scholarly journals A phase-field approach to pneumatic fracture with anisotropic crack resistance

2021 ◽  
Author(s):  
Carola Bilgen ◽  
Kerstin Weinberg
Keyword(s):  
Crack Propagation ◽  
Numerical Simulations ◽  
Crack Resistance ◽  
Phase Field ◽  
Finite Elasticity ◽  
Three Dimensions ◽  
Crack Patterns ◽  
Field Approach ◽  
Phase Field Models ◽  
Fracture Processes

AbstractPhase-field models of fracture allow the prediction of crack propagation and crack patterns. In this contribution, externally driven fracture processes in linear and finite elasticity are investigated. Different approaches to consider pneumatic pressure and materials with non-isotropic crack resistance are studied, combined, and examined in detail. The versatility of the proposed models is proven by a series of numerical simulations in two and three dimensions.

A Phase Field Approach to Fracture with Mass Transport Extension for the Simulation of Environmentally-Assisted Cracking

2017 ◽  
Vol 754 ◽  
pp. 153-156 ◽  
Author(s):  
Rainer Falkenberg
Keyword(s):  
Crack Initiation ◽  
Mass Transport ◽  
Crack Propagation ◽  
Phase Field ◽  
Isotropic Hardening ◽  
Crack Model ◽  
Deformation Model ◽  
Coupling Mechanism ◽  
Crack Patterns ◽  
Field Approach

The fracture mechanics assessment of materials exposed to harmful environments requires the understanding of the interaction between the soluted species and the affected mechanical behaviour. With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase field approach is presented with an embrittlement-based coupling mechanism showing the influence on crack patterns and fracture toughness. Within the phase field approach the modeling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies such as curvilinear crack patterns, without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations. The simulation of showcases demonstrates crack initiation and crack propagation aiming for the determination of stress-intensity factors and crack-resistance curves.

A ξ-vector formulation of anisotropic phase-field models: 3D asymptotics

1996 ◽  
Vol 7 (4) ◽  
pp. 367-381 ◽  
Author(s):  
A. A. Wheeler ◽  
G. B. McFadden
Keyword(s):  
Surface Energy ◽  
Phase Field ◽  
Sharp Interface ◽  
Three Dimensions ◽  
Field Equations ◽  
Pure Material ◽  
Anisotropic Surface ◽  
Phase Field Models ◽  
New Formulation ◽  
Anisotropic Phase

In this paper we present a new formulation of a large class of phase-field models, which describe solidification of a pure material and allow for both surface energy and interface kinetic anisotropy, in terms of the Hoffman–Cahn ξ-vector. The ξ-vector has previously been used in the context of sharp interface models, where it provides an elegant tool for the representation and analysis of interfaces with anisotropic surface energy. We show that the usual gradient-energy formulations of anisotropic phase-field models are expressed in a natural way in terms of the ξ-vector when appropriately interpreted. We use this new formulation of the phase-field equations to provide a concise derivation of the Gibbs–Thomson–Herring equation in the sharp-interface limit in three dimensions.

Phase field approach for nanoscale interactions between crack propagation and phase transformation

Nanoscale ◽  
2019 ◽  
Vol 11 (46) ◽  
pp. 22243-22247 ◽  
Author(s):  
Hossein Jafarzadeh ◽  
Valery I. Levitas ◽  
Gholam Hossein Farrahi ◽  
Mahdi Javanbakht
Keyword(s):  
Phase Transformation ◽  
Surface Energy ◽  
Crack Propagation ◽  
Phase Field ◽  
Scale Effects ◽  
Field Approach ◽  
Nanoscale Interactions

The phase field approach for the interaction of fracture and phase transformation is developed including scale effects and change in surface energy.

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