1. 3/15/2002, Friday Plane Stress Plane Strain J Integral
Hertzberg Chapter 8.6

2. Crack Tip Yielding Energy release rate concept:
Fracture toughness of a material depend on the volume of material capable of plastic deformation prior to fracture.

3. Yielding Zone
As we move towards the center of the sample, the axial stress become non-zero and eventually approach the plane-strain value. The reason that the central portion of a think sample approaches plane strain is that the bulk of the sample, which is lowly stressed compared to the crack tip region, act as clamp preventing Poisson’s concentration in z direction
Three-dimensional view of the yield zone around a crack tip.

4. Dog Bone Yielding Shape

5. Hydrostatic
Von Mises equivalent stress

6. Through Thickness Stress

7. Fracture Toughness KIC, plane-strain fracture toughness.
When the thickness is increased to bring about plastic constraint and plane-strain conditions at the crack tip, the toughness drops. The very important aspect of this low level of toughness is that it does not decrease further with increasing thickness, thereby making this value a conservative lower limit of material toughness in any given engineering application.

8. KIC Test Specimen
A valid plane-strain fracture-toughness test is performed when the specimen thickness and crack length are both greater than a certain minimum value.

9. Three Point Bend

10. Crack Tip Mesh