Issue34

M. Kikuchi et alii, Frattura ed Integrità Strutturale, 34 (2015) 318-325; DOI: 10.3221/IGF-ESIS.34.34 319 but re-meshing process is needed for modeling of growing crack configurations, it has been a bottleneck for the application of FEM to fatigue crack growth problems, especially in three-dimensional field. Recently, several new techniques have been developed to overcome these difficulties. Element Free Galerkin Method [1], X-FEM [2] and Superposion-FEM(S-FEM[3]) have been developed to make re-meshing processes easy, and predict complicated crack paths. Authors have developed fully automatic fatigue crack growth simulation system[4], and applied it to three-dimensional surface crack problem, interaction evaluation of multiple surface cracks[5] and evaluation of crack closure effect of surface crack[6]. This system is developed for residual stress field problem, and Stress Corrosion Cracking process is simulated [7]. Residual stress field is generated by welding, and evaluation of crack growth in Heat Affected Zone (HAZ) is another important problem. In HAZ, grain size is different from other area, and mechanical properties are different from those of base metals. For the evaluation of SCC in such areas, changes of material properties should be considered. In S-FEM, local mesh is re-meshed for each step of crack growth, and local area changes its ’ shape in each step. It seems difficult to change material properties of local mesh following the change of local mesh shape. In this paper, this problem is solved, and crack growth simulation system in heterogeneous material is developed. In the following, this new method is explained briefly, and example problem is simulated and compared with previous works to verify this method. Several practical problems are simulated and effect of existence of interface and changes of material properties are studied and discussed. A PPLICATION OF S-FEM TO HETEROGENEOUS MATERIAL . -FEM is originally proposed by J. Fish [3]. As shown in Fig.1, a structure with a crack is modeled by global mesh and local mesh. Global area, G  , does not include a crack, and course mesh is used for the modeling of global area. A crack is modeled in local area, L  , using fine mesh around crack tip. Local area is superimposed on global area and full model is made. In each area, displacement function is defined independently. In overlapped area, displacement is expressed by the summation of displacement of each area. To keep the continuity at the boundary between global and local area, GL  , displacement of local area is assumed to be zero as shown in the following equation.             0 G G L i G L L i i i L GL i u i u u u i u i (1) Figure 1 : Concept of S-FEM. The derivatives of displacements can be written in the same way. These displacement functions are applied to virtual work principle, as shown in Eq. (2), and .the final matrix form of S-FEM is obtained as shown in Eq. (3) , , , , , , , , G L L L t G G G L i j ijkl k l i j ijkl k l L G L L G tG i j ijkl k l i j ijkl k l i i u D u d u D u d u D u d u D u d u t d                         (2)       0 GG GL G G LG LL L K K u t K K u                                              (3) S