Three-dimensional analyses of plastic constraint for through-thickness cracked bodies

A three-dimensional strip yield model has been proposed to rationalize effects of out-of-plane and in-plane constraints. By use of the model, plastic constraints around a straight-through crack in finite thick plates made of strain hardening materials are analyzed. A global constraint factor α is defined to simulate the three-dimensional effects in two-dimensional analysis. Effects of thickness and stress states on the size of crack-tip plastic zone and α are studied in detail. A unique variation curve of α against normalized thickness is obtained for different combination of materials, load levels and geometry. Influences of the in-plane constraint on the α-thickness curve are analyzed as well. It is shown that the influence of T-stress can be considerable only if the plastic-zone size becomes comparable to the crack length. The difference between the present results and Newman, Bigelow and Shivakumer's three-dimensional finite element results is within 6% over a large range of thickness and stress levels. The three-dimensional shape of the plastic zone is discussed as well. Potential applications of the model are discussed and it is shown by an example that the present model can be used to explain the effects of thickness upon fatigue crack growth.