Brittle Polycrystalline Materials Research Articles

Effects of cleavage plane and material strength on fracture of polycrystalline brittle materials: A phase-field modeling study

A modified phase-field model for fracture is presented which includes the material strength and cleavage planes to quantitatively predict the crack propagation path and the mechanical response in polycrystalline brittle materials. To demonstrate the capability of this model, the crack initiation and propagation and the mechanical response in zirconium diboride bi-crystal and polycrystalline samples are investigated. Using a relationship analogous to the modified Read-Shockley model for grain boundaries with large misorientation angles, the fracture surface energy and the strength of the grain boundaries are made dependent on the misorientation angle of the adjacent grains. In general, the crack path inside each grain follows the orientation of the cleavage plane similar to the experimental observations. At the grain boundaries, a low fracture surface energy and/or a low material strength can result in intergranular crack propagation. Comparing the results of different models show that to have a reasonable mechanical response it is necessary to include the material strength and cleavage planes in the formulations of the model. The proposed phase-field model enables designing texture and engineering grain boundaries to control intergranular and transgranular crack propagations and the macroscopic mechanical response.

Tuning Mechanical Properties in Polycrystalline Solids Using a Deep Generative Framework

A framework for inverse design of tuning mechanical properties of polycrystalline brittle materials is presented using artificial intelligence (AI). Crystalline solids, which often exhibit distinct mechanical properties at different orientations, can be used as building blocks for polycrystalline composites. However, the design space of geometry and crystal misorientations is typically intractable, and all possible solutions cannot be discovered using experiment or numerical simulation. Herein, a framework using deep learning (DL) alongside a genetic algorithm (GA) is adopted to generate composite polycrystalline materials, whereas the raw material is brittle and sensitive to crystalline orientation, to achieve distinct mechanical properties in various combinatorial designs. The DL model, trained by full‐atomistic simulations of crystals with different orientations, evolves autonomously to yield a desirable range of target toughness values, exemplified in maximizing and minimizing toughness, which are validated by molecular dynamics (MD) simulations. It is found that higher crystal misorientations are preferred for high toughness, as opposed to lower overall misorientations for low‐toughness designs. Notably, this shows that a mechanism can be extracted from the AI algorithm. This materiomics method may ultimately change the way nanomaterials are designed, and can be applied to de novo biomaterial design, architected materials, and bioinspired structural materials.

Chip-free surface patterning of toxic brittle polycrystalline materials through micro/nanoscale burnishing

Brittle crystalline materials have important applications in optics and optoelectronics. However, their powders are highly toxic; thus, the chips generated in material removal processes such as cutting, grinding, and polishing are harmful to human health and the environment. In this study, micro/nanoscale burnishing tests were conducted on polycrystalline zinc selenide (p-ZnSe) to explore the feasibility of high-precision surface patterning of a toxic material by local plastic deformation without chip generation. The local deformation behaviours and subsurface damage formation mechanisms were investigated under dry and oil-lubricated conditions. Two types of cracks occurred when the force exceeded a critical value: cracks along the slip planes at the groove bottom and cracks along the cleavage planes at the groove edge. Below the critical force value, however, a crack-free surface was obtained with lower surface roughness than those for diamond-turned surfaces. No phase transformation was detected after burnishing, but lattice distortion appeared in the subsurface layer. A model was developed to predict the activated slip planes by calculating the maximum Schmid factors of the slip systems, and the distribution of subsurface defects was clarified by cross-sectional direct observations. It was also found that the use of a lubricating oil could greatly reduce material pile-ups around the tool. As test pieces, microgrid patterns were fabricated by crossing and overlapping the grooves, and smooth surfaces with surface roughness of 1.85 nm Sa and 4.5 nm Sa, respectively, were achieved. The findings from this study demonstrate the feasibility of chip-free surface patterning on toxic brittle polycrystalline materials by micro/nanoscale burnishing, which is an effective alternative to cutting and grinding for the fabrication of micro structured optical elements and microfluidics.

Phase-field modeling of crack propagation in polycrystalline materials

A phase-field model based on a modified form of the regularized formulation of Griffith’s fracture theory is presented to investigate intergranular and transgranular crack propagations in polycrystalline brittle materials. Grains and grain boundaries are incorporated in the crack initiation and propagation model based on a phase-field model for grain growth, in which the elastic anisotropy varies based on the grain orientation angle, and the grain boundary energy is related to the misorientation angle of the adjacent grains. Correction parameters are utilized in the total free energy functional and mechanical equilibrium equations to consider the effect of material strength on crack nucleation and propagation independent of the regularization parameter. This allows controlling the strength and crack surface energy along the grain boundaries as a function of the misorientation angle in order to mediate intergranular and/or transgranular crack propagation. To demonstrate the capability of the proposed model, intergranular and transgranular crack propagation in ZrB2 bicrystal systems under tensile loading are studied in detail. The effects of grain boundary misorientation angle, grain boundary inclination with respect to initial crack direction, and grain boundary strength (and/or crack surface energy) on the crack propagation path are investigated. Intergranular crack propagation can be promoted by specific combinations of grain boundary strength and crack surface energy, which can contribute to the fracture toughness of polycrystalline materials.

Effects of cyclic loading on subsurface microstructural changes of zirconia polycrystals in nanoscale mechanical processing

Yttria stabilized zirconia (YSZ) is an attractive biomaterial with excellent properties, but its deformation mechanism under repetitive loads is still unclear. In this study, the subsurface microstructural changes of YSZ polycrystals under repetitive loading/unloading were investigated by multi-cyclic nanoindentation. Raman spectroscopy analysis revealed that a tetragonal-to-monoclinic (t-m) phase transformation occurred, and multi-cyclic indentation promoted this transformation significantly. Cross-sectional scanning transmission electron microscopy showed that monoclinic variants were extensively generated beneath the free surfaces outside the indent planes, whereas grain refinement was dominant beneath the indenter tip. In addition, load-displacement curve analysis demonstrated that the t-m phase transformation occurred during unloading rather than loading, and that the phase transformation-induced volume expansion caused an incremental change of residual indent depth. The extension of monoclinic variants was promoted by repetitive shear deformation, resulting in significant pileups, as detected by atomic force microscopy. The effect of sample surface preprocessing on indentation behaviors was also investigated. Microcracking and surface spalling were confirmed around the multi-cyclic indents made on a diamond-turned YSZ sample. Based on the experimental results, a model of subsurface microstructure distribution and evolution was established. The findings from this study help clarify the historical effects in subsurface damaging mechanism of brittle polycrystalline materials caused by cyclic tool-workpiece interactions in nanoscale mechanical processing.

Surface formation mechanism in ultraprecision diamond turning of coarse-grained polycrystalline ZnSe

Zinc selenide is an excellent infrared optical material. In this study, ultraprecision diamond turning experiments were carried out on coarse-grained polycrystalline ZnSe (p-ZnSe) under various conditions and the corresponding surface formation mechanisms were investigated by examining the surface topography, chip morphology, material microstructural change, and cutting forces. Two kinds of surface defects were observed (i.e. plowing-induced micron-scale cleavage craters and tearing-induced submicron-scale tearing pits). It was determined that plowing induced micron-scale cleavage craters could be suppressed by reducing undeformed chip thickness. Furthermore, it was ascertained that tearing-induced submicron-scale tearing pits could be restrained by using a cutting tool with a zero rake angle. The minimal surface roughness was dominated by grain boundary steps formed when the cutting tool crossed twin boundaries at a large angle. A model was proposed for correlating surface defects and boundary steps with crystal orientations and cutting directions. By using a large-nose diamond tool for cutting, a smooth surface of 1.5 nm Sa was obtained. In addition, a zinc blende to cinnabar phase transformation was observed in the cutting chips, and metallization of cutting chips occurred at an extremely small undeformed chip thickness (~20 nm). Moreover, it was discovered that phase transformation inside the workpiece depends on the radius of the tool nose. The findings of this study provide an important reference for ultraprecision machining of brittle polycrystalline materials.

Micromechanical Studies of Strain Rate Dependent Compressive Strength in Brittle Polycrystalline Materials

We propose a novel computational model for the high fidelity prediction of failure mechanisms in brittle polycrystalline materials. A three-dimensional finite element model of the polycrystalline structure is reconstructed to explicitly account for the micro-features such as grain sizes, grain orientations, and grain boundary misorientations. Grain boundaries are explicitly represented by a thin layer of elements with non-zero misorientation angles. In addition, the Eigen-fracture algorithm is employed to predict the crack nucleation and propagation in the grain structure. In the framework of variational fracture mechanics, an equivalent energy release rate is defined at each finite element to evaluate the local failure state by comparing to the critical energy release rate, which varies at the grain boundaries and the interior of grains. Moreover, constitutive models are considered as functions of the local microstructure features. As a result, a direct mesoscale simulation model is developed to resolve the anisotropic response, intergranular and transgranular fractures during the microstructure evolution of brittle materials under general loading conditions. A micromechanics-based interpretation for the rate dependent strength of brittle materials is derived and verified in examples of dynamic compression tests. In specific, the compressive dynamic response of hexagonal SiC with equiaxed grain structures is studied under different strain rates.

Micromechanical modeling of cohesive thermoelastic steady‐state and transient cracking in polycrystalline materials

SummaryIn this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady‐state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results.

Micromechanical modelling of cohesive thermoelastic cracking in orthotropic polycrystalline materials

In this paper a new micromechanical formulation is proposed for modelling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour. Damage evolution along (inter- or trans-granular) interfaces is modelled using thermo-mechanical cohesive laws and, upon failure, non-linear frictional contact analysis is introduced to model separation, stick or slip. Numerical simulations are presented either to demonstrate the validity and study the physical implications of the proposed thermoelastic formulation, in comparison with other numerical methods as well as experimental observations and literature results.

Supershear damage propagation and sub-Rayleigh crack growth from edge-on impact: A peridynamic analysis

Edge-on impact experiments on AlON, a transparent ceramic with superior ballistic performance, show combined intergranular and transgranular fracture. An initial fast-propagating damage front transitions into slower-propagating localized cracks. We develop a peridynamic model for polycrystalline AlON to investigate the failure evolution observed in experiments. We use a computational polycrystalline structure with the same average grain size as the samples used in experiments. The peridynamic model helps explain the reasons behind the observed failure front supershear propagation speed (higher than 2 times the shear wave speed), and the subsequent transition to sub-Rayleigh propagating localized cracks. The computed propagation speeds for the damage front, and the cracks that emanate from it, match very well those measured in experiments. Elastic anisotropy, material microstructure, and brittle failure are the only ingredients used here to determine damage evolution in edge-on impact on brittle polycrystalline materials, under no confinement. Other possible dissipation mechanisms, like twinning, plasticity, friction, are not included in the model. These are likely second-order effects in the evolution of damage and failure for this material and at these impact speeds.

Strength and Deformability of Brittle Polycrystalline Materials in Triaxial Stress-State State

The strength and deformability of brittle polycristalline materials (rock, cement, gypsum) in triaxial stress-strain state are analyzed. It is shown that the strength of such materials increases. The subcritical and postcritical stress-strain curves for polycristalline materials are presented.

Micromechanical boundary element modelling of transgranular and intergranular cohesive cracking in polycrystalline materials

In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi-region boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter- or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. This is the first time inter- and trans-granular fracture are being modelled together by BEM, and DBEM is being extended to include cohesive approach for anisotropic materials. Finally numerical simulations are presented to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.

Micromechanical Boundary Element Modelling of Transgranular and Intergranular Cohesive Cracking in Polycrystalline Materials

In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi region boundary element approach combined with a dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter-or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. Moreover some physical consideration based on cohesive energies were made, in order to guarantee the cohesive model in consideration was appropriate for the purpose of this work. Finally numerical simulations have been performed to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.

Micro-cracking of brittle polycrystalline materials with initial damage

In this paper, the effect of pre-existing damage on brittle micro-cracking of polycrystalline materials is explored. The behaviour of single and multiple cracks randomly distributed within a grain scale polycrystalline aggregate is investigated using a recently developed grain boundary 3D computational framework. Each grain is modelled as a single crystal anisotropic domain. Opening, sliding and/or contact at grain boundaries are modelled using nonlinear cohesive-frictional laws. The polycrystalline micro-morphologies are generated using Voronoi tessellation algorithms in combination with a regularisation scheme to avoid the presence of unnecessary small geometrical entities (edges and faces) usually responsible for excessively refined meshes. Additionally, a semi-discontinuous grain boundary mesh within the Boundary Element framework is employed to reduce the computational time and memory storage, while retaining analysis accuracy. To enhance the analysis convergence, a Newton–Raphson scheme is used. The performed numerical tests produce physically sound micro-cracking evolutions, confirming the potential of the technique for multiscale analysis of polycrystalline material damage and failure.

Microstructure Effects on Cutting Forces and Flow Stress in Ultra-Precision Machining of Polycrystalline Brittle Materials

This paper presents a physics-based analysis to quantitatively describe the effects of grain size, grain boundaries, and crystallographic orientation on the flow stress of the polycrystalline material and thereby on the cutting and thrust forces. The model has been experimentally validated, in terms of the force intensities and sensitivities to microstructure attributes such as the grain size and the misorientation by comparing the forces to measured data in micromachining of polycrystalline silicon carbide (p-SiC). Molecular dynamics (MD) simulations are performed to explore the effects of grain boundaries and misorientation and to validate the modeling analysis in the context of resulting force ratios.

Finite strain analysis of shock compression of brittle solids applied to titanium diboride

A finite strain theory is developed for polycrystalline brittle materials undergoing shock loading. Inelastic deformation arises principally from extension and opening or sliding of microcracks, and depends on pressure as well as deviatoric stress. In the general theory, internal energy depends on a logarithmic measure of finite elastic strain, entropy, and an internal variable associated with fracture. The theory is applied towards planar shock loading of an isotropic sample under possible static pre-stress. An exact analytical solution is derived when inelasticity is idealized as rate independent. The model and solution are applied to describe polycrystalline ceramic titanium diboride. Results provide new insight into experimental shock data, demonstrating importance of elastic nonlinearity and pressure dependent strength. The model describes shock pressure, mean stress, and shear stress in shocked titanium diboride, including the double yield point, with a minimal number of fitting parameters. The analysis predicts an increase in the Hugoniot elastic limit and suppression of inelasticity with increasing compressive pre-stress, in agreement with recent experiments.

Quantifying reliability statistics for electrochemical shock of brittle materials

In brittle polycrystalline materials, anisotropic shape changes—such as those due to thermal expansion, composition changes, and piezoelectricity—can induce stresses severe enough to drive fracture. The stresses developed are microstructurally heterogeneous and develop in proportion to a generalized external stimulus rather than an applied load; as a consequence, traditional Weibull models do not capture the relevant scaling of failure probabilities with respect to applied stimulus or microstructural feature sizes. These limitations are surmounted by a stochastic method, called Finite Element plus Monte Carlo (FE+MC), which enables quantification of reliability statistics in brittle polycrystalline materials subjected to microstructurally heterogeneous stresses which may be driven by non-mechanical stimulii. A finite element analysis computes the stress distributions for a hypothetical defect-free virtual microstructure and a subsequent Monte Carlo analysis distributes flaws throughout the microstructure with sizes chosen from an experimental flaw size distribution. The FE+MC method is validated for uniaxial tensile loading, for which the expected Weibull distribution of failure probability is reproduced. As a demonstration of the utility of this method in a more complex stress state, we consider electrochemical shock of polycrystalline LiXCoO2 electrodes; the computed composition-dependent failure probabilities reproduce key features of experimental acoustic emission measurements not explained by previous modeling approaches.

Crystallographic Effects on Microscale Machining of Polycrystalline Brittle Materials

This paper studies the effects of crystallography on the microscale machining characteristics of polycrystalline brittle materials on a quantitative basis. It is believed that during micromachining of brittle materials, plastic deformation can occur at the tool-workpiece interface due to the presence of high compressive stresses which leads to chip formation as opposed to crack propagation. The process parameters for such a machining process are comparable to the size of the grains, and hence crystallography assumes importance. The crystallographic effects include grain size, grain boundaries (GB), and crystallographic orientation (CO) for polycrystalline materials. The size of grains (crystals), whose distribution is analyzed as a log-normal curve, has an effect on the yield stress of a material as described by the Hall–Petch equation. The effects of grain boundary and orientation have been considered using the principles of dislocation theory. The microstructural anisotropy in a deformed polycrystalline material is influenced by geometrically necessary boundaries (GNB) and incidental dislocation boundaries (IDB). The dislocation theory takes both types of dislocations into account and relates the material flow stress to the dislocation density. The proposed analysis is compared with previously reported experimental data on polycrystalline germanium (p-Ge). This paper aims to provide a deeper physical insight into the microstructural aspects of polycrystalline brittle materials during precision microscale machining.

Hertzian cone crack propagation on polycrystalline materials: Role of R-curve and residual stresses

In this work, the angle of the cone crack produced by Hertzian indentation is studied in relation to the shearing contribution of the crack shielding. This shielding is especially relevant in polycrystalline brittle materials, and may be responsible of the disagreement between previously predicted and actual values of the angle of cone crack. The study was conducted by means of an automated finite-element model of crack propagation, in which an analytical expression of the R-curve was included in the crack path determination. In addition, the influence of extrinsic effects, such as macroscopic residual stresses, was studied. The calculations were compared to crack observations on alumina and alumina-based laminates. Experimental results were in agreement with simulations. Based on this model, a method for quantitative assessment of both mode-I and mode-II crack shielding is proposed.

Modelling Intergranular Microfracture Using a Boundary Cohesive Grain Element Formulation

In this paper, intergranular microfracture evolution in polycrystalline brittle materials is simulated using a cohesive grain boundary integral formulation. A linear cohesive law is used for modelling multiple microcracking initiation and propagation under mixed mode failure conditions, encountering the stochastic e=ects of the grain location, morphology and orientation. Furthermore, in cases where crack surfaces come into contact, slide or separate, fully frictional contact analysis is performed.