Damage In Brittle Materials Research Articles

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement.

Probabilistic analysis of continuum damage mechanics of brittle materials

Uncertainty of material properties in solution of engineering problems is often a fundamental question. Statistical methods give a powerful tool for analysis of uncertainty. Monte Carlo simulations together with Gumbel distribution are used as a possible way to study influence of data dispersion on assessment of damage of brittle materials.

Prediction scheme for the catastrophic failure of highly loaded brittle materials or rocks

Due to broadly distributed heterogeneities, the multistep character of the development of random damage in brittle materials or rocks, reflecting the discrete nature of the fracturing process, enables us to compare the diffusion of damages with the percolation phenomenon. Based on a discrete scale hierarchy, the fracturing process leading to material failure is then identified with a second-order phase transition, enabling prediction. In this connection, this paper presents a prediction scheme for the catastrophic failure or the lifetime of highly loaded materials or rocks. An experimental measurement method and a modelling of bi-phase materials or rocks are proposed. Although this scheme is introduced in the context of materials science, it also works in rock for the prediction of large natural earthquakes and some artificially induced earthquakes and rock bursts due to damming and mining. Results with strong forecasting potential explain for the first time the origin of complex critical exponents through a structural parameter.

A visco-damage model for brittle materials under monotonic and sustained stresses

A theoretical model is proposed to describe the evolution of damage in brittle materials, such as concrete and masonry, subjected to increasing or sustained stresses of relatively high intensity. The model is based on the introduction of suitable damage variables in a rheological model. In this way, it is possible to describe the material behaviour under stresses either increasing or constant in time. The capabilities of the model in describing the mechanical response of material elements subjected to different stress histories are illustrated. Some correlations with experimental data from tests performed on masonry and concrete specimens are presented, to assess the reliability of the theoretical predictions. The results of some numerical applications to non-proportional stress paths are also illustrated. Finally, the limitations of the proposal are discussed and possible further improvements are envisaged. Copyright © 2005 John Wiley & Sons, Ltd.

Damage zone interaction due to non-oriented Vickers indentations on brittle materials

Induced damage in brittle materials due to two interacting Vickers indentations at various orientations was investigated using a three-dimensional finite element model. The model considers ‘tensile cracking and compressive yielding’ behavior of ceramics. Damage evolution due to both the simultaneous and sequential double indentations was studied. The simulation results indicated that the induced damage zone patterns are strongly a function of the relative orientation of the two indenters. The existence of another nearby indentation reduces the crack size on the side closer to the first indentation but increases the overall median damage zone size. These results were validated by sequential Vickers indentation experiments on borosilicate glass. The evolved damage patterns were further rationalized based on Bousinesq and blister field stress fields. Finally, the implication of these results on material removal mechanisms due to simultaneous interaction of several grits in a ceramic grinding process is discussed.

Below Macro: Driving Forces of Micromechanics

Micromechanics has become a driving force in materials science and applied mechanics of fluids, solids, and porous materials. The possibilities offered by micromechanics ‘‘below macro’’ are entering all fields of application, ranging from traditional solid materials to multiphase material systems in geomechanics and biomechanics. At this moment in time, it appears to be useful to explore the state-of-the-art beyond macromechanics of porous materials and explore new approaches in theory and applications. This is in short the focus of the papers in this topical issue of the Journal of Engineering Mechanics. The mechanics analysis of multiphase porous material systems has been traditionally done within the macroscopic context of continuum mechanics, based on the founding works of M. A. Biot and K. Terzaghi. In particular, Biot’s poromechanics theory opened traditional monophasic continuum mechanics to account for couplings induced by a fluid phase saturating the pore space. Ever since, poromechanics has entered a great number of engineering fields, ranging from traditional civil and environmental engineering, to petrol engineering and more recently biomedical engineering. Still, in recent years, a need emerged to go below macro, and relate the macroscopic behavior of a saturated or partially saturated porous medium to the behavior of its microscopic constituents and their mechanical and chemical interactions. In the 1970s, first fundamental answers were developed through homogenization methods of periodic systems, relating both to transport problems and to poromechanical couplings. Almost 25 years later, this topical issue on micromechanics of porous materials explores the state-of-the-art in the field. The papers in this topical issue, which were presented during the 2001 Mechanics and Materials Conference in San Diego as part of the symposium Below Macro: Driving Forces of Micromechanics, focus both on advances in methods and applications. On the methodological front, we can distinguish two or three axes of developments. On one hand, upscaling schemes based on asymptotic expansion ~paper by Auriault! or volume averaging ~paper by Whitaker! today allow the determination of the mathematical form of macroscopic constitutive equations, based on specific assumptions relating to the physics of the phenomena at stake at a very fine scale. On the other hand, if the macroscopic behavior is known, the effective material properties can be determined, provided that the morphology of the microstructure is known. This is the focus of theories dealing with the reconstruction of real porous media ~paper by Adler et al.!, which may well serve in the future for the development of new materials based on homogenization methods. A critical element of poromechanics of saturated or nonsaturated porous media remains the development of methods that allow upscaling the local poromechanical couplings between one fluid phase and the solid phase, or in between fluid phases ~like surface tension! to the macroscopic scale. The problem is well known and solved for linear poroelastic systems ~paper by Berryman!, and recent work focuses primarily on the extension to nonlinear solid material systems ~paper by Deude et al.!, to nonsaturated granular material systems ~paper by Chateau et al.!, and inhomogeneously saturated porous media ~paper by Didwania!. Porous materials remain solid materials with specific strength, fracture, and nonlinear deformation properties. The question of upscaling these properties remains at the forefront of recent developments in micromechanics, situated between theory and applications, to fractured rock masses ~paper by de Buhan et al.!, to the frictional behavior of highly filled composite materials ~paper by Lemarchand et al.!, to a Bingham viscoplastic material ~paper by Perrin!, and to anisotropic damage in brittle materials ~paper by Pensee et al.!. Finally, an application of upscaling schemes to biomaterials ~paper by Hellmich and Ulm!, shows the great potentials of continuum micromechanics for novel engineering mechanics applications. The scene is set by a survey paper by Andre Zaoui, who examines the development of the theory of continuum micromechanics from its very beginning in 1887 to the present day. We are grateful for his contribution, which allows the reader to well situate the different micromechanics approaches in this topical issue in the general context of micromechanics of materials. At the same time, his review paper will remain a source of inspiration for the future.

Simulation of localization failure with strain-gradient-enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro-crack-based anisotropic damage model for rock-like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well-known mesh-sensitivity problem in FEM. In the computation, elements with C1 continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D-non-linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.

Difference in subsurface damage in indented specimens with and without bonding layer

This paper aims to assess the applicability of the bonded–interface technique (BIT) that has been used for examining sub-surface damage in brittle materials. With the aid of the finite element method, the indentation stress fields in alumina specimens with and without a bonded–interface were analysed. It was found that the bonded–interface greatly alters the stress distribution in the neighbourhood of the interface. The high-stress zone shifts away from the interface, and extends to the surface. Both glue layer mechanical properties and bond thickness play a limited role in the overall stress field of the BIT alumina. Comparisons of theoretical predictions with experimental observations showed that, to a great extent, the BIT presents a different pattern of sub-surface damage. The study clarifies the applicability of the BIT and offers a useful guideline for practitioners.

Quantitative evaluation of surface damage in brittle materials by acoustic microscopy

Quantitative evaluation of surface damage in brittle materials by acoustic microscopy

A finite deformation continuum\\discrete model for the description of fragmentation and damage in brittle materials

A dynamic finite element analysis of large displacements, high strain rate deformation behavior of brittle materials is presented in total Lagrangian coordinates. A continuum\\discrete damage model capable of capturing fragmentation at two size scales is derived by combining a continuum damage model and a discrete damage model for brittle failure. It is assumed that size and distribution of potential fragments are known a priori, through either experimental findings or materials properties, and that macrocracks can nucleate and propagate along the boundaries of these potential fragments. The finite deformation continuum multiple-plane microcracking damage model accounts for microcracks within fragments. Interface elements, with cohesive strength and reversible unloading before debonding, between potential fragments describe the initiation of macrocracks, their propagation, and coalescence leading to the formation of discrete fragments. A surface-defined multibody contact algorithm with velocity dependent friction is used to describe the interaction between fragments and large relative sliding between them. The finite element equations of motion are integrated explicitly using a variable time step. Outputs are taken at discrete time intervals to study material failure in detail. The continuum\\discrete damage model and the discrete fragmentation model, employing interface elements alone, are used to simulate a ceramic rod on rod impact. Stress wave attenuation, fragmentation pattern, and overall failure behavior, obtained from the analyses using the two models, are compared with the experimental results and photographs of the failing rod. The results show that the continuum\\discrete model captures the stress attenuation and rod pulverization in agreement with the experimental observations while the pure discrete model underpredicts stress attenuation when the same potential fragment size is utilized. Further analyses are carried out to study the effect of potential fragment size and friction between sliding fragments. It is found that compared with the continuum\\discrete damage model, the discrete fragmentation model is more sensitive to the multi-body discretization.

Maximum depth of cut for ceramics using abrasive waterjet technique

The abrasive waterjet cutting technique is a controlled erosive process in which the impact of high velocity water and abrasives cause cutting of the target material. Advanced engineering ceramic materials have been used in many applications. Cutting of such materials by abrasive waterjet is becoming the recent cutting technique. In the present work, the erosion model by Evans et al. [A.G. Evans, M.E. Gulden, M.E., Rosenblatt, Impact damage in brittle materials in the elastic-plastic response regime, Proc. R. Soc. London, Sec. A, 361 (1978) 343–365] was adopted in order to develop a waterjet cutting model capable of predicting the depth of cut of ceramic materials as a function of the material properties and the process parameters involved. Closed form expression for the maximum depth of cut was obtained. The predicted maximum depths of cut for three ceramic materials were compared with recent experimental results, where both showed an agreement within a maximum deviation of 7.5%. The effect of the process parameters on the maximum depth of cut for a given material was also studied to further investigate the capabilities and limitations of the proposed model.

Computational modelling of impact damage in brittle materials

A Lagrangian finite element method of fracture and fragmentation in brittle materials is developed. A cohesive-law fracture model is used to propagate multiple cracks along arbitrary paths. In axisymmetric calculations, radial cracking is accounted for through a continuum damage model. An explicit contact/friction algorithm is used to treat the multi-body dynamics which inevitably ensues after fragmentation. Rate-dependent plasticity, heat conduction and thermal coupling are also accounted for in calculations. The properties and predictive ability of the model are exhibited in two case studies: spall tests and dynamic crack propagation in a double cantilever beam specimen. As an example of application of the theory, we simulate the experiments of Field (1988) involving the impact of alumina plates by steel pellets at different velocities. The calculated conical, lateral and radial fracture histories are found to be in good agreement with experiment.

Indentation Characterization of Silicon Nitride

Abstract The hardness of hot-pressed silicon nitride ceramics has been measured over a wide range of applied loads, 0.02 to 300 N, for both Vickers and Knoop indenter geometries. The indentation size effect (ISE) was evident for loads less than about 1 N. The Vickers and Knoop hardness values agree provided they are compared at a given penetration of the respective indenter. The influence of the residual stresses of the ceramic surface on the indentation response in the as-machined, polished, and post-annealed state has been investigated. The results are discussed in relation to the characterization of indentation damage in brittle materials and fracture analysis models.

Combining acoustic emission locations and a microcrack damage model to study development of damage in brittle materials : Rock Mechanics Contributions and Challenges: Proc 31st US Symposium, Golden, 18–20 June 1990 P645–651. Publ Rotterdam: A A Balkema, 1990

Combining acoustic emission locations and a microcrack damage model to study development of damage in brittle materials : Rock Mechanics Contributions and Challenges: Proc 31st US Symposium, Golden, 18–20 June 1990 P645–651. Publ Rotterdam: A A Balkema, 1990

A theory of damage in brittle materials

The present paper addresses the geometric representation of damage in brittle solids, its equation of evolution and its incorporation in the constitutive equation. The concept of a damage coordinate is introduced and a thermodynamic derivation of the evolution equation follows. A continuum damage theory ensues. The theory is applied to the case of a thin plate with a central crack under a tensile load in a direction normal to the plane of the crack. The fracture stress is calculated numerically using a finite element code for various crack lengths and a comparison is made with its observed value. Excellent agreement between the two is obtained with the aid of only one damage parameter, the damage propensity constant. A congruence between the theory and linear fracture mechanics is then shown when the damage coordinate is the crack length.

Sandia uses computer models to study crack damage in brittle materials : Anon Ceramic Bulletin, Vol. 66, No. 1, p. 39 (1987)

Sandia uses computer models to study crack damage in brittle materials : Anon Ceramic Bulletin, Vol. 66, No. 1, p. 39 (1987)

The nature of machining damage in brittle materials

The micromechanics of failure emanating from machining-induced cracks in brittle materials is investigated. In situ monitoring of crack response during breaking tests (with use of acoustic wave scattering), strength measurements and post-failure fractography all indicate that the crack response is dominated by residual stresses. Two components of residual stress have been identified: a crack-wedging force due to the plastic zone beneath the strength-controlling machining groove, and a compressive surface layer due to adjacent grooves. The wedging force dominates and causes stable equilibrium crack extension during a breaking test. The implications of the results for non-destructive evaluation of surface damage by acoustic wave scattering is discussed.

Rain erosion damage in brittle materials

In order to understand the processes involved in the high-velocity rain erosion of brittle materials the impact damage produced in soda-lime-silica glass by single and multiple jet impact was studied. The damage was quantified by measuring the post-impact strength of specimens. It is shown that the impact damage depends on the impact velocity, the number of impacts and the specimen dimensions. A new analysis for calculating the velocity dependence of jet/drop impact damage in brittle materials is presented. The model is based on Hertzian contact analysis and dynamic fracture mechanics and takes into account the statistical nature of the flaws in the specimen. A good qualitative agreement with experimental results is obtained.

Impact damage in brittle materials in the elastic-plastic response régime

The impact fracture created in the elastic-plastic response régime has been characterized in terms of its surface extension and penetration. A numerical dynamic analysis has been performed of a typical impact within this régime to indicate some of the principal characteristics of the contact behaviour and the stress field. The damage has then been analysed, by using simplified postulates based on key features of the impact dynamics and basic fracture mechanics concepts. This has enabled the primary material and target parameters affecting the impact fracture to be identified. Thereafter, some implications for strength degradation and erosion have been discussed.

Dynamic solid particle damage in brittle materials: an appraisal

The damage caused by solid projectiles in the elastic and elastic/plastic target response regimes has been characterized and analysed. Semi-empirical methods for establishing the relative importance of the target and properties on the impact damage have been derived, based on quasi-static indentation fracture characterization schemes and the quantification of the impact damage observations.