What precisely does the term "local failure" refer to in the ASME code and how do we evaluate this failure mode? Basically, a ductile material (such as steel) can fail in a brittle manner and we need to check this possibility.

Cauchy Stress Tensor

This stress tensor is a key concept in the linear theory of elasticity and is used for stress analysis of material bodies involving small deformations. The general 9 component stress tensor can be broken down into two other tensors, the hydrostatic stress tensor and the deviatoric stress tensor. The hydrostatic tensor is addresses changes in volume while the deviatoric tensor is concerned with changes in shape as shown below.

The term sigma m in the hydrostatic stress state (which can be either pure tension or pure compression) causes a elastic volume change but no shape change. In addition, sigma m will not affect the yield stress of the material but will affect the value of the fracture strain. Fracture strain is the capability of a material to tolerate deformation before fracture.

Local Failure Methods

Elastic Analysis

The code requires comparing the sum of the three principal stresses to a maximum allowable stress limit.

Elastic Plastic Analysis

The code requires comparing the sum of equivalent plastic strain and forming strain to a limiting triaxial strain.