Prediction of crack growth direction by Strain Energy Sih's Theory on specimens SEN under tension-compression biaxial loading employing Genetic Algorithms

Crack growth direction has been studied in many ways. Particularly Sih's strain energy theory predicts that a fracture under a three-dimensional state of stress spreads in direction of the minimum strain energy density. In this work a study for angle of fracture growth was made, considering a biaxial stress state at the crack tip on SEN specimens. The stress state applied on a tension-compression SEN specimen is biaxial one on crack tip, as it can observed in figure 1. A solution method proposed to obtain a mathematical model considering genetic algorithms, which have demonstrated great capacity for the solution of many engineering problems. From the model given by Sih one can deduce the density of strain energy stored for unit of volume at the crack tip as dW = [1/2E(σ2x + σ2y) - ν/E(σxσy)]dV (1). From equation (1) a mathematical deduction to solve in terms of θ of this case was developed employing Genetic Algorithms, where θ is a crack propagation direction in plane x-y. Steel and aluminium mechanical properties to modelled specimens were employed, because they are two of materials but used in engineering design. Obtained results show stable zones of fracture propagation but only in a range of applied loading.