PSI - Issue 33

860 Domenico Ammendolea et al. / Procedia Structural Integrity 33 (2021) 858–870 Domenico Ammendolea et al./ Structural Integrity Procedia 00 (2019) 000 – 000 crack development. However, the need of managing many interface elements involves relevant computational resources, thus limiting the applicability of such approaches to cases with small geometries. As discussed above, each method has strength and weakness, thus making quite impossible to identify the best option that ensures a suitable compromise between computational cost and reliability of results. Recently, new hybrid methods originated by either the join of standard approaches or the enhancement of classic strategy by advanced numerical techniques have been proposed, such as the SBFEM (Dai et al. (2015), Ooi et al. (2012)). The idea of joining different methods or enhancing standards approaches by innovative numerical techniques represents an exciting opportunity to realize a significant step forward in the development of computational fracture mechanics. This paper presents an innovative FE modeling scheme that merges a standard FE scheme with an advanced numerical strategy based on Moving Mesh (MM) technique (Ammendolea et al. (2020), Ammendolea et al. (2021), Greco et al. (2021a), Greco et al. (2020d)). In particular, the MM uses the Arbitrary Lagrangian-Eulerian Formulation (ALE) because of its ability to move the nodes of the computational mesh according to the evolution of the geometry domain caused by advancing cracks with a reduced amount of remeshing events. One relevant aspect relies on the definition of the crack onset condition and the direction of propagation. It is well known that the M integral is an effective technique to extract fracture variables at the crack front ( i.e ., Stress Intensity Factors and T stress). To this aim, the proposed approach integrates the M -integral method into the ALE technique. Besides, standard fracture criteria are used to identify the crack onset condition and the kinking angle. The paper begins with an overview of the main theoretical concepts forming the proposed procedure (Section 2), followed by a comprehensive description of the numerical implementation (Section 3). Besides, an explanation of the propagation process simulated by the proposed scheme is summarized. Finally, numerical results (Section 4) are reported. In particular, comparison results with experimental data and other numerical approaches reported in the literature are presented. 2 Theoretical Background The following section presents the most important theoretical concepts at the base of the proposed modeling approach. Initially, the governing equations of the thermo-mechanical and fracture mechanics are reported. Next, there is an overview of the Arbitrary Lagrangian-Eulerian technique (ALE), followed by a description of the Interaction Integral method ( M -Integral). The strategy is presented regarding two-dimensional cases. However, the discussion is quite general to be easily extended to three-dimensional problems. Dirichlet and Neumann conditions are applied (Fig. 1-a). Specifically, imposed displacements u and temperature T conditions, while t  and q  are the regions where act tractions t and heat flux q . The body has an initial crack (  C ) that departs from the external boundary and finishes to a crack tip T C . In particular, T C is the origin of a local coordinate system whose horizontal axis is tangent to the crack faces. Under the hypothesis of homogeneous, isotropic, and linear elastic material behavior, and quasi-static conditions as well, the governing equations are the classic ones for structural mechanics and heat transfer, i.e. : ( ) ( ) ( ) 0 : 0 0 sym C u T T I f k T Q       − − + =   −  −  + = (1) u  and T  are the portions where are 2.1 Governing equations of the problem Let’s consider a two-dimensional domain 2 R   , whose external boundary  comprises two sub-sets in which

Eqs. (1) must be solved according to the following boundary conditions:

(

) ) 0

(

: C u T T I n t   − −  = sym

on on

and and

on on

u u T T = =





u

t

(2)

k T n q



−   =



T

q