Brittle Fracture Model Research Articles

Numerical Dynamic Simulation for Three Phase Random Aggregate Model of Concrete

In this paper the concrete under impact load and failure mechanism was studied. Concrete was considered as a three-phase composite material: aggregate, cement mortar and interfacial transmission zone (ITZ).The simulation was based on random polyhedron aggregate model. Mortar and the transition zone were considered as the brittle fracture model material, and the aggregate was considered as plastic material. LS-DYNA finite element program was used to simulate concrete in SHPB experimental device under the impact damage process. It was showed that the reason of the final macro failure was the development of the microcrack, aggregate shape on concrete failure has a certain impact on the failure process.

Finite element modelling of brittle fracture of thick coatings under normal and tangential loading

This paper addresses coating fracture in hard brittle coatings subjected to combined normal and tangential loads through a finite element based methodology. The coating is modelled as an elastic layer perfectly bonded to an elastic substrate with a pre-microcrack, assumed to initiate at the contact trailing edge due to high tensile stress. The predicted results are consistent with previously published coating fracture results. The model predicts a significant effect of coating thickness on crack propagation for coatings with large elastic mismatch and the final propagated crack profile is predicted to depend on friction coefficient, coating fracture toughness and sliding displacement.

A ductile–brittle fracture model for material ductile damage in plastic deformation based on microvoid growth

The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. In this paper, a ductile–brittle fracture criterion derived from a microvoid mechanical model is proposed for microdamage and fracture of metallic material under large elastic–plastic deformation and has been proved to be effective in the analysis of metal forming process. Using this criterion, the analyses of microdamage and ductile–brittle fracture for tensile specimens in complex stress-states have been carried out. The results from these analyses on damage development and fracture are in good agreement with the experimental ones, and from microview point are reasonable for cracked specimens.

Numerical solutions for crack growth based on the variational theory of fracture

Some results concerning numerical experiments based on a variational model for quasi-static Griffith-type brittle fracture are presented. The analysis is essentially based on a formulation of variational fracture given by Francfort and Marigo, the main difference being the fact that we rely on local rather than on global minimization. Propagation of fracture is obtained by minimizing, in a step by step process, a form of energy that is the sum of bulk and interface terms. To solve the problem numerically we adopt discontinuous finite elements based on variable meshes and search for the minima of the energy through descent methods. In order to get out of small energy wells, a mesh dependent relaxation of the interface energy, tending to the Griffith limit as the mesh size tends to zero, is adopted. The relaxation consists in a carefully tailored cohesive type approximation of the interface energy tuned by few parameters. The role of such parameters is investigated.

Bimodal Beremin-type model for brittle fracture of inhomogeneous ferritic steels: Theory and applications

In the present paper two kinds of Beremin-type models are developed to incorporate, in the statistical analysis of brittle fracture, the effect of both microscopic and macroscopic inhomogeneities. The macroscopic inhomogeneities are represented as thin platelets of segregated zones intersecting the crack front. These zones have a strength and fracture properties different from those of the matrix. In the first approach (semi-probabilistic model), an extension of the original Beremin model (1983) is proposed. The distribution of a type of inhomogeneities is deterministic but the fracture behaviour of each component (matrix & inhomogeneities) is described by a Weibull law. Finite element simulations show that for low linear fraction of inhomogeneities and relatively low strength mismatch between the matrix and the inhomogeneities, the crack tip opening displacement of the inhomogeneities and that of the matrix are the same. This produces an elevation of the local stress intensity factor and increases the probability of failure.In the second approach (fully-probabilistic model), inhomogeneities are statistically distributed along the crack front. The probability of failure is calculated by coupling the results of the semi-probabilistic model with those of either Monte-Carlo type simulations or mathematical expressions for the distribution of inhomogeneities. A closed-form solution for the probability of failure is obtained using Poisson’s law. These theoretical calculations predict that the usual size effect (KIC4B=constant, where KIC is the fracture toughness and B is the thickness) is no longer observed. Moreover these calculations reveal that the scatter in the predicted KIC values is largely increased, in particular when the specimen thickness is comparable to the mean distance between inhomogeneities.These theoretical results are compared to two experimental studies. The first one is devoted to the influence of segregated zones on the fracture toughness of a pressure vessel steel (16MND5). In this material the macroscopic inhomogeneities are associated with a bimodal fracture process, which is intergranular in these zones and transgranular cleavage in the matrix. It is shown that the fully-probabilistic model describes reasonably well the scatter in fracture toughness measurements on CT25 specimens, unlike the original Beremin model. The second study is that of the Euro fracture toughness data set. It is confirmed that the original Beremin model is able to describe the variation of the fracture toughness and its scatter with temperature. However this model does not account for some of the observed size effects “anomalies”.

An Advanced Damage Propagation Model of Brittle Fracture

To reduce the coal mining risk, drainage of methane with drills and hydraulic fracture has been put in practice. In the paper, an advanced damage propagation model of brittle fracture is studied based on mode I crack. The localization band of damage is inducted, and the modal of localization of damage around crack-tip is established using fracture and damage mechanics. Besides, the stress distribution in localization of damage is assumed as obeying a quadratic function, thus the stress field around the crack is obtained, and the calculation formula of crack length is presented, which can provide reference for mine production.

A phase-field description of dynamic brittle fracture

In contrast to discrete descriptions of fracture, phase-field descriptions do not require numerical tracking of discontinuities in the displacement field. This greatly reduces implementation complexity. In this work, we extend a phase-field model for quasi-static brittle fracture to the dynamic case. We introduce a phase-field approximation to the Lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase-field. We study the behavior of the model in one dimension and show how it influences material properties. For the temporal discretization of the equations of motion, we present both a monolithic and staggered time integration scheme. We study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments. We also introduce a local adaptive refinement strategy and study its performance in the context of locally refined T-splines. We show that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.

A model for brittle fracture based on the hybrid phase field model

We propose a phase field model for crack propagation based on the hybrid model and justify the model by constructing a family of asymptotic solutions.

Finite element analysis of an atomistically derived cohesive model for brittle fracture

In order to apply information from molecular dynamics (MD) simulations in problems governed by engineering length and time scales, a coarse graining methodology must be used. In previous work by Zhou et al (2009 Acta Mater. 57 4671–86), a traction-separation cohesive model was developed using results from MD simulations with atomistic-to-continuum measures of stress and displacement. Here, we implement this cohesive model within a combined finite element/cohesive surface element framework (referred to as a finite element approach or FEA), and examine the ability for the atomistically informed FEA to directly reproduce results from MD. We find that FEA shows close agreement of both stress and crack opening displacement profiles at the cohesive interface, although some differences do exist that can be attributed to the stochastic nature of finite temperature MD. The FEA methodology is then used to study slower loading rates that are computationally expensive for MD. We find that the crack growth process initially exhibits a rate-independent relationship between crack length and boundary displacement, followed by a rate-dependent regime where, at a given amount of boundary displacement, a lower applied strain rate produces a longer crack length. Our method is also extended to larger length scales by simulating a compact tension fracture-mechanics specimen with sub-micrometer dimensions. Such a simulation shows a computational speedup of approximately four orders of magnitude over conventional atomistic simulation, while exhibiting the expected fracture-mechanics response. Finally, differences between FEA and MD are explored with respect to ensemble and temperature effects in MD, and their impact on the cohesive model and crack growth behavior. These results enable us to make several recommendations to improve the methodology used to derive cohesive laws from MD simulations. In light of this work, which has critical implications for efforts to derive continuum laws from MD simulations, it is shown care must be taken when using a similar approach, and effects of ensemble, temperature and strain rate must be considered.

Model of symmetric crack formation in a plate and a wedge under bending by a point indenter

The energy approach is used to propose a model of brittle fracture of a thin plate (and a wedge) under bending by a point indenter, which permits studying some possible mechanisms determining the number of sectors into which the plate breaks.

Stress localization in BCC polycrystals and its implications on the probability of brittle fracture

The evaluation of the reliability of pressure vessels in nuclear plants relies on the evaluation of failure probability models. Micromechanical approaches are of great interest to refine their description, to better understand the underlying mechanisms leading to failure, and finally to improve the prediction of these models. The main purpose of this paper is to introduce the stress heterogeneities arising within the polycrystal in a probabilistic modeling of brittle fracture. Stress heterogeneities are evaluated from Finite-Element simulations performed on a large number of Statistical Volume Elements. Results are validated both on the measured averaged behavior and on the averaged stresses measured by neutron diffraction in five specific orientations. A probabilistic model for brittle fracture is then presented accounting for the carbide distribution and the stress distribution evaluated previously inside an elementary volume V 0. Results are compared to a “Beremin type” approach, assuming a homogeneous stress state inside V 0.

An experimental and modelling study of brittle cleavage crack propagation in transformable ferritic steel

Flaws that can be present within pressure vessels, pipework and other engineering structures are assessed using the principles of engineering fracture mechanics. It is necessary to support such an approach with an understanding of the underlying fracture mechanisms. Moreover, many of these components are fabricated using transformable steels. In the present paper, the authors describe the fracture of an A508 type steel, heat treated to produce a tempered bainitic microstructure, and subsequently impact tested at −196°C. In particular, focused ion beam microscopy has been used to produce high resolution fractography, combined with information relating to the underlying microstructure and crystallography. The results of cleavage crack propagation across prior austenite grain, lath packet and lath boundaries are described and then correlated with predictions from a three-dimensional geometric model of brittle cleavage fracture in polycrystalline steel. This model includes a consideration of a lath substructure developed within the grains and is based upon a Kurdjumov–Sachs orientation relationship with the parent austenite grain.

About brittle fracture in the vicinity of filled pores

Modeling of brittle fracture of a porous medium (body) under uniaxial compression was performed for the cases of pore filling by fluid or closely packed elastic disks. The second variant of the pore filling represents an example of discrete filling with fracture products often observed in experiments. The effects of pore filling were evaluated on the basis of an analytical description of the appropriate stress fields in the pore vicinities. The estimates showed that both fluid and elastic filling amplify the tendency of the porous medium to brittle fracture under compression.

EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE

Existence and convergence results are proved for a regularized model of dynamic brittle fracture based on the Ambrosio–Tortorelli approximation. We show that the sequence of solutions to the time-discrete elastodynamics, proposed by Bourdin, Larsen & Richardson as a semidiscrete numerical model for dynamic fracture, converges, as the time-step approaches zero, to a solution of the natural time-continuous elastodynamics model, and that this solution satisfies an energy balance. We emphasize that these models do not specify crack paths a priori, but predict them, including such complicated behavior as kinking, crack branching, and so forth, in any spatial dimension.

A micromechanical interpretation of the temperature dependence of Beremin model parameters for french RPV steel

Local approach to brittle fracture for low-alloyed steels is discussed in this paper. A bibliographical introduction intends to highlight general trends and consensual points of the topic and evokes debatable aspects. French RPV steel 16MND5 (equ. ASTM A508 Cl.3), is then used as a model material to study the influence of temperature on brittle fracture. A micromechanical modelling of brittle fracture at the elementary volume scale already used in previous work is then recalled. It involves a multiscale modelling of microstructural plasticity which has been tuned on experimental inter-phase and inter-granular stresses heterogeneities measurements. Fracture probability of the elementary volume can then be computed using a randomly attributed defect size distribution based on realistic carbides repartition. This defect distribution is then deterministically correlated to stress heterogeneities simulated within the microstructure using a weakest-link hypothesis on the elementary volume, which results in a deterministic stress to fracture. Repeating the process allows to compute Weibull parameters on the elementary volume. This tool is then used to investigate the physical mechanisms that could explain the already experimentally observed temperature dependence of Beremin’s parameter for 16MND5 steel. It is showed that, assuming that the hypothesis made in this work about cleavage micro-mechanisms are correct, effective equivalent surface energy (i.e. surface energy plus plastically dissipated energy when blunting the crack tip) for propagating a crack has to be temperature dependent to explain Beremin’s parameters temperature evolution.

An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture

The energy of the Francfort-Marigo model of brittle fracture can be approximated, in the sense of $\Gamma$-convergence, by the Ambrosio-Tortorelli functional. In this work, we formulate and analyze two adaptive finite element algorithms for the computation of its (local) minimizers. For each algorithm, we combine a Newton-type method with residual-driven adaptive mesh refinement. We present two theoretical results which demonstrate convergence of our algorithms to local minimizers of the Ambrosio-Tortorelli functional.

Characterization and prediction of abrasive wear of powder composite materials

Composite materials produced by powder metallurgy provide a solution in many engineering applications where materials with high abrasion and erosion resistance are required. The actual wear behaviour of the material is associated with many external factors (particle size, velocity, angularity, etc.) and intrinsic material properties (hardness, toughness, Young modulus, etc.). Hardness and toughness properties of such tribomaterials are highly dependent from the content of reinforcing phase, its size and from the mechanical properties of the constituent phases. In this study an attempt is made to model the erosion wear behaviour of composite materials, to calculate the wear rate and to correlate erosion rates with experimental results and material parameters. Powder composites cermets and metal–matrix composite materials reinforced with different content of hard phase were used as examples in this research. Wear mechanisms of materials were investigated. Following from the main mechanisms of erosion wear the models of plastic deformation and brittle fracture are developed for prediction of erosion of powder composite materials. It was demonstrated, that the erosion rate of hardmetal-type materials can be predicted using the results obtained by microindentation methods. The use of hardness distribution parameters is justified with materials with low binder content.

Numerical simulations of impacts involving porous bodies: I. Implementing sub-resolution porosity in a 3D SPH hydrocode

In this paper, we extend our Smooth Particle Hydrodynamics (SPH) impact code to include the effect of porosity at a sub-resolution scale by adapting the so-called P – alpha model. Many small bodies in the different populations of asteroids and comets are believed to contain a high degree of porosity and the determination of both their collisional evolution and the outcome of their disruption requires that the effect of porosity is taken into account in the computation of those processes. Here, we present our model and show how porosity interfaces with the elastic-perfectly plastic material description and the brittle fracture model generally used to simulate the fragmentation of non-porous rocky bodies. We investigate various compaction models and discuss their suitability to simulate the compaction of (highly) porous material. Then, we perform simple test cases where we compare results of the simulations to the theoretical solutions. We also present a Deep Impact-like simulation to show the effect of porosity on the outcome of an impact. Detailed validation tests will be presented in a next paper by comparison with high-velocity laboratory experiments on porous materials [Jutzi et al., in preparation]. Once validated at small scales, our new impact code can then be used at larger scales to study impacts and collisions involving brittle solids including porosity, such as the parent bodies of C-type asteroid families or cometary materials, both in the strength- and in the gravity-dominated regime.

A variational model for fracture mechanics: Numerical experiments

In the variational model for brittle fracture proposed in Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46, 1319–1342], the minimum problem is formulated as a free discontinuity problem for the energy functional of a linear elastic body. A family of approximating regularized problems is then defined, each of which can be solved numerically by a finite element procedure. Here we re-formulate the minimum problem within the context of finite elasticity. The main change is the introduction of the dependence of the strain energy density on the determinant of the deformation gradient. This change requires new, more general existence and Γ -convergence results. The results of some two-dimensional numerical simulations are presented, and compared with corresponding simulations made in Bourdin et al. [2000. Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48, 797–826] for the linear elastic model.

Incorporation of Water Content in the Weibull Model for Soil Aggregate Strength

Tillage impacts many components and functions of the soil ecosystem. Thus, the prediction of soil structures produced by tillage may be regarded as a major objective in soil science. Brittle fracture is the desired mode of failure in most tillage operations. Mechanistic or phenomenological models based on the probabilistic Weibull “weakest link” theory are commonly applied to model brittle fracture of air-dry aggregates. The overall objective of this study was to develop a Weibull model to describe the strength of different-sized soil aggregates across a wide range of water contents. Rupture energy data were obtained for aggregates sampled in three field experiments. These included two soil compaction experiments (Bygholm I and II, sandy loam) and a long-term tillage and fertilization experiment (Maury, silt loam). Aggregates were subjected to a crushing test after having been adjusted to matric potentials ranging from −10 kPa to −163 MPa (air dry). Water content strongly affected the characteristic rupture energy (Weibull α parameter), and this relationship was successfully modeled with a power law function. In contrast, water content had little or no effect on the spread of aggregate strengths (Weibull β parameter). Based on these results, we proposed a three-parameter Weibull brittle fracture model for the tested sandy loam and silt loam soils that takes account of the effect of water content for a single aggregate size fraction. This model, in which only α depends on water content, explained on average 89% of the total variation in rupture energy. Further research is needed to fully investigate the influence of water content on the rupture energy of different-sized aggregates.