Introduction to Fracture Mechanics phần 6 ppt

K Dominance Domain of validityThere exists an annular zone where the K solution is valid:... The outer radius, r 0, is the radial distance at which the approximate, asymptotic singular

For Mode I:

Plane Stress:

E

K I2





Plane Strain:

Plane Strain:

2

1 

E

K I

For the general 3-D case, plane strain and anti-plane strain loading:

2









E E

K



For the plane stress case (combination Mode I and Mode II):

E

K

K2  2





K Dominance Domain of validity

There exists an annular zone where the K solution

is valid:

The outer radius, r 0, is the radial distance at which the approximate, asymptotic singular solutions

deviate significantly (say, by more than 10%)

from full elasticity solutions which include higher order terms It is found that,

a

r0  0 1

where is the crack length.a

Example Problem Size Requirements

Consider a low strength steel with σys=350 MPa,

KIc=250 MPa and E = 210 GPa What are the

Minimum specimen size requirements for a valid

KIc measurement?

m

Example Problem Size RequirementsK

Ic Test

ASTM standard E399 (1974) for KIc testing (specimen dimensions large compared to plastic zone):

2

5 2 ,









 K Ic B

b

a



5 2 ,











ys

B b

a



Substitute the known values for σys and KIc Find that

m B

b