Critical Plane Approach

Depending on the material and stress states, the critical planes can be either maximum shear planes or maximum tensile stress planes. Therefore, to assess damage from multiaxial loads, two separate damage models are required. One is for crack growth due to shear, and the other is for crack growth due to tension.

Figure 1. Cracks Driven by Shear and Tensile Stress

Figure 2. Cyclic Torsion, Shear Strain, Tensile Strain, Shear and Tensile Damage

Any damage model can be used in the critical plane approach. The damage models require a search for the most damaging plane. There are two possible damaging (or failure) modes. One on planes that are perpendicular to the free surface which is tensile crack growth. The angle $\theta$ is the angle that a crack is observed on the surface relative to the ${\sigma }_x$ direction. The second failure system occurs on planes oriented 45 degrees to the surface, which is shear crack growth. Both in-plane and out-of-plane shear stresses are considered on this plane. $\theta$ can take on any value on the surface. The shear stress ${\tau }_A$ is an in-plane shear stress and causes microcracks to grow along the surface. The maximum out-of-plane shear, ${\tau }_B$ occurs on a plane that is oriented at 45 degrees from the free surface and causes microcracks to grow into the surface.

Figure 3. In-Plane Shear Stress and Normal Stress at 90 Degree Plane; In-Plane and Out-of-Plane Shear Stress at a 45 Degree Plane