In this work, the phase-field approach to fracture is extended to model fatigue failure in high- and low-cycle regime. The fracture energy degradation due to the repeated externally applied loads is ...introduced as a function of a local energy accumulation variable, which takes the structural loading history into account. To this end, a novel definition of the energy accumulation variable is proposed, allowing the fracture analysis at monotonic loading without the interference of the fatigue extension, thus making the framework generalised. Moreover, this definition includes the mean load influence of implicitly. The elastoplastic material model with the combined nonlinear isotropic and nonlinear kinematic hardening is introduced to account for cyclic plasticity. The ability of the proposed phenomenological approach to naturally recover main features of fatigue, including Paris law and Wöhler curve under different load ratios is presented through numerical examples and compared with experimental data from the author’s previous work. Physical interpretation of additional fatigue material parameter is explored through the parametric study.
•The phase-field staggered algorithm with a residual norm based stopping criterion.•An arbitrary porous steel microstructure exhibiting complex crack paths is analyzed.•The stopping criterion is ...highly important for achieving accuracy and efficiency.•Verification by numerical and experimental results available in literature.•Numerical implementation takes advantage of Abaqus FE software features.
The phase-field approach to fracture modeling circumvents the crack-surface tracking problem by introducing the phase-field variable which separates the broken and unbroken material states through a smooth transition. However, very fine spatial discretization is required to resolve the smooth distribution of the phase-field regulated by a small length scale parameter. Thus, it can be computationally rather expensive when paired with an inefficient solution scheme. This contribution presents a comprehensive discussion on the use of a stopping criterion within the broadly used staggered algorithm. The stopping criterion of the iterative scheme based on the control of the residual norm is introduced and implemented in the finite element software Abaqus. It alleviates the problem of the common single iteration staggered algorithm, which requires fine loading incrementation to produce an accurate solution. The model verification is conducted on several standard benchmark tests and a porous microstructure exhibiting complex crack phenomena. The detailed discussions regarding the proposed implementation’s accuracy and CPU time usage are provided, demonstrating an improvement in computational efficiency with accurate results no longer dependent on the careful selection of loading incrementation. The algorithm codes in the form of the Abaqus user subroutines UMAT and UEL are publicly available on Mendeley data repository linked to this work.
•Recently developed generalised phase-field fracture model is employed.•Realistic microstructural geometries of nodular cast iron are analysed.•Model is able to recover brittle/ductile fracture in ...monotonic and fatigue regime.•By changing material properties, a brittle to ductile fracture transition is observed.•Framework is able to solve contact problems coupled with fracture analysis.
The aim of this work is to model complex fracture and fatigue processes in microstructural geometries of nodular cast iron. Herein, recently developed generalised phase-field formulation for modelling fracture in brittle and ductile solids subjected to both monotonic and cyclic loading is employed. Three different sized microstructural specimens are analysed using different modelling options to investigate the transition between brittle and ductile fracture material behaviour. The results demonstrate the ability of the proposed model to reproduce crack nucleation and complex crack propagation patterns. Moreover, the low- and high-cyclic fatigue regime features are presented in terms of fracture patterns and Wöhler-type curve.
This paper presents an efficient thermo-elastoplastic method for the prediction of welding-induced distortions in a large panel structure. It is based on a shell/3D modeling technique which was ...proposed and experimentally validated in the authors’ previous study. Two numerical examples are analyzed to evaluate the accuracy and efficiency of the present method. In the first example, the recommendations for the estimation of the minimum 3D zone size in the shell/3D model reported in the authors’ previous work are verified, in comparison with the full 3D model, on a T-joint model consisting of plates with different thicknesses. It is shown that the shell/3D modeling technique provides a significant reduction in the computational time needed for the simulation of the welding process and thus enables efficient thermo-elastoplastic analyses on large structures. In the second example, the proposed model is validated on a large panel structure by corresponding the experimental data and inherent strain solutions from the literature.
To assess the integrity of a structure, it is necessary to be familiar with the applied loads on its components. In this paper, an inverse modeling procedure was developed to identify the unknown ...static loads of a cracked component made from a brittle material, using a recently developed phase-field fracture modeling approach. The main goal was to define the optimal number, position, and orientation of the strain gauges on the structural component needed to accurately determine the imposed loads leading to different crack sizes and crack orientations. This enables an accurate assessment of the structural integrity of the components throughout their entire service life, including the process of crack initiation and its stable growth to a critical length. To verify the inverse approach, several numerical benchmark examples as well as the vital components of the wind turbine, such as the axle pin were analyzed. It is shown that the proposed approach with optimally placed strain gauges enables the accurate estimation of complex loads in a fractured component.
•Recently developed phase-field staggered algorithm for fracture modeling is used.•Simplified geometry of a nodular cast iron microstructure is analyzed.•Certain size-effect is observed on various ...sample sizes with average nodule content.•Capabilities of the algorithm to predict complex crack paths are demonstrated.•Stopping criterion is essential for objective, increment-size independent results.
The numerical simulation of fracture phenomena occurring in real microstructures of heterogeneous materials is a particularly complicated problem, involving complex cracking processes. On the basis of recent investigations, it is obvious that the phase-field approach has a strong potential to model these processes. However, it requires fine spatial discretization to resolve the smooth transition of the diffusive crack representation regulated by a small length scale parameter. Thus, it tends to be computationally intensive when combined with an inefficient solution scheme. In this paper, recently developed staggered solution procedure based on the residual norm control has been employed for the fracture analysis of heterogeneous microstructure exhibiting crack initiation and complex crack paths. Four different sample sizes have been analyzed, chosen from the simplified geometry of a nodular cast iron microstructure where the size-effect has been observed. The detailed discussions regarding the accuracy and CPU time usage have been given. An improvement in computational efficiency is demonstrated in comparison to the common single iteration staggered algorithm.
The phase-field approach to fracture modelling has gained much attention in the field of computational fracture mechanics in the past decade. The phase-field approach eliminates the need for the ...numerical tracking of the sharp crack discontinuities by the smooth transition of a scalar damage field whose value differentiates between the broken and intact material states. Its variational based approach has been proven to be thermodynamically consistent and able to solve complex fracture processes. Consequently, many different phase-field fracture models have emerged. In this contribution, a few well-known phase-field models for brittle fracture modelling have been implemented within the staggered algorithm with stopping criterion based on the control of the residual norm, recently developed by the authors. The implementation has been conducted within the commercial finite element software Abaqus and expanded to the three-dimensional settings. The experimental validation of the numerical models is then conducted on the tensile, compact tension (CT) and single edge notched bend (SENB) specimens made of the thermoplastic polymer, polymethylmethacrylate (PMMA). It has been demonstrated that with a suitable choice of the length scale parameter, the developed staggered phase-field fracture models can provide valid prediction of the brittle crack initiation and propagation under quasi-static loading conditions.
The prediction of a crack propagation at the microstructural level of heterogeneous material, as is the case with the nodular cast iron, can be a very demanding problem. Lately, the phase-field ...approach to fracture has been shown a strong potential in modelling such complex crack behaviour in a smeared-crack manner. In this work, the phase-field staggered residual norm based stopping criterion, recently developed by the authors, has been utilized for the numerical simulation of the crack propagation within the heterogeneous microstructural geometry. The geometries have been based on the metallographic images of the nodular cast iron with the graphite nodules considered as porosities. The proposed solution strategy is able to recover the complicated crack nucleation and propagation phenomena within the complex microstructural topology.
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