Objectives 1.Define stress & strain. 2.Utilize Hooke’s Law to calculate unknown stresses and strains. 3.Determine material parameters from a stress-strain.

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Presentation transcript:

Objectives 1.Define stress & strain. 2.Utilize Hooke’s Law to calculate unknown stresses and strains. 3.Determine material parameters from a stress-strain curve. 4.Recognize elastic and plastic components of deformation in a material. 5.Identify the regions of behavior on a stress-strain diagram.

Stress Intensity of Force Stress = ____ /____

Types of Stress Normal : load perpendicular to area

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

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

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

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

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

Why Poisson’s Ratio ?

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

Types of Strain Normal Shear : deformation normal to length

Types of Strain Normal Shear Dilatational (volume change)

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

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

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

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

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

Tensile Test Callister, Materials Science & Engineering

What is Elastic Deformation?

*Recoverable strain (elastic) *Nonrecoverable strain (plastic) Real Material Behavior S e Elastic Elastic/plastic PlasticElastic

Slope of Recovery Line

Unload/Reload Callister, Materials Science & Engineering

Yield Strength from S-e Curve

Everything Together

What is Viscoelastic Deformation?

Creep Test Viscoelasticity

Deformation Types Name Math Model Time Dependency Type Name Math Model Time Dependency Type Elastic Linear/Nonlinear None Recoverable Elastic Linear/Nonlinear None Recoverable Plastic Linear/NonlinearNone Nonrecoverable Plastic Linear/NonlinearNone Nonrecoverable ViscoelasticLinear/Nonlinear Strong Recoverable ViscoelasticLinear/Nonlinear Strong Recoverable ViscoplasticNonlinear Strong Nonrecoverable ViscoplasticNonlinear Strong Nonrecoverable

Representative Modulii Material Modulus (psi) Aluminum 10x10 ^6 Steel 30x10 ^6 Polycarbonate 300 x 10^3