Emilie Ferrié

Extended finite element method for numerical simulation of 3D fatigue crack growth

Abstract This paper is devoted to the presentation of the Extended Finite Element Method (X-FEM) compared to usual Finite Element Method for simulation of 3D fatigue crack propagation under complex loading. This type of situation is very typical of crack propagation in tribological environment. The X-FEM method will be presented in a first part, and two techniques allowing the discretization of cracks will be explained. The interaction integral concept, which allows to compute with a very good accuracy the stress intensity factors KI, KII, KIII, in complex situation will be presented. Once these tools are available, the method can be used very efficiently to simulate crack propagation without remeshing. This property is essential because it guarantees exact energy conservation when the crack is updated. The precise knowledge of individual stress intensity factors KI ,KII and KIII allows deciding the direction of the crack growth (using any crack propagation law). This tool can hence be used to identify the propagation laws in complex cases using comparison between experimental and numerical studies. One example of stress intensity factor computation using a 3D real crack measured by tomography will be shown. 3D crack propagation simulation will be presented. Very recent results will be given for small scale yielding and crack closure situations, which permit to explain, for instance, slowed down crack propagation due to overload.

X-Ray Micro-Tomography Coupled to the Extended Finite Element Method to Investigate Microstructurally Short Fatigue Cracks

In this paper we will present how it is possible to couple a 3D experimental technique with a 3D numerical method in order to calculate the stress intensity factors along the crack front taking into account the real shape of the crack. This approach is used to characterize microstructurally short fatigue cracks that exhibit a rather complicated 3D shape. The values of the stress intensity factors are calculated along the crack front at different stages of crack propagation and it can be seen that the crack shape irregularities introduce rather important fluctuations of the values of KI, KII and KIII along the crack front. The values of KI obtained taking into account the real shape of the crack are significantly different from the ones calculated using an approach based on a shape assumption

Simulation of the Cyclic Response of 316L Single Crystals and Polycrystal Using Three Dimensional Elastic-Plastic Crystalline Finite Element Computations

In the work presented here an elastic-plastic crystalline finite element method is used to simulate the cyclic behavior of 316L austenitic stainless steel single crystals and polycrystal. The evolution of the back stress on each slip system is described using a non linear kinematics hardening law to account for the hardening induced by long range dislocation interactions. As the contribution of short range interactions is assumed to be negligible, the value of the friction stress is kept constant. Three dimensional finite element calculations are performed to simulate the cyclic stress strain curves in the case of a single crystal oriented for multiple slips, as well as for the case of the polycristal. Simulations are compared to experimental data. They seem to be satisfactory for low strain values (εp\2 <10-3) whereas, for εp\2 >10-3, they underestimate the hardening observed experimentally.

Application of X-FEM to 3D Real Cracks and Elastic-Plastic Fatigue Crack Growth

In a general point of view, X-FEM plus level set representation of the interfaces reveals to be of great interest in the aim to couple experimental data with numerical simulations. This can be highly illustrated in the case of 3D fatigue crack growth simulations where the initial 3D “real crack” is extracted from tomo-graphic images. The experimentally observed fatigue crack propagation is compared to numerical simulations. Good agreement is found when a linear variation of closure stress along the crack front is taken into account in the “3D crack propagation law” used for the simulation. Furthermore, in order to take into account plasticity during fatigue crack growth, one develops an augmented Lagrangian formulation in the X-FEM framework that is able to deal with elastic-plastic crack growth with treatment of contact and friction. Numerical issues such as contact treatment and numerical integration are addressed, and finally numerical examples are shown to validate the method.

Characterisation and Modelling of the Three Dimensional Propagation of Short Fatigue Cracks

This paper reports recent results on the characterisation and modelling of the three dimensional (3D) propagation of small fatigue cracks using high resolution synchrotron X ray micro-tomography. Three dimensional images of the growth of small fatigue cracks initiated in two Al alloys on natural or artificial defects are shown. Because of the small size of the investigated samples (millimetric size), fatigue cracks grown in conventional Al alloys with a grain size around 100 micrometers can be considered as microstructurally short cracks. A strong interaction of these cracks with the grain boundaries in the bulk of the material is shown, resulting in a tortuous crack path. In ultra fine grain alloys, the crack shapes tend to be more regular and the observed cracks tend to grow like ”microstructurally long cracks” despite having a small physical size. Finite Element meshes of the cracks can be generated from the reconstructed tomographic 3D images. Local values of the stress intensity factor K along the experimental crack fronts are computed using the Extended Finite Element method and correlated with the crack growth rate.

3D Visualisation of Short Crack Propagation in Al Alloy Using High Resolution Synchrotron X-Ray Microtomography

In-situ fatigue tests monitored by Synchrotron Radiation X-ray microtomography were carried out in order to visualize the three dimensional (3D) shape and evolution of short cracks in the bulk of a cast Al alloy. After the in-situ fatigue test the sample has been infiltrated with liquid Gallium (Ga) in order to visualize the grain structure of the material. Irregularities of the crack advance along the crack front can clearly be correlated to the grain structure of the material.