Themes: Phase-Field Models of Fracture

A PHASE-FIELD MODEL FOR THE MULTISCALE ANALYSIS OF FRACTURE IN SHORT GLASS FIBER REINFORCED POLYMERS [Keynote]

Understanding and modeling the fracture mechanical behavior of short glass fiber reinforced polymers (SFRPs) is challenging: the strong heterogeneity induced by the manufacturing process causes a tight coupling of the material microstructure to the effective response on the component scale. Aiming to account for this microstructural complexity, fracture is approached using a multiscale approach. To resolve the microstructure induced anisotropy and its relationship with the macroscopic material behaviour, an isotropic phase-field fracture model is extended via the fiber orientation interpolation concept. The approach is fed by micromechanical simulations calibrated by experimental data. A validation of the proposed approach is obtained by means of numerical investigations compared to experimental findings.
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AN AUGMENTED PHASE-FIELD MODEL WITH VISCOUS STRESSES FOR DEFECT DYNAMICS

This work begins by applying phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress-strain response. In classical nonlinear elasticity, it is known that subsonic interfaces require a kinetic law, in addition to momentum balance, to obtain unique solutions; in contrast, for supersonic interfaces, momentum balance alone is sufficient to provide unique solutions. However, conventional phase-field models coupled to elastodynamics are unable to model, even qualitatively, the supersonic motion of interfaces. This work identifies the shortcomings in the physics of standard phase-field models to be: (1) the absence of higher-order stress to balance unphysical stress singularities, and (2) the ability of the model to access unphysical regions of the energy landscape.
This work then proposes an augmented phase-field model to introduce the missing physics. The augmented model adds: (1) a viscous stress to the momentum balance, in addition to the dissipative phase-field evolution, to regularize singularities; and (2) an augmented driving force that models the physical mechanism that keeps the system out of unphysical regions of the energy landscape. When coupled to elastodynamics, the augmented model correctly describes both subsonic and supersonic interface motion. This augmented model was then used for fracture simulations.
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SIMULATION OF OFF-AXIS FRACTURE OF THIN-PLY COMPOSITE LAMINATES USING PHASE FIELD

Thin-ply laminates can offer significant advantages for aeronautical design, however, obtaining design allowables for such laminates requires efficient simulation tools. Previous simulation methods used for standard composites pose significant drawbacks when it comes to thin-ply composites, and therefore motivate the advent of new numerical techniques. The Phase Field method, a possible solution, is applied here, in an equivalent single layer approach, to simulate the fracture of multidirectional thin-ply laminates subjected to off-axis loading. The anisotropic nature of the fracture energy multidirectional laminates present is considered through an analytical formulation that feeds the inputs of the method. It is shown that accurate predictions can be obtained compared to experiments for off-axis open-hole tension (OHT) of a hard laminate. But this does not mean the same accuracy will be achieved regardless of the laminate type and lay-up. The issue is nicely illustrated considering a cross-ply laminate that presents the peculiarity of having the same translaminar fracture toughness in the two principal material axes. This creates some inaccuracies in the simulation due to the way the phase field model is formulated. A discussion on this issue and possible ways to circumvent it, under current development, will be presented.
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A SIMPLE ABAQUS PHASE FIELD IMPLEMENTATION FOR THE STUDY OF TRANSVERSE CRACKING IN COMPOSITE LAMINATES

In the recent years, phase-field approach has gained remarkable attention in the field of Fracture Mechanics and has offered solutions to numerous problems involving crack onset and propagation. In the present paper, a Abaqus implementation of the phase-field approach using only a user material subroutine is extended to study intralaminar damage in CFRP composites. To this end, the capability of modeling orthotropic elastic behavior, transverse cracks and residual stresses has been introduced in the formulation. To validate the implementation, mechanical models with three different configurations were considered and Numerical results were compared with the analytical solution of benchmark problems.
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MODELING FRACTURE IN FUNCTIONALLY GRADED MATERIALS WITH PHASE-FIELD METHOD

Phase field fracture predictions in functionally graded plates are carried out using exponential finite element shape functions. The rule of mixtures is employed to estimate the material properties according to the volume fractions of the constituent materials, which have been varied according to given grading profiles. Crack propagation paths and load deflection behaviors are investigated in paradigmatic examples of single-edge notched plate specimens to gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations.
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AN FE-EXPERIMENTAL METHOD FOR DETERMINING QCT-BASED CORTICAL BONE FRACTURE TOUGHNESS AND ULTIMATE STRESS [Keynote]

Cortical bone fracture prediction using Phase Field Models (PFMs) requires the data on the spatial distribution of bone fracture toughness and ultimate stress. However such correlations with qCT parameters or associated bone density are not yet available in the literature. Here, we proposed an FE-Experimental method to determine bone fracture toughness and ultimate stress for different densities and find out potential correlations. Digital Image Correlation (DIC) and diverse standards for KIc calculation show values ranging from 2 to 9 MPa√m. Although it is consistent with reported data in the literature, further work is being conducted using qCT-scans and micro-CT data as well as Finite Element Analysis (FEA) to estimate bone density and determine more accurately the associated fracture toughness and ultimate stress.
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A PHASE FIELD FATIGUE MODEL FOR COMPLEX LOADING SITUATIONS [Keynote]

The phase field method for fracture mechanics has drawn a lot of attention in the past decade because of its simple formulation and easy implementation. Recently, the phase field model is also applied for fatigue fracture for a uniform loading. However, there is still a lack of studies on how to consider complex loading cases in the phase field fatigue model. In this work, we extend the phase field model for non-uniform loading situations by combing it with the rainflow counting algorithm.
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A PHASE FIELD MODEL FOR DAMAGE NUCLEATION IN GEOPOLYMER COMPOSITES

Multi-scale models have been greatly appreciated due to their ability to precisely correlate the microstructure properties with the macroscopic properties of materials. With an aim to verify the structural integrity of geopolymer composites, the microscopic cracks nucleating from the matrix and preexisting pores and the effect on their macroscopic fracture toughness are studied using a computational framework of phase field (PF) in the finite element (FE) context. To assess the effect of random distribution of voids, the representative volume element (RVE) of the composite microstructure is generated using a take and place algorithm. The elastic properties of the composites are obtained by Mori-Tanaka and Self-consistent homogenization schemes. The RVE is then used to simulate a plate under tension to study the damage initiation and propagation in geopolymer composites. The PF model investigates the crack nucleation and branching from the already-existing voids in the composites. A qualitative validation of the approach by means of crack patterns is also presented.
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