Phase field cohesive zone modeling for fatigue crack propagation in quasi-brittle materials

Baktheer, Abedulgader; Martínez-Pañeda, Emilio; Aldakheel, Fadi

doi:10.1016/j.cma.2024.116834

Cited by 22 publications

(2 citation statements)

References 99 publications

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“…During compression or unloading, the irreversibility condition is required to ensure a monotonically increasing phase field variable. Consequently, a strain-history field H(x, t) [20,27], defined as shown below, was introduced:…”

Section: Governing Equationsmentioning

confidence: 99%

“…The non-local damage models applied to Griffith's theory are based on the variational formulation developed by Francfort and Marigo [17,18] and implemented by Bourdin et al [19]. Complex fracture processes in two-and three-dimensional [20] solids, such as crack initiation, propagation, and branching, can be processed automatically without any additional ad hoc strategies.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation

Kriaa,

Hersi,

Ammar

et al. 2024

Applied Sciences

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In this paper, experimental tensile tests for pre-cracked high Carbon steel ‘C90’ specimens were performed for quasi-static and dynamic loading. High loading velocity affects the crack patterns by preventing deflection. On the other hand, an efficient numerical tool based on the phase field model was developed and validated to predict brittle fracture trajectories. A staggered numerical scheme was adopted to solve the displacement and damage fields separately. Implementation efficiency in initiating and propagating cracks, even from an undamaged microstructure, was proved. The effect of the critical fracture energy density Gc on the crack path was tested; with smaller Gc, the crack patterns become more complex. In addition, the impact of loading velocities was examined, and earlier and faster crack formation and greater crack branching is observed with higher impact velocity. In this study, bidimensional plane stress cases were treated. The phase field model with hybrid formulation was able to predict crack pattern and especially crack arrest and branching found in the literature. The developed model accurately determined the transition zone of the crack path topology that has been observed experimentally.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation

Kriaa,

Hersi,

Ammar

et al. 2024

Applied Sciences

View full text Add to dashboard Cite

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Dual phase‐field model for immiscible fluid flow through fractured unsaturated porous media

Peters,

Heider,

Markert

2024

Proc Appl Math and Mech

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The immiscible multiphase fluid flow in intact and fractured porous media is relevant to numerous engineering sectors, including industrial processes, geo‐engineering, and civil engineering. These encompass crucial applications that pose significant challenges in modeling, such as carbon dioxide () storage in underground reservoirs, contaminant transport, and desiccation‐induced hydraulic fracturing in unsaturated soils. In this work, a macroscopic framework is developed to describe the transport of immiscible and multiphase fluids in intact and fractured porous materials. The modeling approach utilizes the embedding of two phase‐field models within the continuum Theory of Porous Media (TPM). The case of negligible capillary pressure in the macroscopic scale is associated with many numerical challenges in solving this nonlinear DAEs system, which forms the major subject of the current work. Hence, the problem of the neglected capillary pressure is defined as a target problem. To deal with this, a thermodynamically consistent modified problem is defined, which incorporates an additional artificial macroscopic capillary pressure based on the Cahn–Hilliard phase‐field approach. To increase the robustness and stability of the numerical solution, the Newton–Raphson method is replaced by a homotopy method that allows a gradual transformation of a simpler, solvable problem into the original target problem that usually converges poorly. The sharp crack topology in the fracture regions is approximated by another phase‐field method, which forms a diffusive transition zone across the crack edges of the deformable porous material. For the solid matrix, we consider a small strain assumption with a heterogeneous distribution of the permeability parameter. The inclusion of heterogeneity allows for a more realistic modeling of crack propagation and fluid‐fluid interaction. For the numerical framework, the coupled DAE system is approximated by the finite element method (FEM), implemented in the open‐source project FEniCSx. Appropriate stabilization techniques are also discussed.

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A review of recent trends and challenges in numerical modeling of the anisotropic behavior of hardened 3D printed concrete

Baktheer,

Classen

2024

Additive Manufacturing

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Phase field cohesive zone modeling for fatigue crack propagation in quasi-brittle materials

Cited by 22 publications

References 99 publications

Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation

Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation

Dual phase‐field model for immiscible fluid flow through fractured unsaturated porous media

A review of recent trends and challenges in numerical modeling of the anisotropic behavior of hardened 3D printed concrete

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