The Role of Finite Deformation Analysis in Plane Stress and Strain Fractures

A full nonlinear analysis, geometric as well as constitutive, of cracked plates in plane stress and strain is given. The theory is formulated in a Lagrangian frame of reference. The Newton-Rahpson method is used to solve for generalized displacements in the resulting nonlinear equilibrium equations. An elastic-perfectly plastic behavior is assumed.

An example of a plate containing a sharp crack and subjected to tensile load is solved using a developed finite element computer program. The analysis reveals the extent to which linear elastic-plastic approximation can be used with confidence. The inclusion of changes of large geometry results in higher and more intense strains directly ahead of the crack tip. Also a limited value of stress is achieved in the near crack tip zone. In general, the full nonlinear analysis presents a better representation of ductile fracture mechanisms than does linear elastic-plastic analysis.