Evaluation of Crack Tip Stress Field Using Combination of Advanced Implementation of Over-Deterministic Method and FE Analysis

Abstract

Creation of an automatic utility to determine the values of coefficients of higher order terms of Williams power series by usage of over-deterministic method applied to results of finite element analysis is a main goal of this research. The developed procedure based on the support of Java programming language considerably simplifies analyses on optimization of selection of FE nodal results for improvement of accuracy of the near-crack-tip fields’ approximation using Williams series.

Multi-parameter approximation of stress field in a cracked specimen using purpose-built Java applications

“…4 and 5; the progress of g-function is strongly influenced by the used type of distance distribution and the place of interest (determined by the initial angle, the selection sector and the relative crack length). In this aspect the results are in accordance with the conclusions in [16]; this is the reason for choosing three different values of  for stress the field analysis using the ReFraPro application. Note that the FE model, before it was used for evaluation of the stress field via ODM, was successfully verified for the value of the first term of William expansion in previous works (e.g.…”

“…Components of the displacement vector u a v in the selected nodes of the finite-element mesh and also their coordinates serve as inputs to this technique and values of the coefficients of the terms of the series A n , where 1, n N  present its outputs. In the case of this study, the number of the selected nodes k was set to 49 (due to keeping consistence with previous studies in [15,16]) and maximal order of the Williams series term was N = 12, so the system of equations was strongly over-determined (the condition of the over-determination is 2k > N). For the FE calculations the ANSYS computational software [17] was employed.…”

“…In both these issues the distance from the crack tip plays a significant role. The ODeMApp application is created for arbitrary number of nodes picked from the FE model; however, k was set to 49 in this study (explained above, adopted from [15,16]). The space of the parametric study presented in the paper consists of several directions/axes.…”

Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance

“…Published study [19] on WPS approximation with nodal selection from more than one ring around the crack tip resulted into next studies. Another type of nodal selection was considered in subsequent works by the authors [20,21,22]; the nodes were selected from specific parts of the test specimen body with specific distribution functions of their distance and angular position from the crack tip. This way was employed with expectations that the fields will be better (more accurately/efficiently) approximated.…”

“…This way was employed with expectations that the fields will be better (more accurately/efficiently) approximated. An automatic utility to determine the values of coefficients of the higher order terms of WPS using the over-deterministic method was developed [20] to enable multi-parameter description of stress field, where the coefficients of WPS terms are calculated from several layers and angular sections. And the distance distribution of the nodal selection is governed by various functions.…”