Phase Field Approach For Fracture Research Articles

An acceleration scheme for the phase field fatigue fracture simulation with a concurrent temporal homogenization method

The phase field approach for fracture has been adapted for fatigue fracture in recent years. In this work, we propose an efficient acceleration scheme for this approach based on concurrent time-scale homogenization. In this scheme, the fatigue fracture problem is decomposed into a macrochronological problem and a microchronological problem, and is accelerated with the macrochronological time steps adaptively determined. The macrochronological time step is monitored during the whole simulation, and is corrected by a predictor–corrector strategy if necessary. Numerical examples demonstrate that this scheme is able to accelerate fatigue fracture simulations without sacrificing much accuracy, and can be up to 200 times faster than direct numerical simulations in some cases. For certain force-controlled examples, the proposed scheme, equipped with the arc-length control, is able to reproduce Paris’ law with a correlation coefficient higher than 0.91 in the logarithmic scale.

Fracture tailoring in 3D printed continuous fibre composite materials using the Phase field approach for fracture

Additive Manufacturing is a technology with high potential since it offers a lot of benefits going from lower material waste to flexibility in the component fabrication process. The continuous Carbon Fibre (CF) deposition is an interesting approach since it allows to depose continuous CF bundles following different geometries and avoiding the limitations of current composite manufacturing techniques. Choosing the CF deposition path means also giving the designer the possibility to reinforce areas of the designed component which are subjected to stress concentrations, thus increasing its fracture resistance. In this work, a study on the reinforcement capabilities of this technology is performed, considering different specimen geometries and different geometries for the CF deposition path. Two different geometries are analysed: a V-notch and an Open-Hole specimen, both subjected to tensile loading. To model the fracture scenario, a Phase Field framework is exploited. The V-notch simulation demonstrates the capability of Phase Field to catch both the fracture path and the mechanical response reported in experiments from the literature. In the second part of the paper, the Open Hole Tension test is simulated numerically by means of the same tools described above, taking into consideration different geometries for the reinforcement around the hole. The specimens with different reinforcement geometries show different mechanical responses and crack patterns, thus highlighting the influence of the continuous CF reinforcement geometry on the fracture scenario.

In-situ strength effects in long fibre reinforced composites: A micro-mechanical analysis using the phase field approach of fracture

Transverse intralaminar cracks in layers with perpendicular orientation referred to the main loading direction have a significant effect on the apparent ultimate strength of the corresponding composite laminate. This effect stems from the fact that such transverse cracks generally promote the occurrence of other failure mechanisms leading to the specimen collapse in subsequent stages of the loading process. With the aim of conducting a careful investigation regarding the onset and progression of transverse intralaminar cracking events, a micro-mechanical analysis of cross-ply laminates is herein proposed. Particularly, the cross-ply laminates belonging to the family [0°2/90°n/0°2] are considered via the generation of high-fidelity micro-mechanical models, which reproduce the internal fiber arrangements related to the reference results in Saito et al. 2012, Experimental evaluation of the damage growth restraining in 90° layer of thin-ply CFRP cross ply laminates, Adv. Comp Mat, 21:1,57–66. Differing from alternative approaches, current predictions are equipped with the combined used of two fracture-based modeling methods: (i) the variational phase field (PF) approach for triggering crack events into the matrix, and (ii) the bilinear cohesive zone model (CZM) for the simulation of fibre-matrix decohesion failures. Relying on this computational methodology, the focus of this work is to analyze the influence of the transverse ply thickness (n) on the onset and propagation of damage under tensile conditions, in conjunction with the transition from micro-cracking to meso-scale damage states. For this purpose, several models are generated into the FE package ABAQUS using user-defined capabilities, replicating configurations of specimens included in previous experimental investigations, i.e. through the consideration of different transverse ply thickness (n = 1, 2, 4). Present results show the potential of the proposed methodology to predict the transverse matrix cracking phenomena and the ability and reliability for capturing the delay of the crack with thinner plies, a phenomenon which is usually denominated as in-situ effect in the related literature.

A micromechanical analysis of inter-fiber failure in long reinforced composites based on the phase field approach of fracture combined with the cohesive zone model

The nature of failure in long fiber-reinforced composites is strongly affected by damage at the micro-scale. The presence of different phases at different length scales leads to a significant complexity in the failure progression. At the micro-scale, the complexity is due to the presence of different points of initiation for damage and the presence of cracks propagating both in the matrix and along the fiber–matrix interfaces. This scenario gives also the opportunity to improve the material design by modifying the properties of the different constituents in order to inhibit or delay some failure mechanisms. In view of this complexity, the development of predictive numerical tools with high capabilities in terms of reliability becomes of notable importance. In order to address this aspect, the combination of the phase-field approach for fracture and the cohesive zone model is herein exploited to demonstrate its capability and accuracy for the study of failure initiation at the micro-scale. Single-fiber problems subjected to transverse loading are considered as benchmark for the prediction of the sequence of stages of failure initiation, the size effect of the fiber radius on the apparent strength, the effect of a secondary tensile transverse load and the effect of a secondary neighbouring fiber. Numerical predictions are found to be in very good agreement with experimental trends and finite fracture mechanics predictions available in the literature.

Fracture analysis of thin films on compliant substrates: A numerical study using the phase field approach of fracture

In this work, the phase field (PF) approach for brittle fracture in the bulk coupled with the cohesive zone model (CZM) for pre-existing interfaces is exploited for the simulation of fracture of thin films on compliant substrates, which are structural configurations of extensive use in many engineering systems such as protecting layers for vessels, stretchable electronic devices, among many others. Due to the coupling between the two aforementioned models for fracture, the proposed approach enables capturing bulk damage and crack deflection or penetration at the prescribed interfaces in a robust and reliable manner, these scenarios depending on the particular mechanical properties of the system via a sensitivity analysis. In this concern, it is shown that the proposed approach is capable of predicting several complex crack paths for different fracture modes, concerning the 2D and 3D thin film fracture problems herein investigated: (i) deflection/delamination, (ii) penetration and (iii) deflection/delamination at the prescribed interface in combination with penetration. Moreover, the effect of the interface fracture energy on the predicted crack path has been carefully investigated.

Phase field modeling of crack growth with double-well potential including surface effects

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way to the interfacial stresses in phase transformations. The differences in the modeling of crack growth with considering the surface stresses and without it are discussed. It is shown how the surface stresses affect the stress fields and consequently the crack nucleation and propagation. The finite element method is utilized to solve the coupled equations of mechanics and crack phase field. It is emphasized that the surface stresses affect the driving force for both the crack nucleation and propagation by disturbing the momentum balance. Thus, a different external loading is required in the presence of the surface stresses.

Crack Patterns in Heterogenous Rocks Using a Combined Phase Field-Cohesive Interface Modeling Approach: A Numerical Study

Rock fracture in geo-materials is a complex phenomenon due to its intrinsic characteristics and the potential external loading conditions. As a result, these materials can experience intricate fracture patterns endowing various cracking phenomena such as: branching, coalescence, shielding, and amplification, among many others. In this article, we present a numerical investigation concerning the applicability of an original bulk-interface fracture simulation technique to trigger such phenomena within the context of the phase field approach for fracture. In particular, the prediction of failure patterns in heterogenous rock masses with brittle response is accomplished through the current methodology by combining the phase field approach for intact rock failure and the cohesive interface-like modeling approach for its application in joint fracture. Predictions from the present technique are first validated against Brazilian test results, which were developed using alternative phase field methods, and with respect to specimens subjected to different loading case and whose corresponding definitions are characterized by the presence of single and multiple flaws. Subsequently, the numerical study is extended to the analysis of heterogeneous rock masses including joints that separate different potential lithologies, leading to tortuous crack paths, which are observed in many practical situations.

Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The discrete crack limit case is approached for a small length-scale parameter that controls the width of the transition region between the fully broken and the undamaged phases. From a computational standpoint, this necessitates fine meshes, at least locally, in order to accurately resolve the phase-field profile. In the classical approach, phase-field models are computed on a fixed mesh that is a priori refined in the areas where the crack is expected to propagate. This on the other hand curbs the convenience of using phase-field models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multi-level hp-refinement technique that enables a dynamically changing mesh which in turn allows the refinement to remain local at singularities and high gradients without problems of hanging nodes. Yet, in case of complex geometries, mesh generation and in particular local refinement becomes non-trivial. We address this issue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multi-level hp-refinement and the FCM in the context of phase-field simulations.

Phase‐Field Modeling of Hydraulic Fracture

AbstractHydraulically driven fracture has gained more and more research activity in the last few years, especially due to the growing interest of the petroleum industry. Key challenge for a powerful simulation of this scenario is an effective modeling and numerical implementation of the behavior of the solid skeleton and the fluid phase, the mechanical coupling between the two phases as well as the incorporation of the fracture process. Existing models for hydraulic fracturing can be found for example in [1], where the crack path is predetermined, or in [2] who use a phase field fracture model in an elastic framework, however without incorporating the fluid flow. In this work we propose a new compact model structure for the Biot‐type fluid transport in porous media at finite strains based on only two constitutive functions, that is the free energy function ψ and a dissipation potential ϕ that includes the incorporation of an additional Poiseuille‐type fluid flow in cracks. This formulation is coupled to a phase field approach for fracture and is fully variational in nature, as shown in [3]. In contrast to formulations with a sharp‐crack discontinuity, the proposed regularized approach has the main advantage of a straight‐forward modeling of complex crack patterns including branching. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)