13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- High Cycle Fatigue Simulation using Multi-temporal Scale Method coupled with Continuum Damage Mechanics Dong Qian1,*, Sagar Bhamare2 1 Department of Mechanical Engineering, University of Texas at Dallas, Richardson, TX 75080, USA 2 Innova Engineering, Inc., Irvine, CA 92614, USA * Corresponding author: dong.qian@utdallas.edu Abstract A multiple temporal scale computational approach for assessing the fatigue life of engineering materials and components is presented. This full-scale simulation approach is developed in light of the challenges in employing the traditional computational method based on Finite Element Method (FEM)) and semi-discrete schemes for fatigue design and analysis. Simulating loading conditions with cycles on the order of hundreds of thousands and beyond is generally an impractical task for FEM even with the high-performance computing platform. Two critical aspects are addressed, i.e., the multiple time scales associated with the fatigue loading condition and the fatigue initiation/growth representations. Detailed implementation of integrating a multiscale space-time representation with a robust material model for the fatigue failure is outlined and demonstrated in the context of a common choice of industrial metal. Keywords Space-time FEM, High Cycle Fatigue, Multi-temporal Scale Method, Enrichment 1. Introduction In fatigue-based design of mechanical components and structures, safe-life and damage-tolerance approaches have been widely employed in practice. In safe-life approach, stress or strain are related to the number of cycles to failure under fatigue loading. Empirical curves developed from such a kind of relation are utilized to predict the life or acceptable level of fatigue load. Damage-tolerance approach based itself on the fracture mechanics concepts established by Griffith [1] and Irwin [2]. Using these concepts, Paris [3] proposed the relationship between the rate of crack growth and the range of applied stress intensity factor, which is used to predict the fatigue crack growth under cyclic loading history. While both methodologies have been widely used by the industry, they have significant limitations due to the empirical nature of the method. In addition, there can be significant scatterings in the fatigue test, which makes the curve-fitting unreliable. Further, the extrapolation of constant amplitude (CA) test data to predict life under variable amplitude (VA) and random loading conditions is a challenging task [4]. Motivated by these limitations, a multiple temporal scale computational approach is developed to assess the fatigue life of structural components. Examples include columns, beams, plates, and shells that are extensively used in assembly of mechanical components. This full-scale simulation approach is established in light of the challenges in employing the traditional computational method based on Finite Element Method (FEM) and semi-discrete schemes for fatigue design and analysis. Semi-discrete schemes such as the popular central difference or Newmark-β methods are known to suffer from either the time-step constraints or lack of convergence due to the oscillatory nature of the fatigue loading condition. As such, simulating loading conditions with cycles on the order of hundreds of thousands and beyond is generally an impractical task for FEM even with the high-performance computing platform. On the other hand, there is a great demand for such a computational capability as factors such as stress history and triaxiality, nonlinear coupling among the loads, complex geometry are known to critically influence the fatigue failure and generally not
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