Issue 50

G. Khandouzi et alii, Frattura ed Integrità Strutturale, 50 (2019) 29-37; DOI: 10.3221/IGF-ESIS.50.04 30 I NTRODUCTION n most civil or mining projects such as blasting, road tunnels excavation, flying rocks and support systems, the type of the forces applied are dynamic. There are several methods to predict the effect of dynamic loads on structures with a flaw. One of the most important of these methods is introduced by the International Society of Rock Mechanics (ISRM) in 2012. This method uses semicircular specimens with a pre-existing crack under dynamic load. Measurement of dynamic failure parameters such as stress intensity factor, crack start and crack propagation velocity when analyzing the behavior of a dynamically loaded structure is important. While a dynamic load distribution model increases the level of complexity and the existing analytical solutions are mainly suitable for simple problems, numerical modeling is considered as a suitable tool for solving these problems. According to Jing [1], a valid numerical model requires complete knowledge of the geometric and physical properties of fractured rock masses. The main challenge is not to build a perfect model, but to create a model that is suitable for the main purpose [1]. For analyzing the fracture, there are a variety of numerical methods for cracking process modeling such as NMM (Numerical Manifold Method) [2], DDA (Discontinuous Deformation Analysis) [3], BEM (Boundary Element Method) [ 4], RFPA (Rock Failure Process Analysis) [5], PFC (Particle Flaw Code) [6], X-FEM [7, 8], and several other in-house codes based on the LEFM Criteria [9]. In addition to creating system equations, two main tasks include evaluating the stress intensity factors (SIF) and fracture growth simulation based on determining the mode of fracture (I, II and III) and different criteria for fracture growth such as maximum tensile strength or energy release rate [1]. So, based on the requirements listed above, as well as Jing expressed in numerical modeling, in this study, XFEM method is used for modeling crack propagation. Failure mechanism consists of two parts start failing and the damage assessment based on the maximum principal stress fracture and power-law fracture criteria. The displacement extrapolation method has been used to determine initiation stress intensity factor and CSOD plot for modeling verification. CDP model is adapted to estimate the failure area in the specimen and comparison between kinetic energy and internal energy for verification of the CDP model. E XTENDED FINITE ELEMENT METHOD odeling of fixed discontinuities, such as cracks, using the conventional finite element method, requires that the mesh is compatible with geometric discontinuities. Therefore, a high mesh density is required in the neighborhood of the crack edge to capture the singular asymptotic fields properly. Moreover, modeling of a growing crack is even more complex as the mesh ought to be updated continuously to fit the geometry of the fracture as the crack progresses [10]. The extended finite element method (XFEM) reduces the problems associated with the meshing of crack surfaces [10]. Nowadays, the X-FEM has developed as a powerful numerical method for the analysis of crack propagation [11]. This method mixed finite element and meshless method. Modeling of crack explicitly in this method isn't by the mesh, but it uses the crack geometry implicit description, compatible with any crack path, regardless of its prior condition [12-13]. One of the major benefits of X-FEM on Finite Element Method is the flexibility and versatility in modeling, which does not need to be aligned with the element edges. This method is based on the enrichment of the FE model with additional degrees of freedom (DOF) connected with the nodes of the elements intersected to the discontinuity [14]. Failure criterion in X-FEM X-FEM model uses the maximum principal stress criterion for the damage initiation criterion and also a power-law criterion for calculation of damage assessment law. Eqn. (1) illustrates the maximum principal stress criterion : 0 Max Max f          (1) Where 0 Max σ shows the maximum principal stress allowed. The Macaulay bracket with the ordinary interpretation is represented by the symbol . To signify compressive stress that does not initiate damage the Macaulay brackets are used. Initiation of damage is assumed to begin when the maximum stress ratio is equal to one [10]. The Abaqus uses the power - law model described in Eqn. (2): I M