Poisson's ratio, n

1
Poisson's ratio, n
Poisson's ratio, n
(Isotropic materials only)
metals n 0.33ceramics n 0.25polymers n
0.40
Units E GPa or psi n dimensionless

• ? gt 0.50 density increases
• ? lt 0.50 density decreases
  (voids form)

2
Derivative Relationship
3
Other Elastic Properties
Elastic Shear modulus, G
t G g
4
Plastic (Permanent) Deformation
(at lower temperatures, i.e. T lt Tmelt/3)
Simple tension test
ElasticPlastic
at larger stress
engineering stress, s
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
5
Yield Strength, sy

• Stress at which noticeable plastic deformation
  has
• occurred.

when ep 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.
6
Tensile Strength, Tult
Maximum stress on engineering stress-strain
curve.
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
Plastic tensile strain at failure
Adapted from Fig. 6.13, Callister 7e.
8
Toughness
Ability to absorb energy before fracturing
Approximated by the area under the stress-strain
curve.
Brittle fracture elastic energyDuctile
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

• Ability of a material to store energy
• Energy stored best in elastic region

If we assume a linear stress-strain curve this
simplifies to
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
An increase in sy due to plastic deformation.
Curve fit to the stress-strain response (flow
curve)
K is stress at e 1
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

where n is the number of data points