# Fracture and Failure Theory. Defining Failure Failure can be defined in a variety of ways: Unable to perform the to a given criteria Fracture Yielding.

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Fracture and Failure Theory

Defining Failure Failure can be defined in a variety of ways: Unable to perform the to a given criteria Fracture Yielding ……

Failure of Structural Materials Yielding is often considered “impending failure” The deformations associated with yield provide a warning The service life is effectively ended if a materials yields under service, in most cases.

Tresca Yield Criterion Ductile Materials Assumes slip occurs during yielding “yielding begins when max. shear stress reaches the shear stress obtained in a simple tension test at yield”  max = (σ 1 –σ 2 )/2

Tension in x and y directions   xx yy

  xx yy

von Mises Yield Criterion Separates “hydrostatic pressure” from “distortion stresses” Bases on “Energy of distortion is equal to energy of distortion at yield of a simple tension test”

Comparison of Theories

Surface Energy and Fracture Energy required to generate new surfaces Griffith crack theory Crack will propagate if elastic strain energy is equal to energy of newly created surface

2a rr   Real Distribution Plastic Zone

Stress Intensity The Stress Intensity Factor is a constant that defines the stress distribution near a crack 2a rr   r = distance from crack tip.

Fracture Toughness, K Ic Fracture toughness, K Ic Material property  Used to predict the crack size that can be tolerated  c = K Ic /(  a) 1/2 K Ic increases with thickness K Ic decreases with temperature increase

Stress Concentrations Stress risers occur at discontinuities SCF is related to hole shape and size 2a rr    max  ave

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