-stressandstrainstress and strain -...
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![Page 1: -StressandStrainStress and Strain - SKKUhome.skku.edu/~femlab/lecture/introduction_mse/lecture14.pdf · 7.2 Stress and Strain Stress, σ: Force per unit area Strain, ε: Unit deformation](https://reader033.vdocuments.site/reader033/viewer/2022042520/5ae8a3647f8b9a3d3b90408e/html5/thumbnails/1.jpg)
Chapter 7. Mechanical PropertiesChapter 7. Mechanical Properties
- Stress and StrainStress and Strain
![Page 2: -StressandStrainStress and Strain - SKKUhome.skku.edu/~femlab/lecture/introduction_mse/lecture14.pdf · 7.2 Stress and Strain Stress, σ: Force per unit area Strain, ε: Unit deformation](https://reader033.vdocuments.site/reader033/viewer/2022042520/5ae8a3647f8b9a3d3b90408e/html5/thumbnails/2.jpg)
7.1 Introduction
Important Mechanical Properties: strength, hardness, ductility and stiffness
Load: tensile, compressive, shearp
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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
![Page 4: -StressandStrainStress and Strain - SKKUhome.skku.edu/~femlab/lecture/introduction_mse/lecture14.pdf · 7.2 Stress and Strain Stress, σ: Force per unit area Strain, ε: Unit deformation](https://reader033.vdocuments.site/reader033/viewer/2022042520/5ae8a3647f8b9a3d3b90408e/html5/thumbnails/4.jpg)
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Geometric consideration
⎟⎞
⎜⎛ +
==′2cos1cos2 θσθσσ ⎟
⎠⎜⎝
==2
cos σθσσ
⎟⎞
⎜⎛ 2sin θ
⎟⎠⎞
⎜⎝⎛==′
22sincossin θσθθστ
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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
![Page 7: -StressandStrainStress and Strain - SKKUhome.skku.edu/~femlab/lecture/introduction_mse/lecture14.pdf · 7.2 Stress and Strain Stress, σ: Force per unit area Strain, ε: Unit deformation](https://reader033.vdocuments.site/reader033/viewer/2022042520/5ae8a3647f8b9a3d3b90408e/html5/thumbnails/7.jpg)
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dFE ⎟⎞
⎜⎛
0rdr
E ⎟⎠⎞
⎜⎝⎛∝
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Ex 7.1
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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
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Ex 7.2