PSI - Issue 33

Domenico Ammendolea et al. / Procedia Structural Integrity 33 (2021) 858–870 Domenico Ammendolea et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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1 Introduction In many engineering applications, especially when high-temperature gradients are present, the integrity of materials can be seriously compromised. Indeed, widely used engineering materials have either manufacturing or service induced internal cracks, which are ready to expand under severe thermal gradients. This phenomenon is of great concern since materials degrade faster up to complete failure. In such cases, failure events can occur suddenly, with no evidence, thereby involving massive economic losses and severe safety hazards. For this reason, rational predictions of the fracture behavior of materials under thermal loadings are of utmost importance to enhance the overall performances meanwhile avoiding unsafe scenarios. Recently, numerical simulations have become the principal mean of analysis to investigate the fracture behavior of materials in view of the relevant economic advantages assured (De Maio et al. (2020a), Greco et al. (2018a), Greco et al. (2018b)). Indeed, experimental tests are expensive and tricky to conduct, especially considering the difficulties of setting up specific environmental temperatures. Most numerical approaches have been developed in the framework of the Finite Element (FE) method. Commonly, FE methods are collected in two categories, i.e. , smeared crack and discrete approaches (Borst et al. (2004), Greco et al. (2020a)). Such methods differ from each other depending on the way they represent the crack. Smeared crack approaches account for the presence of cracks by using proper constitutive laws (reproducing nonlinear strain-softening behavior), which reduce material properties once that fracture conditions occur. Such methods are straightforward and computationally cheap (Mazars and Pijaudier ‐ Cabot (1989), Scuro et al. (2018a), Scuro et al. (2018b)). However, they have some weaknesses that affect their reliability. Indeed, the local character of the constitutive material (and then the damage as well) implicates that such models suffer from mesh dependency issues. This drawback relies on the fact that once fracture conditions occur, damage localizes in finite elements close to failure points. In the absurd case of extreme mesh refinements, the damage zone reduces accomplishing, thus involving a progressively vanishing of the dissipated fracture energy (Červenka et al. (2005)) . To avoid such an issue, implicit models adopt energy regularization procedures (Bažant and Oh (1983), Peerlings et al. (1996)) . Regularization procedures introduce additional variables acting as localization limiters, thus providing a more suitable dissipated fracture energy quantification. Despite such procedures address mesh dependency issues, the smeared crack models lose the capability to capture smooth crack trajectories. Discrete models simulate internal cracks by including strain or displacement discontinuity fields into standard finite element formulations. Basically, there are two family approaches currently being adopted in FE methods, i.e. , ( i ) intra-element and ( ii ) inter-element approaches. Intra-element approaches reproduce crack discontinuities within the finite elements. Prominent examples of such approaches are the eXtended Finite Element Method (X-FEM) (Bordas et al. (2007)), and the Strong Discontinuities Approaches (SDA) (Sancho et al. (2007)). Intra-element methods reproduce crack initiation and propagation accurately. However, they suffer from difficulties in performing numerical integrations because of the necessity of using highly refined mesh frames to account for the arbitrarily of growing cracks. On the other hand, inter-element approaches trace advancing cracks between the boundaries of the finite elements that form the mesh frame. Specifically, such approaches make use of interface elements (equipped by proper constitutive laws) that reproduce detachment mechanisms. Probably, the most used method is the cohesive zone model proposed by Dugdale (Dugdale (1960)) and Barenblatt (Barenblatt (1962)). In the traditional use, interface elements are inserted along with prescribed mesh frame boundaries before the analysis. For this reason, this strategy is effective for reproducing fracture propagation mechanisms in problems with known crack paths, such as debonding phenomena (Pascuzzo et al. (2020)). If crack paths are unknown in advance, so that cracks can grow arbitrarily, special techniques must be used. One option entails the use of adaptive procedures that update the mesh frame consistent with the crack configuration and insert cohesive elements according to specific insertion criteria (Camacho and Ortiz (1996), Kuutti and Kolari (2012)). Although adaptive strategies address the issues of handling random growing cracks, they are computationally expensive because of the necessity for continuous remeshing actions. Another option relies on the insertion of cohesive elements everywhere in the mesh frame before that analysis starts (De Maio et al. (2019a), De Maio et al. (2020b), De Maio et al. (2019b), Greco et al. (2020b)). Such strategies, known as diffuse interface element methods, avoid remeshing actions, providing a more natural representation of