A micromechanics-based non-local damage to crack transition framework for porous elastoplastic solids

Abstract

The failure process of ductile porous materials is simulated by representing the damage nucleation, growth and coalescence stages up to crack initiation and propagation using a physically-based constitutive model. In particular, a non-local damage to crack transition framework is developed to predict the fracture under various loading conditions while minimising case-dependent calibration process. The formulation is based on a discontinuous Galerkin method, making it computationally efficient and scalable. The initial stable damage process is simulated using an implicit non-local damage model ensuring solution uniqueness beyond the onset of softening relying on the Gurson-Tvergaard-Needleman (GTN) model. Once the coalescence criterion is satisfied, which can physically arise before or during the softening stage, a cohesive band is introduced. Within the cohesive band, a void coalescencebased governing law is solved, accounting for the stress triaxiality state and material history, in order to capture the near crack tip failure process in a micromechanically sound way. Two coalescence models are then successively considered and compared. First, with a view to model verification towards literature results, a numerical coalescence model detects crack initiation at loss of ellipticity of a local model, and the crack opening is governed by ad-hoc parameters of the GTN model. Alternatively, the Thomason criterion is used to detect crack nucleation during the softening stage while the Thomason coalescence model governs the crack opening process. This latter model is able to reproduce slant and cup-cone failure modes in plane-strain and axisymmetric specimens, respectively.

A two characteristic length nonlocal GTN model: Application to cup–cone and slant fracture

“…Nucleation parameters for the local and non local models are compared in table 2. This fit leads to a relatively good agreement of the global responses for both test cases with the reference results as well as results from the literature [21,57], as can be seen in figures 3 and 4.…”

“…where ∂Ω and ⃗ n respectively designate the boundary of the body Ω and its outer normal vector. Let us note that the gradients are calculated on the current configuration and not on the initial configuration as considered by [21,22]. Besides, this model introduces two characteristic lengths in equations 10 and 11, l ω and l κ , respectively associated to void growth and nucleation mechanisms.…”

“…They have been selected because they result in complex crack paths, with cupcone fracture for the axisymmetric specimen and slant fracture for the plane strain specimen. In addition, the tests have been used in literature [21,56,57] as a reference to identify and study ductile fracture models.…”

“…Another solution is based on implicit gradient methods [11,12] which facilitate the use of integral methods as originally proposed in [13,14]. These methods have been used to model ductile fracture for metals within a finite strain framework [15][16][17][18][19][20][21] although they were initially developed for quasi-brittle failure. Using an implicit gradient formulation, the local constitutive equations are preserved at the cost of small adaptations.…”

A nonlocal approach of ductile failure incorporating void growth, internal necking, and shear dominated coalescence mechanisms

“…The evolution laws for void characteristics under the shear driven coalescence mode could be enhanced with a more complex micromechanics-based model. When the damage indicator is close to its critical value, the transition to crack will be considered by an energy consistent framework as considered by Wu et al (2014); Leclerc et al (2018Leclerc et al ( , 2020.…”