Research Article: Full thermo-mechanical coupling using eXtended finite element method in quasi-transient crack propagation

Date Published: July 3, 2018

Publisher: Springer International Publishing

Author(s): Fakhreddine Habib, Luca Sorelli, Mario Fafard.


This work aims to present a complete full coupling eXtended finite element formulation of the thermo-mechanical problem of cracked bodies. The basic concept of the extended finite element method is discussed in the context of mechanical and thermal discontinuities. Benchmarks are presented to validate at the same time the implementation of stress intensity factors and numerical mechanical and thermal responses. A quasi-transient crack propagation model, subjected to transient thermal load combined with a quasi-static crack growth was presented and implemented into a home-made object-oriented code. The developed eXtended finite element tool for modeling two-dimensional thermo-mechanical problem involving multiple cracks and defects are confirmed through selected examples by estimating the stress intensity factors with remarkable accuracy and robustness.

Partial Text

The interest in fracture mechanics and its applications has gained considerable importance in recent years in various industries: aerospace engineering, automobile industry, civil engineering, etc. This attention is due to the high cost caused by the presence of cracks and defects, which require more energy, time, substantial efforts and dedicated strategies regarding intervention, maintenance, repair, etc. Practically, taking into account the real environmental conditions in service has become essential, when the material is subject to a significant gradient of temperature. For instance, temperature change in real structures, where the deformation are constrained, can engender a mechanical load and a high-stress concentration around crack tips. Subsequently, crack can propagate with a, a priori, not known orientation, direction, intensity etc. Since, cracks cannot be eliminated under any circumstances; this prompts engineers to guide our efforts towards winning strategies in prevention, design and especially analysis that can be provided by the tool of numerical modeling.

A set of thermo-mechanical examples are herein discussed by considering a strong material discontinuity; for a static adiabatic crack and in propagation state of an isotropic material. Validation of the results is fulfilled by a comparison with the computation of the stress intensity factors which allows validating both mechanical and thermal responses as well as the quantification of the linear elastic fracture mechanics (LEFM) parameters. The computation domains chosen for the benchmarks are extracted from the literature and meshes are generated using Gmsh [52]. A hybrid object-oriented code has been developed in a monolithic multi-physical philosophy treating each step starting from the mesh generated from Gmsh, the definition of the enrichment-zone, the XFEM matrix computation blocks associated to each physical segment and to each coupled part, the computation of fracture mechanics quantities and post-processing context.

A new thermo-mechanical crack propagation model in a cracked body was presented which can be applied, for instance, to ensure the safety of structures subjected to thermal loading. The developed geometrical eXtended finite element method was successfully applied to model crack growth and achieving the expected optimal rate of convergence by confirming the benefit of the fixed enrichment area approach on the computation of stress intensity factor profile. Numerical development and various matrices in full coupling were presented for each sub-problems, mechanical and thermal, and for the full coupled XFEM part. The criteria for crack growth, as well as for the direction of the virtual crack extension are described, and their performance in the context of the XFEM is discussed. From three examples, various benchmarks result in a cracked domain are examined and validated from the existing results in the literature. The robustness and the accuracy of the model implementation to extract the thermo-mechanical responses and to compute the associated stress intensity factors for stationary crack, with and without holes, as well as the effect of crack length and hole position on the SIFs are proved. Furthermore, a quasi-transient load example governed by mode-I is presented and the contribution of this loading on the profile of the SIFs until reaching thermal equilibrium is analyzed. Finally, an example of multiple mixed-mode cracks growth and multiple holes that may be present as small flaws in the material manufacturing stage is examined; only the limiting cases of stable crack are discussed. When the heat flow is distributed by the presence of the cracks, we observe a high local intensification of thermal gradients followed by an intensification of thermo-mechanical stress around them, which may lead to the crack growth or inevitable collapse of the structure.




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