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.
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Failure Criterion: A criterion used to hypothesize the failure.
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Failure Theory: A Theory behind a failure criterion.
Why Need Failure Theories? •
To design structural components and calculate margin of safety.
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To guide in materials development.
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To determine weak and strong directions.
Failure Mode •
Yielding: a process of global permanent plastic deformation. Change in the geometry of the object.
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Low stiffness: excessive elastic deflection.
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Fracture: a process in which cracks grow to the extent that the component breaks apart.
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Buckling: the loss of stable equilibrium. Compressive loading can lead to bucking in columns.
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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
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Plastic deformation at room temperature Creep at elevated temperatures Yield stress is the important design factor
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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