ME85-lecture12a

# ME85-lecture12a - LECTURE 12 Axial Deformation Axial Stress...

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Axial Deformation Axial Deformation LECTURE 12 Stress and Strain – Axial Loading

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Fundamental Concepts: What is Strain ? What is Displacement , and what is deformation.
What is Strain ? Definition 1: DISPLACEMENT is the change of position of a material point during a motion. Definition 2: DEFORMATION is the relative displacement. ) ( ) ( X u X X u = + Δ ) ( ) ( X u X X u + Δ 1. , there is no deformation, the bar is experienced a rigid-body motion. 2. , the infinitesimal segment either elongates or shortens

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Definition of normal strain Normal Strain is a measure of relative deformation Average strain
Normal Strain is a measure of relative deformation, and strain is a point-wise quantity. dx du x x u x x u x x = + = Δ ε ) ( ) ( lim ) ( 0

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Normal Strain strain normal stress = = = = L A P δ ε σ L A P A P = = = 2 2 L L A P δδ = = = 2 2
Stress-Strain Test

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Tensile Test
Strain Gauge

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Stress-Strain Diagram: Ductile Materials

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Stress-Strain Relation
Mechanics Model: Deformable Solid 1. Elasticity theory, 2. Plasticity theory, 3. Visco-elasticity theory, 4. Elasto-plastic theory, 5. Soft matter theory 6. …………

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Soft matter: A liquid crystal drop
What is elasticity ?

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Hooke’s Law: Modulus of Elasticity Below the yield stress Elasticity of Modulus or Modulus Youngs = = E E ε σ Strength is affected by alloying, heat treating, and manufacturing process but stiffness (Modulus of Elasticity) is not.
Constitutive Models Linear elastic perfectly or rigid plastic ε σ E = Hooke’s law

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Constitutive Models Linear elastic-perfectly plastic
Stress-Strain Diagram: Brittle Materials

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Elastic vs. Plastic Behavior
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ME85-lecture12a - LECTURE 12 Axial Deformation Axial Stress...

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