Brittle Polycrystalline Materials Research Articles

A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials

AbstractIn this paper, a cohesive grain boundary integral formulation is proposed, for simulating intergranular microfracture evolution in polycrystalline brittle materials. Artificially generated polycrystalline microstructures are discretized using the proposed anisotropic boundary element method, considering the random location, morphology and material orientation of each grain. Each grain is assumed as a single crystal with general elastic orthotropic mechanical behaviour. Crack initiation and propagation along the grain boundaries interfaces are modelled using a linear cohesive law, considering mixed mode failure conditions. Furthermore, a non‐linear frictional contact analysis is performed over cracked grain interfaces to encounter cases where crack surfaces come into contact, slide or separate. The effect of randomly located pre‐existing flaws on the overall behaviour and microcracking evolution of a polycrystalline material is also investigated for different Weibull moduli. The stochastic effects of each grain morphology‐orientation, internal friction and randomly distributed pre‐existing flaws, under different loading conditions, are studied probabilistically by simulating various randomly generated microstructures. Copyright © 2006 John Wiley & Sons, Ltd.

On the mean cluster size of a network of cracks

Brittle polycrystalline materials such as rocks, ceramics, and certain metals contain microcracks that can grow and coalesce under sufficiently high stress, resulting in failure and, possibly, fragmentation. Such processes are idealized in this paper by treating the cracks as circular disks whose coalescence forms clusters and can terminate growth after a number of intersections. A non-linear recurrence relation for the probability of cluster size is developed and solved by means of a generating function, providing information on the mean size of the crack clusters and the standard deviation. This solution leads to a simple expression for the percolation threshold. The probability of clusters of size n is also determined. Above the percolation threshold the probabilities of finite and infinite clusters are treated separately. Explicit expressions for the probabilities can be approximated by taking a Laplace transform in a simple case, thus clarifying the behaviour of the solution. Appendices show the relation of the theory to practical problems, Monte Carlo approaches, the probability of infinite clusters, and discuss the uniqueness of solutions to such geometrical problems, i.e. Bertrand's Paradox. Copyright © 2005 John Wiley & Sons, Ltd.

The shock response of float-glass laminates

Interfaces within glass targets give rise to variations in the mode of failure of material components. The wide use of such laminates merits further investigation of the failure mechanism. It is already known that when shocked above a threshold of 4GPa, glass fails under compression behind a propagating front following the compression front. Work is presented which indicates how this failure process is altered by bonding together two plates to introduce an interface, rather than leaving a monolithic target. After crossing an internal interface, the failure wave propagates only after a delay in soda-lime glass and the failed strength of the material is increased at the inner interface compared with that at the impact face. Addition of a second interface illustrates these effects. Recent work has shown that failure of more than two plates bonded together during impact shapes the pulse transmitted through materials. Indeed it has been suggested that glass sheets bonded together show some of the features of polycrystalline brittle materials. In this work, the stress has been monitored at different stations in the laminate to ascertain the effect of varying the number of tiles within the laminate. It is found that the pulse rises to ca. 4GPa quickly and then is ramped more gradually as the number of glass sheets is increased.

419 有限要素法による多結晶体の破壊強度の評価(応力破壊解析,学術講演)

419 有限要素法による多結晶体の破壊強度の評価(応力破壊解析,学術講演)

Mesoscale Modeling of Dynamic Fracture of Ceramic Materials

The dynamic propagation and branching of a mode I crack in polycrystalline brittle materials like ce- ramics are investigated numerically using a 2-D explicit grain-based cohesive/volumetric finite element scheme. The granular microstructure of the ceramics is taken into account and the crack is restricted to propagate along the grain boundaries. Special emphasis is placed on study- ing the effect of grain size and cohesive parameters on the crack branching instability.

A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: Numerical examples

Numerical aspects of the grain level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of grain level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/or layers.

A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementation

A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo grain level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.

Three-dimensional simulation of crack extension in brittle polycrystalline materials

Crack extension resistance in brittle polycrystals was investigated from the viewpoint of three-dimensional microcrack evolution. Even in the case of macroscopically two-dimensional cracks, inhomogeneous distribution of microscopic stress along the crack front gives rise to three-dimensional structures of extended crack surfaces. Numerical simulations of macroscopic crack extension were carried out, which showed that three-dimensional distribution of grain-by-grain thermal stress leads to a significant increase in the crack extension resistance. It was concluded that three-dimensional interpretation on the microscopic inhomogeneity is necessary for the correct comprehension of macroscopic crack extension behavior in brittle polycrystals.

Wave propagation, damage evolution, and dynamic fracture extension. Part I. Percussion drilling

Percussion drilling, wave propagation in damageable media, and the evolution of damage caused by repeated impacts during percussion drilling in brittle disordered materials are investigated. Analytic, numerical, and experimental works complementing each other in clarifying the complex dynamic process of damage evolution and fracture network development in polycrystalline brittle materials are presented. Rock samples from field tests were sectioned and a microscopic investigation of the damage and fracture zones at the bottom and circumference of the borehole was performed. On the basis of experimental findings, we develop a three-dimensional numerical simulation scheme which incorporates wave propagation in dissimilar granular arrangements, dynamic impact phenomena, and accumulation of brittle damage to the rock grains. The combination of brittle damage continuum mechanics with the theory of propagation of elastic wave proves to be a very suitable approach for the description of impact destruction of rock and rocklike materials showing brittle behavior. The developed 3D finite-block numerical code enables one to simulate single and multiple impacts on personal computers. Further development will include the impact of a sequence of bits and the implementation of time-varying elastic properties in the wave propagation model. The results of experimental field tests are in good agreement with numerical model simulations.

Effects of residual stress on toughening of brittle polycrystals

The effects of residual stress on toughening of brittle polycrystalline materials, in the absence of microcracking, were investigated by considering the mode I stress intensity factor reduction at the tip of a stationary crack under combined applied and residual stress loading. Toughness enhancement associated with a number of model singular and non-singular residual stress fields was evaluated. The singular residual stress fields were used to model grain-sized thermal expansion anisotropy due to grain-orientation differences in a polycrystal. The numerical results indicate that residual stress can significantly toughen a stationary crack against initiation. For the same average value of residual stress, toughness enhancement due to singular residual stress fields is more substantial than that due to non-singular residual stress fields. Sample toughness enhancement results are presented for a single-phase polycrystal failing by intergranular fracture.

Probability of intergranular fracture in intrinsically brittle materials

A simple model for estimating the probability of intergranular fracture has been presented. This model predicts that intrinsically brittle polycrystalline materials exhibit intergranular fracture even if the fracture energy of the grain boundary is equivalent to that of the cleavage plane. Furthermore, less symmetric crystals will be more prone to intergranular fracture than those with many possible cleavage favourably oriented loading directions.

Cracking at grain boundaries in polycrystalline brittle materials

The cracking of grain boundary facets in polycrystalline materials showing anisotropic thermal expansion behaviour is controlled by several microstructural factors in addition to the intrinsic thermal and elastic properties. Of specific interest are the relative orientation of the two grains meeting at the facet, and the size of the facet; these factors thus introduce two statistical aspects to the problem. The criteria for facet fracture are critically reviewed. The statistical factors are then introduced to give quantitative data on crack density vs temperature. The theory is compared briefly with limited experimental measurements of Young's modulus for various rocks as a function of temperature.

Effect of sample testing conditions on the form of the relationship of strength to grain size for brittle polycrystalline materials

Effect of sample testing conditions on the form of the relationship of strength to grain size for brittle polycrystalline materials

Fracture in the compression of columnar gained ice

Failure behavior of fine-grained columnar ice is investigated under compression. A special experimental set-up is used to achieve a uniform stress (strain) state in the specimen. The strength is then determined at several constant temperatures and strain rates. Three failure mechanisms have been identified: cleavage fracture, plastic flow, and linkage of grain boundary cracks. The failure mechanism is believed to be a material property. The failure mode, however, is dependent on the specimen geometry and the loading condition. Thorough investigation is made on the failure modes of ice specimens (4 × 8 × 12 cm blocks). A major conclusion is that ice is an excellent material to be used in the investigation of the failure of brittle polycrystalline materials.

The influence of press-powder grain composition on the physicomechanical properties of magnesia refractories

1. Investigations with the aid of the simplex-lattice method of experimental design and a mathematical formalization permitted an elucidation of the nature of changes in the bending strength, Young's modulus, and true porosity of periclase-spinel ceramic over a range of limiting values of the fractional compositions of the original press powders. 2. Graphs of the distribution of the properties make it possible to choose press powder compositions over a wide range which will ensure a constant level of the properties of the material under test. 3. It was shown that it is necessary to take into account the statistical aspects in research on changes in the strength properties of brittle polycrystalline materials due to variation in the grain structure.

Structure and strength of brittle polycrystalline inorganic materials (attempt at classification)

The effect of structure features of brittle polycrystalline materials on their strength is discussed. The classification of structure features is proposed based on relationship between the strength of basic crystalline and binding phases and also on the bonding strength of these phases into solid body.

Effect of Cylindrical Porosity on Young's Modulus of Polycrystalline Brittle Materials

Effect of Cylindrical Porosity on Young's Modulus of Polycrystalline Brittle Materials

A Strength–Porosity Relation Involving Different Pore Geometry and Orientation

A number of empirical and semiempirical expressions which relate the strength of brittle polycrystalline materials to the total porosity have been proposed by various investigators. The present study demonstrates from a purely theoretical point of view that not only the total porosity but the pore shape and orientation are important factors affecting the strength. A strength‐porosity relation is derived that takes pore shape and orientation into account. Examples of how various types of pores should affect the strength are presented.