Behavior Of Brittle Materials Research Articles

Influence of the Erodent Shape on the Erosion Behavior of Ductile and Brittle Materials

Solid particle erosion is identified as a major wear process occurring in numerous industrial applications. A number of test parameters influence the behavior of the materials during this wear process. Particle shape is one of the key factors, which is often discussed for ductile or brittle materials in the literature, but a comparative study of ductile and brittle materials showing an effect of particle shape has not been addressed in detail until now. The present work discusses the influence of erodent shape on the wear behavior of a ductile (Ti-6Al-4 V alloy) and a brittle (TiN coating) material during the erosion process. Investigations are performed in an erosion test rig where the ductile and brittle materials are charged with spherical and angular SiO2 particles at normal impact. Results show an inverse erosion behavior of ductile and brittle materials with the variation in particle shape. Ductile materials show low material removal with spherical particles, whereas brittle materials show low material removal rates with angular ones. This work also provides an analysis of the material removal phenomenon to understand the effect of particle shape on tested materials. Since materials removal phenomenon in ductile materials is often reported in the literature, this work addresses the material removal behavior especially in ceramic coatings.

Analysis on the Effects of Grinding Wheel Speed on Removal Behavior of Brittle Optical Materials

It is often desired to increase the machining rate while maintaining the desired surface and subsurface integrity during fabricating high-quality optical glass components. This paper proposed a high-speed high-efficiency low-damage grinding technology for machining brittle optical materials, which consists of three grinding processes: rough grinding, semifinishing grinding, and finishing grinding. Grinding characteristics are investigated with respect to grinding forces, specific cutting energy, surface roughness, ground surface quality, subsurface damage, and material removal mechanisms in grinding of fused silica optical glasses with this technology at grinding speeds of up to 150 m/s. These indications are thoroughly discussed by contacting the undeformed chip thickness. The results indicate that the level of these indications is significantly improved with an increase in the wheel speed due to the decrease of the undeformed chip thickness. It is also found that the improvement of ground surface quality is limited when the wheel speed increases from 120 m/s to 150 m/s, which may be due to the influence of vibration caused by the higher wheel speed. For different grinding processes, these results are also substantially improved with the change of grinding conditions. It is found that the material removal mechanism is dominated by brittle fracture at rough and semifinishing grinding processes, while ductile flow mode can be observed at the finishing grinding process. There are some differences between the experimental results and the previous predicted model of subsurface damage depth.

Experimental Validation of RVE Based Failure Simulations of Macro‐Porous Materials

AbstractConnections between inhomogeneities and the failure behavior of brittle material may be investigated by finite element simulations of representative volume elements. Representative volume elements are typically subjected to periodic boundary conditions. Moreover, representative volume elements are often chosen as planar, i. e., two dimensional in order to reach reasonable statistics with regard to random distributions of inhomogeneities. The significance of such strongly simplified simulations needs to be validated, especially if the matrix failure is potentially dominated by defects, as is the case, e. g., in macro‐porous ceramics. We propose a quasi‐periodic concept to design specimens with cylindrical pores, which reproduce the stress state in a two dimensional representative volume element. This is achieved by a partial periodic replication of the region of interest. We suggest that material models used in simulations can be assessed by comparison between simulated and experimentally observed failure. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Development of material model for assessment of brittle cracking behavior of plexiglas

The objective of this study is to investigate the brittle cracking behavior of Plexiglas material when subjected to indentation loading. Indentation tests were conducted on Modified Vickers testing machine to acquire the experimental data in the form of load-displacement curve. Several mechanical properties such as hardness, yielding stress and fracture toughness have been ascertained from the analysis of the experimental data. The experimental data then used to create a mathematical model of Plexiglas for its brittle cracking behavior with indentation loading. Furthermore, a numerical simulation based study was carried out to simulate the brittle cracking in Plexiglas plate when subjected to indentation loading. The simulations were performed in the FE solver Abaqus. The brittle cracking model in Abaqus/Explicit is used which determines the required force and displacement to produce crack in Plexiglas. Finally a comparison of simulation results was made to the experimental data to validate the FEA procedures and accuracy of predictions. The numerical predictions of load-displacement curve found remarkably consistent with experimental results.

Tool Load Sensitivity Against Multidimensional Process Influences in Microblanking of Copper Foils With Silicon Punches

The continuous trend toward miniaturization of metallic microparts of high quality at low costs results in the need of appropriate production methods. Mechanical manufacturing processes like forming and blanking meet these demands. One major challenge for the application of them are the so-called size effects. Especially, the downsizing of the required manufacturing tools and adequate positioning cause higher effort with increasing miniaturization. One promising approach for downsizing of tools is the transfer of knowledge from microsystems technology. This study shows the process behavior of etched silicon punches in microblanking operations. For the application as tool material especially, the brittle material behavior and sensitivity against tensile stresses have to be considered. These mechanical loads favor wear in form of cracks and breaks at the cutting edge of the punch and thus decreasing tool life. In a special test rig these wear phenomena were observed in microblanking of copper foils. Although, high positioning accuracy between tools and workpiece can be assured within this test rig, scatter of tool life is observable. Therefore, a finite element (FE) analysis of the tool load in the microblanking process with special respect to tensile stresses was performed. Within the 3D FE model multidimensional positioning errors like tilting between punch and die were integrated. Their influence on the tool load in form of increasing tensile stresses is evaluated with respect to the type and magnitude of positioning error and verified by experimental results concerning wear. Furthermore, the effect of small outbreaks at the cutting edge on the process behavior and tool load is analyzed.

A comparative study of the r-adaptive material force approach and the phase-field method in dynamic fracture

This contribution presents a comparison between a discrete and a smeared approach to approximate a crack in finite element simulations including the contribution of inertia to the behavior of brittle material under transient loading in the case of fracture. The discrete approximation of a crack is based in this case on a node duplication technique triggered by the evaluation of the so-called “material force” at the crack tip. The smeared approximation of a crack bases on the diffuse description of the crack by a phase-field approach. The governing equations under consideration of transient contributions are shown and the procedure for the finite element implementation is outlined. Numerical simulations investigate the capabilities and limitations of both methods. Firstly, the procedure to introduce initial cracks in a structure and the setup necessary to make them interact with stress waves properly, are under investigation. Moreover, this study deals with the evaluation of the velocity of the crack propagation and its comparison to experimental data. Finally, the phenomenon of crack branching is studied. The presentation and discussion of the results of the simulations provide an overview on the potential of both approaches with respect to an efficient and a realistic simulation of fracture processes in dynamic problems.

Experimental and Numerical Investigation of Float Glass–GFRP Hybrid Beams

Despite the great potentials of glass as a construction material, its brittle material behaviour poses major challenges to structural engineers when designing load-bearing glass structural members. This paper presents the load response and the failure behaviour of float glass–GFRP hybrid beams, when used as a mean of improving strength and ductility of float glass. Hybrid beams made from two layers of float glass sheets and an adhesively-bonded semi-transparent pre-cured GFRP interlayer were tested in four-point bending. The experimental results showed that double layer hybrid beams continued to take load even after the formation of the first major crack, and the beams were stronger and ductile than conventional single and multilayer float glass beams. Once the bottom glass layer has cracked the combination of the GFRP and the top glass layer carried the applied load whilst the gradual decrease in the stiffness due to the formation of new cracks ensures a ductile failure. Experimentally-validated finite element (FE) models that predict the evolution of stresses, stiffness and failure load of single and double layer glass beams, and glass– GFRP hybrid beams are also presented.

The influence of loading conditions on fracture initiation, propagation, and interaction in rocks with veins: Results from a comparative Discrete Element Method study

AbstractWe present the results of a comparative study of loading conditions on the interactions between extension fractures and veins. We model the fracture behavior of brittle discrete element materials each containing a tabular vein body of variable orientation and strength in two different loading conditions. The first is uniaxial tension, applied with servo‐controlled sidewalls. The second is a boudinage boundary condition in which a tensile triaxial stress state is induced in the brittle model volume by quasi‐viscous extensional deformation in the adjacent layers. Most of the fracture‐ vein interactions observed in uniaxial tension also exists in boudinage boundary conditions. However, the importance of each interaction mechanism for a given configuration of relative strength and misorientation of the vein may differ according to the loading mechanism. Nucleation and internal deflection is under both boundary conditions the dominating fracture‐vein interaction style in weak veins. In uniaxial tension models, strong veins tend to alter the fracture path by external deflection, while under boudinage loading these veins are more likely overcome by the fracture step over mechanism. Dynamic bifurcation of fractures was observed in uniaxial tension models but never for boudinage boundary conditions. This is because the acceleration of fracture tips in these conditions is suppressed by interaction with distributed fractures as well as viscous damping by the neighboring layers.

Numerical simulation of mesomechanical behavior of porous brittle materials

The influence of the types of porous structure on the features of deformation, damage accumulation and fracture of mesovolumes of brittle materials is studied. At the mesoscale, the pores of different shape are taken into account explicitly. The digital models were made using random values of coordinates and radii of spherical voids or solid spheres. For numerical modeling of the mechanical behavior up to failure, the evolutionary approach is applied with considering the nonlinear constitutive equations to describe damage accumulation and its influence on the degradation of the strength properties of the frame of porous ceramics. The calculated averaged stress-strain diagrams were shown to be sensitive not only to the value of porosity but also to the shape of pores. The simulation results are validated with experimental data for zirconia and alumina ceramics. Good qualitative and quantitative agreement of modeling results with experimental data suggests that taking into account of two-scale porosity in the form of explicit consideration of large pores at the mesoscale and implicit integrated consideration of tiny pores and cracks from the microscale in the form of accumulated damage is quite sufficient in the framework of the hierarchical modeling.

Study on the Ductile Removal Behavior of K9 Glass with Nano-Scratch

Ductile removal behavior of hard and brittle material in the process of machining has always been a sticking topic. A series of nanoscratch tests of K9 glass were conducted with Berkovich probe on nanoindenter XP to investigate the ductile removal process, material deformation and crack damage. It was found that the scratches surface was free from crack damage in the range of the selected scratching parameters and excellent machinability of K9 glass was obtained. The observation also showed that the stable chips were distributed on the sides of the scratches and the deformation of chips was much larger than that obtained in the conventional machining. Meanwhile, a pile-up phenomenon was obvious and the residual depth of scratches was decreased with the increasing of scratch velocity under the same normal load condition.

A Comprehensive Study on Crack Tip Parameters of Modified Ring Specimen for Mixed-Mode Fracture Toughness Tests on Brittle Materials

Abstract Modified ring (MR) specimen was suggested for investigating the mixed-mode (I/II) fracture behavior of brittle materials by rotating the crack orientation with respect to the loading direction. Crack tip fracture parameters (KI, KII, and T stress) of MR were calculated for different geometric dimensions. To verify the numerical modeling procedure, two sets of comparisons were drawn between the results of prior studies on MR Mode I fracture behavior and those of this study, showing good agreement between the results. Through some graphs, the effects of geometric parameters on YI, YII, and T* (dimensionless crack tip parameters) and also on βII (pure Mode II crack angle) were studied. In addition, the biaxiality ratio (B), as an influential factor in the generalized maximum tangential stress (GMTS) criterion, was calculated for the whole range of mode mixity in the MR specimens. Next, fracture behavior of the specimen was discussed by means of the GMTS criterion in terms of the results obtained for the biaxiality ratio (B). At the end, as an appendix, the entire results obtained for YI, YII, T*, and βII were presented.

Multi-scale modeling of microstructure dependent intergranular brittle fracture using a quantitative phase-field based method

The fracture behavior of brittle materials is strongly influenced by their underlying microstructure that needs explicit consideration for accurate prediction of fracture properties and the associated scatter. In this work, a hierarchical multi-scale approach is pursued to model microstructure sensitive brittle fracture. A quantitative phase-field based fracture model is utilized to capture the complex crack growth behavior in the microstructure and the related parameters are calibrated from lower length scale atomistic simulations instead of engineering scale experimental data. The workability of this approach is demonstrated by performing porosity dependent intergranular fracture simulations in UO2 and comparing the predictions with experiments.

Finite element implementation of the Hoek–Brown material model with general strain softening behavior

A numerical implementation of the Hoek–Brown criterion is presented, which is capable of modeling different post-failure behaviors observed in jointed rock mass. This is done by making the material parameters a function of the accumulated plastic strain. The implementation is for use in finite element calculations, and is based on the return mapping framework. The updated stress state together with the consistent constitutive matrix is found in principal stress space based on the principles of boundary planes. The implementation is verified through the simulation of a tunnel excavation for perfectly-plastic, brittle and strain softening material behavior and the results are compared with known solutions.

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB).Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior.The goal of this paper is to present a new combined experimental–numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment.Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.

Numerical-experimental study on the mechanisms of material removal during magnetic abrasive finishing of brittle materials using extended finite element method

Magnetic abrasive finishing (MAF) is an advanced machining process efficiently used for finishing of hard-to-machine materials. In this method, material removal takes place through nano-/microindentations in the presence of a controllable magnetic field generated via a permanent or an electronic magnet. Understanding the material removal mechanisms of the process is of particular importance for achievement of a high-quality surface with minimum surface defects. Therefore, in this work a numerical-experimental study was performed toward this issue using the extended finite element method (X-FEM). In this regard, the MAF operation was simulated as an indentation and sliding process of a sharp abrasive and the prevailing material removal mechanisms were obtained during MAF of BK7 optical glass. The constitutive material model for the specimen was defined according to the elastic-plastic-cracking model, which takes into account the tensile cracking and compressive yielding behavior of brittle materials. The X-FEM analysis revealed that both microcutting and microfracture mechanisms exist during MAF process of brittle materials depending on the process parameters. Among various parameters, magnetic particles size and abrasives size were the most influential factors affecting the dominant mechanism of material removal. The obtained numerical results were then validated experimentally by using scanning electron microscopy (SEM). The SEM observations revealed good performance of X-FEM analysis in prediction of material removal mechanisms during MAF of brittle materials.

The behavior of ultra-high-strength reinforced concrete columns under axial and cyclic lateral loads

In general Ultra High Strength Concrete (UHSC) is a new class of concrete that has been developed in recent decades. UHSC is characterized by extraordinary mechanical and durability properties. The UHSC-Matrix is very brittle material behavior. In this research an experimental program consists of twelve square UHSC columns is being carried out to study the behavior of UHSC columns subjected to constant axial load combined with cyclic lateral loading in order to simulate the case of seismic action. The main parameters of this program were: longitudinal reinforcement ratio, percentage of steel fiber, stirrups ratio, axial load level and concrete compressive strength. In this experimental program each specimen represents a column extending on both sides from the beam-column connection to the location of the point of inflection. Particular attention is paid to the effect of each variable on the strength enhancement, stiffness degradation, energy dissipation capacity, curvature ductility and displacement ductility of the tested columns. Valuable conclusions were obtained from the research results. By increasing the concrete compressive strength the column capacity increases accompanied by a decreasing in the ductility aspects, increasing the longitudinal steel ratio from 2% to (3.6% and 4.5%) leading to an increase in the column capacity and ductility aspect of the tested columns. Using steel fiber between (1.33–2.67)% is recommended in UHSC columns in seismic zones. The Egyptian concrete code of practice limits for the columns stirrups is suitable in seismic zones for columns subjected to a low axial load level.

Experiments and modeling of ballistic penetration using an energy failure criterion

One of the most intricate problems in terminal ballistics is the physics underlying penetration and perforation. Several penetration modes are well identified, such as petalling, plugging, spall failure and fragmentation (Sedgwick, 1968). In most cases, the final target failure will combine those modes. Some of the failure modes can be due to brittle material behavior, but penetration of ductile targets by blunt projectiles, involving plugging in particular, is caused by excessive localized plasticity, with emphasis on adiabatic shear banding (ASB). Among the theories regarding the onset of ASB, new evidence was recently brought by Rittel et al. (2006), according to whom shear bands initiate as a result of dynamic recrystallization (DRX), a local softening mechanism driven by the stored energy of cold work. As such, ASB formation results from microstructural transformations, rather than from thermal softening. In our previous work (Dolinski et al., 2010), a failure criterion based on plastic strain energy density was presented and applied to model four different classical examples of dynamic failure involving ASB formation. According to this criterion, a material point starts to fail when the total plastic strain energy density reaches a critical value. Thereafter, the strength of the element decreases gradually to zero to mimic the actual material mechanical behavior. The goal of this paper is to present a new combined experimental-numerical study of ballistic penetration and perforation, using the above-mentioned failure criterion. Careful experiments are carried out using a single combination of AISI 4340 FSP projectiles and 25[mm] thick RHA steel plates, while the impact velocity, and hence the imparted damage, are systematically varied. We show that our failure model, which includes only one adjustable parameter in this present work, can faithfully reproduce each of the experiments without any further adjustment. Moreover, it is shown that the most common failure criterion based on a critical strain is simply inadequate to reproduce the results, due to the linear nature of the damage evolution. The advantages of the energy-based failure criterion are discussed in detail.

Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression

Fracture coalescence, which plays an important role in the behavior of brittle materials, is investigated by loading rock-like specimens with two and three pre-existing flaws made by pulling out the embedded metal inserts in the pre-cured period. Different geometries are obtained by changing the angle of the flaws with respect to the direction of loading and the spacing. With reference to the experimental observation of crack initiation and propagation from pre-existing flaws, the influences of the third pre-existing flaw on the cracking processes was analyzed. It was found during the test that: with the increase of the angle of the rock bridge, the rock specimen takes a turn from wing crack propagation failure to crack coalescence failure, and it will be more obvious with the increase of the prefabricated crack angle. According to the different geometries of pre-existing cracks, seven types of coalescence have been identified based on the nature of the cracks for the specimen with two pre-existing flaws. The multi-crack interaction results in the continuous degradation of the macroscopic mechanical properties of the rock mass. On one hand, it weakens the trend of relative sliding of the coplanar cracks, and on the other hand, it changed the coalescence patterns of the fractured specimen. The research reported here provides increased understanding of the fundamental nature of rock mass failure in compression.

Numerical and analytical investigation on the dynamic buckling behavior of glass columns under blast

Current applications in buildings of structural glass elements often require design rules and formulations able to provide acceptable predictions for phenomena complex to describe, which generally depend on combination of several geometrical and mechanical aspects. The estimation of the buckling resistance of glass elements, for example, represents a topic of large interest for researchers, due to typical high slenderness ratios, limited tensile strength and brittle material behavior. In the paper, the buckling response of glass columns under impulsive orthogonal pressures (e.g. blast) and combined static compressive vertical loads (e.g. gravity loads or further service loads) is investigated. The dynamic buckling behavior of columns in out-of-plane bending is primarily analyzed. Advanced numerical nonlinear dynamic simulations are then performed on various laminated columns, by means of 3D numerical FE-models able to take into account the interaction of simultaneous loads and possible glass cracking. Analytical calculations are also carried-out by means of single-degree-of-freedom (SDOF) formulations derived from structural dynamics theories, in order to properly estimate blast and second-order effects on maximum deflections and corresponding tensile stresses. Finally, based on the rather good correlation generally found between numerical and analytical calculations, a design approach is proposed for practical estimation of buckling strength of glass elements in the analyzed loading and boundary conditions.

Inverse pseudo Hall-Petch relation in polycrystalline graphene.

Understanding the grain size-dependent failure behavior of polycrystalline graphene is important for its applications both structurally and functionally. Here we perform molecular dynamics simulations to study the failure behavior of polycrystalline graphene by varying both grain size and distribution. We show that polycrystalline graphene fails in a brittle mode and grain boundary junctions serve as the crack nucleation sites. We also show that its breaking strength and average grain size follow an inverse pseudo Hall-Petch relation, in agreement with experimental measurements. Further, we find that this inverse pseudo Hall-Petch relation can be naturally rationalized by the weakest-link model, which describes the failure behavior of brittle materials. Our present work reveals insights into controlling the mechanical properties of polycrystalline graphene and provides guidelines for the applications of polycrystalline graphene in flexible electronics and nano-electronic-mechanical devices.