Showing papers on "Fracture (geology) published in 2017"

A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Abstract: Being one of the most promising candidates for the modeling of localized failure in solids, so far the phase-field method has been applied only to brittle fracture with very few exceptions. In this work, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics. Specifically, the crack phase-field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context. The energy dissipation functional due to crack evolution and the stored energy functional of the bulk are characterized by a crack geometric function of polynomial type and an energetic degradation function of rational type, respectively. Standard arguments of thermodynamics then yield the macroscopic balance equation coupled with an extra evolution law of gradient type for the crack phase-field, governed by the aforesaid constitutive functions. The classical phase-field models for brittle fracture are recovered as particular examples. More importantly, the constitutive functions optimal for quasi-brittle failure are determined such that the proposed phase-field theory converges to a cohesive zone model for a vanishing length scale. Those general softening laws frequently adopted for quasi-brittle failure, e.g., linear, exponential, hyperbolic and Cornelissen et al. (1986) ones, etc., can be reproduced or fit with high precision. Except for the internal length scale, all the other model parameters can be determined from standard material properties (i.e., Young’s modulus, failure strength, fracture energy and the target softening law). Some representative numerical examples are presented for the validation. It is found that both the internal length scale and the mesh size have little influences on the overall global responses, so long as the former can be well resolved by sufficiently fine mesh. In particular, for the benchmark tests of concrete the numerical results of load versus displacement curve and crack paths both agree well with the experimental data, showing validity of the proposed phase-field theory for the modeling of damage and quasi-brittle failure in solids.

Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

Abstract: The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.

Phase field modeling of fracture in anisotropic brittle solids

Abstract: A phase field model of fracture that accounts for anisotropic material behavior at small and large deformations is outlined within this work. Most existing fracture phase field models assume crack evolution within isotropic solids, which is not a meaningful assumption for many natural as well as engineered materials that exhibit orientation-dependent behavior. The incorporation of anisotropy into fracture phase field models is for example necessary to properly describe the typical sawtooth crack patterns in strongly anisotropic materials. In the present contribution, anisotropy is incorporated in fracture phase field models in several ways: (i) Within a pure geometrical approach, the crack surface density function is adopted by a rigorous application of the theory of tensor invariants leading to the definition of structural tensors of second and fourth order. In this work we employ structural tensors to describe transverse isotropy, orthotropy and cubic anisotropy. Latter makes the incorporation of second gradients of the crack phase field necessary, which is treated within the finite element context by a nonconforming Morley triangle. Practically, such a geometric approach manifests itself in the definition of anisotropic effective fracture length scales. (ii) By use of structural tensors, energetic and stress-like failure criteria are modified to account for inherent anisotropies. These failure criteria influence the crack driving force, which enters the crack phase field evolution equation and allows to set up a modular structure. We demonstrate the performance of the proposed anisotropic fracture phase field model by means of representative numerical examples at small and large deformations.

Modeling of internal mechanical failure of all-solid-state batteries during electrochemical cycling, and implications for battery design

Abstract: This is the first quantitative analysis of mechanical reliability of all-solid state batteries. Mechanical degradation of the solid electrolyte (SE) is caused by intercalation-induced expansion of the electrode particles, within the constrains of a dense microstructure. A coupled electro-chemo-mechanical model was implemented to quantify the material properties that cause an SE to fracture. The treatment of microstructural details is essential to the understanding of stress-localization phenomena and fracture. A cohesive zone model is employed to simulate the evolution of damage. In the numerical tests, fracture is prevented when electrode-particle's expansion is lower than 7.5% (typical for most Li-intercalating compounds) and the solid-electrolyte's fracture energy higher than Gc = 4 J m−2. Perhaps counter-intuitively, the analyses show that compliant solid electrolytes (with Young's modulus in the order of ESE = 15 GPa) are more prone to micro-cracking. This result, captured by our non-linear kinematics model, contradicts the speculation that sulfide SEs are more suitable for the design of bulk-type batteries than oxide SEs. Mechanical degradation is linked to the battery power-density. Fracture in solid Li-ion conductors represents a barrier for Li transport, and accelerates the decay of rate performance.

Fractal characterization of dynamic fracture network extension in porous media

Abstract: Fracture network and fractured porous media as well as their transport properties have received great attentions in many fields from engineering application and basic theoretical researches. Fracture will dynamically extend in length and aperture to form complex fracture network under some external conditions such as percussion drilling, wave propagation, desiccation and hydrofracturing. The complexity of fracture network can be well quantitatively characterized by fractal dimension. In this work, the dynamic characterization of fracture network extension in porous media under drying process is measured by the improved box-counting technique, and fractal dimensions of fracture network are respectively related to drying time, average aperture, moisture content and fracture porosity. The fractal dimension increases exponentially with drying time and average aperture, and decreases with moisture content in the form of power law. Specially, the fractal dimension is approximatively increased with porosity in t...

Numerical evaluation of the phase-field model for brittle fracture with emphasis on the length scale

Abstract: The phase-field model has been attracting considerable attention due to its capability of capturing complex crack propagations without mesh dependence. However, its validation studies have primarily focused on the ability to predict reasonable, sharply defined crack paths. Very limited works have so far been contributed to estimate its accuracy in predicting force responses, which is majorly attributed to the difficulty in the determination of the length scale. Indeed, accurate crack path simulation can be achieved by setting the length scale to be sufficiently small, whereas a very small length scale may lead to unrealistic force-displacement responses and overestimate critical structural loads. This paper aims to provide a critical numerical investigation of the accuracy of phase-field modelling of brittle fracture with special emphasis on a possible formula for the length scale estimation. Phase-field simulations of a number of classical fracture experiments for brittle fracture in concretes are performed with simulated results compared with experimental data qualitatively and quantitatively to achieve this goal. Furthermore, discussions are conducted with the aim to provide guidelines for the application of the phase-field model.