Plane Stress vs Plane Strain
Definition
In thin sections the crack-tip region contracts freely in the thickness direction (plane stress), giving higher apparent toughness. In thick sections that contraction is constrained (plane strain), producing a conservative lower-bound toughness used in structural codes.
- Thin section behaviour
- Plane stress, free contraction at crack tip
- Thick section behaviour
- Plane strain, constrained contraction
- Toughness effect
- Plane strain gives a conservative lower-bound value
- Design use
- Plane-strain fracture toughness used in structural codes
Common questions
Why would using a thin-section toughness value on a thick structural part be dangerous?+
Thin-section testing can report an artificially high apparent toughness because the material can contract freely near the crack tip, so applying that number to a thick, constrained part would overestimate its real resistance to fracture.
How does a failure investigator determine which condition applied at fracture?+
They compare the actual section thickness against the material's plane-strain thickness criterion, and examine the fracture surface, since plane-strain fractures tend to be flatter with less shear lip than plane-stress fractures in the same material.
Related terms
- Elastic-Plastic Fracture Mechanics (EPFM)
- The extension of fracture mechanics to ductile materials where significant plasticity occurs before fracture. The J-integral and crack tip opening displacement (CTOD)...
- Fracture Toughness (K_IC)
- The critical stress intensity factor measured under plane-strain conditions. It is a material property representing the maximum K a component can tolerate...
- Griffith Criterion
- The energy-balance condition derived by A.A. Griffith in 1921: a crack extends when the elastic strain energy released per unit area of...
- Linear Elastic Fracture Mechanics (LEFM)
- The branch of fracture mechanics valid when the plastic zone at the crack tip is small relative to the crack length and...
- Stress Intensity Factor (K)
- A parameter, in MPa√m, describing the amplitude of the stress field near a crack tip for a given geometry and load. When...