I. Fundamentals of Mechanical Properties of Materials
Four types of mechanical properties of thin films are of interest. The first type is the elastic constants, in which the typical property is Young’s modulus. The other three types are strengths including yield strength, σy , ultimate tensile strength, σu , fracture strength, σf , ductility, i.e., elongation, δ, and reduction of area, ψ or RA, and toughness, i.e., fracture toughness, K IC or G C , and impact energy, which correspond to stress, strain and energy, respectively.
1. Stress-strain Curve
Two definitions of stresses and strains are widely used in academia and industry, namely, engineering (or nominal) stresses and engineering (or nominal) strains, and true stresses and true strains. The basic test to characterize mechanical properties of materials is the tensile test. Figure 2-1 shows a general stress-strain curve obtained from a uniaxial tensile test. In the first stage, stress increases linearly with strain with the slope of Young’s modulus. For brittle-ductile materials, if the stress-strain curve is smooth, yield strength (σy ) is determined by an engineering standard and it is the stress under an offset strain, which is usually taken as 0.2 %. Thus, the yield strength is marked as σ0.2. The ultimate tensile strength represents the ability of a sample to resist uniform deformation under tension, which is calculated from the maximum load (P max ) and the original cross section area (A 0), i.e., σu =P max /A 0. The ultimate tensile strength is the critical point, at which necking occurs and uniform deformation is ended in the tested sample.
Referring to Fig. 1, the conventional tensile test gives the following mechanical properties defined as follows:
Ultimate tensile strength: σu = P max /A 0, (1) Yield strength: σy = P y /A 0, (2) Elongation: δ = (L f -L 0)/L 0, (3) Reduction of area: RA = ψ = (A 0 -A f )/A 0, (4)
where A 0 and L 0 are respectively the original cross sectional area and gauge length, A f and L f are respectively the final cross sectional area and gauge length at fracture, and δ and ψ are the parameters to evaluate ductility. Since the cross sectional area (A) and the gauge length (L) change during tensile testing, true stress (σ) and true strain (ε) are defined as:
σ = P/A (5)
)/ln(/00
L L L dL L
L ==∫ε.
(6)
Nominal (engineering) stress and nominal (engineering) strain are defined as:
σ’=P/A 0, (7) ε’=ΔL/L 0=(L-L 0)/L 0=(L/L 0)-1. (8)
Combining Eqs. (6) and (8) yields
ε=ln(1+ ε’). (9)
