Issue 32

N. Bisht et alii, Frattura ed Integrità Strutturale, 32 (2015) 1-12; DOI: 10.3221/IGF-ESIS.32.01 3 automatically. The number of elements around the circumference is taken as 32. The FE modelling parameters are optimized on the basis of the error analysis presented in Fig. 3 for two edge cracks. Figure 2 : Plane 82 element with 8-nodes. Figure 3(a) : Variation of stress intensity factor with number of crack tip elements. Figure 3(b) : Variation of stress intensity factor with radius of first row of elements, K I,FEM and K I, THE are finite element and theoretical based computations of mode I stress intensity factor The error analysis has been done by varying the radius of the first row of the crack tip element and number of elements in the first row and computing the stress intensity factor for various parameters. The density of the FE mesh is modified by varying the number of the elements of the first row as 16, 20, 24, 32 and 40, keeping the radius of the first row as a /8 where a has been taken as 10 mm. Also, the radius of the first row ( a/n ) around the crack tip is varied, taking n= 8, 10, 12, 16 and 20 with 32 number of elements. For comparison K I is calculated theoretically from the relation given for two collinear edge cracks [30]. It is found that the K I calculation errors stay below 0.8% for all meshing strategies. Fig. 3(a-b) show variation of the normalized K I (FE based computation to the actual (theoretical) Mode I stress intensity factor) for different mesh configurations. It can be observed from Fig. 3 that, on average, the calculation with the radius of first element as 1.25 mm (i.e. a / 8=1.25) and number of elements around the crack tip as 32 yields least error i.e. closest to unity amongst the other meshing strategies. It is mentioned by Miranda et al. [32] that calculation error and associated standard deviation tend to increase for higher mesh density. These increasing errors are a result of an ill conditioned numerical problem [32]. The increasing error due to the decrease in first crack tip radius may be due to the stress singularity that is present at the crack tip and the linear elastic fracture mechanics concept fails to predict the stress intensity factor. The other FE modelling parameters are shown in Fig. 4 and 5. In Fig. 5 node 1 is the crack tip node and the nodes 2, 3, 4 and 5 are used to represent the crack path for evaluating the fracture parameters. The nodes are essentially taken in this order when a full crack model is employed. For the numerical simulation, a uniform pressure intensity of 1.0 MPa (80 N) is applied to the upper and lower edges in the vertical direction (y axis). The material properties are Young’s Modulus E=70 GPa, Poisson’s ratio=0.33. The mode I and mode II stress intensity factors are computed from the following relations using the displacement extrapolation method.