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Fracture and Failure Theory

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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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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.

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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

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Tension in x and y directions xx yy

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xx yy

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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”

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Comparison of Theories

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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

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2a rr Real Distribution Plastic Zone

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

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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

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

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Fracture Mechanics and Size Effect of Concrete

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