Module-4-Mechanical-Properties-of-Materias
Group 2 - Material Science and Engineering
Focuses on Mechanical Properties of Materials
Content Overview
Elastic Deformation and Plastic Deformation
Interpretation of Tensile Stress-Strain Curves
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.