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Objectives

Objectives. Define stress & strain. Utilize Hooke’s Law to calculate unknown stresses and strains. Determine material parameters from a stress-strain curve. Recognize elastic and plastic components of deformation in a material. Identify the regions of behavior on a stress-strain diagram.

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Objectives

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  1. Objectives • Define stress & strain. • Utilize Hooke’s Law to calculate unknown stresses and strains. • Determine material parameters from a stress-strain curve. • Recognize elastic and plastic components of deformation in a material. • Identify the regions of behavior on a stress-strain diagram.

  2. Stress Intensity of Force Stress = ____ /____

  3. Types of Stress Normal : load perpendicular to area

  4. Types of Stress • a) Normal • b) Shear : load parallel to area

  5. Types of Stress • a) Normal • b) Shear • c) Hydrostatic (uniform pressure)

  6. Strain: Intensity of Deformation e = ____/_____ =dl / lo

  7. Types of Strain Longitudinal Strain e = u / l Transverse Strain e = v / l Normal : deformation in the the direction of length

  8. Transverse Strain Materials tend to expand/contract in the directions perpendicular to the load application. Poisson’s Ratio  = - _____________ axial strain

  9. Why Poisson’s Ratio ?

  10. Poissons Ratio Values • = 0.5 constant volume • = 0.3 good guess for most materials

  11. Types of Strain • Normal • Shear : deformation normal to length

  12. Types of Strain • Normal • Shear • Dilatational (volume change)

  13. Relating Stress and Strain Called a “Constitutive Model” Simple Linear Model: “Hooke’s Law”

  14. Relating Stress and Strain Normal S = E e Stress = Young’s modulus x strain

  15. Relating Stress and Strain Shear Hooke’s Law  = G  Shear Modulus G = E / [2 (1+  )]  = shear stress G = shear modulus  = shear strain

  16. Relating Stress and Strain Dilatational (hydrostatic) Hooke’s Law P = K  K= E/3(1-2) P = pressure K = bulk modulus  = V/ Vo

  17. Real Material Behavior -Hookean to a limiting strain -Proportional limit : Deviation from linear -After PL *Linear *Flat *Non linear

  18. Tensile Test Callister, Materials Science & Engineering

  19. What is Elastic Deformation?

  20. Real Material Behavior *Recoverable strain (elastic) *Nonrecoverable strain (plastic) Elastic Elastic/plastic S Plastic Elastic e

  21. Slope of Recovery Line

  22. Unload/Reload Callister, Materials Science & Engineering

  23. Yield Strength from S-e Curve

  24. Everything Together

  25. What is Viscoelastic Deformation?

  26. Creep Test Viscoelasticity

  27. Deformation Types Name Math Model Time Dependency Type Elastic Linear/Nonlinear None Recoverable Plastic Linear/Nonlinear None Nonrecoverable Viscoelastic Linear/Nonlinear Strong Recoverable Viscoplastic Nonlinear Strong Nonrecoverable

  28. Representative Modulii

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