Ductile damage modelling with locking‐free regularised GTN model

Abstract

The major goal of this work is to develop a robust modelling strategy for the simulation of ductile damage development including crack initiation and subsequent propagation. For that purpose, a Gurson-type model is used. This model class, as many other damage models, leads to significant material softening and must be used within a large deformation framework due to the ductile character of the materials. This leads to 2 main difficulties that should be dealt with carefully: mesh dependency and volumetric locking. In this work, a logarithmic finite strain framework is adopted in which the Gurson-Tvergaard-Needleman constitutive law is reformulated. Then a nonlocal formulation with regularisation of hardening variable is applied so as to solve mesh dependency and strain localization problem. In addition, the nonlocal model is combined with mixed "displacement-pressure-volume variation" elements to avoid volumetric locking. Thereby, a mesh-independent and locking-free finite strain framework suitable for the modelling of ductile rupture is established. Attention is paid to mathematical properties and numerical performance of the model. Finally, the model parameters are identified on an experimental database for a nuclear piping steel. Simulations of standard test specimens (notched tensile bars and compact tension and single edge notched tensile cracked specimens) are performed and compared to experimental results. KEYWORDSductile damage, GTN model, mesh dependency, mixed finite element, nonlocal regularisation, volumetric locking

Modelling of localized ductile fracture with volumetric locking‐free tetrahedral elements

“…On this basis, a three-field (u∕̃h∕p) mixed method with localizing gradient enhancement is presented. The proposed method is a departure from existing work in the literature, 10,12,43 which adopted conventional gradient enhancement. The mesh sensitive regularization of the proposed method is demonstrated with a uniformly tapered plate test.…”

“…In the literature, the combination of the three-field mixed element and conventional gradient enhancement has been reported to resolve both mesh sensitivity and volumetric locking issues. 10,12,43 Besides, the mesh-sensitive regularization capacity of localizing gradient enhancement has been demonstrated in Xu and Poh. 21 In this section, the performance of the proposed three-field mixed element with localizing gradient enhancement is further investigated with a uniformly tapered plate.…”

“…There are two major classes of nonlocal enhancements adopted in literature for ductile fracture: (a) integral formulation 1,[5][6][7][8] and (b) gradient formulation. [9][10][11][12][13][14][15][16] In a nonlocal formulation, the size of the interaction domain is characterized by a length scale parameter, which serves as a localization limiter. Conventionally, a constant interaction domain (length scale parameter) is adopted throughout the loading process.…”

“…In parallel, a similar framework combining both u∕̃h mixed field and gradient enhancement has been adopted for finite strain ductile fracture problems with tetrahedral elements, to resolve both volumetric locking and mesh sensitivity issues. 10,12,43 This study focuses on the simulation of ductile fracture with 10-node tetrahedral elements. The performance of F-bar and mixed field methods are accessed.…”

“…) and(12), the linearization of Kirchhoff stress can be determined asd ij = ds im (I mj + 2e mj ) + 2s im de mj = [  imkl (I mj + 2e mj ) + 2s im I mkjl ] de…”