A global/local model reduction approach dedicated to 3D fatigue crack growth with crack closure effect

Abstract

Experimental and numerical study of fatigue crack propagation in a thick-walled cylinder under cyclic hoop stress I Salam, M A Malik, M Abid et al.Study on the relationship between stress intensity factor and J integral for mixed mode crack with arbitrary inclination based on SBFEM C L Zhu, J B Li, G Lin et al. Abstract. It has been known for decades that fatigue crack propagation in elastic-plastic media is very sensitive to load history since the nonlinear behavior of the material can have a great influence on propagation rates. However, raw computations of millions of nonlinear fatigue cycles on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose a global model reduction strategy, mixing both the a posteriori and a priori approaches in order to drastically decrease the computational cost of these types of problems. IntroductionThe accurate prediction of the fatigue lifetime of components or structures is of great interest for mechanical engineering applications. In this respect, it is now more and more needed to be able to simulate accurately 3D fatigue crack growth in complicated structures. Moreover, realistic problems are submitted to complicated spectrum loadings. In those cases, fatigue crack propagation in elastic-plastic media is particularly sensitive to the localized nonlinear phenomena that take place in the vicinity of the crack tip [1,2]. Indeed, contact and frictional effects along the crack faces as well as the confined plasticity are non-negligible issues in fatigue problems. As a consequence, numerical models for fatigue crack analysis need to be able to couple the characteristic lengths of the structure, the area of interest linked to the crack and its possible propagation, and the characteristic lengths of the confined nonlinearities close to the crack front. Obviously, such simulations are very challenging since raw computations of millions of nonlinear fatigue cycles on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose here to apply the so-called general idea of model reduction, in order to decrease this computational cost.The model reduction methods are used when many resolutions of similar problems are needed. They make use of the information contained in some solutions to make the other computations faster. Those methods can be put in two general categories: the a posteriori and a priori approaches. In the a posteriori approach, some preliminary computations are performed first to build a basis of a reduced subspace approximating the solution space associated with the considered problem. This is called the offline phase, it possibly has a high numerical cost, but it is performed only once. Then, the reduced model can be used in an online phase, many times,