Computer Simulation of Fracture in Brittle Polycrystalline Solids: Effect of Modulus Anisotropy
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Computer Simulation of Fracture in Brittle Polycrystalline Solids: Effect of Modulus Anisotropy Shiun Ling and Michael P. Anderson Exxon Corporate Research Science Laboratories Annandale, New Jersey 08801, U.S.A.
ABSTRACT A simulation procedure based on the spring network model has been developed for studying the fracture behavior in brittle, polycrystalline solids. In this 2-D model, the effect of crystalline symmetry is accounted for by imparting to individual bonds a constitutive relationship using the material compliance matrix. Using this model, it was found that the fracture morphology becomes more intragranular in nature with increasing modulus anisotropy. Careful analysis suggests that this is due to the wider stress distributions, and the resulting larger number of cracks generated in the interior of anisotropic grains.
INTRODUCTION The fracture processes in brittle polycrystalline solids are controlled by the material properties (modulus, fracture energies), and the microstructural features (crystallite orientations, second phase distributions). An in-depth understanding of the complex interactions between these controlling factors and the failure processes is critical to the engineering of structural components. Numerical simulations using the spring network model provide a powerful tool for this investigation. This is because this type of model allows for spontaneous crack growth, and can include the details of real material microstructures. The spring model had been employed by numerous researchers [1-5]. In their models the spring interactions typically consist of a central force term augmented by a bondbending three body force term. By choosing appropriate values for the force constants, these models can describe isotropic mechanical behavior. These model have also been extended to simultaneously use several different types of springs, so that collectively the springs can describe the anisotropic mechanical behavior found in many materials [3, 61. This approach, however, has the problem that once a spring is broken, the remaining other types of springs can no longer reproduce the intended behavior. In this work a simulation procedure based on the spring network model is developed for studying the effect of modulus anisotropy due to crystalline symmetry. In this approach every spring is made to individually possess the desired modulus property, and thus avoiding the problem pointed out above. This model is described in details in the methodology section. Here it is employed to study the brittle fracture behavior in polycrystalline solids as functions of modulus anisotropy, and fracture energies.
MODELLING METHODOLOGY A 2-D computer image of the polycrystalline microstructure is first generated. This can be done by mapping the continuum grain structure onto a discrete lattice as shown in Fig. 1(a). In the present work we have chosen to work with a square lattice. To each lattice site is then assigned a number, Q, that represents the crystallographic orientation of the grain in which the site is embe
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