-StressandStrainStress and Strain -...
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Chapter 7. Mechanical Properties Chapter 7. Mechanical Properties - Stress and Strain Stress and Strain
Transcript of -StressandStrainStress and Strain -...
Chapter 7. Mechanical PropertiesChapter 7. Mechanical Properties
- Stress and StrainStress and Strain
7.1 Introduction
Important Mechanical Properties: strength, hardness, ductility and stiffness
Load: tensile, compressive, shearp
7.2 Stress and Strain
Stress, σ : Force per unit area
Strain, ε : Unit deformation. Elastic strain is recoverable; plastic strain is
permanent.
0AF
=σ
0
ll
llli Δ=
−=ε
00 ll
F
0AF
=τ
Geometric consideration
⎟⎞
⎜⎛ +
==′2cos1cos2 θσθσσ ⎟
⎠⎜⎝
==2
cos σθσσ
⎟⎞
⎜⎛ 2sin θ
⎟⎠⎞
⎜⎝⎛==′
22sincossin θσθθστ
Elastic Deformation
7.3 Stress-Strain behavior
εσ E= Hook’s lawεσ E=
E : modulus of elasticity, or Young’s modulus
Hook s law
• Metal and ceramics : 45 Gpa ~ 407 Gpa
• Polymer : 0 007 Gpa ~ 4 GpaPolymer : 0.007 Gpa 4 Gpa
Atomic scale : small changes in the interatomic spacing and
the stretching of interatomic bonds <= interatomic bonding forcesthe stretching of interatomic bonds < interatomic bonding forces
γτ G=
G : shear modulus
dFE ⎟⎞
⎜⎛
0rdr
E ⎟⎠⎞
⎜⎝⎛∝
Ex 7.1
7.5 Elastic properties of materials
z
y
z
x
εε
εεν −=−=
ν : Poisson’s raio
)1(2 ν+= GE
0.25< ν < 0.5
In most of metals G 0 4EIn most of metals, G ~ 0.4E
Ex 7.2
