Stress ratio contributes to fatigue crack growth in dentin
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如何解决疲劳效应英语作文Title: Strategies to Combat Fatigue Effect。
Fatigue effect, the depletion of mental and physical energy over time, poses a significant challenge to individuals in various aspects of life, be it academic, professional, or personal. Addressing this issue requires a multifaceted approach encompassing lifestyle adjustments, cognitive strategies, and self-care practices. In this essay, we will delve into effective methods to tackle fatigue effect and enhance overall well-being.Firstly, establishing a balanced lifestyle is paramount in combating fatigue. Adequate sleep is fundamental for replenishing energy levels and sustaining cognitive function. Research suggests that adults should aim for 7-9 hours of sleep per night for optimal health. Additionally, maintaining a consistent sleep schedule, even on weekends, helps regulate the body's internal clock, promoting better sleep quality and reducing daytime fatigue.Moreover, incorporating regular physical activity into one's routine is beneficial for combating fatigue. Exercise stimulates the release of endorphins, neurotransmittersthat elevate mood and energy levels. Engaging in activities such as jogging, yoga, or swimming not only enhances physical fitness but also boosts mental clarity and alertness. Even short bouts of exercise throughout the day can mitigate feelings of fatigue and improve overall productivity.In conjunction with lifestyle modifications, adopting cognitive strategies can mitigate the impact of fatigue on cognitive function. Time management techniques, such as the Pomodoro Technique, involve breaking tasks into manageable intervals separated by short breaks. This method prevents burnout and enhances focus by capitalizing on the brain's natural rhythm of attention.Furthermore, implementing mindfulness practices can counteract the cognitive effects of fatigue. Mindfulness meditation, characterized by non-judgmental awareness ofthe present moment, promotes mental clarity and resilience to stress. Studies have shown that regular meditation reduces fatigue and enhances cognitive flexibility, enabling individuals to navigate challenges with greater ease.In addition to lifestyle and cognitive interventions, self-care practices play a crucial role in combatingfatigue effect. Nutrition plays a pivotal role in sustaining energy levels throughout the day. Consuming a balanced diet rich in whole grains, lean proteins, fruits, and vegetables provides essential nutrients that support optimal brain function and mitigate fatigue.Moreover, practicing self-compassion and setting realistic expectations are vital components of self-care. Perfectionism and excessive self-criticism can contribute to burnout and exacerbate feelings of fatigue. Cultivating self-compassion involves treating oneself with kindness and understanding, particularly during periods of heightened stress or fatigue.Furthermore, establishing boundaries and prioritizing self-care activities is essential for preventing burnout. Carving out time for leisure activities, social connections, and relaxation fosters resilience and replenishes depleted energy stores. Whether it's reading a book, spending time with loved ones, or engaging in hobbies, prioritizing activities that bring joy and fulfillment is essential for maintaining well-being.In conclusion, addressing fatigue effect necessitates a comprehensive approach encompassing lifestyle adjustments, cognitive strategies, and self-care practices. Byprioritizing sleep, exercise, mindfulness, nutrition, and self-compassion, individuals can mitigate the impact of fatigue and cultivate resilience in the face of challenges. Empowering oneself with effective coping mechanisms is keyto sustaining energy levels and optimizing overall well-being.。
Men and Women, Who are more fatigued?While men and women lead different roles in our daily life, who do you think are more fatigued? To be objective, I think men take more pressure than women for the higher expectation of society, greater family responsibility and the lack of ability to let off the stress.First of all, generally speaking, our society set much higher expectation for men. From our traditional notion, men are born to endeavor to work to achieve fame and wealth while women are only required to take good care of her husband and children.A survey conducted by China Survey Website, almost 90% of workplace especially some hazard and demanding jobs, such as firefighters, police officer, are taken in charge by men. That is to say, men have a large field to pay attention to . More pressure as they take, they are usually likely to feel fatigued.Secondly, while we acknowledge that women do play a significant role in family life, so do men. As a leader in family, not only should men support the extended family financially but also smooth the tension between family numbers. You know, sometimes it is quite challenging for men to settle the contradiction between his mother and wife, which in some degree increases his mental pressure.Thirdly, as an old saying goes that, the true man never shed tears easily, to show their machismo and mature character, men can not show their fragility directly in public. An article in American Psychological Magazine pointed out that facing pressure, men are more likely to escape or being angry while women choose to share with their buddies. Therefore, Powerless reaction to get off pressure also contributes to they more fatigue than women.In a nutshell, we can not deny that men do confront with bigger pressure which means more fatigue and they really need more understanding and care at the same time.。
背应力英文术语In the realm of engineering and physics, the term "back stress" refers to a residual stress that opposes the direction of the applied load. This concept is particularly significant in the study of materials and their mechanical properties, as it influences how materials deform under stress and recover once the stress is removed.Back stress is a key factor in the phenomenon known as Bauschinger effect, where the yield strength of a material in compression becomes different from the yield strength in tension after a plastic deformation has occurred. This effect is named after the German engineer Johann Bauschinger, who first described it in the late 19th century.Understanding back stress is crucial for predicting the behavior of materials under cyclic loading, which is common in many industrial applications. For instance, metal components in machinery or structures are often subjected to repeated loading and unloading cycles, leading to what is known as fatigue. The accumulation of back stress during these cycles can lead to unexpected failures if not properly accounted for in the design process.In metallurgy, back stress plays a role in work hardening, also known as strain hardening, where a metal becomes stronger and harder after being plastically deformed. This is due to the increase in dislocation density within the metal's crystal structure, which creates an internal back stress that opposes further dislocation movement.Moreover, back stress is a critical consideration in the field of plasticity theory, which deals with the permanent deformation of materials. The mathematical modeling of back stress involves complex equations that describe how materials yield and flow under various stress states. These models are essential for engineers to design safe and reliable products.In summary, back stress is a fundamental concept in the study of material science and engineering. It affects how materials respond to external loads, their strength, and their durability. A thorough understanding of back stress and its implications is necessaryfor the development of advanced materials and the design of structures and components that can withstand the demands of modern engineering challenges.The study of back stress is not only limited to metals but also extends to polymers, composites, and other materials. Each material exhibits unique back stress characteristics, influenced by its microstructure, composition, and processing history. Researchers continue to explore the effects of back stress on new materials, seeking to enhance their performance for various applications.In the aerospace industry, for example, the control of back stress is vital for the development of lightweight yet strong materials that can endure the extreme conditions of flight. Similarly, in the automotive industry, understanding back stress contributes to the creation of vehicles that are both fuel-efficient and safe.In conclusion, back stress is a complex but essential aspect of material behavior. Its study and application are integral to the advancement of technology and the improvement of our daily lives through better, more resilient materials and products. As research progresses, our grasp of back stress and its management will continue to evolve, leading to innovations that will shape the future of engineering and design. 。
Daily exercise is an essential part of maintaining a healthy lifestyle.It not only strengthens our bodies but also boosts our spirits and improves our overall wellbeing. Heres a detailed English essay on the importance of daily exercise and how it can benefit us in various ways.Title:The Importance of Daily Exercise for a Strong PhysiqueIntroductionIn todays fastpaced world,where technology and sedentary lifestyles have become the norm,the significance of daily exercise cannot be overstated.Exercise is the cornerstone of a healthy life,offering a myriad of benefits that extend beyond just physical health.Physical Benefits1.Strengthening Muscles and Bones:Regular physical activity helps to build and maintain strong muscles and bones.It increases bone density and muscle mass,which is particularly important as we age to prevent conditions like osteoporosis and sarcopenia.2.Weight Management:Daily exercise is crucial for maintaining a healthy weight.It helps to burn calories and fat,which is essential for preventing obesity and related health issues.3.Cardiovascular Health:Engaging in regular exercise improves heart health by strengthening the heart muscle,lowering blood pressure,and reducing the risk of heart diseases.4.Enhanced Immune System:Physical activity can boost the immune system,making it more effective in fighting off infections and diseases.Mental Health Benefits1.Stress Relief:Exercise is a natural stress reliever.It releases endorphins,which are chemicals in the brain that act as natural painkillers and mood elevators.2.Improved Mood and Mental Clarity:Regular physical activity can help to alleviate symptoms of depression and anxiety,and it can also improve cognitive function, including memory and concentration.3.Better Sleep:Daily exercise can contribute to better sleep quality by reducing stressand promoting a healthy sleep cycle.Social Benefitsmunity Engagement:Participating in group exercises or sports can foster a sense of community and belonging,which is important for social wellbeing.2.Improved SelfEsteem:Achieving fitness goals can boost selfesteem and confidence,as individuals take pride in their physical abilities and accomplishments.LongTerm Benefits1.Disease Prevention:Regular exercise can help prevent chronic diseases such as type2 diabetes,high blood pressure,and certain types of cancer.2.Longevity:Studies have shown that individuals who engage in regular physical activity tend to live longer,healthier lives.ConclusionIncorporating daily exercise into our routines is not just about achieving a fit body its about nurturing a fit mind and spirit.Its about investing in our health and wellbeing for the long term.Whether its a brisk walk in the park,a yoga session,or a gym workout, every bit of movement counts.Lets make a commitment to move more and sit less, embracing a lifestyle that prioritizes health and happiness through daily exercise.。
考试影响心情的英语作文八年级The Impact of Exams on Eighth Grade Students' MoodExaminations play a crucial role in the education system, serving as a milestone to measure a student's knowledge and academic progress. However, it is undeniable that these tests can sometimes take a toll on students' emotions and overall well-being. In this essay, we will explore the effects of exams on eighth-grade students' moods, analyzing the challenges they face and suggesting possible coping strategies.To begin with, the pressure to perform well in exams can significantly impact a student's mood. The fear of failure and the desire to meet parents' or teachers' expectations create immense stress among eighth graders. As the examination approaches, feelings of anxiety and nervousness tend to intensify, affecting their daily routine and mental health.In addition to being overwhelmed by stress, some studentsmay also experience feelings of self-doubt during exam periods. They may question their abilities and competence, which can lead to decreased self-esteem. The constant comparison with peers who seem to excel academicallyfurther exacerbates these negative emotions.Moreover, the rigorous study routine often required for exams can cause exhaustion and burnout among eighth graders. Long hours spent studying without breaks can result in physical and mental fatigue, leading to irritability and frustration. Lack of sleep due to late-night cramming sessions further deteriorates their mood and hampers concentration during exams.Furthermore, the heavy workload associated with exam preparation may leave little time for hobbies or activities that bring joy to students' lives. This deprivation of leisure time can lead to feelings of monotony or boredom, negatively impacting their overall mood.Nevertheless, there are various strategies students can employ to positively manage their emotions duringexamination periods:Firstly, maintaining a balanced study schedule is crucial. Allocating specific times for studying while also allowing breaks for relaxation or pursuing hobbies helps prevent burnout and maintains motivation levels.Secondly, practicing effective stress management techniques, such as deep breathing exercises or meditation, can help alleviate anxiety and promote a calm state of mind. Finding a healthy outlet for stress, such as engaging in physical activities or confiding in a trusted friend or family member, also contributes to improved emotional well-being.Moreover, setting realistic expectations is essential. Students should aim for improvement rather than perfection and understand that exams do not define their worth as individuals. Celebrating small victories along the way and acknowledging personal growth can boost self-confidence and positively influence mood.Lastly, engaging in activities that provide joy andrelaxation is vital to maintaining a positive mindset. Whether it is listening to music, reading a book for leisure, or practicing a hobby, incorporating enjoyable activities into one's routine helps counterbalance the stress of exams.In conclusion, while exams have a significant impact on eighth-grade students' moods, it is crucial to recognize and address these emotional challenges. By implementing effective coping strategies and maintaining a healthy mindset, students can navigate through exam periods with less stress and negative emotions.。
如何减压英语作文Reducing stress is an important aspect of maintaining a healthy lifestyle. There are several effective ways to relieve stress, and in this essay, I will discuss some of the most effective methods.Firstly, exercise is a great way to reduce stress. Engaging in physical activities such as jogging, swimming, or playing sports can help release endorphins, which are known as "feel-good" hormones. Regular exercise not only improves physical health but also enhances mental well-being. It helps to clear the mind and allows individuals to focus on something other than their stressors.Secondly, practicing mindfulness and meditation can significantly reduce stress levels. Mindfulness involves being fully present in the moment and accepting one's thoughts and feelings without judgment. Meditation, on the other hand, focuses on deep breathing and relaxation techniques to calm the mind and body. Both practices canhelp individuals gain a sense of inner peace and reduce anxiety.Additionally, maintaining a healthy lifestyle can contribute to stress reduction. Eating a balanced diet, getting enough sleep, and avoiding excessive consumption of caffeine and alcohol are all important factors in managing stress. A well-nourished body and a good night's sleep can greatly improve one's ability to cope with stress.Furthermore, engaging in hobbies and activities that bring joy and relaxation can be highly effective in reducing stress. Whether it's reading, painting, listening to music, or gardening, finding activities that provide a sense of pleasure and distraction can help individuals unwind and forget about their worries.Moreover, seeking support from friends, family, or professionals can be beneficial for stress reduction. Talking to someone about one's problems and concerns can provide emotional support and different perspectives. Therapists or counselors can offer guidance and techniquesto manage stress effectively.Lastly, it is essential to set realistic goals and prioritize tasks. Often, stress arises from feeling overwhelmed by a long list of responsibilities. By breaking tasks into smaller, manageable steps and focusing on one thing at a time, individuals can reduce stress and increase productivity.In conclusion, there are various effective ways to reduce stress. Engaging in regular exercise, practicing mindfulness and meditation, maintaining a healthy lifestyle, pursuing hobbies, seeking support, and managing tasks effectively are all helpful strategies. By incorporating these methods into our daily lives, we can effectively manage stress and lead a healthier, more balanced life.。
肥胖原因的英语作文In today's fast-paced world, obesity has become a growing concern affecting people of all ages. The reasons behind this epidemic are multifaceted and complex. Here is an essay that delves into the causes of obesity:The Rising Tide of Obesity: Unraveling the CausesObesity, a condition characterized by excessive body fat, has been on the rise globally. The World Health Organization (WHO) reports that obesity has nearly tripled since 1975, making it a significant public health issue. Several factors contribute to this alarming trend, and understanding them is crucial for developing effective prevention and intervention strategies.1. Unhealthy DietOne of the primary reasons for the increase in obesity is the shift towards unhealthy diets. The availability andaffordability of high-calorie, nutrient-poor foods have madeit easier for individuals to consume more calories than they burn. Fast food, sugary beverages, and processed snacks are often the culprits, as they are rich in fats, sugars, andsalts but lack essential nutrients.2. Sedentary LifestyleModern lifestyles have become increasingly sedentary. With the advent of technology, physical activity has been replaced by screen time. Office jobs, long commutes, and leisure activities that involve watching television or playing video games contribute to a lack of exercise. This sedentary behavior leads to a decrease in energy expenditure, which can result in weight gain.3. Genetic PredispositionResearch has shown that genetics play a role in the development of obesity. Certain genes may predispose individuals to gain weight more easily or affect their metabolism. While genetic factors cannot be changed, understanding one's genetic risk can help in making informed lifestyle choices.4. Psychological FactorsEmotional eating is another factor that contributes to obesity. Stress, depression, and other psychological issues can lead to overeating as a coping mechanism. Comfort foods, often high in calories, are sought after during times of emotional distress, leading to weight gain.5. Socioeconomic StatusThere is a correlation between socioeconomic status and obesity. Lower-income individuals may have limited access to healthy food options and safe spaces for physical activity.Additionally, they may face barriers such as time constraints and lack of resources, which can hinder their ability to maintain a healthy lifestyle.6. Environmental FactorsThe environment in which we live also influences our eating habits and physical activity levels. Urban sprawl, lack of green spaces, and poor public transportation systems can make it difficult for individuals to engage in regular physical activity. Furthermore, aggressive marketing of unhealthy foods can lead to increased consumption.ConclusionAddressing the obesity epidemic requires a multifaceted approach that considers the various contributing factors. It is essential to promote healthy eating habits, encourage regular physical activity, and create supportive environments that facilitate these behaviors. By understanding the causes of obesity, we can work towards developing strategies to combat this global health issue.This essay provides a comprehensive overview of the causes of obesity, highlighting the importance of a holistic approach to tackle this complex health challenge.。
作业负担太重而造成的困扰建议英语作文全文共3篇示例,供读者参考篇1The heavy burden of homework has been a longstanding issue in education and it is a problem that affects students of all ages. From elementary school to college, students are often overwhelmed by the amount of homework they are assigned.One of the main reasons for the heavy homework burden is the pressure to excel academically. In today's competitive world, students are pushed to achieve high grades and excel in every subject. This often leads to teachers assigning a large volume of homework in order to ensure that students have a strong grasp of the material.However, the excessive amount of homework often has negative consequences. Students may experience high levels of stress, anxiety, and even burnout from trying to balance their academic workload with other responsibilities such as extracurricular activities, jobs, and social lives. This can have a detrimental impact on their overall well-being and mental health.In order to address this issue, it is important for educators and policymakers to take a closer look at the amount and type of homework that is assigned to students. Instead of focusing solely on quantity, it is important to consider the quality of the assignments and how they contribute to students' learning.One possible solution is to implement a more balanced approach to homework assignments. This could involve assigning fewer but more meaningful and engaging assignments that encourage critical thinking, creativity, and problem-solving skills. In addition, teachers could provide students with more flexibility in how they complete their assignments, allowing them to choose topics that interest them or to demonstrate their understanding in alternative ways.Another important aspect to consider is the impact of homework on students' mental health. Teachers should be mindful of the workload they assign and take into consideration the individual needs and abilities of their students. Providing support and resources for students who are struggling with the homework load can help alleviate some of the stress and pressure they may be experiencing.In conclusion, the heavy burden of homework is a significant issue that needs to be addressed in order to ensure thewell-being and academic success of students. By taking a more balanced and student-centered approach to homework assignments, educators can help alleviate some of the stress and anxiety that students may be experiencing. By working together to find solutions to this problem, we can create a more supportive and nurturing learning environment for all students.篇2The Heavy Burden of Homework and Suggestions for ReliefIntroductionHomework is an essential part of education, helping students to reinforce their understanding of concepts learned in class. However, in recent years, the burden of homework has become increasingly heavy, leading to a variety of issues for students. This essay will discuss the problems caused by an excessive amount of homework and provide some practical suggestions to alleviate this burden.The Problems Caused by Excessive Homework1. Lack of Time for Rest and RelaxationOne of the most obvious problems caused by an excessive amount of homework is the lack of time for rest and relaxation.Students who are overwhelmed with assignments often find themselves having to sacrifice their leisure time in order to keep up with their workload. This can lead to increased stress levels, fatigue, and a lack of motivation to learn.2. Negative Impact on HealthThe heavy burden of homework can also have a negative impact on students' health. Lack of sleep, poor nutrition, and high levels of stress can all contribute to physical and mental health problems, such as headaches, stomachaches, and anxiety. Over time, these issues can have a detrimental effect on students' overall well-being and academic performance.3. Reduced Interest in LearningWhen students are bombarded with too much homework, they may begin to view learning as a chore rather than a source of enjoyment. This can lead to a decrease in motivation, engagement, and academic achievement. Students may also feel overwhelmed and demoralized, leading to a loss of interest in their studies.Suggestions for Relief1. Limit the Amount of HomeworkOne way to alleviate the burden of homework is to limit the amount assigned to students. Educators should carefully consider the purpose of each assignment and prioritize quality over quantity. By assigning fewer, but more meaningful tasks, students can focus on mastering key concepts and developing critical thinking skills.2. Provide Support and ResourcesTeachers should provide students with the necessary support and resources to help them complete their homework effectively. This could include study guides, extra help sessions, online resources, and access to tutoring services. By offering students the assistance they need, educators can help to reduce the stress and anxiety associated with homework.3. Encourage Time Management and OrganizationTo help students manage their workload more effectively, educators should teach them valuable time management and organizational skills. By setting realistic goals, creating schedules, and prioritizing tasks, students can learn to balance their academic responsibilities with other commitments. This can help to reduce procrastination, improve productivity, and increase overall academic performance.4. Foster a Positive Learning EnvironmentFinally, creating a positive learning environment is essential for reducing the burden of homework. Educators should encourage collaboration, communication, and creativity in the classroom, fostering a sense of community and support among students. By promoting a culture of learning and growth, educators can help students to develop a love of learning and a desire to succeed.ConclusionIn conclusion, the heavy burden of homework can have a variety of negative consequences for students, including stress, poor health, and reduced interest in learning. By implementing the suggestions provided in this essay, educators can help to alleviate this burden and create a more positive and supportive learning environment for their students. By working together to address the issue of excessive homework, we can ensure that students have the time and resources they need to thrive academically and personally.篇3Title: Suggestions for Alleviating the Heavy Homework BurdenIn recent years, the issue of excessive homework burden has become a hot topic of discussion among parents, teachers, and students. The heavy workload of assignments and projects has caused immense stress and anxiety among students, leading to concerns about their mental and physical well-being. In this essay, we will explore the reasons behind the heavy homework burden and provide suggestions on how to alleviate this problem.There are several factors contributing to the heavy homework burden faced by students. One of the main reasons is the relentless pursuit of academic excellence by schools and parents. With the increasing competition in the education system, there is a growing pressure on students to excel in their studies. As a result, teachers assign a large volume of homework to ensure that students are constantly engaged in learning and revision. Additionally, the use of standardized tests and exams as a measure of academic performance has further exacerbated the problem, as students feel the need to constantly prepare for these assessments by completing numerous assignments.Another factor that contributes to the heavy homework burden is the lack of coordination among teachers. Oftentimes, students are assigned multiple tasks from different subjects,each with its own deadline. This lack of coordination leads to a situation where students are overwhelmed with work and struggle to meet the deadlines. Furthermore, the increasing emphasis on extracurricular activities and social events adds to the time constraints faced by students, leaving them with little time to complete their assignments.To address the issue of heavy homework burden, it is essential for schools to adopt a more holistic approach to education. This includes developing a comprehensive curriculum that focuses on the overall well-being of students, rather than just academic achievement. Schools should also encourage collaboration among teachers to ensure that assignments are spread out evenly across subjects and do not overlap in terms of deadlines. Additionally, schools should provide students with adequate support and resources to help them manage their workload effectively.In addition to the responsibilities of schools, parents also play a crucial role in alleviating the heavy homework burden faced by students. Parents should communicate with teachers regularly to understand the expectations and requirements of assignments. They should also encourage their children to prioritize their tasks and develop effective time managementskills. By creating a conducive environment at home, parents can help reduce the stress and anxiety experienced by students when dealing with their homework.Furthermore, students themselves can take proactive steps to manage their workload and reduce the impact of heavy homework burden. They should create a study schedule that allocates sufficient time for each assignment and allows for breaks in between tasks. By breaking down their workload into smaller, more manageable chunks, students can prevent themselves from feeling overwhelmed and ensure that they complete their assignments on time. Additionally, students should seek help from teachers or peers if they are struggling with any particular assignment, rather than trying to tackle it alone.In conclusion, the heavy homework burden faced by students is a complex issue that requires a collaborative effort from schools, parents, and students to address. By adopting a more holistic approach to education, developing effective communication among teachers and parents, and empowering students to manage their workload effectively, we can alleviate the stress and anxiety caused by excessive homework. Only byworking together can we create a healthier and more balanced learning environment for students to thrive in.。
远离疲倦呼唤健康作文英语Title: Embracing Health: A Journey Away from Fatigue。
In the hustle and bustle of modern life, it's easy to succumb to fatigue. The demands of work, social obligations, and personal responsibilities can leave us feeling drained and depleted. However, it's essential to prioritize our health and well-being to combat this fatigue and embrace vitality. In this essay, we will explore strategies for maintaining and enhancing health to ward off fatigue andlive life to the fullest.First and foremost, a balanced diet lays the foundation for good health. Consuming a variety of nutrient-rich foods provides the body with the energy and nourishment it needsto function optimally. Incorporating plenty of fruits, vegetables, whole grains, and lean proteins into our meals ensures that we obtain essential vitamins, minerals, and antioxidants. Moreover, staying hydrated by drinking an adequate amount of water throughout the day is crucial forsupporting bodily functions and combating fatigue.In addition to proper nutrition, regular exercise is paramount for maintaining physical and mental well-being. Engaging in physical activity not only boosts energy levels but also releases endorphins, which are natural mood elevators. Whether it's brisk walking, jogging, cycling, swimming, or practicing yoga, finding activities that we enjoy makes it easier to stay motivated and consistent. Aim for at least 30 minutes of moderate-intensity exercise most days of the week to reap the benefits of an active lifestyle.Furthermore, adequate rest and sleep are essential components of a healthy lifestyle. Many people underestimate the importance of quality sleep in combating fatigue and promoting overall health. Establishing a consistent sleep schedule, creating a relaxing bedtime routine, and optimizing sleep environment can facilitate better sleep quality. Aim for seven to nine hours of sleep per night to allow your body and mind to recharge fully.Moreover, managing stress effectively is crucial for preventing burnout and maintaining optimal health. Chronic stress not only contributes to fatigue but also weakens the immune system and increases the risk of various health problems. Incorporating stress-reduction techniques such as mindfulness meditation, deep breathing exercises, progressive muscle relaxation, and spending time in nature can help alleviate stress and promote relaxation.Additionally, nurturing social connections andfostering a supportive network of family and friends can significantly impact our health and well-being. Strong social ties provide emotional support, reduce feelings of loneliness, and increase resilience in the face of challenges. Make time for meaningful interactions with loved ones, whether it's through shared activities, conversations, or simply spending quality time together.Furthermore, it's essential to listen to our bodies and prioritize self-care. Pay attention to physical and emotional cues, and take breaks when needed to rest and recharge. Engage in activities that bring joy andfulfillment, whether it's pursuing hobbies, practicing gratitude, or indulging in self-care rituals. Remember that self-care is not selfish but necessary for maintaining overall health and well-being.In conclusion, embracing health is the key to warding off fatigue and living a vibrant life. By prioritizing proper nutrition, regular exercise, adequate sleep, stress management, social connections, and self-care, we can cultivate resilience and vitality in the face of life's challenges. Let us commit to making conscious choices that support our health and well-being, allowing us to thrive and enjoy all that life has to offer.。
极端通勤的弊端,英语作文Extreme commuting has become an increasingly common phenomenon in many cities and metropolitan areas around the world. As the cost of living continues to rise in urban centers, more and more individuals are forced to live further away from their places of employment, leading to longer and more arduous commute times. While some may see this as a necessary trade-off to secure affordable housing, the drawbacks of extreme commuting can be significant and far-reaching.One of the primary issues associated with extreme commuting is the toll it takes on an individual's physical and mental health. Spending hours each day sitting in traffic or crammed into crowded public transportation can be physically exhausting, leading to increased levels of stress, fatigue, and even chronic health problems such as back pain or cardiovascular issues. The sedentary nature of the commute also contributes to a more sedentary lifestyle, which can have negative impacts on overall fitness and well-being.In addition to the physical strain, extreme commuting can also take asignificant emotional and psychological toll. The time spent away from home and family can lead to feelings of isolation, loneliness, and a sense of disconnection from one's personal life. The constant stress of navigating traffic, dealing with delays, and adapting to ever-changing commute schedules can contribute to increased anxiety, depression, and burnout. This can have a detrimental effect on an individual's relationships, work performance, and overall quality of life.Another major drawback of extreme commuting is the financial burden it places on individuals and households. The costs associated with owning and operating a vehicle, purchasing fuel, and paying for public transportation fares can quickly add up, often accounting for a significant portion of a person's monthly budget. This can make it increasingly difficult to save for other important financial goals, such as retirement, home ownership, or unexpected expenses.Furthermore, the environmental impact of extreme commuting cannot be overlooked. The increased reliance on personal vehicles and the resulting rise in greenhouse gas emissions contribute to the ongoing climate crisis. The congestion on roads and highways caused by extreme commuting also leads to increased air pollution, which can have negative health consequences for both commuters and the wider community.Beyond the individual and environmental impacts, extreme commuting can also have broader societal implications. The time spent commuting is time that could otherwise be spent engaging in more productive or fulfilling activities, such as pursuing education, volunteering, or spending time with family and friends. This can lead to a decrease in community engagement and social cohesion, as individuals have less time and energy to devote to local organizations, events, and civic duties.Additionally, the concentration of employment opportunities in urban centers can exacerbate economic disparities, as individuals living in more affordable but distant suburbs or rural areas may have fewer job options and face longer commutes to access higher-paying positions. This can perpetuate cycles of poverty and limit social mobility, further widening the gap between the haves and the have-nots.In conclusion, the drawbacks of extreme commuting are numerous and far-reaching. From the negative impacts on physical and mental health to the financial and environmental costs, the burden of lengthy and arduous commutes can take a significant toll on individuals, families, and communities. As cities and metropolitan areas continue to grapple with the challenges of urban growth and housing affordability, it is crucial that policymakers, urban planners, and employers work together to develop innovative solutions thatprioritize sustainable and accessible transportation options, reduce commute times, and improve the overall quality of life for those affected by extreme commuting.。
Stress ratio contributes to fatigue crack growth in dentin D.Arola,W.Zheng,N.Sundaram,J.A.RoulandDepartment of Mechanical Engineering,University of Maryland Baltimore County,1000Hilltop Circle, Baltimore,Maryland21250Received10April2004;revised11August2004;accepted16November2004Published online2March2005in Wiley InterScience().DOI:10.1002/jbm.a.30269Abstract:An experimental study of fatigue crack growth in dentin was conducted,and the influence of stress ratio(R) on the crack growth rate and mechanisms of cyclic extension were examined.Double Cantilever Beam(DCB)fatigue specimens were sectioned from bovine molars and then subjected to high cycle fatigue loading(105ϽNϽ106) under hydrated conditions.The evaluation consisted of Mode I loads with stress ratios that ranged fromϪ0.5to0.5. The fatigue crack growth rates were measured and used to estimate the crack growth exponent(m)and coefficient(C) according to the Paris Law model.The fatigue crack growth rates for steady-state extension(Region II)ranged from1E-7 to1E-4mm/cycle.It was found that the rate of cyclic exten-sion increased significantly with increasing R,and that the highest average crack growth rate occurred at a stress ratio of0.5.However,the crack growth exponent decreased with increasing R from an average of4.6(Rϭ0.10)to2.7(Rϭ0.50).The stress intensity threshold for crack growth de-creased with increasing R as well.Results from this study suggest that an increase in the cyclic stress ratio facilitates fatigue crack growth in dentin and increases the rate of cyclic extension,both of which are critical concerns in min-imizing tooth fractures and maintaining lifelong oral health.©2005Wiley Periodicals,Inc.J Biomed Mater Res73A: 201–212,2005Key words:dentin;fatigue;fracture;stress ratio;restoration failureINTRODUCTIONThe significance and clinical implications of tooth fracture have been of considerable importance to the field of restorative dentistry for many years.In fact, the“cracked tooth syndrome”has been coined in recognition of this special class of tooth failures.1–3 Although fracture is not the primary cause of restored tooth failure,it is often considered the most detrimen-tal due to the likelihood that it will warrant complete extraction.4As the number and average age of fully dentate patients continues to rise,5an understanding of the primary mechanisms contributing to tooth frac-ture becomes increasingly important.Tooth fractures may occur due to a single dynamic load,or as a result of stresses that exceed the strength of the hard tissues or restorative replacement.Al-though possible,these forms of fracture are rather uncommon.Mechanical failures of a restored tooth are much more likely to result from fatigue,which is a cumulative process comprised of damage initiation and/or propagation.In restored teeth,fatigue and fatigue failures are expected to result from cyclic loads that are associated with typical oral activities.In fact, fatigue crack growth within dentin has been cited as a likely contributor to the failure of teeth with restora-tions;dentin is the hard tissue occupying the majority of the human tooth.In a numerical evaluation offirst molars with MOD amalgam restorations,Arola et al.6 found that if cracks as small as25m were introduced in the dentin during a cavity preparation fatigue crack growth may enable cusp fracture within25years (postplacement).Also,flaws that exceeded100m in length were estimated to enable cusp fracture within5 years.Flaws of this size are well within the range that may be introduced in the enamel and dentin with conventional burrs.7,8Nevertheless,the numerical study was conducted assuming that the fatigue prop-erties of dentin are consistent with those of monolithic structural ceramics;the fatigue crack growth proper-ties of dentin were unknown.Consequently,the re-sults should be considered to provide afirst-order estimate of fatigue response that emphasize the poten-tial importance of fatigue crack growth to restored tooth failures.In comparison to the number of evaluations on the hardness and elastic modulus,there have been rela-Correspondence to:D.Arola;e-mail:darola@ Contract grant sponsor:the Whitaker Foundation(a bio-medical engineering research grant)Contract grant sponsor:the National Science Foundation; contract grant numbers:BES9900296,0238237©2005Wiley Periodicals,Inc.tively few studies on the fatigue and fracture behavior of dentin.9In fact,the fatigue properties of tooth tis-sues and dental restorative materials are just begin-ning to receive meaningful attention.The mechanics of fatigue crack growth and fracture in dentin was recently evaluated by Arola et al.,10and it was found that there was a host of complex mechanisms contrib-uting to crack extension under monotonic and cyclic loads.A complementary study by Arola and Rou-land11identified that the average fatigue crack growth rate in bovine dentin was approximately5E-6mm/ cycle and dependent on the dentin tubule orientation. Although there was no significant difference in the rate of crack growth with dentin tubule orientation, there was a definite tendency for crack curving and alignment of the crack perpendicular to the tubules. Fatigue cracks have also been extended across the dentin–enamel junction(DEJ)to study crack deflec-tion.12The fatigue properties of human dentin have been examined by Nalla et al.,13,14in which both the stress-life response and fatigue crack growth behavior of dentin were quantified.These investigators found that the stress-life response was largely time,rather than frequency dependent,and that the fatigue life decreased with presence of a tensile mean stress;the endurance strength for human dentin was reported to be between25and45MPa.The authors also evaluated fatigue crack growth in human dentin where the av-erage growth rate reported was approximately5E-6 mm/ing experimental results,an evaluation of restored tooth failure due to fatigue crack growth was conducted to identify the potential importance to restored tooth failures.The analysis resulted in life estimates that were longer than those reported by Arola et al.,6but did signify the detrimental effects of flaws in dentin to the fatigue life of restored teeth.If aflaw of adequate length is introduced within the dentin during a cavity preparation or restorative pro-cedure,the entire fatigue life is comprised of cyclic crack propagation only;the stress-life response is not relevant.Many engineering materials exhibit an in-crease in the cyclic crack growth rate with increasing stress ratio(R),which is the ratio of the minimum stress to the maximum stress over a fatigue cycle.The relative sensitivity to R is material dependent.15In general,materials subjected to fully reversed fatigue with superposition of tensile monotonic stresses (which increases the stress ratio;RՆ0)fail more readily.15Although potentially relevant to the failure of restored teeth,the influence of R on fatigue crack growth in dentin has not been examined.In this investigation,the fatigue crack growth prop-erties of dentin have been studied as a function of the cyclic stress ratio.The primary objective of the study was to establish the influence of R on the cyclic crack growth rate and stress intensity threshold.Both are important parameters that help characterize fatigue crack growth in dentin.A quantitative description of the changes in fatigue crack growth in dentin with R is presented and the significance of the study to restor-ative dentistry is discussed.MATERIALS AND METHODSBovine dentin was used in this study due to its availability and the similarity in structure with human dentin.16,17Bo-vine and human dentin are both hard tissues of the tooth, and are approximately40to45%inorganic,35%organic, and20to25%water by volume.18The organic and inorganic components are comprised of a collagenfibril network and an apatite crystalline matrix,respectively.The dentin of both human and bovine molars is traversed by tubules that ex-tend from the pulp outwards towards the DEJ.The tubules exist as open channels(1to2m internal diameter)that are surrounded by a hypermineralized ring of tissue referred to as the peritubular dentin.In bovine dentin the peritubular cuff surrounding each tubule is between0.5to1m in wall thickness,which is consistent with that of human dentin. Additional details concerning the structure of dentin is available in ref.18.Although the microstructure of human and bovine dentin is quite consistent,the density of tubules in bovine molars appears to be lower.A recent evaluation of fatigue crack growth in the dentin of bovine molars identi-fied tubule densities ranging from1700to20,000tublues/ mm2,11in comparison to the density for coronal dentin of human molars,which generally exceeds20,000tubules/ mm2.18Fully erupted maxillary molars were sectioned from the upper jaw of mature cows(1–3years of age)within12h of slaughter.The number of specimens obtained from each donor(cow)varied.In general,one to three acceptable mo-lars were obtained from each donor,and no more than two specimens were obtained from each molar.In total,molars from more than15donors were used in the investigation. Noncarious molars were stored immediately in a calcium-buffered saline bath at2°C.The teeth were then cast within a cylindrical ring using a polyester resin to provide a foun-dation for sectioning[Fig.1(a)].Primary sectioning was performed using a numerically controlled slicer/grinder (K.O.Lee Model S3818EL)under continuousflood coolant. Teeth were sectioned along the mesial-distal or buccal-lin-gual axis to obtain slices as shown in Figure1(b).Secondary sections were introduced as necessary to form double can-tilever beam(DCB)specimens from the visible dentin(Fig.2).A longitudinal groove with0.30-mm width was intro-duced in the specimens to channel the direction of crack growth under cyclic loading.Through preliminary experi-ments it was found that a channel was required to preclude crack curving/deflection and to maximize the extent of sta-ble cyclic extension achieved.The holes used for application of the cyclic loads were counterbored on the back of the specimen to the notch depth.This modification centered the load within the crack growth ligament and maintained sym-metric Mode I loads through the crack growth ligament.To facilitate stable crack initiation,the notch tip of each speci-men was sharpened using a razor blade and1m diamond202AROLA ET AL.paste.According to evaluation of the notch tip using elec-tron microscopy,typically the notch root radius was less than 20m.An additional description of the methods used for specimen preparation is available in ref.11.All loading was performed using a universal testing sys-tem (EnduraTEC Model ELF 3200)with an electromagnetic actuator,a maximum load capacity of 225N ,and a sensitiv-ity of Ϯ0.01N .Specimens were submerged in a calcium-buffered saline bath at room temperature to maintain mois-ture content during fatigue loading.Load control fatigue was used with maximum pin loads of between 8and 12N and frequency fixed at 5Hz for all experiments.Just prior to loading,the expected crack path was stained with an indel-ible marker to improve visual contrast between the crack and dentin.The actuator displacement was monitored visu-ally after the beginning of cyclic loading,as crack initiation was often evident through an increase in the specimen’s compliance.After a specific number of fatigue cycles the saline bath was drained and the notch tip was observed for crack initiation using a scaled optical microscope (60ϫ).Accentuation of the crack was accomplished via a focused white light beam incident from behind the specimen for back illumination.19Once a crack was evident at the razornotch,its initial length (a i )was measured on the front of the specimen with the microscope and recorded.Measurements of the change in crack length (⌬a )were made over specific intervals of fatigue loading until complete specimen frac-ture.During each crack length measurement the specimen was subjected to cyclic loading at 1Hz to help identify the crack tip;the load cycle remained the same during crack length measurements.The number of cycles between mea-surements (⌬N )was chosen according to the observed crack growth rate,and typically ranged between 10,000and 25,000cycles.A single experiment typically lasted between 3to 6days,and depended on the time required for crack initiation,rate of crack growth,the extent of stable crack growth achieved,and the incidence of crack divergence or curving.The fatigue crack growth experiments were completed within 3weeks of harvesting the molars.The fatigue crack growth rate (da/dN )was modeled using the Paris Law 20according toda dNͯ1,2,RϭC ͑⌬K ͒m(1)Figure 1.Preparation of double cantilever beam (DCB)specimens from a bovine molar.(a)Bovine molar with mesial–distal sections;(b)a single slice and potential specimenoutlined.Figure 2.The double cantilever beam (DCB)specimen geometry:(a)dimensions;(b)a complete specimen.STRESS RATIO AND FATIGUE CRACK GROWTH IN DENTIN 203where ⌬K is the stress intensity range (⌬K max Ϫ⌬K min ),and da and dN represent the incremental changes in crack length (⌬a )and number of cycles (⌬N ),respectively.The Paris Law parameters C and m represent the fatigue crack growth coefficient and exponent,respectively,and are considered material constants.The stress intensity range was estimated according to⌬K ϭͫ12a 223⅐͑P max 2ϪP min 2͒ͬ12(2)where P max and P min are the minimum and maximum open-ing load and a is the average crack length.The quantities B and h are the crack path thickness and half beam height,respectively.21The crack growth rate (da/dN )and Paris Law parameters were evaluated with respect to the dentin tubule orientation and stress ratio (R ).As evident from Equation (1),the tubule orientation was defined with relation to the fracture surface (Fig.3)in terms of two angles including anout-of-plane (1)and in-plane tubule angle (2).Because the orientation was not known prior to cyclic loading,visual measurements of tubule angles were made after fracture of the specimens using a scanning electron microscope (SEM;JEOL Model JSM-5600).Crack growth rates for each speci-men were plotted as a function of stress intensity range (⌬K )on a log–log scale to identify the three characteristic regions of fatigue crack growth,namely Region I though Region III.The Region I response is comprised of crack initiation and precedes the Region II response.23Region II represents the steady-state region of crack growth,and is often referred to as the “Paris”region.In evaluating a fatigue crack growth response Region II is the portion of growth that exhibits the lowest slope.23Thus,the portion of growth history with minimum slope distinguished Region II of each fatigue crack growth response.A power law trend-line was fit to the Region II data to obtain least-squares error estimates of the fatigue crack growth exponent (m )and coefficient (C ).In addition,the Region I fatigue response was used to establish the stress intensity threshold (⌬K th ),which defines the min-imum stress intensity range necessary to enable fatigue crack growth.In an unrestored tooth the natural cyclic stress ratio is expected to be R ϭ0(P min ϭ0)and the fatigue crack growth rate is a function of the maximum cyclic load (P max )imposed during occlusion.However,a constant stress is also poten-tially present,especially in restored teeth.Polymerization shrinkage of composite restoratives,volumetric expansion of restorative materials with hydration and physical inter-ference fits (posts,inlays,etc.)are potential sources of con-stant stresses in teeth that superpose with the cyclic compo-nent.To account for the potential influence of stress ratio on fatigue crack growth in dentin,the specimens were sub-jected to Mode I fatigue loads with stress ratios that ranged from Ϫ0.5ՅR Յ0.5[Fig.4(a)].The stress ratio (R )is defined according toR ϭmin max(3)where min and max are the minimum and maximum nom-inal stress of the fatigue cycle,respectively.The numberofFigure 3.Definition of the dentin tubuleorientation.Figure 4.Fatigue loading and stress ratio.(a)Cyclic Mode I loading;(b)illustration of stress ratio.204AROLA ET AL.specimens and specific stress ratios used in the study are listed in Table I.Assuming that the predominant response is linear elastic,the stress ratio is equivalent to the correspond-ing cyclic load ratio(P min/P max).A schematic diagram illus-trating the relationship between cyclic load and stress ratio is shown in Figure4(b).Through preliminary experiments it was found that crack initiation occurred more rapidly at a specific⌬K using a stress ratio of0.5.Consequently,fatigue crack initiation was achieved at the razor sharpened notch through load control fatigue with Rϭ0.5,after which the load cycle was changed to that of the stress ratio of interest. The maximum load for any particular specimen(and R)was based on two factors.After crack initiation the load was incrementally increased to initiate fatigue crack growth and identify the stress intensity threshold.Then,the load wasincreased to foster fatigue crack growth and a desired time interval between crack measurements;the corresponding minimum load for a particular maximum load was adjusted according to the desired R.Note that the crack was extended an appreciable length after initiation(and prior to Region II growth)to minimize contributions from the razor sharpened notch and potential effects from the growth at Rϭ0.5.A simple comparison of the fatigue crack growth param-eters including C and m[Eq.(1)]was conducted as a func-tion of R using the Student’s t-test.Although more than one DCB specimen was obtained from a few of the donors,all specimens were treated with equal weight in conducting the statistical analysis.It is worthwhile mentioning that there are other statistical measures that may be used in evaluating differences in the crack growth parameters associated with stress ratio.Yet,the t-test served as an adequate method of comparison at the present point of the investigation.The stress intensity threshold(⌬K th)was also estimated from the cumulative results obtained for each stress ratio.The quan-tity⌬K th defines the minimum stress intensity required for cyclic crack growth.There are empirical models that have been developed to account for the influence of R on cyclic crack growth in engineering structural materials.22Many of these models are well known,but they have not been em-ployed to quantify the effects of R on fatigue crack growth in hard tissues,especially in dentin.Analytical treatments of the effects from R on fatigue crack growth in dentin will be addressed in future studies.After completion of the fatigue tests the SEM was used to determine the dentin tubule orientation(1,2)with relation to the fracture surface.The fracture surface morphology was also examined to establish differences in the mechanisms of fatigue crack growth associated with R.The fractured DCB specimens were sputtered with gold palladium to enhance conductance of the fracture surface.RESULTSA typical fatigue crack growth response for a bovine DCB specimen is shown in Figure5.The three char-acteristic regions of cyclic extension(Regions I,II,and III)are highlighted to emphasize the extent of stable crack growth(Region II)with respect to the other two regions.In addition,the three parameters used in characterizing the cyclic response(⌬K th,m,and C)are identified in Figure5for clarity as well.All of the dentin DCB specimens exhibited well-definedRegion Figure5.A typical fatigue crack growth response from a bovine dentin DCB specimen.This particular specimen was subjected to cyclic loading with Rϭ0.10.Figure6.Cyclic crack growth response of all specimens.TABLE INumber of DCB Specimens Examinedat Each Stress RatioStress ratioϪ0.50Ϫ0.250.100.240.380.50Specimens66207610STRESS RATIO AND FATIGUE CRACK GROWTH IN DENTIN205II and Region III responses.However,the initiation region (Region I)was less evident,especially for fa-tigue crack growth in specimens with R Ն0.1.The fatigue crack growth responses for the dentin specimens are presented in Figures 6and 7.In partic-ular,the cumulative results from all experiments are shown in Figure 6.To highlight the influence of stress ratio on the Region II response,results for specimens subjected to fatigue with R ϭ0.10and R ϭ0.50are shown in Figure 7.Note that only the steady state component (Region II)of the cyclic crack extension is shown in Figures 6and 7for clarity.From a compar-ison of the responses in these two figures it is evident that the rate of fatigue crack growth increased with R .It is also evident that crack growth required less driv-ing force with increasing R as evident from the crack growth responses in Figures 6and 7.Note that growth that occurred at lower stress intensity range (⌬K )with increasing R .Under conditions of cyclic loading where Ϫ0.5ՅR Յ0.1fatigue crack growth occurred for ⌬K Ն1.0MPa ⅐m 0.5.However,with increasing posi-tive stress ratio fatigue crack growth occurred at amuch lower stress intensity;cyclic crack growth in the dentin specimens from experiments with R ϭ0.50occurred for 0.4Յ⌬K Յ1.0MPa ⅐m 0.5.As evident from Figure 6,the largest overall fatigue crack growth rate occurred for cyclic loading with the largest stress ratio (R ϭ0.50).The average Paris Law parameters for the dentin specimens including the fatigue crack growth expo-nent and coefficient are listed in Table II.According to the power law description,the increase in growth rate with R was largely associated with an increase in the crack growth coefficient (C ),which increased by more than a factor of magnitude from the zero-to-tension fatigue (R ϭ0.10)to tension–tension (R ϭ0.50)con-ditions.Despite the increase in fatigue crack growth rate,the Paris law exponent decreased with increasing R from approximately 4.6(R ϭ0.10)to 2.7(R ϭ0.50).The differences in m for R Ͼ0.1are all statistically significant with respect to m for R ϭ0.10(p Յ0.01).In addition to the growth rate parameters,the average ⌬K th for the growth responses at each stress ratio was determined and are listed in Table II.Interestingly,the ⌬K th decreased with increasing R from 1.05MPa ⅐m 0.5at R ϭ0.10to 0.43MPa ⅐m 0.5at R ϭ0.50.Similar to the differences in m ,differences in ⌬K th for R Ͼ0.1are statistically significant with p Յ0.01.Yet,there was no significant difference between m ,C ,or ⌬K th for fatigue crack growth responses with R ϭ0.10and R ϭϪ0.25or R ϭϪ0.50.Micrographs obtained from the fractures surfaces of the bovine dentin specimens after fracture are pre-sented in Figure 8.Two different micrographs are shown,each of which have been obtained from a specimen in which fatigue crack growth occurred in plane with the dentin tubules (1ϭ0°).In fact,all of the specimens tested in the study resulted in 1ϭ0°and in general,2was approximately 45°.The micro-graph in Figure 8(a)was obtained from a specimen subjected to cyclic loading with R ϭϪ0.50,whereas the specimen in Figure 8(b)underwent fatigue loading with R ϭ0.24.In contrast to expectation,there were no drastic differences in the fracture surface morphology from a comparison of specimens that underwent fa-tigue crack growth at the different stress ratios.As is evident from both micrographs,crackexten-Figure parison of experimental fatigue crack growth in the bovine dentin for R ϭ0.5and R ϭ0.1.TABLE IIAverage Fatigue Crack Growth Parameters of the DCB SpecimensStress Ratio C(mm/cycle)⅐(MPa ⅐m 0.5)Ϫmm ⌬K th(MPa ⅐m 0.5)Ϫ0.50 2.26E-06Ϯ0.56E-06 4.64Ϯ0.380.98Ϯ0.10Ϫ0.25 2.49E-06Ϯ0.49E-06 4.43Ϯ0.160.97Ϯ0.100.10 1.12E-06Ϯ0.84E-06 4.57Ϯ0.61 1.05Ϯ0.140.24 4.81E-06Ϯ1.41E-06 3.94Ϯ0.790.69Ϯ0.060.3817.1E-06Ϯ3.93E-06 2.95Ϯ0.150.52Ϯ0.030.5027.9E-06Ϯ12.6E-062.73Ϯ0.650.43Ϯ0.06206AROLA ET AL.sion occurred predominantly through the peritubular cuff and across the lumen rather than at the interface or intertubular boundary.On the mesoscopic level the fatigue crack growth surfaces were relatively smooth and did not exhibit the characteristic fatigue striations or beach marks that are typically found on the surface of more common engineering materials.23However,during the crack length measurements microcracking was observed in front of the crack tip as well as bifurcation of the crack in which propagation occurred along multiple parallel paths.At these locations,the fatigue crack growth surface exhibited bundles of tu-bules that served as tethers that bridged the adjacent crack surfaces.The bundles underwent extension and cantilever bending during opening mode extension.The fatigue crack growth surfaces at locations of crack bridging (evident from the crack growth measure-ments)were documented using the SEM postfailure,an example of which is shown in Figure 8(b).An identification of crack bridging in the fracture of den-tin is not uncommon.In fact,the mechanisms of crack growth resistance through bridging have been docu-mented and described in detail by others in evalua-tions of stable crack growth.24,25In general,the ap-pearance of bridging elements appeared less often on specimens subjected to tension–tension fatigue loads than for specimens where R Ͻ0.1.These observations are supported by fewer bridging elements evident on the fractures surfaces of specimens loaded with R Ͼ0.1as noted from the comparison of the fractures surfaces in Figure 8(a)and Figure 8(b).Interestingly,the bridging elements fractured perpendicular to the axis of the tubules as apparent in Figure 8(b),inde-pendent of whether the tubules were oriented parallel to the specimen’s primary axis defined by the direc-tion of crack growth.DISCUSSIONAn experimental study of fatigue crack growth in bovine dentin was conducted and the effects of stress ratio on particular features of cyclic extension were quantified.Overall,the fatigue crack growth rates ranged from approximately 1E-7to 1E-4mm/cycle.A comparison of the crack growth rates for all stress ratios is shown in Figure 9and was constructed using the average Paris Law parameters (Table II).As evi-dent from this figure,the lowest average growth rates resulted from zero-to-tension (R ϭ0.10)fatigueload-Figure 9.A comparison of the average cyclic growth rates over the range of stress ratios considered in thestudy.Figure 8.Typical micrographs from the fatigue crack growth surfaces.The direction of crack growth was from right to left.(a)Microscopic view of the fracture surface (1,2ϭ0°,45°);(b)top view of bridging elements (1,2ϭ0°,45°);R ϭ0.24.STRESS RATIO AND FATIGUE CRACK GROWTH IN DENTIN 207ing.The crack growth rate and Paris Law parameters(C and m)for Rϭ0.10(Table II)compare well withthose reported in earlier studies on bovine and humandentin.The authors recently reported results from ananalysis on fatigue crack in bovine dentin in terms oftubule orientation where the mean exponent includingall orientations was4.56Ϯ0.6.11Similarly,the stressintensity threshold was reported and appeared to be afunction of tubule orientation as well.For dentin spec-imens with tubules oriented parallel to the fracturesurface(1ϭ0°)the lower bound was approximately 1MPa⅐m0.5.These earlier results are in good agree-ment with those for Rϭ0.10of the present study.Theresults also compare well with the range of publishedvalues of m for compact bone,which reportedlyranges between2.8to5.1.26As previously mentioned,Nalla et al.13used compliance measurements to exam-ine fatigue crack growth rate in human dentin andreported a⌬K th(for Rϭ0.1)of1.06MPa⅐m0.5.However,the crack growth exponent(m)was esti-mated to be8.76,which is nearly twice that estimatedfor bovine dentin.Similarly,Sundaram and Arola27reported results from a fatigue crack growth analysisin human dentin using methods identical to thoseused in the present study.The average crack growthexponent comprised of growth in dentin with threedifferent tubule orientations(1ϭ0°,45°,and90°)was 7.6.Differences in m between bovine and human den-tin and compact bone may suggest that there are sub-tle structural differences that contribute to the mech-anisms of cyclic extension.The dentin of bovine molars appears to exhibit a lower tubule density than human dentin,and would result in a lower mineral content per unit volume of tissue.Also,peritubular dentin is harder than intertubular dentin.9These fac-tors could promote a reduction in theflaw sensitivity of bovine dentin,which would be manifested through a lower fatigue crack growth exponent.Similar to dentin,bone is composed of type-I collagenfibers bound and impregnated with carbonated apatite nanocrystals.28,29Yet,bone is not traversed by the same hypermineralized tubular network that exists in dentin.Based on the influence of tubule orientation on crack growth in bovine dentin11and perceived influ-ence of tubule density,the lower m reported for fa-tigue crack growth in bone indicates that structure is important to the mechanisms of fatigue crack growth in hard tissues.At present,these comments are spec-ulative,and differences in fatigue crack growth in hard tissues related to structure requires further eval-uation.Nevertheless,the average growth rates and ⌬K th reported for both bovine and human dentin(Rϭ0.1)are in agreement and suggests that fatigue crack growth in bovine dentin can serve as a useful model for human dentin.A comparison of the fatigue crack growth responsesfor the bovine dentin in Figures6and7shows that the stress ratio played an important role on the fatigue crack growth rate.As expected,the rate of crack growth increased with R for RՆing the Paris Law model,the growth rates for each R were de-scribed in terms of the growth exponent and coeffi-cient(m,C).The value of m for a material signifies the sensitivity in crack growth rate(da/dN)to the stress intensity range(⌬K).22,23In general,m is lower for ductile materials(typically around3),and increases to above10for extremely brittle materials such as ceram-ics or concrete.15,22,23The average exponent for the dentin specimens evaluated with Rϭ0.10(mϭ4.57) indicates that the bovine dentin response spans the ductile–brittle range.However,there is a reduction in m with increasing R,signifying that there are potential changes in the growth mechanisms within Region II as a result of R.Generally,stress ratio effects are domi-nant in Region I and Region III where the stress in-tensity threshold and critical stress intensity often de-crease with increasing R.However,results from the study suggest that the stress ratio was important to all three regions of the cyclic response.Consequently,the growth characteristics are worthwhile to discuss with regards to each region separately.As expected,there were significant changes in the ⌬K th with R and the dependence of⌬K th on R for the bovine dentin is shown in Figure10(a).For tension-compression cyclic loading(RՅ0)there is essentially no dependence on the stress ratio relative to Rϭ0.10. However,for RՆ0.1the experimental results show that the⌬K th continues to decrease with increasing stress ratio.All of the reductions in⌬K th for RϾ0.1 were statistically significant(pՅ0.01)with respect to that estimated from results for Rϭ0.10.Many mate-rials exhibit a critical stress ratio(R cr),beyond which there is no further change in the stress intensity threshold;15at R cr,a global stress intensity threshold can be defined in which fatigue crack growth will not occur at any R(provided⌬KՅ⌬K th).But results for the bovine dentin withϪ0.5ՅRՅ0.5indicate that R cr and a global⌬K th may not exist.Thus,oral conditions comprised of cyclic loading with a high stress ratio (which result from the addition of a large constant tensile stress)may enable fatigue crack growth in re-stored teeth at an extremely low stress intensity range or from smallflaws.Another interpretation of the unique Region I re-sponse for the bovine dentin is shown in Figure10(b) where the ratio of fracture toughness(K c)to⌬K th is presented in terms of R.An average value for K c of1.9 MPa⅐m0.5has been used based on related results obtained with bovine dentin.30A high ratio of K c to ⌬K th signifies a material that is sensitive to smallflaws. The ratio of these two parameters for traditional struc-tural materials ranges between10and100.15,23Inter-estingly,for the bovine dentin the ratio of K c to⌬K th is approximately equal to2,and appears almost constant208AROLA ET AL.。