Analysis of sensitivity and numerical stability in the calculation of factors of tension intensity in a case of fracture mechanics

Abstract

The article studies the calculation of stress intensity factors in a case of fracture mechanics in steel plates under uniform load configuration. The sensitivity of the first mode factor of stress intensity K_I with respect to the relationships a/w, a/h, h/w (a: initial fracture size, w: plate width, h: vertical distance between fracture and the loading line) is explored. We perform comparisons of the results obtained by different methodologies such as the analytical obtained from the literature, the method of placement of the contour implemented in the free software MAXIMA and the finite element method implemented through a model in ANSYS. Since the method of positioning the contour incorporates a generalized least squares solution, we could observe some problems of numerical instability associated mainly to cases in which the size of the initial fracture is considerable with respect to the width of the loaded plate. The most relevant contributions are given regarding the particular sensitivity analysis of the case, the analysis of problems of numerical instability in specific situations of K_I calculation, implementations of free software codes such as MAXIMA and implementation of finite element models in ANSYS using Quarter Elements Point. The results obtained are reported by numerical and graphical comparisons of the behavior of the K_I factor for the different relationships studied under different methodologies. The article concludes on what are the significant relations in the sensitivity of the stress intensity factor K_I and the origin of the problems of numerical instability of the placement method by the parametric study associated to the condition number of the system of the global matrix of the same method.