Elastic Stress-Strain Relationships

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Presentation transcript:

Elastic Stress-Strain Relationships CON 251 Materials Testing

Stress and Strain Stress: Intensity of the internal force, measured by force per unit area Strain: Elongation per unit length Nominal Stress: Force divided by the original cross sectional area True Stress: Force divided by the actual cross sectional area

Formulas for Stress and Strain For an axially loaded member: P

More Definitions Stress vs. Strain Diagrams: Plot of stress vs. strain for a given material. Linear (Elastic) Range: Range of stress-strain diagram in which stress is (generally) proportional to strain. Nonlinear (Plastic) Range: Range of stress-strain diagram in which stress is NOT proportional to strain.

“Linear” and “Elastic” Stress is proportional to strain. 0   Elastic after unloading, no permanent deformation. 0 

The Linear (Elastic) Range

Modulus of Elasticity Unit: lb/in2 Constant of proportionality (slope of a line) in elastic range. Unit: lb/in2 It is also called as Young’s Modulus. For a linear material, the relationship between stress and strain: and

Typical Stress-Strain Curves for Materials (a) Mild Steel (b) Iron (c) Rubber

Strength in Elastic Range Proportional limit: The point beyond which stress is no longer proportional to strain. Elastic Limit: The point beyond which permanent deformation will result when the load is removed.

Stress Strain Terminology