Symposium 12: Phase-Field Models of Fracture

Assessment of phase-field numerical errors to classical Griffith’s theory is essential to obtain feasible solutions which do not require an excessive computational cost. This work analyses the phase-field fracture approach to Westergaard’s problem in terms of crack growth initiation under mode I and mixed mode I+II loading conditions.
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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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Accurate modelling and prediction of both statistical trends in damage formation and damage site initiation
is critical in both the design, microstructure optimization and lifetime management of components and
welded joints for nuclear power stations. This paper presents a coupling between a strain-gradient based
crystal plasticity formulation and a phase field fracture model to predict damage initiation sites, damage
propagation and void initiation statistics that match electron microscopy experimental results for grain
boundary damage from a 316H stainless steel creep test specimen. The interplay between the grain
misorientation and the presence of carbides at the grain boundaries is investigated. A range of novel
variations are incorporated into this approach that can isolate damage from varying mechanisms, including
slip, creep, and contributions from plastic or elastic deformation within the simulated microstructure. The
local effect of carbides, forming on specific grain boundary types, on void cavitation is included by using
a misorientation-dependent critical energy release rate. The direct comparison with electron backscatter
diffraction experiments clarifies what the most important damage mechanisms are and the quantitative
fracture energy reduction as a function of carbide density. The extension of this model to ferritic steel
microstructures is also explored.
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Accurate modeling of fracture in polymer nano-composites entails the consideration of numerous complex phenomena including the branching and coalescence of multiple cracks. This contribution employs a graded interphase enhanced phase-field fracture approach (PFF-GI) to capture a wide spectrum of experimentally observed fracture behaviors including particle debonding. Herein the overall fracture response of the composite material is controlled via the degree of grading, i.e. continuous variation in material properties, within an interphase region of finite thickness around the filler particle.
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The poker-chip experiments of Gent and Lindley (1959) – in which they bonded thin disks of elastomers to metal plates at two ends and applied tension – jump-started investigations into the phenomenon of cavitation. Despite their importance, these experiments and other similar experiments have yet to be fully explained. One likely reason for their elusiveness is that it had long been mistakenly presumed that cavitation in elastomers could be explained on the basis of an elastic instability. Another reason is that a unified nucleation and propagation fracture theory in large deformations to explain cavitation as a fracture phenomenon had not existed. Recently, Kumar, Francfort, and Lopez-Pamies (2018) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in elastomers undergoing arbitrarily large quasistatic deformations. In this work, we quantitatively analyze the poker-chip experiments using this theory and showcase the theory’s ability to model nucleation and propagation in a unified manner.
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The dynamic aspect of crack propagation is a topic of deep interest in material science. The phase field fracture modeling has shown encouraging results in a dynamic framework but remains challenging in terms of the time discretization resolution. Though the implicit time integration methods are mainly used in the literature, they become limiting in nonlinear problems due to the resolution of the system of equations required. Thus, explicit time integration schemes are an alternative to avoid these massive matrix operations. This paper presents the approaches set up to adapt the coupled formulation to a full explicit time integration for both equations.
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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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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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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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