Damage In Brittle Materials Research Articles

A 3-DOF spreading precision positional stage for ductile end-face fly-cutting of quartz glass

Ductile removal is widely employed to eliminate subsurface damage in brittle materials. Achieving this requires the cutting depth to be set extremely low, presenting significant challenges for error compensation and precise feeding of the machine tool. In this paper, a novel three-degree-of-freedom spreading precision positioning stage is developed to mitigate the effects of workpiece deflection errors and feed resolution on the depth of cut during the end-face fly-cutting process. First, a bridge and half-bridge composite structure is designed to facilitate the planar spreading of the spatial motion mechanism. A mathematical model of the composite structure is developed based on elastic beam theory. Second, the effects of various structural parameters on the amplification ratio of the structure are investigated. The accuracy of the theoretical model is verified by finite element analysis. Finally, ductile fly-cutting experiments on quartz glass are conducted using a precision 5-axis machine tool.

Three-dimensional modeling of impact fractures in brittle materials via peridynamics

Accurate prediction of the impact fracture behavior of brittle materials is crucial in various industries. The paper employs the peridynamic method to model the penetration and damage in brittle materials during impact. The proposed three-dimensional peridynamic impact fracture model (3D-PDIFM) overpasses other numerical models by adopting a new computational technique to couple the impact collisions of different types of projectiles with the peridynamic method. Moreover, the 3D-PDIFM is highly efficient in impact fracture simulations by focusing on the effects of the projectile without simulating its particles, thereby saving more computational efforts. Validation through comparison with experimental measurements and observations ensures that the 3D-PDIFM accurately represents the real-world impact fracture behavior of brittle materials. The paper also highlights the efficiency of the 3D-PDIFM in comparison to traditional mesh-based numerical simulations. Therefore, the 3D-PDIFM can be significant for practical engineering applications as efficient simulations can save time and computational resources. Using the validated model, the impact fracture behavior of PMMA under various conditions, such as changes in panel thickness, impact area, and projectile velocity, is investigated. This analysis gains more insights into how these factors affect the brittle material's response to impact. Moreover, the impact fracture behaviors of tempered glass and float glass panels are examined under different conditions of impact loadings. This study also explains the penetration and impact fracture phenomena in brittle materials. Overall, using the 3D-PDIFM as a modeling and simulation tool can help engineers and researchers analyze the behavior of glass panels under various impact scenarios, thus allowing for optimization of design parameters to improve impact resistance.

A Lagrangian DG-Method for Wave Propagation in a Cracked Solid with Frictional Contact Interfaces

We developed a discontinuous Galerkin (DG) numerical scheme for wave propagation in elastic solids with frictional contact interfaces. This type of numerical scheme is useful in investigations of wave propagation in elastic solids with micro-cracks (cracked solid) that involve modeling the damage in brittle materials or architected meta-materials. Only processes with mild loading that do not trigger crack fracture extension or the nucleation of new fractures are considered. The main focus lies on the contact conditions at crack surfaces, including provisions for crack opening and closure and stick-and-slip with Coulomb friction. The proposed numerical algorithm uses the leapfrog scheme for the time discretization and an augmented Lagrangian algorithm to solve the associated non-linear problems. For efficient parallelization, a Galerkin discontinuous method was chosen for the space discretization. The frictional interfaces (micro-cracks), where the numerical flux is obtained by solving non-linear and non-smooth variational problems, concerns only a limited number the degrees of freedom, implying a small additional computational cost compared to classical bulk DG schemes. The numerical method was tested through two model problems with analytical solutions. The proposed Lagrangian approach of the nonlinear interfaces had excellent results (stability and high accuracy) and only required a reasonable additional amount of computational effort. To illustrate the method, we conclude with some numerical simulations on the blast propagation in a cracked material and in a meta-material designed for shock dissipation.

Micro-mechanical fracture dynamics and damage modelling in brittle materials.

This study explores the interplay between wave propagation and damage in brittle materials. The damage models, based on micro-mechanical fracture dynamics, capture any possible unstable growth of micro-cracks, introducing a macroscopic loss of stability. After stating the non-dimensional mathematical problem describing the wave propagation with damage, we introduce a non-dimensional number, called the microscopic evolution index, which links the micro and macro scales and discriminates the microscopic scale behaviour. For large values of microscopic evolution index, corresponding to a microscopic quasi-static process coupled with a macroscopic dynamic one, the macroscopic dynamic system could lose its hyperbolicity or become very stiff and generate shock waves. A semi-analytical solution to the one-dimensional wave propagation problem with damage, which could be very useful in the accuracy evaluation of the numerical schemes, was constructed. Concerning the asymptotic behaviour of the dynamic exact solution on the microscopic evolution index (or on the strain rate), an important strain rate sensitivity was found: the pulse loses its amplitude for decreasing strain rate and, starting with a critical value, the micro-scale model is rate independent. A possible regularization technique to smooth the shock waves at low and moderate strain rates is discussed. Finally, some numerical results analyse the role played by the the friction on the micro-cracks in the damage modelling of blast wave propagation. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Nonlocal phase field approach for modeling damage in brittle materials

In this work, we present a nonlocal phase field model for damage in brittle materials. We define a non-conservative order parameter for representing the damage. The Helmholtz free energy functional of the Ginzburg-Landau type that incorporates a new degradation function for the elastic strain energy is considered. The hypothesis of strain equivalence and strain energy equivalence from continuum damage mechanics are adopted to predict the evolution of damage. A conjugate force to damage is derived for both these hypothesis to arrive at a damage criterion. The strong interrelation between phase field models and gradient damage models has been brought out. The solution of the nonlinear system of coupled equation is achieved by a change in the modified Arc-length method and considering a staggered approach. In this approach a linearization of the Crisfield Arc-length quadratic equation for calculation of load increment factor results in an unique root. Numerical examples are presented to demonstrate the usefulness of the proposed damage model.

Modelling of Contact Damage in Brittle Materials Based on Peridynamics

Modelling of Contact Damage in Brittle Materials Based on Peridynamics

Scratching of SiC ceramics at two dimensional pre-stressing

A stress field model was built to study the effects of pre-stressing value, normal and tangential load on the three principal stresses and maximum shear stress when the silicon carbide (SiC) ceramics were scratched under two dimensional pre-stressing, and the scratching tests of SiC ceramic were conducted by using a Rockwell diamond indenter at different pre-stress values and normal loads. Scratching induced damage was assessed and characterised via destructive inspection techniques and progressive lapping techniques combined with the digital microscope. Acoustic emission (AE) technology was also used for the online monitoring of the damage. The results showed that, for a given scratching load, the amplitude of AE signals was reduced as the pre-stress values increasing, and surface/subsurface damage of SiC ceramics induced by two dimensional pre-stress scratching was less than that by conventional scratching. So one can believe that the two dimensional pre-stress method can contribute to decreasing the machining damage of brittle materials.

A numerical damage model for initially anisotropic materials

Significant progresses have been realized during the last decades on both macroscopic and micro-mechanical modeling of induced damage in brittle materials. Most damage models developed so far were devoted to initially isotropic materials. This work is devoted to modeling of induced damage in an initially anisotropic material. A numerical micro-mechanical damage model is proposed, using an Eshelby inclusion solution based homogenization method. Based on the numerical integration of the exact Green’s function and using an appropriate coordinate frame rotation method, an efficient numerical algorithm is proposed to determine the Hill tensor for an arbitrarily oriented family of cracks embedded in a transversely isotropic elastic matrix. Based on this, the effective elastic properties of cracked materials are determined through a rigorous up-scaling procedure using three different homogenization schemes, and taking into account interactions between the initial material anisotropy and induced cracks. A specific damage criterion is then defined in the framework of irreversible thermodynamics to describe the progressive growth of damage. The proposed model is finally implemented in a computer code and applied to study mechanical responses of cracked materials in different loading paths. Again, effects of the initial anisotropy and homogenization schemes are investigated.

Implementation of a rate dependent tensile failure model for brittle materials in ABAQUS

Plate impact tests present the dynamic response of materials under impact loading conditions. Commercial finite element software can be used to simulate plate impact test and implement the desired constitutive or damage model of materials. Implementation of plate impact tests also allows researchers to study the dynamic response of heterogeneous materials in micro-scale. A plate impact test for brittle materials has been simulated in this study using ABAQUS software. Micro-cracking in the brittle ceramic materials causes the samples to behave inelastically under compressive shock loading. The release waves from the free surface of the flyer and rear surface of the target release the compressed materials. Consequently, micro-cracks rapidly open and extend, causing the damage to grow. Thus, the Taylor–Chen–Kuszmaul (TCK) model was implemented using a VUMAT FORTRAN ABAQUS/Explicit subroutine with respect to tension with damage growth and to compression plasticity for ceramic plates (target). The objective of the study is to describe the implementation of a state- and pressure-dependent constitutive model that describes tensile damage in brittle materials using a finite element method. An iteration second-order Runge–Kutta method has been developed for further implementation. Some parameters, such as damage nucleation and strain rate sensitivity, are calibrated based on the ability of the model to reproduce the experimental results. The damage model introduced in this study has been employed successfully to match the experimental results for an AD-85 ceramic target material.

Modeling of Rockburst by Elastoplastic Damage Theory at Finite Strains

Rockburst is modeled in this paper by the theory of elastoplastic damage at finite stains. Isotropic damage coupled with elastoplasticity is assumed and multiplicative kinematics in a purely mechanical setting is further applied. Merging the finite strain plasticity framework of Simo and the thermodynamics with internal variables of Lemaitre in definition of damage including processes, the Helmholtz free energy is additively decomposed to characterize the basic mechanism of elasto-plasticity and damage of brittle materials. The numerical simulations for granite burst are conducted by finite element technique.

Effect of surface scratches on the characteristics of nonlinear Rayleigh surface waves in glass

Using nonlinear Rayleigh waves, the effect of surface scratches on the propagation of nonlinear ultrasonic waves in a glass plate was investigated. The results showed that the amplitudes of the fundamental and second harmonics of the nonlinear Rayleigh waves decreased with increasing average width of surface scratches due to the interaction between scratch-induced cracks and wave propagation. The increase of the nonlinearity with the average scratch width suggests that the surface scratches caused the decrease of apparent Young's modulus near the glass surface. Nonlinear Rayleigh surface waves could be a potential method for the quantitative and rapid measurement of surface and subsurface damage in brittle materials.

Shock loading on AlN ceramics: A large scale molecular dynamics study

The nanoscale structure of shock waves in high strength AlN ceramics is studied using molecular-dynamics simulations. Impacts using four independent crystallographic directions, with particle velocities in the range 0.8–4.0km/s, reveal the generation of a well-defined two-wave structure, consisting of an elastic precursor followed by a wurtzite-to-rocksalt structural transformation wave (STW). Impacts with particle velocities below 0.8km/s or above 4.0km/s generate single elastic or single overdriven shock waves, respectively. The latter propagates faster than the longitudinal sound velocity along the impact direction. The structure of the STW exhibits a strong anisotropy with respect to the crystallographic directions. Results show distinct shock front features from a steady, sharp and well defined STW front for impact at the basal plane to a rough STW front with the formation of an intermediate metastable fivefold coordinated phase or the generation and propagation of dislocations from the shock front for impact at other directions. These results indicate that shock-induced damage in brittle materials can be highly intricate even in defect-free systems. Simulations show no deformation twinning or other well defined plastic wave as found in experiments on polycrystalline AlN suggesting that interfaces and defects strongly affect the materials response to shock loading.

Nonlocal damage model using the phase field method: Theory and applications

A new nonlocal, gradient based damage model is proposed for isotropic elastic damage using the phase field method in order to show the evolution of damage in brittle materials. The general framework of the phase field model (PFM) is discussed and the order parameter is related to the damage variable in continuum damage mechanics (CDM). The time dependent Ginzburg–Landau equation which is also termed the Allen–Cahn equation is used to describe the damage evolution process. Specific length scale which addresses the interface region in which the process of changing undamaged solid to fully damaged material (microcracks) occurs is defined in order to capture the effect of the damaged localization zone. A new implicit damage variable is proposed through the phase field theory. Details of the different aspects and regularization capabilities are illustrated by means of numerical examples and the validity and usefulness of the phase field modeling approach is demonstrated.

Thermal Fatigue and Waste Heat Recovery via Thermoelectrics

Using thermoelectrics to directly convert heat energy into useful electricity faces a number of challenges. In addition to the optimized thermal and electrical transport parameters that are needed to boost energy conversion efficiency, thermoelectric (TE) materials must possess sufficient mechanical integrity to survive hundreds or thousands of in-service heating and cooling cycles (thermal fatigue). The nature of TE materials themselves makes it problematic for them to survive under thermal fatigue conditions since TE materials typically (1) are brittle semiconductors or ceramics and (2) have low thermal conductivity which acts to enhance the dimensionless figure of merit ZT but also leads to high stress in response to thermal transients. In addition, many TE materials, including chalcogenide compounds and intermetallic compounds, have relatively high thermal expansion coefficients which also generates high stresses when TE materials are exposed to thermal gradients and transients. The problem of thermal fatigue has been discussed (but not studied directly) in terms of thermal shock parameters, where thermal shock refers to a single thermal cycle and thermal fatigue refers to many thermal cycles. The differences between thermal shock and thermal fatigue are profound in part since the physical mechanisms that lead to good thermal shock resistance are defeated by thermal fatigue. This paper presents a description of (i) the inadequacies of both the thermoelastic model and the energy balance model in addressing thermal fatigue problems as well as (ii) strategies that have been successful in reducing thermal fatigue damage in brittle materials.

A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects

Abstract This paper is devoted to micromechanical modeling of isotropic damage in brittle materials . The damaged materials will be considered as heterogeneous media composed of solid matrix weakened by isotropically distributed microcracks . The original contribution of the present work is to provide a proper micromechanical thermodynamic formulation for damage-friction modeling in brittle materials with the help of Eshelby’s solution to matrix-inclusion problems. The elastic and plastic strain energy involving unilateral effects will be fully determined. The condition of microcrack opening–closure transition will be determined in both strain-based and stress-based forms. The effect of spatial distribution of microcracks will also be taken into account. Further, the damage evolution law is formulated in a sound thermodynamic framework and inherently coupled with frictional sliding . As a first phase of validation, the proposed micromechanical model is finally applied to reproduce basic mechanical responses of ordinary concrete in compression tests.

A three-dimensional micromechanics model for the damage of brittle materials based on the growth and unilateral effect of elliptic microcracks

Abstract Based on the analysis of a representative elliptic microcrack embedded in a RVE, the additional compliance tensor induced by an embedded opening/closed microcrack is derived, and that corresponding to the kinked growth of a closed elliptic microcrack is also derived by making use of its approximately equivalent simplification. The effect of the microcracks is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A three-dimensional micromechanics damage model is obtained for brittle materials, assuming numerous randomly distributed elliptic microcracks and taking into account their deformation, frictional sliding, growth and kinked growth.

Homogenization‐based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks

AbstractThis paper is devoted to micromechanical modeling of induced anisotropic damage in brittle geomaterials. The formulation of the model is based on a proper homogenization procedure by taking into account unilateral effects and interactions between microcracks. The homogenization procedure is developed in the framework of Eshelby's inclusion solution and Ponte‐Castaneda and Willis (J. Mech. Phys. Solids 1995; 43:1919–1951) estimate. The homogenization technique is combined with the thermodynamics framework at microscopic level for the determination of damage evolution law. A rigorous crack opening–closure transition condition is established and an energy‐release‐rate‐based damage criterion is proposed. Computational aspects on the implementation of micromechanical model are also discussed. The proposed model is evaluated by comparing numerical predictions with experimental data for various laboratory tests on concrete. Parametric studies on unilateral effects and influences of microcracks interactions are finally performed and analyzed. Copyright © 2008 John Wiley & Sons, Ltd.

Simulation of high speed impact into ceramic composite systems using cohesive-law fracture model

A numerical study for the analysis of oblique metal/ceramic/metal three layer composite systems against a long-rod has been performed. The study was done using a three-dimensional dynamic program NET3D, which uses the finite element Lagrangian method with explicit time integration. To model the discrete nature for fracture and damage of brittle materials, we implemented cohesive-law fracture model with a node separation algorithm for the tensile failure and Mohr–Coulomb model for the compressive loading. A tetrahedral element implemented in the code provides more potential fracture surfaces than a hexahedral element. As a verification of the scheme, an oblique impact into the composite system was conducted and the calculated penetration depth and propagating crack paths were found to be in good agreement with experiment. Next a series of three-dimensional numerical simulations have been conduced to examine the ballistic performance of three layer composite systems. The residual velocity and residual length of the rod were computed for different plate thickness ratios of equal areal density. The impact velocities considered are 1.5, 1.8 and 2.2 km/s. The oblique angle of the plate is 0° and 45°. The optimum thickness ratios of ceramic to metal are very similar to those obtained from the previous experiment.

A micromechanics-based non-local anisotropic model for unilateral damage in brittle materials

The present Note is devoted to the formulation of a micromechanics-based model of non-local anisotropic damage and its application to concrete materials and structures. We first formulate a local anisotropic unilateral damage model on the basis of a suitable homogenization scheme which takes into account interactions between penny-shaped microcracks as well as their spatial distribution. The damage surface is built by using an energy release rate-based criterion. Then a non-local extension of the model is proposed by replacing the local energy release-rate for each family of microcracks by its average over a characteristic volume V of the material centered at a given point. In order to demonstrate the efficiency of the non-local model in mesh-independent simulation of failure process in structures, some applications concerning failure of concrete materials and structures are presented. To cite this article: Q.-z. Zhu et al., C. R. Mecanique 336 (2008).

Dynamics of the Size and Orientation Distribution of Microcracks and Evolution of Macroscopic Damage Parameters

We are dealing with damage of brittle materials caused by growth of microcracks. In our model the cracks are penny-shaped. They can only enlarge but not heal. For a single crack a Rice–Griffith growth law is assumed: There is crack growth only if tension is applied normally to the crack surface, exceeding a critical value. Our aim is to investigate the effect of crack growth on macroscopic constitutive quantities. A possible approach taking into account such an internal structure within continuum mechanics is the mesoscopic theory. A distribution of crack lengths and crack orientations within the continuum element is introduced. Macroscopic quantities are calculated as averages with the distribution function. A macroscopic measure of the progressing damage, i.e., a damage parameter, is the average crack length. For this scalar damage parameter we derive an evolution equation. Due to the unilateral growth law for the single crack, it turns out that the form of this differential equation depends explicitly on the initial crack length distribution. In order to treat biaxial loading, it is necessary to introduce a tensorial damage parameter. We define a second-order tensor damage parameter in terms of the crack length and orientation distribution function.