Theories of failure from my som book

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Theories of Failure Theory at a Glance (for IES, GATE & PSUs) 1. Introduction •

Failure: Every material has certain strength, expressed in terms of stress or strain, beyond which it fractures or fails to carry the load.

Failure Criterion: A criterion used to hypothesize the failure.

Failure Theory: A Theory behind a failure criterion.

Why Need Failure Theories? •

To design structural components and calculate margin of safety.

To guide in materials development.

To determine weak and strong directions.

Failure Mode •

Yielding: a process of global permanent plastic deformation. Change in the geometry of the object.

Low stiffness: excessive elastic deflection.

Fracture: a process in which cracks grow to the extent that the component breaks apart.

Buckling: the loss of stable equilibrium. Compressive loading can lead to bucking in columns.

Creep: a high-temperature effect. Load carrying capacity drops.

Failure Modes: Excessive elastic deformation 1. Stretch, twist, bending 2. Buckling 3.

Vibration

or

Yielding

Fracture

• •

Plastic deformation at room temperature Creep at elevated temperatures Yield stress is the important design factor

• • •

Sudden fracture of brittle materials Fatigue (progressive fracture) Stress rupture at elevated temperatures Ultimate stress is the important design factor

2. Maximum Principal Stress Theory (W. Rankin’s Theory- 1850) – Brittle Material The maximum principal stress criterion: •

Rankin stated max principal stress theory as follows- a material fails by fracturing when the largest principal stress exceeds the ultimate strength σu in a simple tension test. That is, at the onset of fracture, |σ1| = σu OR |σ3| = σu


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