MECHANICAL PROPERTIES OF MATERIALS Department of Physics KL University

Objectives Identification of elastic and plastic behaviour of materials through molecular level Behaviour of ductile and brittle materials with external load Measurement of various properties like hardness and toughness of materials

Basic Terms Stress Strain Types of Stress Types of Strain Hooke’s law Elasticity Plasticity Ductility Brittleness Hardness Toughness Fatigue Creep Fracture

Elasticity Plasticity Regains to original shape Deforms permanently

Elastic deformation Molecular approach 1. Initial 2. Small load 3. Unload F d bonds stretch return to initial Elastic means reversible

Plastic deformation Molecular approach 1. Initial 2. Small load 3. Unload p lanes still sheared F d elastic + plastic bonds stretch & planes shear plastic Plastic means permanent Process of plastic deformation in crystals is by slip process (motion of dislocation) and in non-crystalline solids, the plastic deformation is by viscous flow mechanism.

Stress: The internally developed forces per unit area of a material due to the application of external force. Its SI unit is Pascal (or) N/m2

Strain Fractional change in the dimensions of a material due to the application of external force. It has no unit

Types of Stress & Strain Tensile stress – Longitudinal Strain Compressive Stress – Volume Strain Shear stress – Shear Strain

Tensile Stress – Longitudinal Strain Tension F W Equal and opposite forces directed away from each other

Compressive Stress Longitudinal strain Compression F W Equal and opposite forces directed towards each other

Shear Stress – Shear Strain Tangential force

Hooke’s Law Within elastic limit, Stress α Strain Stress = E x Strain E - Modulus of elasticity, Unit : N/m2

Different modulli of elasticity

Modulus of elasticity of materials depends on bond strength between atoms, stronger the bond, larger will be the modulus of elasticity. Values of the modulus of elasticity for ceramic materials are about the same as for metals; for polymers they are lower. These differences are a direct consequence of the different types of atomic bonding in the three materials types.

Increase in temperature of material, decreases the modulus of elasticity.

Poisson’s Ratio: If lateral strain along x- and y- directions is same loaded unloaded If lateral strain along x- and y- directions is same (ε x = ε y),material may be isotropic.

Material – thin wires – withstands plastic deformation DUCTILITY Material – thin wires – withstands plastic deformation

Fractures without deformation BRITTLENESS Fractures without deformation

Hardness:. - withstand plastic deformation or Hardness: - withstand plastic deformation or indentation produced in the material. Creep: - time dependent deformation at constant load

Strength : Ability to withstand loads Types of strength 1.Yield strength : Strength beyond which it exhibits plasticity 2. Tensile strength (or) Ultimate strength : Strength at which the material breaks or fractures

Tensile Strength TS engineering stress strain engineering strain • Maximum stress on engineering stress-strain curve. y strain Typical response of a metal F = fracture or ultimate strength Necking acts as stress concentrator engineering TS stress engineering strain • Metals: TS occurs when noticeable necking starts. • Polymers: TS occurs when polymer chains are aligned and about to break.

Toughness : Energy absorbed up to fracture Toughness : Energy absorbed up to fracture. Fatigue: Failure under cyclic (or) repeated stress Fracture: Breakage of a material into separate parts under the action of stress

Engineering Stress-Strain Diagram ultimate tensile strength 3 necking Slope=E Strain Hardening yield strength Fracture 5 2 Elastic region slope =Young’s (elastic) modulus yield strength Plastic region ultimate tensile strength strain hardening fracture Plastic Region Stress (F/A) Elastic Region 4 1 Strain ( ) (DL/Lo)

Stress – strain curve – brittle and ductility

Engineering and True Stress-Strain Engineering stress (σn ) = F/A0 A0 – original area of cross section Engineering strain εn = (L-L0)/L0

Engineering and True Stress-Strain Curve

Hardness Tests Indentation Method Brinell Hardness Test Rockwell Hardness Test Vicker Test

VH = 1.854F/d2 , d = (d1+d2)/2