Determination of stress intensity factors in cracked plates by the finite element method

Abstract

Stress fields near crack tips in an elastic body can be specified by the stress intensity factors which are closely related to the stress singularities arising from the crack tips. These singularities, however, cannot be represented exactly by conventional finite element models. A new method for the analysis of stresses around cracks is proposed in this paper on the basis of the superposition of analytical and finite element solutions. This method is applied to several two-dimensional problems whose solutions are obtained analytically, and it is shown that their numerical results are in excellent agreement with analytical ones. Sufficiently accurate results can be obtained by the conventional finite element analysis with rather coarse mesh subdivision. Computational efforts are then considerably reduced compared with other methods.

Morphological aspects of fatigue crack propagation Part II—effects of stress biaxiality and welding residual stress

“…The stress field ahead of the crack tip is analyzed, and not only the stress intensity factors but also the higher order stress field parameters are determined by the method of superposition of analytical and finite-element solutions [5], so that a curved crack-growth path can be predicted by applying the results to the first order perturbation solution of slightly curved crack extension [6], [7]. The local symmetry criterion for a fatigue crack-propagation path, which has been proposed in [3], is used in the present simulation.…”

“…Comparing the curves A and B, we can see the effect of the residual stress on the fatigue crack propagation. The curve A is obtained disregarding the residual stress, while the curve B takes into account the effect by using (5). In both cases, (3) is used as the crack-growth equation.…”

“…A two-dimensional cracked domain is analyzed by the finite element method, and the stress field ahead of the current crack tip is analyzed by taking into account the higher order stress field parameters at the crack tip (Yamamoto and Tokuda [5]). A curved crack increment can be determined by using the first order perturbation solution (Sumi, Nemat-Nasser, and Keer [6], and Sumi [7]) together with the local symmetry criterion used as a fatigue crack-path criterion [3].…”

Stress intensity factors for three-dimensional cracks

“…They have applied this method for the analysis of stress intensity factors in two-dimensional and axisymmetric bodies [13][14][15][16][17]. In the present paper, they propose a method for the analysis of three-dimensional distributions of the stress intensity factor on the basis of the concept of the method of superposition.…”

Improvement of stress intensity factors computed from path‐independent integrals by Richardson's extrapolation

“…The independence between I and the ordered pair (w, t) permit us to take w h (grid size) and t l (crack length) in equation (5). Because the grid size h goes to zero, the series expansions of H x and H y have the following form:…”