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

Abstract

A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.