A micromechanical multi-physics model for ceramics has been recalibrated and used to simulate impact experiments with boron carbide in abaqus . The dominant physical mechanisms in boron carbide have been identified and simulated in the framework of an integrated constitutive model that combines crack growth, amorphization, and granular flow. The integrative model is able to accurately reproduce some of the key cracking patterns of Sphere Indentation experiments and Edge On Impact experiments. Based on this integrative model, linear regression has been used to study the sensitivity of sphere indentation model predictions to the input parameters. The sensitivities are connected to physical mechanisms, and trends in model outputs have been intuitively explored. These results help suggest material modifications that might improve material performance, prioritize calibration experiments for materials-by-design iterations, and identify model parameters that require more in-depth understanding.

Failure criteria for a crack between two dissimilar materials are presented. Test data from three different material pairs are considered. The first two consist of an interface crack between glass and epoxy and two dissimilar ceramic clays. For the third material pair, there is a delamination between two unidirectional carbon fiber polymer-reinforced plies with fibers in the 0 deg and 90 deg directions. Failure criteria for these materials have been presented previously. In this study, invariant parameters are used in the failure criteria. It is seen that the invariant length parameter has values which are unrealistically large and small. The preferred criterion is based on first principles.

Knowledge of crack initiation, propagation, and corresponding thermal shock failure evolution is prerequisite for effective maintenance of civil engineering so as to avoid disaster. Experimental analysis of the cracking in the ceramic sheets subsequent to water quenching has been conducted. Based on statistical mesoscopic damage mechanics, it was revealed that there are four stages in the process of thermal shock evolution of ceramics subjected to water quenching. The multiple cracks interaction mechanism has been analyzed from the viewpoint of the evolution of the elastic strain energy and stress intensity factor.

In ferroelectroelastic ceramics, the process of fracture is accompanied by significant inelastic deformation due to domain switching. This leads to an apparent toughening of the material, which is known as R-curve behavior. A promising approach to predict R-curves is based on one parameter fracture criteria. The scope of this paper is the examination of the physical validity of these criteria for realistic material behavior. Besides a general discussion of the problem, fracture of the lead zirconate titanate ceramic PIC151 is examined. Thereby, restriction is made to purely mechanical material behavior. The results indicate that the usage of one parameter fracture criteria is questionable. This is due to a conflict between the length scale of the zone wherein the asymptotic crack tip singularity dominates in the field solution of the continuum model and the length scale associated with the fracture process zone. It is concluded that an incorporation of the fracture process into the used fracture mechanics model is necessary to capture transient fracture of ferroelectroelastic ceramics properly.

One observation from interface defeat experiments with thick ceramic targets is that confinement and prestress becomes less important if the test scale is reduced. A small unconfined target can show similar transition velocity as a large and heavily confined target. A possible explanation for this behavior is that the transition velocity depends on the formation and growth of macro cracks. Since the crack resistance increases with decreasing length scale, the extension of a crack in a small-scale target will need a stronger stress field, viz., a higher impact velocity, in order to propagate. An analytical model for the relation between projectile load, corresponding stress field, and the propagation of a cone-shaped crack under a state of interface defeat has been formulated. It is based on the assumption that the transition from interface defeat to penetration is controlled by the growth of the cone crack to a critical length. The model is compared to experimentally determined transition velocities for ceramic targets in different sizes, representing a linear scale factor of ten. The model shows that the projectile pressure at transition is proportional to one over the square root of the length scale. The experiments with small targets follow this relation as long as the projectile pressure at transition exceeds the bound of tensile failure of the ceramic. For larger targets, the transition will become independent of length scale and only depend on the tensile strength of the ceramic material. Both the experiments and the model indicate that scaling of interface defeat needs to be done with caution and that experimental data from one length scale needs to be examined carefully before extrapolating to another.

It has been demonstrated that significant weight reductions can be achieved, compared to conventional glass-based armor, when a transparent ceramic is used as the strike face on a glass-polymer laminate. Magnesium aluminate spinel (MgAl2O4) and AlON are promising candidate materials for application as a hard front layer in transparent armor. Comprehensive, systematic investigations of the fragmentation of ceramics have shown that the mode of fragmentation is one of the key parameters influencing the ballistic resistance of ceramics. In the study described here, the fragmentation of AlON and three types of spinel was analyzed: two types of fine grained spinel with nominal average grain sizes 0.6 μm and 1.6 μm and a bimodal grain-sized spinel with large grains of 250 μm size in a fine grain (5–20 μm) matrix were examined. The ceramic specimens of 6-mm thickness were glued to an aluminum backing and impacted with armor piercing (AP) projectiles of caliber 7.62 mm at two different velocities—850 m/s and 1100 m/s. The targets were integrated into a target box, which allowed for an almost complete recovery and analysis of the ceramic fragments. Different types of high-speed cameras were applied in order to visualize the different phases of fragment formation and ejection. A laser light-sheet illumination technique was applied in combination with high-speed cameras in order to determine size and speed of ejected ceramic fragments during projectile penetration. The application of the visualization techniques allowed for the analysis of the dynamics of the fragment formation and interaction with the projectile. A significant difference in the fragment size distributions of bimodal grain-sized spinel and AlON was observed.

A simple and easy-to-use analytical (“mathematical”) predictive model has been developed for the assessment of the size of an inelastic zone, if any, in a ball-grid-array (BGA) assembly. The BGA material is considered linearly elastic at the strain level below the yield point and ideally plastic above the yield strain. The analysis is carried out under the major assumptions that, as far as the estimated size of an inelastic zone is concerned, (1) the inhomogeneous (“discrete”) BGA structure can be substituted by a homogeneous (continuous) bonding layer of the same thickness (height) and (2) only the longitudinal cross-section of the package-substrate assembly can be considered. The numerical example carried out for a 30 mm long surface-mount package and a 200 μm thick lead-free solder indicated that, in the case of a high expansion PCB substrate, about 7.5% of the interface's size experienced inelastic strains, while no such strains could possibly occur in the case of a low expansion ceramic substrate. The suggested model can be used to check if the zone of inelastic strains exists in the design of interest and, if inelastic strains cannot be avoided, how large this zone is, before applying a Coffin-Manson-type of an equation (such as, say, Anand's model in the ANSYS software) with an objective to evaluate the BGA material lifetime.

A continuum model is developed for describing deformation and failure mechanisms in crystalline solids (ceramics and minerals) with the cubic spinel structure. The constitutive model describes the response under conditions pertinent to impact loading: high pressures, high strain rates, and, possibly, high temperatures. Nonlinear elasticity, anisotropy, thermoelastic coupling, dislocation glide, twinning, shear-induced fracture, and pressure-induced pore collapse are addressed. The model is applied to enable an improved understanding of transparent ceramic aluminum oxynitride (AlON). Calculations demonstrate an accurate depiction of hydrostatic and shear stresses observed experimentally in shock-loaded polycrystalline AlON. Various choices of initial resistances to slip, twinning, or shear fracture that result in similar predictions for average stresses in polycrystals but different predictions for defect densities (accumulated dislocations and twin volume fractions) are investigated. Predictions for single crystals provide insight into grain orientation effects not available from previous experimental investigations.

Ceramic materials applied by air plasma spray are used as components of thermal barrier coatings. As it has been found that such coatings also dissipate significant amounts of energy during vibration, they can also contribute to reducing the amplitude of resonant vibrations. In order to select a coating material for this purpose, or to adjust application parameters for increased dissipation, it is important that the specific mechanism, by which such dissipation occurs, be known and understood. It has been suggested that the dissipative mechanism in air plasma sprayed coatings is friction, along interfaces arising from defects between and within the “splats” created during application. An analysis, similar to that for the dissipation in a lap joint, is developed for an idealized microstructure characteristic of such coatings. A measure of damping (loss modulus) is extracted, and the amplitude dependence is found to be similar to that observed with actual coating materials. A critical combination of parameters is identified, and variations within the microstructure are accounted for by representing values through a distribution. The effective or average value of the storage (Young’s) modulus is also developed, and expressed in terms of the parameters of the microstructure. The model appears to provide a satisfactory analytical representation of the damping and stiffness of these materials.

The ability of a ceramic to resist penetration by projectiles depends, in a coupled manner, on its confinement and its mechanical properties. In order to explore the fundamental inter-relationships, a simulation protocol is required that permits the microstructure and normative properties (hardness and toughness) to be used as input parameters. Potential for attaining this goal has been provided by a recent constitutive model, devised by Deshpande and Evans (DE) [2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanics-Based Dynamic Constitutive Model,” J. Mech. Phys. Solids, 56, pp. 3077–3100 ] that incorporates the contributions to the inelastic strain from both plasticity and microcracking. Before implementing the DE model, various comparisons with experimental measurements are required. Previously, the model has been successfully used to predict the quasistatic penetration of alumina by hard spheres. In the present assessment, simulations of the dynamic penetration of confined alumina cylinders are presented as a function of microstructure and properties and compared with literature measurements of the ballistic mass efficiency. It is shown that the model replicates the measured trends with hardness and grain size. Motivated by this comparison, further simulations are used to gain a basic understanding of the respective roles of plasticity and microcracking on penetration and to elucidate the phenomena governing projectile defeat.

The mechanics of frictional attachment between surfaces with pillars, inspired by the head fixation system of dragonflies, is analyzed. The system consists of two surfaces of interdigitating pillars held together through friction, as by the densely packed bristles of two brushes when pressed together. The adhesive strength of the system is promoted by high elastic modulus, high friction coefficient, large aspect ratio, and dense packing of the fibers. However, the design is limited by the compressive buckling, the compressive indentation or cracking of the contacting pillars, yielding in shear or similar mechanisms that limit the achievable friction stress, and tensile failure of the pillars upon pull-out. Maps, which summarize the strength of the adhesive system and the failure limits and illustrate the trade-off among the design parameters, are presented. Case studies for steel, nylon, and ceramic pillars show that useful strength can be achieved in such attachments; when buckling during assembly and contact failure can be avoided, adhesive performance as high as 30% of the tensile strength of the pillar material may be possible.

Plate impact experiments and impact recovery experiments were performed on 92.93 wt. % aluminas using a 100 mm dia compressed-gas gun. Free surface velocity histories were traced by a velocity interferometry system for any reflector (VISAR) velocity interferometer. There is a recompression signal in free surface velocity, which shows evidence of a failure wave in impacted alumina. The failure wave velocities are 1.27 km ∕ s and 1.46 km ∕ s at stresses of 7.54 GPa and 8.56 GPa , respectively. It drops to 0.21 km ∕ s after the material released. SEM analysis of recovered samples showed the transit of intergranular microcracks to transgranular microcracks with increasing shock loading. A failure wave in impacted ceramics is a continuous fracture zone, which may be associated with the damage accumulation process during the propagation of shock waves. Then a progressive fracture model was proposed to describe the failure wave formation and propagation in shocked ceramics. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. Numerical simulation of the free surface velocity was performed in good agreement with the plate impact experiments. And the longitudinal, lateral, and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

In metal-ceramic systems the constraint on plastic flow leads to so high stress triaxialities that cavitation instabilities may occur. If the void radius is on the order of magnitude of a characteristic length for the metal, the rate of void growth is reduced, and the possibility of unstable cavity growth is here analyzed for such cases. A finite strain generalization of a higher order strain gradient plasticity theory is applied for a power-law hardening material, and the numerical analyses are carried out for an axisymmetric unit cell containing a spherical void. In the range of high stress triaxiality, where cavitation instabilities are predicted by conventional plasticity theory, such instabilities are also found for the nonlocal theory, but the effects of gradient hardening delay the onset of the instability. Furthermore, in some cases the cavitation stress reaches a maximum and then decays as the void grows to a size well above the characteristic material length.

Recently, three-dimensional structured ceramic composites with large threshold strengths (i.e., stress below which there is zero probability of failure) have been fabricated utilizing an architecture consisting of relatively stress-free, elongated prismatic domains, separated by thin compressive walls. We build upon prior work on laminate architectures, with the common feature that these structures are all susceptible to fracture. Typically, these three-dimensional structures consist of thin shells of mullite that surround alumina. Cracks, originating from large flaws within the ceramic body, are arrested by the surrounding compressive layers until a specific stress level is attained (i.e., the threshold strength), resulting in a truncation of the strength distribution in the flaw region. A preliminary stress intensity solution has shown that this arrest is caused by a reduction of the crack driving force by the residual compression in the compressive walls. This solution also predicts that the threshold strength is dependent not only on the magnitude of the residual compression in the walls but also on the dimensions of both phases. A finite element model is presented that utilizes a penny-shaped crack in the interior of such a structure or half-penny-shaped crack emanating from the edge of such a structure. Ongoing analytical and experimental work that is needed to more fully understand this arrest phenomenon and its application towards the development of reliable, damage-tolerant ceramic components are discussed.

A three-dimensional solution for the problem of transversely loaded, all-round clamped rectangular plates of arbitrary thickness is presented within the linear, small deformation theory of elasticity. The Ritz minimum energy principle is employed to derive the governing equation of the plate made of functionally graded materials. In theory, if we employ an infinite number of terms in the displacement series, the exact solution can be determined. However, a practical limit always exists due to numerical implementation. The solution has a validity comparable to some higher order theories. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent are investigated.

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad hoc, tedious, and time consuming. Here, we present an algorithm that obtains a scaling law in the form of a power law from experimental data (including simulated experiments). The proposed algorithm integrates dimensional analysis into the backward elimination procedure of multivariate linear regressions. In addition to the scaling laws, the algorithm returns a set of dimensionless groups ranked by relevance. We apply the algorithm to three examples, in each obtaining the scaling law that describes the system with minimal user input.

Field singularities of collinear and collinear periodic interface cracks between an electrode and a piezoelectric matrix are studied in terms of the Stroh formalism for mixed boundary conditions. In contrast to the relevant work done previously on this subject, the problem is solved based on the assumption that the upper and lower planes embedding the electrode consist of two arbitrary piezoelectric materials, and the cracks are assumed to be permeable. The problem is reduced to an interfacial crack problem equivalent to that in purely elastic media. Explicit expressions are presented for the complex potentials and field intensity factors. All the field variables exhibit oscillatory singularities, and their intensities are dependent on the material properties and the applied mechanical loads, but not on the applied electric loads.

The thermal fracture behavior in functionally graded yttria stabilized zirconia–NiCoCrAlY bond coat alloy thermal barrier coatings was studied using analytical models. The response of three coating architectures of similar thermal resistance to laser thermal shock tests was considered. Mean field micromechanics models were used to predict the effective thermoelastic and time-dependent (viscoplastic) properties of the individual layers of the graded thermal barrier coatings (TBCs). These effective properties were then utilized in fracture mechanics analyses to study the role of coating architecture on the initiation of surface cracks. The effect of the surface crack morphology and coating architecture on the propensity for propagation of horizontal delamination cracks was then assessed. The results of the analyses are correlated with previously reported experimental results. Potential implications of the findings on architectural design of these material systems for enhanced thermal fracture resistance are discussed.