Poisson's ratio, n • Poisson's ratio, n: Units: (Isotropic materials only) metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40 Units: E: [GPa] or [psi] n: dimensionless  > 0.50 density increases  < 0.50 density decreases (voids form)

Derivative Relationship

Other Elastic Properties simple torsion test M t G g • Elastic Shear modulus, G: t = G g • Elastic Bulk modulus, K: pressure test: Init. vol =Vo. Vol chg. = DV P P = - K D V o • Special relations for isotropic materials: 2(1 + n) E G = 3(1 - 2n) K

Plastic (Permanent) Deformation (at lower temperatures, i.e. T < Tmelt/3) • Simple tension test: Elastic+Plastic engineering stress, s at larger stress Elastic initially permanent (plastic) after load is removed ep engineering strain, e plastic strain Adapted from Fig. 6.10 (a), Callister 7e. Most metals – elasticity only continues until strains of about 0.005

Yield Strength, sy y = yield strength sy Stress at which noticeable plastic deformation has occurred. when ep = 0.002 tensile stress, s engineering strain, e sy p = 0.002 y = yield strength Note: for 2 inch sample e = 0.002 = z/z  z = 0.004 in Adapted from Fig. 6.10 (a), Callister 7e.

Tensile Strength, Tult Tult engineering stress strain • Maximum stress on engineering stress-strain curve. y strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering Tult stress engineering strain Adapted from Fig. 6.11, Callister 7e. • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbone chains are aligned and about to break.

Ductility x 100 L EL % - = • Plastic tensile strain at failure: e s Lf o f - = • Plastic tensile strain at failure: Engineering tensile strain, e E ngineering tensile stress, s smaller %EL larger %EL Lf Ao Af Lo Adapted from Fig. 6.13, Callister 7e. • Another ductility measure: 100 x A RA % o f - =

“Toughness” • Ability to absorb energy before fracturing • Approximated by the area under the stress-strain curve. very small toughness (unreinforced polymers) Engineering tensile strain, e E ngineering tensile stress, s small toughness (ceramics) large toughness (metals) Adapted from Fig. 6.13, Callister 7e. Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Note: Not fracture toughness, not notch toughness

Effect of Temperature on “Toughness” Figure 6.14 from text: Engineering stress-strain for iron at three temperatures

Resilience, Ur 2 1 U e s @ Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @ Adapted from Fig. 6.15, Callister 7e.

Elastic Strain Recovery Adapted from Fig. 6.17, Callister 7e.

True Stress & Strain S.A. changes when sample stretched True stress True Strain Adapted from Fig. 6.16, Callister 7e.

Hardening ( ) s e • An increase in sy due to plastic deformation. large hardening small hardening y 1 • Curve fit to the stress-strain response (flow curve): K is stress at e = 1 s = K e ( ) n “true” stress (F/A) “true” strain: ln(L/Lo) Strain hardening coefficient: n = 0.15 (some steels) to n = 0.5 (some coppers) Strain hardening coefficient: slope of log-log plot

Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics Mean Standard Deviation All samples have same value Because of large variability must have safety margin in engineering specifications where n is the number of data points