fracture and failure theory. defining failure failure can be defined in a variety of ways: unable to...
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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= (σ1 –σ2)/2
Tension in x and y directions
xy
Tension in x and y directions
xy
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”
2231
232
221 2 y
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
r
Kr
2
1
rr
Real Distribution
Plastic Zone
Stress Intensity
The Stress Intensity Factor is a constant that defines the stress distribution near a crack
2a
r
Kr
2
1
rr
FactorIntensity Stress 1 aK
r
Kr
2
1
r = distance from crack tip.
Fracture Toughness, KIc
Fracture toughness, KIc
Material property Used to predict the crack size that can be
tolerated c = KIc/(a)1/2
KIc increases with thickness KIc decreases with temperature
increase
Stress Concentrations
Stress risers occur at discontinuities
SCF is related to hole shape and size 2a
rr
max
ave
Factorion Concentrat Stress ave
max
TK