Issue 41

A.S. Chernyatin et alii, Frattura ed Integrità Strutturale, 41 (2017) 293-298; DOI: 10.3221/IGF-ESIS.41.39 295 (5) where r , θ and x , y are local polar and Cartesian coordinates related to the crack tip, the plane x0y is perpendicular to the crack front line; κ is the parameter of the stress state. It should be noted that   1 2 I K a ,  2 4 Т а . The program in the MATLAB environment, so called "Williams", in conjunction with macro "Crack" provides the calculation of the coefficients of stress field expansion terms (Eq. (5) in the vicinity of the crack tip. The "Williams" interacts with the macro in ANSYS software, which enables collection of the displacements and stresses at measuring points surrounding the crack tip in plane x0y . The determination of the coefficients of expansion (5) is carried out by means of least squares method that provides comparison of these data and data calculated via expression (5). These calculations are performed in many planes which are perpendicular to the crack front for estimation of the SIF and T- stress distribution along front. Algorithm of numerical crack propagation simulation Control program (with GUI) that provides collaboration between program elements of ANSYS and MATLAB software is developed in MATLAB. A schematic diagram of its implementation is given in Fig. 1. The data files with special structures are formed at the beginning for initialization of different data, namely, sizes and geometry of the model, the crack, elements, material properties, options of loading (minimum and maximum value of cyclic loading and residual stresses distribution along thickness) and other data. The solution begins with the start of the control program and "Williams". Next step is the launching of ANSYS in the background mode for creation of the FE-model and solution of minimum and maximum values for the loading cycle. The collected data in the analyzed points are transiting to "Williams". Figure 1 : The algorithm of numerical solution for the crack propagation problem. After computing the coefficients of William’s expansion for the minimum and maximum loads per cycle (as well as K min, T max , K max ), the control program calculates values of the fatigue crack increment at each points of the crack front in accordance with Eq. (4). The new configuration of the crack front is formed and saved in the data file for the "Crack" macro. This specified sequence of procedures in ANSYS and MATLAB are executing repeatedly.