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

• 2. Interpretation of Tensile Stress-Strain Curves

• 3. 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.