1. 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
 > density increases
 < density decreases (voids form)

2. Derivative Relationship

3. 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

4. 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 (a),
Callister 7e.
Most metals – elasticity only continues until strains of about 0.005

5. 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 = = z/z
 z = in
Adapted from Fig (a),
Callister 7e.

6. 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.

7. Ductility x 100 L EL % - = • Plastic tensile strain at failure: e s Lfo 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 - =

8. “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

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

10. 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.

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

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

13. 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

14. 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