Numerical Simulation of Mixed-Mode Crack Propagation in Functionally Graded Materials

2009 ◽  
Vol 631-632 ◽  
pp. 121-126 ◽  
Author(s):  
Li Ma ◽  
Zhi Yong Wang ◽  
Lin Zhi Wu
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Crack Propagation ◽  
Crack Growth ◽  
Functionally Graded Materials ◽  
Mixed Mode ◽  
Fracture Criterion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Specific Fracture

This paper addresses the numerical simulation of mixed-mode crack propagation in Functionally Graded Materials (FGMs) by means of eXtended Finite Element Method (XFEM), endowed with elastic and toughness properties which gradually vary in space. The method allows to follow crack paths independently of the finite element mesh, this feature is especially important for FGMs, since the gradation of the mechanical properties may lead to complex propagation paths also in simple symmetric tests. Each step of crack growth simulation consists of the calculation of the mixed-mode stress intensity factor by means of a non-equilibrium formulation of the interaction integral method, determination of the crack growth direction based on a specific fracture criterion. A specific fracture criterion is tailored for FGMs based on the assumption of local homogenization of asymptotic crack-tip fields in FGMs. The present approach uses a user-defined crack increment at the beginning of the simulation. Crack trajectories obtained by the present numerical simulation agree well with available experimental results for FGMs. The computational scheme developed here serve as a guideline for fracture experiments on FGM specimens (e.g. initiation toughness and R-curve behavior).

scholarly journals Mixed-Mode Crack Propagation in Functionally Graded Materials

2005 ◽  
Vol 492-493 ◽  
pp. 409-414 ◽  
Author(s):  
Jeong Ho Kim ◽  
Glaucio H. Paulino
Keyword(s):  
Numerical Simulation ◽  
Crack Propagation ◽  
Crack Growth ◽  
Functionally Graded Materials ◽  
Mixed Mode ◽  
Fracture Criterion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Mixed Mode Crack ◽  
Specific Fracture

This paper presents numerical simulation of mixed-mode crack propagation in functionally graded materials by means of a remeshing algorithm in conjunction with the finite element method. Each step of crack growth simulation consists of the calculation of the mixedmode stress intensity factors by means of a non-equilibrium formulation of the interaction integral method, determination of the crack growth direction based on a specific fracture criterion, and local automatic remeshing along the crack path. A specific fracture criterion is tailored for FGMs based on the assumption of local homogenization of asymptotic crack-tip fields in FGMs. The present approach uses a user-defined crack increment at the beginning of the simulation. Crack trajectories obtained by the present numerical simulation are compared with available experimental results.

A New Interaction Integral Method for Analysis of Cracks in Orthotropic Functionally Graded Materials

2003 ◽  
Author(s):  
B. N. Rao ◽  
S. Rahman
Keyword(s):  
Finite Element ◽  
Functionally Graded Materials ◽  
Mixed Mode ◽  
Functionally Graded ◽  
Mixed Mode Fracture ◽  
Arbitrary Geometry ◽  
Smooth Functions ◽  
Graded Materials ◽  
Element Discretization ◽  
Element Method

This paper presents two new interaction integrals for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional orthotropic functionally graded materials of arbitrary geometry. The method involves the finite element discretization, where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as meshless method, boundary element method, and others. Three numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed interaction integrals. Comparisons have been made between the SIFs predicted by the proposed interaction integrals and available reference solutions in the literature, generated either analytically or by finite element method using various other fracture integrals or analyses. An excellent agreement is obtained between the results of the proposed interaction integrals and the reference solutions.

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