Issue 17

E. Benvenuti et alii, Frattura ed Integrità Strutturale, 17 (2011) 23-31; DOI: 10.3221/IGF-ESIS.17.03 23 A brittle fracture criterion for PMMA V-notches tensile specimens based on a length-enriched eXtended Finite Element approach E. Benvenuti, R.Tovo, P. Livieri Università di Ferrara A BSTRACT . A criterion for the prediction of the static failure loads in tensile PMMA specimens with sharp notches is presented. The proposed criterion is based on a regularized version of the eXtended Finite Element Method (XFEM), which has been previously applied to concrete-like materials. The main feature of the proposed approach is that the cracking process is not treated as a local process, but it is modeled by assuming that macro-cracks stem from the interaction of micro-cracks within a finite width process zone. The case of a brittle materials with thin process zone is tackled by assuming one layer of enriched finite elements. Preliminary results concerning PMMA specimens subjected to mode-one loading are presented. K EYWORDS . Static failure criteria; PMMA; XFEM. I NTRODUCTION harp notches in tensile structural elements trigger crack initiation and influence the global load bearing capacity. Hence the necessity of formulating reliable and effective static failure criteria for structures with sharp notches emerges. In particular, if the case of notched components made of brittle materials is considered, criteria based on the evaluation of the local maximum value of a stress scalar fail, owing to the presence of infinite values of the stress field components. As argued by Neuber [1], effective static fracture criteria can be introduced by assuming that crack initiation is governed by volume, or surface, averages of the local stress scalar field, which is most representative of the expected failure mode. For instance, Seweryn [2] proposed a criterion based on the evaluation on the maximum value of the stress scalar, which is obtained by averaging the stress component normal to the crack direction along the crack path. A further extension of this approach can be envisaged in the critical distance criteria proposed by Taylor et al. [3]. The introduction of volume averages of stress scalars can be alternatively interpreted as the adoption of a non-local fracture criterion, where the critical value of a certain scalar field at a point depends not only on the local value of that field at the current point, but also on the values that the scalar field reaches at the surrounding points [4, 5]. The non-local continuum concept has been especially exploited in the numerical analysis of components made of elasto-damaging materials. Specifically, two variants of non-local models have been intensively used: integral models and gradient models. Inspired by the approach proposed by Peerlings et al. [6], Tovo et al. [7, 8] proposed an implicit gradient static failure criterion which is very reliable, as it can be easily implemented by using standard tools for solving partial differential equations within usual finite element codes. An advantage of the implicit gradient static failure criterion is that the non- local equivalent stress can be obtained over the entire spatial domain without a priori assumption of the position of the critical points [7]. An alternative approach to overcome the stress singularity at the crack tip is represented by the adoption of a cohesive crack model [9-11]. In the cohesive crack model, a traction-separation law is introduced along the crack path. The S