Module-4-Mechanical-Properties-of-Materias

Group 2 - Material Science and Engineering

  • Focuses on Mechanical Properties of Materials

Content Overview

    1. Elastic Deformation and Plastic Deformation

    1. Interpretation of Tensile Stress-Strain Curves

    1. Yielding under Multi-Axial Stress, Yield Criteria, Macroscopic Aspects of Plastic Deformation, and Property Variability & Design Considerations

Types of Deformation

Temporary/Recoverable Deformation

  • Mechanical Loads:

    • Deformation Time Independent: Elastic

    • Deformation Time Dependent:

      • Anelastic (Under Load)

      • Elastic Aftereffect (After Removal of Load)

  • Combination of Recoverable and Permanent:

    • Time Dependent: Visco-Elastic Deformation

  • Permanent Time Independent: Plastic

  • Time Dependent: Creep (Under Load)

Stress and Strain

Engineering Stress and Engineering Strain

  • Engineering Stress (σ): Load divided by original area

  • Engineering Strain (ε): Percent change in length

  • Changes in object dimensions under applied load affect stress and strain calculations.

True Stress and True Strain

  • Defined to give an accurate representation of instantaneous conditions.

Elastic Deformation

Basics of Elastic Deformation

  • Elastic deformation is reversible.

  • Characterized by the relationship of stress (σ) and strain (ε).

  • Elastic Modulus (E): Proportionality constant between stress and strain, varies with material type.

  • Secant and Tangent Modulus used for non-linear stress-strain materials.

Theoretical Basis

  • Involves reversible displacements of atoms and stretching of atomic bonds.

  • Elastic modulus indicates material stiffness and resistance to atomic separation.

  • Changes with temperature; elastic moduli decrease with increased temperature.

Shear and Bulk Modulus

  • Shear Modulus (G): τ = Gγ (τ: shear stress, γ: shear strain)

  • Bulk Modulus (K): Ratio of mean stress to volumetric strain (K = σm/∆).

  • Poisson’s Ratio (ν): Ratio of lateral strain to linear strain.

Plastic Deformation

Deformation Mechanisms

  • Crystalline solids deform through slip and twinning, while amorphous solids deform via viscous flow without directional characteristics.

  • Elastic and Plastic deformation involves complex interactions between atomic bonds, dislocation movements, and strain rates.

Stress-Strain Relationship

  • Constitutive equations relate stress and strain in plastic deformation.

Tensile Stress-Strain Curve

Curve Characteristics

  • Key Points:

    • A: Starting Point

    • E: Tensile Strength

    • F: Fracture Point

    • B: Proportional Limit

    • G: 0.2% Offset Strain

    • H: Yield Strain

    • C: Elastic Limit

    • D: Yield Limit

  • Resilience (Ur): Ability to absorb energy under elastic deformation

  • Toughness (Ut): Ability to absorb energy under plastic deformation, combining strength and ductility.

Yielding Under Multi-Axial Stress

  • When necking occurs, uniaxial stress becomes triaxial, needing adjustments in the flow curve according to Bridgman’s corrections.

Yield Criteria

Von Mises and Tresca Criteria

  • Von Mises Criterion: Yielding occurs when the second invariant of the stress deviator (J2) reaches a critical value (distortion energy criterion).

  • Tresca Criterion: Yielding occurs when maximum shear stress equals that under uniaxial stress.

Macroscopic Aspects of Plastic Deformation

  • Observations from plastic deformation include:

    • Dimensional changes

    • Change in grain shapes

    • Formation of cell structures in grains

Property Variability

  • Variability influenced by test methods, specimen fabrication, operator bias, and calibration.

  • Designing for variability involves considering safety factors (N) and design factors (N').

Design Considerations

Tailoring Parameters

  • Values for safety factor (N) typically range from 1.2 to 4.0.

  • Higher N values decrease design efficiency (excess material or strength).

  • Factors influencing design include previous experience, accuracy of mechanical forces, material properties, and the impact of failure.

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