveform. PSD is expressed in g2/Hz versus frequency for acceleration waveforms.3.19 prohibited features: Design details, materials, construction features, or installation characteristics that have resulted in seismic induced failure or malfunction of the equipment to maintain its structural integrity and perform its specified function at earthquake or test excitations up to and including the defined seismic capacity level.3.20 qualified life: The period of time, prior to the start of a design basis event (DBE), for which the equip-ment was demonstrated to meet the design requirements for the specified service conditions.3.21 reference equipment: The equipment used to establish a reference equipment class.3.22 reference equipment class: A group of equipment sharing common attributes as defined by a set of inclusion rules and prohibited features.3.23 reference site: A site containing equipment or items used to establish a reference equipment class.3.24 required response spectrum (RRS): The response spectrum issued by the user or the user’s agent as part of the specifications for qualification or artificially created to cover future applications. The RRS con-stitutes a requirement to be met.3.25 resonant frequency: A frequency at which a response peak occurs in a system subjected to forced vibration. This frequency is accompanied by a phase shift of response relative to the excitation.3.26 response spectrum: A plot of the maximum response, as a function of oscillator frequency, of an array of SDOF damped oscillators subjected to the same base excitation.3.27 rigid equipment: Equipment, structures, and components whose lowest resonant frequency is greater than the cutoff frequency on the response spectrum.3.28 safe shutdown earthquake (SSE): An earthquake that is based upon an evaluation of the maximum earthquake potential considering the regional and local geology and seismology and specific characteristics of local subsurface material. It is that earthquake that produces the maximum vibratory ground motion for which certain structures, systems, and components are designed to remain functional. These structures, sys-tems, and components are those necessary to ensure the following:a)Integrity of the reactor coolant pressure boundaryb)Capability to shut down the reactor and maintain it in a safe shutdown conditionc)Capability to prevent or mitigate the consequences of accidents that could result in potential off-siteexposures comparable to the guideline exposures of 10 CFR—Chapter 1, Part 10073.29 seismic capacity: The highest seismic level for which required adequacy has been verified.3.30 seismic ruggedness: The ability to resist the damaging effects of an earthquake imparted by robust design and manufacture.3.31 seismic vulnerability: A physical and/or electrical characteristic that renders an equipment item sus-ceptible to structural damage or malfunction from the effects of an earthquake.3.32 sine beats: A continuous sinusoid of one frequency, amplitude modulated by a sinusoid of a lower frequency.7Information on references can be found in Clause 2.。

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Framework using functional formsof hardening internal state variables in modelingelasto-plastic-damage behaviorGeorge Z.Voyiadjis *,Robert J.DorganDepartment of Civil and Environmental Engineering,Louisiana State University,Baton Rouge,LA 70803,USAReceived 23April 2006;received in final revised form 4January 2007Available online 18March 2007Dedicated to Professor Dusan Krajcinovic.AbstractThis work gives the thermodynamically consistent theoretical formulations and the numerical implementation of a plasticity model fully coupled with damage.The formulation of the elasto-plas-tic-damage behavior of materials is introduced here within a framework that uses functional forms of hardening internal state variables in both damage and plasticity.The damage is introduced through a damage mechanics framework and utilizes an anisotropic damage measure to quantify the reduc-tion of the material stiffness.In deriving the constitutive model,a local yield surface is used to deter-mine the occurrence of plasticity and a local damage surface is used to determine the occurrence of damage.Isotropic hardening and kinematic hardening are incorporated as state variables to describe the change of the yield surface.Additionally,a damage isotropic hardening is incorporated as a state variable to describe the change of the damage surface.The hardening conjugate forces (stress-like terms)are general nonlinear functions of their corresponding hardening state variables (strain-like terms)and can be defined based on the desired material behavior.Various exponential and power law functional forms are studied in this formulation.The paper discusses the general concept of using such functional forms.however,it does not address the relevant appropriateness of certain forms to solve different problems.The proposed work introduces a strong coupling between damage and plasticity by utilizing damage and plasticity flow rules that are dependent on both the plastic and damage potentials.However,in addition to that the coupling is further enhanced through the use of the functional forms of the hardening variables introduced in this formulation.0749-6419/$-see front matter Ó2007Published by Elsevier Ltd.doi:10.1016/j.ijplas.2007.03.012*Corresponding author.Tel.:+12255788668;fax:+12255789176.E-mail addresses:voyiadjis@ (G.Z.Voyiadjis),rdorgan@ (R.J.Dorgan).International Journal of Plasticity 23(2007)1826–1859/locate/ijplasG.Z.Voyiadjis,R.J.Dorgan/International Journal of Plasticity23(2007)1826–18591827The use of this formulation in solving boundary value problems will be presented in future work. The fully implicit backward Euler scheme is developed for this model to be solved in a Newton–Raphson solution procedure.Ó2007Published by Elsevier Ltd.Keywords:Constitutive behavior;Anisotropic material;Damage;Plasticity;Finite elements1.IntroductionOne of thefirst important contributions to phenomenological damage modeling is that given by Kachanov(1958)and Rabotnov(1968).Damage models with two separate uncoupled damage and plastic loading surfaces(e.g.Chow and Wang,1987;Hansen and Schreyer,1994;Zhu and Cescetto,1995;Murakami et al.,1998,etc.)present a week coupling between plasticity and damage.Strong coupling between plasticity and damage is obtained by using one single smooth generalized yield surface for the plasticity and dam-age evolutions(e.g.Gurson,1977;Hesebeck,2001;Mahnken,2002;Tvergaard,1982; Reusch et al.,2003;Wen et al.,2005).Another approach to achieve this strong coupling is by using separate plasticity and damage surfaces with separate non-associatedflow rules in such a way that both damage and plasticityflow rules are dependent on both the plastic and damage potentials.Voyiadjis and Deliktas(2000)introduced a formulation for such an approach.Menzel et al.(2005)also introduced coupling of plasticity and damage through a frame of multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage.Clayton(2005,2006)proposed micromechanical based models that demonstrated the influences of interfacial separation,random crystallographic orienta-tion,and grain morphology.This framework distinguishes between the effects of inter-granular damage at grain and phase boundaries and transgranular damage.However, the work proposed here is not addressing such microstructural effects.The following are but a very few of the numerous researchers that pioneered work in different areas of continuum damage mechanics such as brittle materials(Krajcinovic and Foneska,1981;Krajcinovic,1983,1996)and ductile materials(Andrade Pires et al., 2004;Bonora,1997,1999;Bonora et al.,2005;Brunig,2003a,b;Brunig and Ricci,2005; Lemaitre,1992;Kachanov,1986;Murakami et al.,1998).In the1990s coupling of contin-uum damage mechanics to plasticity appeared(e.g.Voyiadjis and Kattan,1992;Lubarda and Krajcinovic,1995;Zhu and Cescetto,1995;Voyiadjis and Deliktas,2000;Menzel et al.,2002;Nesnas and Saanouni,2002).The readers are referred to the book by Krajci-novic(1996)for details about the different existing damage models.In addition the readers can also refer to his book for his seminal works on damage mechanics and its application to different materials.The proposed work introduces a strong coupling between damage and plasticity by uti-lizing damage and plasticityflow rules that are dependent on both the plastic and damage potentials.However,in addition to that the coupling is further enhanced through the use of the functional forms of the hardening variables introduced in this formulation.Continuum damage mechanics introduces a continuous damage variable which is used as a measure of micro-cracks and micro-voids.In the simplest case,this damage variable is introduced as a scalar.This scalar measure has been used to adequately solve many mechanics problems in the literature(e.g.Kachanov,1958;Lemaitre,1984;Krajcinovic,1828G.Z.Voyiadjis,R.J.Dorgan/International Journal of Plasticity23(2007)1826–18591996,etc.).However,in reality,all materials have been shown to accumulate damageanisotropically,and a second order damage tensor is required to properly define theproblem.A simple plot of the uniaxial stress-strain behavior for a material with both coupledplasticity and damage is presented in Fig.1.Plasticity does not begin to occur until afterthe stress reaches the critical value,r yp.However,as seen in this plot,the stress-straincurve begins to have a nonlinear behavior before this point and after it reaches a criticalvalue,r yd.This is due to the accumulation of micro-cracks and micro-voids which reducethe elastic stiffness tensor from the original,undamaged elastic stiffness,e E.This problem is most apparent in brittle and not ductile materials,primarily due to micro-fracturing.However,it may also occur in ductile materials with initial micro-voids.Removal of theexternal loading conditions will not return the state to its original state as not all of themicro-cracks and micro-voids will close;the state of the damaged material will follow alinear path defined by the damaged elastic stiffness modulus,E.Thus,when the materialexperiences a combination of plasticity and damage,the irrecoverable strains consist of aninelastic component due to damage,e id,and an inelastic component due to plasticity,e p.The total irrecoverable component of strain is denoted here as the inelastic damage andplastic strain,e pd.The total recoverable part of the strain,e e,can be decomposed intoan elastic strain due to the effective undamaged material,~e e,and an additional elasticstrain,e ed,due to the change in the elastic stiffness modulus(with closure of some cracksand voids).The change in the damage surface can be explained in terms of the accumulation ofmicro-cracks and micro-voids with loading.Loading causes the micro-cracks andmicro-voids to generate,to propagate,and to interact.The ease with which the micro-cracks are able to move determines the damage hardness of the material.With an increaseG.Z.Voyiadjis,R.J.Dorgan/International Journal of Plasticity23(2007)1826–18591829 in the micro-damage density,there begins to be more interactions between the micro-cracks and between the micro-voids such that damage increase becomes more difficult and the stress required to produce additional micro-damage increases.The material exhib-its hardening due to the arresting of micro-cracks because of their respective interactions.A damage material model can be used to describe this behavior by defining the evolution of a damage tensor through a damage criterion such that a damage surface is defined as well as the change in size,shape,and position of the damage surface.In this work,a J2 type of damage criterion is used with isotropic hardening corresponding to the change in the size of the damage surface.The constitutive model is derived using consistent thermodynamics in the same fashion as a classical rate-independent continuum J2plasticity model(e.g.Doghri,1993;Simo and Hughes,1998;Belytschko et al.,2000;Voyiadjis et al.,2004).Based on thefirst law of ther-modynamics,the Helmholtz free energy is introduced to describe the current state of energy in the material(Malvern,1969;Coussy,1995),and is a function of the strain and the internal state variables under consideration.In order to derive the model equa-tions,the thermodynamics of irreversible processes is followed by introducing a local state consisting of state variables(Malvern,1969;Lemaitre and Chaboche,1994;Coussy,1995; Doghri,2000;Mahnken,2002;Eftis et al.,2003;Bjerke et al.,2002;Cauvin and Testa, 1999).A thermodynamic potential is used which allows the state laws to be defined based on the state variables.The evolution of the thermodynamic conjugate forces are then obtained by assuming the physical existence of the dissipation potential at the macroscale and through the use of the theory of functions of several variables with a Lagrange mul-tiplier.A fully implicit backward Euler scheme is then developed to be solved in a New-ton–Raphson solution procedure.For convenience in developing the constitutive model and thefinite element algorithm, tensorial notation will be used.Boldface terms indicate tensors of order one or greater, while italicized terms indicate scalars.Einstein’s summation convention is used unless otherwise indicated.2.Continuum damage mechanicsDamage may be attributed to either or both micro-cracks and–voids as shown in Fig.2.for either metals or metal matrix composites.In Fig.2a damage in metals due to micro-voids is shown while in Fig.2b dislocations in metals are observed.In Fig.2c metal matrix composites(MMCs)with variousfiber sizes are shown.Finally in Fig.2d micro-cracks in MMCs are observed in the metal matrix as well as at thefiber interface.The MMC used in Fig.2d is a titanium aluminide with silicon carbidefibers.The reader is referred to the work by Voyiadjis et al.(1995)and Voyiadjis and Venson(1995)for details in reference to MMCs.The damage characterization material parameters maybe obtained through the series of experiments outlined by Voyiadjis and Venson(1995).For the char-acterization of the hardening plasticity parameters the reader is referred to the work by Voyiadjis and Abu Al-Rub(2003)for the particular case of316L stainless steel material. However,the same procedure maybe used for other similar metals.In order to allow one to develop constitutive equations within the concept of contin-uum mechanics such that there is a degradation of the material during loading due to micro-damage,the real,damaged state of the material is represented by afictitious, effective undamaged state with a continuum damage measure,u,representing themicro-damage.The material used in this case for a one-dimensional case of a damaged bar with a uniform cross-section of area A ,transformation from the damaged state to the effective state is defined through a scalar damage measure (Kachanov,1958);however,as engineering materials tend to have anisotropic material behavior,damage tends to develop differently in different directions.In order to capture this behavior,a different damage measure should be used for each of the directions leading to a second-order aniso-tropic damage measure (e.g.Sidoroff,1981;Cordebois and Sidoroff,1979,1982;Mura-kami and Ohno,1981;Murakami,1983;Krajcinovic,1983;Voyiadjis and Kattan,1992,1993;Voyiadjis and Park,1997,1999;Voyiadjis and Deliktas,2000,etc.).In order to define this anisotropic measure,consider a representative volume element (RVE)of the damaged material such that each face of the RVE has a normal in the direc-tion of a global coordinate system axis,x i ,as shown in Fig.3a.For anisotropic damage,each face of this RVE will have a different damage distribution.Thus,a vector q can be used to represent the micro-damage density such that each component of the vector rep-resents the density of the micro-damage on the i th surface and can be written as follows (Voyiadjis and Venson,1995):q i ¼A D i A i ¼A i Àe A i A i ðno sum over i Þð1Þwhere for the i th surface,A i is the total damaged area,e Ai is the effective net area which resists a load,and A Di is the area of the micro-damage.For a general case of anisotropicdamage,the damage measure can be written in terms of these damage densities such that (Voyiadjis and Venson,1995;Voyiadjis et al.,1995):Fig.2.(a)Damage due to micro-voids in metals;(b)dislocation density in metals;(c)metal matrix composites,MMCs;(d)damage due to micro-cracks in MMCs (Dorgan,2006).1830G.Z.Voyiadjis,R.J.Dorgan /International Journal of Plasticity 23(2007)1826–1859u ¼ffiffiffiffiffiffiffiffiffiffiffiffiq q p ð2ÞThis damage tensor u is a real symmetric tensor such that the eigenvalues of this tensor areall real ð^u 1;^u 2;^u 3Þand there always exists at least three real eigenvectors ð^e 1;^e 2;^e 3Þ.Thus,for an RVE consisting of a general damage state defined by u ,there always exists a cor-responding RVE rotated to the principal directions,such that the normals of the principalRVE are defined by the vectors ^e 1,^e 2,and ^e 3as shown in Fig.3b.Thus,a damage tensor ^ucan be defined in the orthogonal principal directions as a diagonal tensor such that:^u¼^u 1000^u 2000^u3264375ð3ÞIn order to rotate the damage tensor from the principal directions to the global direc-tions,an orthogonal transformation tensor Q is used through the following equation:u ¼Q T Á^u ÁQ ð4Þwhere the transformation tensor is written in terms of the components of the eigenvectors such that:½Q ¼^e 11^e 12^e 13^e 21^e 22^e 23^e 31^e 32^e 33264375ð5ÞThus,the tensor used to represent the damage in a body has been defined.This tensor will be used to transform the stresses and the strains in the actual configuration to the fic-titious undamaged configuration.Under uniaxial loading,the strain at a given stress has two parts:a recoverable elastic strain,and an irreversible plastic strain (Fig.1).The reversible part is related to the stress through the usual linear elastic equations using a damaged elastic stiffness tensor.It will be shown that this fourth order tensor can be defined as a function of the damage tensor,u ,through the inverse of the damage effect tensor,M .In this work,additive decomposition of the total observable strain,e ,into its internal variable components is assumed:e ¼e e þe pd ð6ÞG.Z.Voyiadjis,R.J.Dorgan /International Journal of Plasticity 23(2007)1826–185918311832G.Z.Voyiadjis,R.J.Dorgan/International Journal of Plasticity23(2007)1826–1859where e e is the reversible thermo-elastic component of the strain and e pd is the irreversible component of the strain due to both plasticity and damage.The elastic strain can be fur-ther decomposed into an elastic strain corresponding to the undamaged configuration,~e e, and an additional component due to the reduction of the elastic stiffness tensor,e ed.Sim-ilarly,the total irrecoverable component of strain,e pd,can be further decomposed into an inelastic component due to damage,e id,and an inelastic component due to plasticity,e p.3.Thermodynamic state variablesThe local coupled plasticity-damage model is defined through the use of the method of material local state identification.In this method,a model is developed such that the ther-modynamic state at a given point in space and time is completely determined by a given set of state variables at that point in space and time.The set of state variables are separated into a set of observable state variables and a set of internal state variables.The observable variables are those that can be measured and which appear regardless of the material phe-nomena.The observable state variables used here are the temperature denoted by the sca-lar T,the total strain denoted by the second-order tensor e,and the damage tensor denoted by the second-order tensor u.For pure elasticity,this set of observable state variables entirely defines the point;how-ever,for elasto-plasticity coupled with damage,the material has a history dependency which requires an additional set of internal state variables.For this coupled damage-plas-ticity model,the internal state variables will consist of plasticity hardening variables and a damage hardening variable.The hardening internal state variables are unitless,strain-like quantities and are accumulated into a set of plasticity related measures,V p and a set of damage related measures,V d,as follows:V p¼½r;a ;V d¼½j ð7Þwhere the internal state variables considered here are the plasticity related variables repre-senting thefluxes of the isotropic and kinematic hardening behaviors denoted by the scalar r and the second-order tensor a,respectively,and the damage related variable representing theflux of the isotropic hardening behavior denoted by the scalar j.The isotropic hard-ening term r(Hill,1950)corresponds to the change in the size of the yield surface,the kine-matic hardening term a(Prager,1956)corresponds to the change in the location of the yield surface,and the isotropic hardening term j.corresponds to the change in the size of the damage surface.4.Thermodynamic equations of stateIn order to determine state laws which relate the internal state variablefluxes to their stress-like conjugate thermodynamic forces,a thermodynamic potential defined as the Helmholtz free energy is introduced which is a state function of a thermodynamic system (Malvern,1969;Lemaitre and Chaboche,1994;Coussy,1995;Doghri,2000).This thermo-dynamic potential is used to describe the current state of energy in the material,and is a function of the observable state variables and the internal state variables under consideration:w¼wðe;T;e pd;e e;u;V p;V dÞð8ÞHowever,as the strains are decomposed for this coupled plasticity-damage model as given by Eq.(6),this Helmholtz free energy is rewritten as follows:w¼wðe e;T;u;V p;V dÞð9ÞThe second law of thermodynamics imposes restrictions on the constitutive relations. From the second law of thermodynamics,the Clausius–Duhem inequality can be written as follows:r:_eÀqð_wþs_TÞÀqÁr TTP0ð10Þwhere r is the second order Cauchy stress tensor,q is the mass density,q is the heatflux vector,s is the entropy per unit mass representing the amount of disorder or randomness in a system,$T is the temperature gradient,and_w is the time derivative of w,such that:_w¼o wo e e :_e eþo wo T_Tþo wo u:_uþo wo V pÁ_V pþo wo VÁ_V dð11ÞThe dot in the fourth andfifth terms indicates that this term is summed over the com-ponents of the sets,V p and V d,of macroscopic measures of irreversible ing this relationship along with the strain decomposition given by Eq.(6),the Clausius–Duhem inequality can be expanded in the following form:r:_e pdþrÀq o w o e e:_e eÀq o wo Tþs_TÀq o wo u :_uÀqo wo V pÁ_V pÀq o wo VÁ_V dÀqÁr TTP0ð12ÞIn order to obtain thermodynamic laws,independent processes are assumed that satisfy this inequality.Thefirst independent process is a case of elastic loadingð_e pd¼0;_u¼0; _V p¼0;_V d¼0Þoccurring at a constant,uniform temperatureð_T¼0;r T¼0Þ.Thus,for the Clausius–Duhem inequality to hold at any given elastic strain increment,the following thermo-elastic state law must be true:r¼q o wo e eð13ÞThe next independent process is that of uniform thermal loadðr T¼0Þin addition to the elastic loadingð_e pd¼0;_u¼0;_V p¼0;_V d¼0Þ.Assuming Eq.(13)holds,the Clau-sius–Duhem inequality holds at any given temperature increment only if the following thermo-elastic state law is true:s¼Ào wo Tð14ÞThus,from the last two equations,the stress,r,and the enthalpy,s,are defined as the conjugate forces corresponding to the state variables e e and T,respectively.A conjugate force,Y,is also defined corresponding to the damage measure,u,as follows:Y¼Àq o wo uð15ÞSimilarly,sets of conjugate forces,A p and A d,are defined which correspond to the plas-ticity hardening internal state variables and damage hardening internal state variables, respectively,such that:G.Z.Voyiadjis,R.J.Dorgan/International Journal of Plasticity23(2007)1826–18591833A p ¼½R ;X ;A d ¼½K ð16Þwhere the scalar R measures the expansion or contraction of the yield surface in the stress space while maintaining its shape and having a fixed center,the second-order tensor X measures the movement and distortion of the yield surface,and the scalar K measures the expansion or contraction of the damage surface in the stress space.Whereas the inter-nal state variables are unitless,strain-like quantities,the thermodynamic conjugate forces are a set of stress-like quantities that are related to the state variables as the stress is related to the strain.These conjugate forces are defined in the Clausius–Duhem inequality by the following set of state laws:A p ¼q o w o V p ;A d ¼q o wo V d ð17Þ5.Stress transformationsFor a general state of anisotropic damage,the Cauchy stress is transformed to the effec-tive Cauchy stress through a linear transformation such that (Murakami and Ohno,1981;Murakami,1983):~r ¼M :r ð18Þwhere M is the fourth order damage effect tensor in terms of the second order damage ten-sor,u .This tensor can be written by transforming the damage effect tensor,c M ,which is defined with reference to the principal direction coordinate system:M ¼Q T ÁQ T Ác M ÁQ ÁQ ð19ÞEq.(19)allows the use of the diagonal form of the damage tensor as given in Eq.(3).Var-ious forms for the principal damage effect tensor have been given in the literature.Sidoroff(1981),Cordebois and Sidoroff(1982),and Lee et al.(1986)expressed the components of this matrix in the following form:½c M ijkl ¼d ik d jl ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1À^u ik Þð1À^u jl Þp ðno sum over i ;j ;k ;l Þð20ÞAlternate forms for the components of this damage effect tensor have been presented by Voyiadjis and Park (1997)as follows:½c M ijkl ¼d ik d jl ½ð1À^u jl Þþð1À^u ik Þ 2ð1Àu ik Þð1Àu jl Þðno sum over i ;j ;k ;l Þð21Þ½c M ijkl ¼2d ik d jl ð1À^u ik Þþð1À^u jl Þðno sum over i ;j ;k ;l Þð22ÞThe differences between these forms of the damage effect tensor are brought about by the symmetrization procedure used as discussed in Voyiadjis and Park (1997).In the rest of this work,it is assumed that the components of the damage effect tensor are as described by Eq.(22);however,similar formulations can be performed for the other rep-resentations.Thus,using this form of the principal damage tensor,the components of theterm o c M =o ^uare found by taking derivatives of the components given by Eq.(22)such that:1834G.Z.Voyiadjis,R.J.Dorgan /International Journal of Plasticity 23(2007)1826–1859o½c M ijkl o^u ab ¼2d ik d jlðd ia d kbþd ja d lbÞ½ð1À^u ikÞþð1À^u jlÞ 2ðno sum over i;j;k;lÞð23ÞAs this model incorporates plasticity in addition to damage,it will be necessary in eval-uating the yield criterion to define the deviatoric components of the effective stress.Given the Cauchy stress tensor and the effective Cauchy stress tensor,the deviatoric parts are defined here as follows:s¼IÀ131 1:rð24Þ~s¼IÀ131 1:~rð25ÞSubstituting the transformation relation,Eq.(18),into Eq.(25),a linear relationship be-tween the Cauchy stress tensor and the effective deviatoric stress tensor is obtained such that:~s¼N:rð26Þwhere the fourth order tensor N is a linear operator defined as follows:N¼MÀ131 1:Mð27ÞUtilizing Eq.(24)in Eq.(26),the following relationship is obtained for the effective deviatoric stress:~s¼M:sþ13M:1 1:rÀ131 1:M:rð28ÞThis equation cannot be manipulated to obtain a linear transformation between the devi-atoric stress and the effective deviatoric stress,and it will thus be required to use Eq.(26) for the transformation of the deviatoric stress.The isotropic hardening and kinematic hardening conjugate forces must also be written in terms of the effective configuration.As the isotropic hardening conjugate force repre-sented by the scalar R is a scalar,a transformation to the effective configuration is per-formed as follows:e R¼R1Àk u kð29Þwhere e R is the isotropic hardening conjugate force in the effective configuration.The norm of the damage tensor is used in this transformation as a scalar measure of damage,u eq. The kinematic hardening conjugate force represented by the second-order tensor X is a second-order tensor which can be linearly transformed using the same method as for the Cauchy stress such that:e X¼M:Xð30Þwhere e X is the backstress conjugate force in the effective configuration.It will be beneficial in the formulation of the yield condition to define the backstress tensor in terms of the fourth order tensor N from Eq.(27).As the backstress conjugate force is a deviatoric ten-sor,M can be replaced with N such that:G.Z.Voyiadjis,R.J.Dorgan/International Journal of Plasticity23(2007)1826–18591835e X¼N:Xð31ÞGiven the damaged and the effective Cauchy stress tensor as well as the damaged and the effective backstress conjugate force,the damaged and the effective relative stress ten-sors are defined here as follows:~n¼~sÀe Xð32Þn¼sÀXð33ÞSubstituting the transformation relations,Eqs.(26)and(31),into Eq.(32),the fol-lowing transformation of the relative stress tensor to the effective configuration is obtained:~n¼~sÀe X¼N:ðrÀXÞð34ÞThe norm of this effective relative stress will be used in the effective configuration yield condition and is defined as follows:k~n k¼k~sÀe X k¼k N:ðrÀXÞkð35Þ6.Elastic strain transformationsThe transformation of the strains from the damaged state to the effective state in this work is derived through the use of the concept of elastic energy equivalence(Sidoroff, 1981).This concept assumes that the elastic energy in the damaged state and in the effec-tive state are equivalent such that:1 2~r:~e e¼12r:e eð36ÞSubstitution of Eq.(18)into this equation gives the transformation relation for the elas-tic strain from the damaged configuration to the effective configuration as follows: ~e e¼MÀT:e eð37ÞIt is assumed that the following Hookean relation holds for both the damaged config-uration and for the effective configuration:r¼C e:e eð38Þ~r¼e C e:~e eð39Þwhere C e is the damaged elasticity modulus and e C e is the effective,undamaged elasticitymodulus.For isotropic elasticity,the effective,undamaged elasticity modulus is written here as follows:e C e¼j e1 1þ2l e I D¼k e1 1þ2l e Ið40Þwhere1and I D are the second-order identity tensor and the fourth-order deviatoric iden-tity tensors,respectively.The two independent material constants k e and l e are the Lame´constants.Substituting Eqs.(38)and(39)into Eq.(36)and utilizing the transformation Eq.(37), the assumption of elastic energy equivalence gives the transformation relation between the。