Numerical investigation on corner singularities in cracked plates using the G-theta method with an adapted θ field

Determination of the fracture toughness of a 9Cr ODS steel fuel cladding using the pin loading Tension test

“…A second method, used, e.g., by Cravero and Ruggieri [30], is based on the direct evaluation of the 𝐽 integral. It will be referred to as the "𝐺 𝜃 method" [31]. In this section, both methods are applied and compared.…”

A method to compute mixed‐mode stress intensity factors for nonplanar cracks in three dimensions

“…As seen in the previous section, estimate (49) may not be tight when u h B is computed using FEM (ie, m = 1∕2). Under conditions discussed in Grossman-Ponemon, 52 because  is an affine functional, we can apply a duality argument and show that…”

“…It is very common in the literature to approximate the pointwise value of G (or a stress intensity factor) by its weighted average over a small section of the crack front. 14,30,36,38,41,[43][44][45][46] Less frequently found are approaches in which G is approximated as a function in a finite element space over  and v is any function in its dual, 24,[47][48][49] which leads to the need to invert the mass matrix of the shape functions over  . Of course, in some cases, it is possible to regard the former as a mass-lumped version of the latter.…”

“…Meanwhile, Davis et al 53 used a separate set of basis functions other than those associated with the nodes along the crack front when using the virtual crack extension method for 3D crack growth simulations. The G-theta method used by Vu et al 49 allows the use of separate spaces for the energy release rate and for the virtual crack extensions, both of which need not be related to the bulk finite element discretization. A secondary effect of the decoupling of the meshes is that we are no longer restricted in how we discretize the fields over the crack front; for example, we may use piecewise affine Lagrange finite elements in the bulk discretization while approximating the stress intensity factors in a spectral basis along the crack front.…”