Dugdale model for three equal collinear straight cracks: An analytical approach

• To provide analytical solution of multiple cracks under general yielding conditions.
• Load bearing capacity of an infinite plate containing three equal collinear straight.
• Stress intensity factor and crack tip opening displacement are evaluated theoretically and numerically.

In the paper, solution of three collinear equal straight cracks has been investigated on the basis of Dugdale’s hypothesis. These cracks damage an infinite isotropic elastic perfectly plastic plate. Crack tips are very sensitive about loads applied at the infinite boundary of the plate. Each crack tip opens in mode-I type deformation on the application of repeated loads at the boundary of the plate, as a result yield zones develop at each crack tip. To stop further opening of cracks, the rims of the developed yield zones are subjected to yield stress distribution. Muskhelisvili’s complex variable method is used to derive analytical expressions for complex potential function, stress intensity factor (SIF), components of displacement and crack tip opening displacement (CTOD) at each crack tip. Some of the analytical expressions are validated with previously published work. Numerical results are obtained for load bearing capacity, yield zone length and CTOD. These results are analyzed and reported graphically for different cracks lengths.