Strain Energy Decomposition Influence in the Phase Field Crack Modelling at the Microstructural Level of Heterogeneous Materials

2019 ◽  
Vol 827 ◽  
pp. 482-487
Author(s):  
Karlo Seleš ◽  
Zdenko Tonković ◽  
Ante Jurčević ◽  
Jurica Sorić
Keyword(s):  
Phase Field ◽  
Heterogeneous Materials ◽  
Nodular Cast Iron ◽  
Stopping Criterion ◽  
Energy Decomposition ◽  
Initiation And Propagation ◽  
Decomposition Models ◽  
Residual Norm ◽  
Complex Crack ◽  
Metallographic Images

The prediction of a crack initiation and propagation occurring on the microstructural level of heterogeneous materials can be a very demanding problem. According to the results of recent investigations, the emerging phase field approach to fracture has a strong potential in modelling the complex crack behaviour in a simple manner. In this study, recently developed phase field staggered solution scheme with the residual norm stopping criterion has been employed for the fracture analysis of heterogeneous microstructure exhibiting complex crack phenomena. The microstructural geometries based on the metallographic images of the nodular cast iron and the material properties of an academic brittle material have been used in numerical simulations where the graphite nodules have been considered as porosities. Two commonly used energy decomposition models, the spectral decomposition and the spherical-deviatoric split, and their effects on the results of the phase field modelling are investigated. Numerical results show that the proposed algorithm recovers the complicated crack path driven by the complex microstructural topology.

scholarly journals A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1913
Author(s):  
Yousef Navidtehrani ◽  
Covadonga Betegón ◽  
Emilio Martínez-Pañeda
Keyword(s):  
Phase Field ◽  
Crack Nucleation ◽  
Crack Density ◽  
Contact Problems ◽  
Element Mesh ◽  
Robust Implementation ◽  
Current Implementation ◽  
User Material Subroutine ◽  
Complex Crack ◽  
Monolithic Solution

We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus’ in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed is made freely available.

scholarly journals Improvement of preconditioned bi-Lanczos-type algorithms with residual norm minimization for the stable solution of systems of linear equations

2021 ◽  
Author(s):  
Shoji Itoh
Keyword(s):  
Relative Error ◽  
Conjugate Gradient ◽  
Linear Equations ◽  
Stable Solution ◽  
Stopping Criterion ◽  
Type Method ◽  
Stabilized Method ◽  
Norm Minimization ◽  
Systems Of Linear Equations ◽  
Residual Norm

AbstractIn this paper, improved algorithms are proposed for preconditioned bi-Lanczos-type methods with residual norm minimization for the stable solution of systems of linear equations. In particular, preconditioned algorithms pertaining to the bi-conjugate gradient stabilized method (BiCGStab) and the generalized product-type method based on the BiCG (GPBiCG) have been improved. These algorithms are more stable compared to conventional alternatives. Further, a stopping criterion changeover is proposed for use with these improved algorithms. This results in higher accuracy (lower true relative error) compared to the case where no changeover is done. Numerical results confirm the improvements with respect to the preconditioned BiCGStab, the preconditioned GPBiCG, and stopping criterion changeover. These improvements could potentially be applied to other preconditioned algorithms based on bi-Lanczos-type methods.

scholarly journals Phase-field fracture modelling of crack nucleation and propagation in porous rock

2020 ◽  
Vol 224 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Alex Spetz ◽  
Ralf Denzer ◽  
Erika Tudisco ◽  
Ola Dahlblom
Keyword(s):  
Numerical Model ◽  
Phase Field ◽  
Crack Nucleation ◽  
Phase Field Model ◽  
Experimental Tests ◽  
Shear Cracks ◽  
Rock Samples ◽  
Fine Grained ◽  
Propagation Pattern ◽  
Complex Crack

AbstractIn this work, we suggest a modified phase-field model for simulating the evolution of mixed mode fractures and compressive driven fractures in porous artificial rocks and Neapolitan Fine Grained Tuff. The numerical model has been calibrated using experimental observations of rock samples with a single saw cut under uniaxial plane strain compression. For the purpose of validation, results from the numerical model are compared to Meuwissen samples with different angles of rock bridge inclination subjected to uni-axial compression. The simulated results are compared to experimental data, both qualitatively and quantitatively. It is shown that the proposed model is able to capture the emergence of shear cracks between the notches observed in the Neapolitan Fine Grained Tuff samples as well as the propagation pattern of cracks driven by compressive stresses observed in the artificial rock samples. Additionally, the typical types of complex crack patterns observed in experimental tests are successfully reproduced, as well as the critical loads.

Multi-Scaling Homogenization Process for Nodular Cast Iron Using BEM

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1740005
Author(s):  
Adrián Alberto Betancur Arroyave ◽  
Carla Tatiana Mota Anflor
Keyword(s):  
Cast Iron ◽  
Effective Properties ◽  
Heterogeneous Materials ◽  
Nodular Cast Iron ◽  
External Boundary ◽  
Element Formulation ◽  
Modeling Tools ◽  
Homogenization Process ◽  
Nodule Shape ◽  
Good Agreement

In this work, a multi-scaling homogenization process using boundary element formulation (BEM) for modeling a two-dimensional multi-phase microstructure containing irregular’s inclusions is presented. The BEM is very attractive for multiscale modeling tools for heterogeneous materials. In this approach, the iterative inhomogeneity discretization of the external boundary is disregarded, leading to a computational low cost. This approach was used for solving the elastic problem of a representative volume element (RVE) and the field theory medium. The main goal relies on finding the effective properties of micro-heterogeneous materials within a homogeneous and orthotropic matrix. Expressions for evaluating the effective properties under Plane Stress (PT) for orthotropic materials were also presented. Generally, the numerical models consider the graphite nodules as voids for GGG-40 and the roundness is close circular geometry. In this sense, a nodular cast iron GGG-40 microgram was obtained by X-ray computed tomography and Laser Confocal Microscope System, allowing the modeling of the true nodule shape. The numerical results showed good agreement with the experimental tests. The inclusions of graphite were considered as voids in the material matrix. Experimental stress–strain tests and micrographic analysis were used to determine the Young’s modulus, spatial distributions, as well as, nodule shape. The numerical in this work was compared with the obtained experimental results in this work. The comparison between the obtained experimental data with those available in the literature also showed good agreement.

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