Mechanical Properties of Solids

Mechanical Properties of Solids

• Elasticity: A material's ability to regain its original shape and size after a deforming force is removed.
• Deforming Force: A force that changes the shape or size of a body.
• Restoring Force: Internal forces that try to return a body to its original shape and size.
• Perfectly Elastic Body: A body that completely regains its original shape and size when the deforming force is removed (Examples: steel, quartz, glass).
• Perfectly Plastic Body: A body that does not regain its original shape or size after the deforming force is removed.
• Stress: Internal restoring force per unit area of a deformed body.
• Strain: Change in dimension of a body divided by the original dimension. (It is a ratio so it has no units).
• Stress-Strain relationship: Within the elastic limit, strain is directly proportional to stress, i.e., stress is proportional to strain.

Types of Stress

• Longitudinal (or Normal) Stress: Stress that acts perpendicular to the cross-sectional area of a body.
  • Tensile Stress: Increase in length due to applied force.
  • Compressional Stress: Decrease in length due to applied force.
• Tangential (or Shear) Stress: Stress that acts parallel to the surface of a body.
• Volume (or Bulk) Stress: Stress applied uniformly from all sides to a body.

Types of Strain

• Longitudinal Strain: Change in length divided by the original length.
• Volumetric Strain: Change in volume divided by the original volume.
• Shearing Strain: Tangential applied force over the area of force.

Modulus of Elasticity

• A measure of a material's stiffness, defined as the ratio of stress to strain within the elastic limit.
• Young's Modulus (Y): Ratio of longitudinal stress to longitudinal strain.
• Bulk Modulus (B): Ratio of bulk stress to bulk strain.
• Rigidity Modulus: Ratio of tangential stress to shearing strain.

Hooke's Law

• Within the elastic limit, strain is directly proportional to stress.
• Stress = k * Strain, where k is the modulus of elasticity for the material.

Stress-Strain Curve

• Describes the behavior of a material under stress.
• Elastic Limit: Point on the curve where material no longer obeys Hooke's law.
• Yield Point: The point on the curve where a material begins plastic deformation.
• Ultimate Tensile Strength: The maximum stress a material can withstand before failure.
• Fracture Point: The point at which the material breaks.

Poisson's Ratio

• The ratio of lateral strain to longitudinal strain.
• A measure of how much a material deforms in one direction when stressed in another.