Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics

Agrawal, Vaibhav; Dayal, Kaushik

doi:10.1007/s10704-017-0234-y

Cited by 22 publications

(9 citation statements)

References 21 publications

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“…Effects of local inertia observed in the present work will also be applicable for phase-field methods used for dynamic fracture. We are pleased to note that the phase field modelers started tending to the same conclusion of the necessity to cancel material inertia together with the material stiffness -see [1] and [8].…”

Section: Role or Inertiamentioning

confidence: 87%

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The effect of local inertia around the crack-tip in dynamic fracture of soft materials

2019

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Phase-field or gradient-damage approaches offer elegant ways to model cracks. Material stiffness decreases in the cracked region with the evolution of the phase-field or damage variable. This variable and, consequently, the decreased stiffness are spatially diffused, which essentially means the loss of the internal links and the bearing capacity of the material in a finite region. Considering the loss of material stiffness without the loss of inertial mass seems to be an incomplete idea when dynamic fracture is considered. Loss of the inertial mass in the damaged material region may have significant effect on the dynamic failure processes. In the present work, dynamic fracture is analyzed using a theory, which takes into account the local loss of both material stiffness and inertia. Numerical formulation for brittle fracture at large deformations is based on the Cosserat point method, which allows suppressing the hourglass type deformation modes in simulations. Based on the developed algorithms, the effect of the material inertia around a crack tip is studied. Two different problems with single and multiple cracks are considered. Results suggest that in dynamic fracture the localized loss of mass plays an important role at the crack tip. It is found, particularly, that the loss of inertia leads to lower stresses at the crack tip and, because of that, to narrower cracks as compared to the case in which no inertia loss is considered. It is also found that the regularized problem formulation provides global convergence in energy under the mesh refinement. At the same time, the local crack pattern might still depend on the geometry of the unstructured mesh.

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Section: Role or Inertiamentioning

confidence: 87%

“…= 0.05 is used for element deletion. 1 Contours of ρ/ρ 0 are shown in Fig. 8 for S 1 to S 3 at t = 167 μs, in the reference configuration.…”

Section: Case IImentioning

confidence: 99%

The effect of local inertia around the crack-tip in dynamic fracture of soft materials

2019

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“…Ziaei-Rad et al (2016) used the non-maximum suppression technique from an image processing field to detect the ridge of the phase-field profile and then applied cubic spline fit to determine the crack path representation with reasonable success to identify crack branching as well as crack tips within the mesh resolution limits. Agrawal and Dayal [368] partially explained the relationship between phase-field and crack opening displacement and irreversibility in the phase-field model. Yoshioka et al [369] presented two approaches -a line integral and a level-set method, to compute the crack opening displacement that is required in hydraulic fracturing simulations and demonstrated that both approaches computed the crack opening temporal growth accurately.…”

Section: Challengesmentioning

confidence: 97%

“…Fast crack propagation under dynamic loading: For some fast crack propagation simulations, e.g. [368], the calculated fracture velocity overestimated the fracture energy dissipation.…”

Section: Specific Challenges For Phase-field Fracture Modelmentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Diehl¹,

Lipton²,

Wick³

et al. 2021

Preprint

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Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, The Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities with their relative advantages and challenges are summarized.

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“…This approach corresponds to static equilibrium with respect to stress fields and conjugate forces to order parameters; hence, propagation speeds of crack fronts and twin boundaries are not quantitatively reproduced. Phase field formulations fully accounting for inertia and time-dependent kinetics are discussed elsewhere for brittle fracture [ 35 , 36 ] and deformation twinning [ 37 , 38 ]. Elastic strain energy density is expressed in terms of a linearized strain tensor, a representation assumed sufficient for problems of brittle fracture addressed herein, to be contemplated further upon inspection of numerical results.…”

Section: Phase Field Theory: Bulk Grains and Matrix Materialsmentioning

confidence: 99%

A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites

et al. 2021

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Diamond-silicon carbide (SiC) polycrystalline composite blends are studied using a computational approach combining molecular dynamics (MD) simulations for obtaining grain boundary (GB) fracture properties and phase field mechanics for capturing polycrystalline deformation and failure. An authentic microstructure, reconstructed from experimental lattice diffraction data with locally refined discretization in GB regions, is used to probe effects of local heterogeneities on material response in phase field simulations. The nominal microstructure consists of larger diamond and SiC (cubic polytype) grains, a matrix of smaller diamond grains and nanocrystalline SiC, and GB layers encasing the larger grains. These layers may consist of nanocrystalline SiC, diamond, or graphite, where volume fractions of each phase are varied within physically reasonable limits in parametric studies. Distributions of fracture energies from MD tension simulations are used in the phase field energy functional for SiC-SiC and SiC-diamond interfaces, where grain boundary geometries are obtained from statistical analysis of lattice orientation data on the real microstructure. An elastic homogenization method is used to account for distributions of second-phase graphitic inclusions as well as initial voids too small to be resolved individually in the continuum field discretization. In phase field simulations, SiC single crystals may twin, and all phases may fracture. The results of MD calculations show mean strengths of diamond-SiC interfaces are much lower than those of SiC-SiC GBs. In phase field simulations, effects on peak aggregate stress and ductility from different GB fracture energy realizations with the same mean fracture energy and from different random microstructure orientations are modest. Results of phase field simulations show unconfined compressive strength is compromised by diamond-SiC GBs, graphitic layers, graphitic inclusions, and initial porosity. Explored ranges of porosity and graphite fraction are informed by physical observations and constrained by accuracy limits of elastic homogenization. Modest reductions in strength and energy absorption are witnessed for microstructures with 4% porosity or 4% graphite distributed uniformly among intergranular matrix regions. Further reductions are much more severe when porosity is increased to 8% relative to when graphite is increased to 8%.

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Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics

Cited by 22 publications

References 21 publications

The effect of local inertia around the crack-tip in dynamic fracture of soft materials

The effect of local inertia around the crack-tip in dynamic fracture of soft materials

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites

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