Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials...

Lecture 26, summer 2007Mechanical Properties I: Metals & Ceramics

ENGR 145, Chemistry of MaterialsCase Western Reserve University

Reading assignment: Callister 6.1-6.3, 6.5-6.9, 13.8-13.9

Learning objectives:• Understand the difference between elastic and plastic

deformation• Know how to determine mechanical properties from the results of

a tensile test• Elastic modulus • Yield strength • Tensile strength • Strain to failure

• Understand how the mechanical properties of ceramics differ from those of ductile metals

Lecture 26: Mechanical Properties I: Metals & Ceramics



Engineering Stress & Strain [Callister 6.2]

from Callister

F

A0

L

L0

tension compression



Elasticity vs. Plasticity [Callister 6.2]

• Elastic behavior• 0 when 0• Reversible deformation — no permanent shape change after

load is removed

• Plastic behavior• ≠0 when 0 • Some strain remains after load has been removed



Poisson’s Ratio [Callister 6.5]

• Elastic dimensional change will occur transverse to applied uniaxial load:

v

x

z

y

z

Poisson’s ratio



• Stress-strain curve for loading …

• … is retraced on unloading

• Linear elastic behavior: Hooke’s law

Elastic Behavior [Callister 6.3]

Callister Fig. 6.5

E

• Note: not all elastic behavior is linear (see e.g. Callister Figure 6.6) …

• … but all elastic behavior is reversible

modulus of elasticity(a.k.a. Young’s

modulus)



Modulus of Elasticity and the Interatomic Potential [Callister 6.3]

• Recall that energy between atoms depends on their separation• Recall also that

Minimum in energy zero net force

Callister Fig. 2.8b

tensioncompression

F d(energy)

d(separation)

Applying tension or compression

raises energy of material



• F = d(energy)/dr• Modulus of elasticity dF/dr E d2(energy)/dr2

— curvature of interatomic potential near ro

d E d

Callister Fig. 2.8 a

d dF

A

dL dr

dL r

E d

d r

A

dF

dr




• Modulus of elasticity dF/dr

Callister Fig. 6.7


high modulus

low modulus



Mechanical Properties of Metals — Elastic Behavior

• High modulus strong bonding (high curvature of interatomic potential near ro)

(from Callister)



Elastic Modulus: Temperature Dependence [Callister 6.3]

Callister Fig 6.8

Callister Fig. 2.8

• E gradually as T



• Plastic behavior: some strain remains after removal of load

Mechanical Properties of Metals [Callister 6.5]

0.2% yield strength

0.002=0.2%)

• Yield strength: stress that will result in a specified residual strain



Callister Fig. 6.11

• Plastic behavior in a tensile test• Yielding• Tensile strength (M) (a.k.a. ultimate tensile strength)

• Necking• Fracture (F)




Callister Fig. 6.13

• Brittle vs. ductile Two measures of ductility:% elongation

% area reduction

0

0

% 100fl lEL

l

0

0

% 100fA ARA

A




Mechanical Properties of Metals — Plastic Behavior



Callister Fig. 6.14

Plastic Behavior: Effects of Temperature



Callister Fig. 6.15

Modulus of Resilience [Callister 6.6]

• Measure of a material’s capacity to absorb mechanical energy elastically

• Area under stress-strain curve has units of energy per unit volume

• Approximate this integral with:

0

y

rU d

U

r1

2

y

y

y

2

2E



Callister Fig. 6.13

• A measure of energy absorbed during fracture

• Area under stress-strain curve has units of energy per unit volume

• Approximate this area as

Modulus of Toughness [Callister 6.6]

UT ut %EL

UT y ut

2%EL

or



True Stress and Strain [Callister 6.7]

• Engineering stress and strain: based on initial dimensions

• True stress and strain: based on instantaneous dimensions (i)

F

A0

L

l0

l l

0

l0

T F

Ai

Tln

li

l0

Callister Fig. 6.1



• Engineering stress and strain: based on initial dimensions

• True stress and true strain: based on instantaneous dimensions

Callister Fig. 6.16

Start of necking

True Stress and Strain [Callister 6.7]



Mechanical Properties of Ceramics [Callister 13.8]

• Virtually no plasticity at room T

• Strain to failure typically < 0.2%

• Linear to fracture

Callister Fig. 13.29



• Flexural strength: measured in 3-point bending

• a.k.a. modulus of rupture, 3-point bend strength, fracture strength

Callister Fig. 13.28

Compression

Tension


fs 3Ff L

2bd 2

rectangularcross-section

circularcross-section fs

Ff L

R3




• Moduli usu. higher than for metals • Wide spread in strengths

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Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials...

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