fracture and failure theory. defining failure failure can be defined in a variety of ways: unable to...

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