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Recently, phase field modeling of fatigue fracture has gained a lot of attention from many researches and studies, since the fatigue damage of structures is a crucial issue in mechanical design. Differing from traditional phase field fracture models, our approach considers not only the elastic strain energy and crack surface energy, additionally, w...
Citations
... Van Paepegem et al [64] propose to choose the global ∆N based on a percentile of the cumulative distribution of the local cycle-jump sizes. In [67], within an adaptive cycle stepping scheme, a cycle count increment is obtained based on a stage-wise defined allowed damage increment, again relying on a crucial user choice for the latter. Other approaches are implicit; i.e. ...
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... In the past two decades, the phase field multiphysics fracture model has been applied in various analyses in computational fracture mechanics, including (1) modeling the growth of cracks in brittle materials such as ceramics and rocks [26,27], (2) modeling fractures in ductile materials, such as metals and alloys [28], (3) simulating fatigue crack growth in metals [29,30], (4) simulating crack growth in biomedical materials, such as bone and teeth [31,32], and (5) simulating the growth of cracks at different scales, such as micro-cracks, meso-cracks, and macro-cracks [33,34]. ...
This work introduces a novel phase-field solution for simulating and predicting fractures in elastic solids. In this phase-field fracture model, the crack growth is driven by the material energy–momentum flux, or the configurational force, inspired by a null divergence conservation law and its variational theory, as opposed to employing the commonly-used strain energy degradation-based crack-driving force. By doing so, the crack growth or material configuration change is solely determined by the physics-based Eshelby energy–momentum tensor density or the Rice J-integral flux, which aligns with the energy release criterion of the celebrated Griffith–Eshelby–Rice (GER) theory. The proposed method not only preserves the integrity of the balance of linear momentum principle at the crack tip region but also provides a correct stress asymptotic field in front of the crack tip, while accurately capturing the crack growth.
The key idea of this approach is to use the monotonically increasing and irreversible phase field as the marker of the configurational change and form a phase field variational principle that couples the strain energy density with the configurational strain energy density. By doing so, we only damage the displacement field as a form of diffused crack, as opposed to damaging the stress field in the existing phase-field method. Moreover, from numerical simulations, we discovered two different forms of energy release rates: one drives crack growth by enforcing the crack-tip traction loading condition, and one drives crack growth by enforcing the crack-tip deformation condition, demonstrating the ability of the proposed method to naturally capture two distinct modes of fractures due to two different near-crack tip loading conditions. These advancements and contributions reveal previously unknown insights into fracture mechanics.
... • FEMFAT provides a unified framework for modeling fatigue crack growth. It covers the entire fracture evolution, including nucleation, propagation, branching, and kinking [69]. • FEMFAT takes into account the influence of residual stress distribution near the crack tip. ...
Fatigue crack growth modeling is critical for assessing structural integrity in various engineering applications. Researchers and engineers rely on 3D software tools to predict crack propagation accurately. However, choosing the right software can be challenging due to the plethora of available options. This study aimed to systematically compare and evaluate the suitability of seven prominent 3D modeling software packages for fatigue crack growth analysis in specific applications. The selected software tools, namely ABAQUS, FRANC3D, ZENCRACK, LYNX, FEMFAT, COMSOL Multiphysics, and ANSYS, were subjected to a comprehensive analysis to assess their effectiveness in accurately predicting crack propagation. Additionally, this study aimed to highlight the distinctive features and limitations associated with each software package. By conducting this systematic comparison, researchers and engineers can gain valuable insights into the strengths and weaknesses of these software tools, enabling them to make informed decisions when choosing the most appropriate software for their fatigue crack growth analysis needs. Such evaluations contribute to advancing the field by enhancing the understanding and utilization of these 3D modeling software packages, ultimately improving the accuracy and reliability of structural integrity assessments in relevant applications.
... In other works like [13,14], the fatigue degradation function and history variable are chosen differently, but they are still used to reduce the fracture energy term. Different from those phase field formulations for fatigue fracture, Schreiber et al. [15,16], Yan et al. [17] follow the path from Kuhn and Müller [6] the sum of additional driving forces caused by fatigue damage. One major advantage of this formulation is that it directly couples the phase field model with the fatigue parameters of experiments, allowing us to handle complex environmental influences on crack growth. ...
... In this work, we show that the phase field fatigue model can take the effects of loading frequency and loading temperature into consideration. Additionally, the adaptive cycle number adjustment algorithm (ACNAA) [17] is employed in favor of efficient computations. It is shown that results from phase field simulations agree with existing experimental data. ...
... In Section 4, a thermomechanical fatigue phase field model is presented, and in Section 5, conclusions are drawn and directions for future work are given. It is noted that since the original phase field fatigue model has been well presented in [15,17,23], we do not repeat the details of the model here in order to minimize any overlaps. ...
... A similar approach was recently published in [65,66], where nonlinear kinematic and isotropic hardening were considered. Further advancements in phase field modeling targeting both brittle and ductile fatigue failure can be explored in [67][68][69][70][71]. ...
The phase field method has gathered significant attention in the past decade due to its versatile applications in engineering contexts, including fatigue crack propagation modeling. Particularly, the phase field cohesive zone method (PF-CZM) has emerged as a promising approach for modeling fracture behavior in quasi-brittle materials, such as concrete. The present contribution expands the applicability of the PF-CZM to include the modeling of fatigue-induced crack propagation. This study critically examines the validity of the extended PF-CZM approach by evaluating its performance across various fatigue behaviors, encompassing hysteretic behavior, S-N curves, fatigue creep curves, and the Paris law. The experimental investigations and validation span a diverse spectrum of loading scenarios, encompassing pre-and post-peak cyclic loading, as well as low-and high-cyclic fatigue loading. The validation process incorporates 2D and 3D boundary value problems, considering mode I and mixed-modes fatigue crack propagation. The results obtained from this study show a wide range of validity, underscoring the remarkable potential of the proposed PF-CZM approach to accurately capture the propagation of fatigue cracks in concrete-like materials. Furthermore, the paper outlines recommendations to improve the predictive capabilities of the model concerning key fatigue characteristics.
... Within the first type, Yan et al. [22] have adopted a concept of "cycle jump" for the model by Schreiber et al. [20], where the process is characterized by an ever-increasing fatigue damage field. More precisely, the process is divided into three stages named elastic stage, transient stage, and fatigue fracture stage, with different cycle increments in each stage. ...
... Such process will continue until ∆t trial i satisfies (21) or ∆t trial i = T . Finally, we remark that α ′ in (17), (21), and (22) can be replaced by the total macrochronological rateα, especially if∂α/∂t is comparable to α ′ . ...
... Then (21) is obtained by setting t = t i = t i−1 + ∆t trial i and requiring the difference between the two approximations [the last term of (20)] be small enough. If (21) is not satisfied, the time increment ∆t trial i should be corrected in (22), which is obtained by limiting the difference between the two approximations within tol. identically zero. ...
... After the crack nucleation stage, the parameters q and b are parameters controlling how intense the additional fatigue energy drives the crack. A discussion of different choices of the parameters q and b can be found in [34]. The degradation function h(s) -similarly as g(s) -models the loss of the stiffness of broken material due to cyclic fatigue. ...
... The degradation function h(s) -similarly as g(s) -models the loss of the stiffness of broken material due to cyclic fatigue. A discussion of different choices of the degradation functions can be found in [34,36]. ...
... However, the cycle number increment is usually determined by a trade-off between the computing time of simulation and the accuracy of the result. The choice of the number of the cycle increment is critical in the phase field fatigue model, not only because it determines the simulation time, but also because it has a strong influence on the crack topology [34]. ...
Fatigue failure is one of the most crucial issues in manufacturing and engineering processes. Stress cycles can cause cracks to form and grow over time, eventually leading to structural failure. To avoid these failures, it is important to predict fatigue crack evolution behavior in advance. In the past decade, the phase field method for crack evoluation analysis has drawn a lot of attention for its application in fracture mechanics. The biggest advantage of the phase field model is its uniform description of all crack evolution behaviors by one evolution equation. The phase field method simultaneously models crack nucleation and crack propagation which will be particularly useful manufacturing problems. In this work, we show that the phase field method is capable to reproduce the most important fatigue features, e.g., Paris’ law, mean stress effect, and load sequence effects. For efficient computing, a “cycle”- “time” transformation is introduced to convert individual cycle numbers into a continuous time domain. In order to exploit the symmetry property of the demonstrated examples, a phase field model in cylindrical coordinates is presented. Finally, the fatigue modeling approach presented is applied to study a cold forging process in manufacturing.
... ( In addition to the models in Table 3, there also exist fatigue PFMs considering the elasto-plastic coupling [149][150][151][152][153], different phase field constitutive relations [77], new damage accumulation strategies [154], and efficient numerical algorithms [80,155]. ...
... To reduce the computing effort of the models developed by Schreiber et al. [69,142], Yan et al. [155] further proposed an efficient implementation method, where the simulation step was defined as a certain increment of load cycles, and the fatigue failure 39 simulation is divided into three stages according to the evolution of the fatigue damage D. When the fatigue damage D is below the threshold Dc, the increment of the cycle number should be as large as possible. When D is close to the limit threshold Dc, the cycle number increment should be chosen to ensure that the damage increment dD is small enough. ...
Phase field fracture models have demonstrated great capacities in simulating crack nucleation, propagation, branching, and joining in brittle and ductile materials subjected to external stimulations. Because of their great flexibility, phase field fracture models can incorporate various material properties including anisotropy, elastoplasticity, viscoelasticity, hyperelasticity, piezoelectricity, etc. Recently, the models have been extended to fatigue, one of the most common material failure mechanisms in structural engineering. The purpose of this paper is to provide a comprehensive review of recent work on phase field models for fatigue damage and failures. Following a brief introduction to the development of phase field fracture models as well as the theories and models of fatigue, the fundamentals of the models for elastic and elasto-plastic cases are presented, including basic theories, formulas, tension–compression splits, and numerical implementations. Then, the emphasis is placed on different aspects of the phase field models for fatigue fracture involving the approaches of introducing fatigue damage, the descriptions of crack nucleation and propagation, the coupling of cyclic plasticity and phase field models, and the acceleration algorithms. Finally, the future research directions of phase field models for fatigue fracture and the major challenges to be conquered in their engineering applications are discussed.
... The block size was adaptively selected to control the damage rate. Yan et al. [57] developed an adaptive cyclic incremental adjustment algorithm, which can reduce the computational cost of the simulation without sacrificing accuracy. The whole simulation is divided into three stages: elastic stages, transition phase, and fatigue stages. ...
Fatigue fracture simulation based on phase field methods is a promising numerical approach. As a typical continuum approach, phase field methods can naturally simulate complex fatigue fracture behavior. Moreover, the cracking is a natural result of the simulation without additional fracture criterion. This study first introduced the phase field fracture principle, then reviewed some recent advances in phase field methods for fatigue fracture modeling, and gave representative examples in macroscale, microscale, and multiscale structural simulations. In addition, some strategies to improve the performance of phase field models were summarized from different perspectives. The applications of phase field methods to fatigue failure demonstrate the ability to handle complex fracture behaviors under multiple loading forms and their interactions, and the methods have great potential for development. Finally, an outlook was made in four aspects: loading form, fatigue degradation criterion, coupled crystal plasticity, and performance improvement.
... Schreiber et al. [25] added the damage accumulation evolution to phase field model for simulating the FCG behavior. Furthermore, they proposed [26] an efficient phase field method for FCG that only requires moderate computational cost without sacrificing accuracy. Wang et al. [27] presented a local approach to analyze the FCG rate through the characterization on the dissipative process of the crack tip zone. ...
