Simulations of microcracking in the process region of ceramics with a cell model

Microcracking around a macrocrack and the consequential toughening in polycrystalline ceramics are simulated. The objective is to check the hypothesis that the suppression mechanism for opening of off-side microcracks does not work in certain ceramic materials because cracks open up, assisted by residual stresses, at a much reduced load in some grains, while, still encountering a high resistance to crack growth at the grain boundaries. A two-dimensional cell model of a polycrystalline material is investigated. Each cell represents one grain. The load-deformation law for the cell is assumed to contain two load peaks. The first peak is associated with microcrack nucleation in the grain, while the second peak is related to the resistance that the microcrack meets at the grain boundary. The cells are included in a finite element model. Grain to grain variations, for instance due to residual stresses, are taken into account by a Weibull distribution of the first load peak. Results from the simulations show that variations of the propensity for microcrack nucleation between different grains constitute a major factor responsible for the generation of microcrack clouds. Such cloud formation would otherwise be impeded by unloading effects from central microcracks. In addition, and in accordance with observations, the simulations also show high fracture energies (compared to what would be expected for a typically brittle material), as well as a period of stable crack propagation.     

Acoustic microscopy of low-ductility materials

Acoustic microscopy offers materials scientists not only high resolution, but also the ability to image sub-surface and surface features by its unique elastic contrast mechanisms. It is a particularly powerful tool for detecting discontinuities such as voids and cracks, and for characterizing interfacial boundaries between different phases. This paper describes the application of acoustic microscopy to two important classes of low-ductility material: engineering ceramics and ceramic-fibre composites. Images of a wide range of near-surface defects are presented for the six ceramics studied, including porosity and microcracks. An application to crack length determination during indentation tests is also discussed. In the composites, there were systematic variations in contrast from the fibre-matrix interface, which appeared to correlate with changes in interfacial strength. Finally, the line-focus microscope was used to demonstrate how the Rayleigh velocity and attenuation can be used to characterize the microstructure of ceramics and ceramic composites.     

Effects of moisture-assisted slow crack growth on ceramic strength

An investigation was made of strength degradation caused by moisture-assisted slow crack growth of surface flaws in two dense polycrystalline ceramics. Specimen sizes were varied. The observed strength degradation of each ceramic was predictable usingK _IC as a material property in fracture-mechanics relations, suggesting that the only material variable involved was critical flaw size. The strength of one of the ceramics in water decreased significantly with increased specimen size, but its Weibull modulus was essentially unaffected by specimen size and slow crack growth.     

Quantitative fractography of mixed-mode fracture in an R-curve material

Mixed-mode fracture surfaces of an R-curve material were quantitatively assessed using fractography. The R-curve material chosen was a mica glass ceramic. Vickers indentation cracks of different sizes were introduced at the center of tensile surface of glass ceramic bars fractured in flexure. The bars were fractured in flexure by generating mixed-mode (I/II) loading conditions at crack tips by orienting indentation cracks at various angles with respect to the tensile axis. Quantitative fractography indicated that crack-to-mirror size ratios were a function of crack length and mode mixity. Stress intensity at branching for the mirror–hackle transition during mixed-mode (I/II) fracture condition was a constant and was less than the corresponding stress intensity at branching in mode I loading. An empirical relationship is derived for the effective geometric factors in mixed-mode fracture of ceramics from surface cracks in flexure.     

Structural-simulation modeling of the fritting and fracture of a ferroelectric ceramic

Results are presented from a structural-simulation modeling of the processes that occur during the fritting and fracture of ferroelectric ceramics BaTiO₃ and PbTiO₃. A study was made of anomalous grain growth and the effect of these grains on the spontaneous cracking of the materials. Also examined are features of the propagation of a macrocrack in the modeled structure with allowance for the microcrack region formed in the neighborhood of the crack tip. Alternative microcrack patterns that lead to a change in the strength of the material are discovered, and estimates are obtained for different strength characteristics: crack density; the dimensions of the prefracture region; the crack resistance of the ceramic; local strengthening and shielding of the macrocrack by the microcrack region at its tip.Translated from Problemy Prochnosti, No. 8, pp. 77–86, August, 1994.     

结构陶瓷磨削表面微裂纹的研究

结构陶瓷的磨削表面微裂纹是较常见和较危险的磨削损伤，本文应用压痕断裂力学。磨削表面热应务陶瓷微观结构的有关知识分析了结构陶瓷表面裂纹的形成机理、形状特征及奖表面的延伸，并对几种典型结构民磨削表面层的微观状态进行了大量的ＳＥＭ观察，结果表明：（１）磨削微裂纹与陶瓷的断裂韧性Ｋ１Ｃ和显微硬度Ｈ之比、陶瓷的热特性及磨削工艺参数有关；（２）磨削微裂纹的 压痕效应径向裂纹、热裂纹、（３）细晶陶瓷多为穿晶裂纹     

Weibull modulus of fracture strength of toughened ceramics subjected to small-scale contacts

The Weibull modulus of toughened ceramics was evaluated. The fracture of the toughened ceramics was assumed to be initiated by surface cracks induced during small-scale contacts such as grinding and polishing and an exponential function was selected to describe the R-curve behavior. Based on a brief theoretical analysis, a numerical simulation procedure was designed to predict the fracture strength for toughened ceramics with different R-curve characteristics. The Weibull modulus of each toughened ceramic was estimated and compared with that of the un-toughened base material. It was concluded that an increase in Weibull modulus can always result from toughening. The increase in Weibull modulus was found to be related directly to the relative crack tolerance, i.e., the ratio of the initial crack size to the critical crack size. This suggests that the improvement in crack stability due to toughening is the main reason for the increased Weibull modulus.     

Effect of porosity on the crack pattern and residual strength of ceramics after quenching

The effect of porosity on the crack characteristics of ceramics after water-quenching is studied by measuring the cracks in ceramic sheets. The result reveals that the pore volume fraction has a slight effect on the enhancement of thermal shock resistance of ceramics when the porosity ranges from 0 to 20 %, because the length and density of the long crack in porous alumina are always slightly less than that in dense alumina. This result is in agreement with the prediction based on the minimum potential energy principle using experimentally measured data. Moreover, the proportion of the strength reduction in the third regime decreases significantly with increasing porosity, because the strength of unquenched specimens decreases more rapidly than that of quenched specimens with increasing porosity. The results of this study may help to further understand the thermal shock behavior of ceramics.     

Probabilistic model of early fatigue crack growth

A model is developed in this paper to describe the nucleation and early growth of fatigue cracks. Polycrystalline materials are modelled as a set of elements (grains) with random properties. It is assumed that the resistance to damage of neighboring elements is mutually independent and follows the same probability distribution, except for the elements situated near the surface whose resistance is lower and which are subjected to higher scattering. Damage accumulation in each element due to cyclic loading is considered, and an element is treated as ruptured when a critical damage level is attained; then the ruptured element is included in the cracked domain. The finite element technique is applied to realize the modelling. Numerical results exhibit all the principal features of early fatigue crack growth such as nonmonotonous change of crack growth rates, statistical scatter of crack dimensions and growth rates, and stabilization of the process when a considerable number of grains enter the cracked domain.     

Crack propagation in ceramics under cyclic loads

Stable crack growth is observed in notched plates of polycrystalline alumina subject to fully compressive far-field cyclic loads at room temperature in a moist air environment andin vacuo. The fatigue cracks propagate at a progressively decreasing velocity along the plane of the notch and in a direction macroscopically normal to the compression axis. The principal failure events leading to this effect are analysed in terms of notch-tip damage under the far-field compressive stress, microcracking, frictional sliding and opening of microcracks, and crack closure. An important contribution to such Mode I crack growth arises from the residualtensile stresses induced locally at the notch-tip when the deformation within the notch-tip process zone leaves permanent strains upon unloading from the maximum nominal compressive stress. It is shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials. The mechanisms of fatigue in ceramics are compared and contrasted with the more familiar examples of crack propagation under far-field cyclic compression in metallic systems and the implications for fracture in ceramic-metal composites and transformation toughened ceramic composites are highlighted. Strategies for some important applications of this phenomenon are recommended for the study of fracture mechanisms and for the measurement of fracture toughness in brittle solids.     

Mechanics and micromechanisms of fatigue crack growth in brittle solids

This paper is concerned with the mechanics and micromechanisms of stable mode I crack growth in brittle solids subjected to compression-compression fatigue and tension-tension fatigue loads. Constitutive models, results of finite element analyses, and experimental observations are described for monolithic ceramics and ceramic-matrix composites, plain concrete, and a transformation-toughened ceramic in an attempt to deduce a general theory on the origin of mode I fracture in notched plates under uniaxial cyclic compression at room temperature. An analysis of the residual stress field which develops at elevated temperatures in response to power law creep and far-field compressive cyclic loads is also presented. The principal driving force for mode I fracture in cyclic compression is the generation of a near-tip zone of residual tension, when the deformation at the notch-tip leaves permanent strains upon unloading from the far-field compressive stress. The results indicated that materials with very different microscopic deformation mechanisms, i.e., microcracking, dislocation plasticity, martensitic transformation, interfacial debonding/slip, or creep, exhibit a macroscopically similar, stable fracture under far-field cyclic compression because the zone of residual tension is embedded in material which is elastically strained in compression. It is shown that cyclic compression loading offers a unique method for fatigue precracking notched specimens of brittle solids prior to tensile fracture testing, whereby an unambiguous interpretation of the critical stress intensity factors for crack initiation and growth can be achieved. Fatigue crack growth characteristics of a transformation-toughened ceramic and a creeping ceramic composite under tension-tension fatigue loads are also discussed.     

Microstructural aspects of crack propagation in ceramics

X-ray microradiographic examination supported by optical and SEM observations was used to study crack propagation in various ceramics, including glasses and cubic and noncubic polycrystalline bodies of different grain sizes. The nature of crack propagation in ceramics was often extremely complex. While cracks in glassy materials were generally simple, as would be expected, in cubic and non-cubic polycrystalline specimens both wandering and branching of cracks was observed. In cubic materials, wandering and branching occurred on the scale of the grain size, while in fine grain, non-cubic materials these were on a multi-grain scale. Results are consistent with the grain size dependence of fracture energy. Elastic anisotropy and thermal expansion anisotropy were suggested as major factors in crack wandering and branching.     

Effects of microstructural through‐thickness non‐uniformity and crack size on fatigue crack propagation and fracture of rolled Al‐7075 alloy

Some of the fatigue tests performed using the standard compact tension (CT) and a non‐standard specimen made of rolled 7075 aluminium alloy exhibit fatigue crack growth (FCG) lagging in a small region along the crack front. Through‐thickness microstructural evaluation shows that material grains in this region did not flatten as much as other regions. In the non‐standard specimen, surface cracks are either grown under fatigue loading or broken under monotonically increasing quasi‐static loads at different crack sizes. The aforementioned lagging also exists in a narrow region of 3‐D FCG for specimens with microstructural through‐thickness non‐uniformity. A more important feature for this type of specimen with surface crack is the deflection of fast fracture direction into the grain interfaces, namely from L‐T orientation to S‐L and S‐T directions. It is proved that this is due to significant levels of second principal stresses near the free surface for small cracks and lower fracture toughness of the material in S‐L and S‐T directions.     

Formability of a high-strain-rate superplastic Al–4.4Cu–1.5Mg/21SiCW composite under biaxial tension

The cavitation behavior and forming limits of a high-strain-rate superplastic 21 vol.% SiC whisker-reinforced Al–4.4Cu–1.5Mg (Al–4.4Cu–1.5Mg/21SiC_W) under biaxial stress states were investigated in this paper. The composite sheet was bulged using dies with aspect ratios of 1:1, 4:3 and 2:1 at the constant applied stress of 4 MPa and at the optimal temperature of 793 K determined from superplastic tensile tests. The thickness distributions of bulged diaphragms were measured at different strain levels. For diaphragms deformed equibiaxially, a good agreement between experimental thickness distributions and the theoretical predictions of Cornfield and Johnson (Int. J. Mech. Sci. 12 (1970) 479) was observed at fractional heights of the deformed diaphragms ranging from 0.4 to 1.0. The cavitation behavior of the composite under biaxial tension was compared with that of uniaxial tension. It was found that at a similar effective strain, the amount of cavities obtained under equibiaxial tension is slightly greater than that under uniaxial tension, and the cavity growth rate parameter under uniaxial tension was also slightly larger than that of uniaxial tension. The influence of stress state on cavity growth rate was discussed. Limit strains of Al–4.4Cu–1.5Mg/21SiC_W at different stress ratios were predicted based on a plastic damage model recently developed for superplastic materials (Chan and Chow, Int. J. Mech. Sci., submitted). The trend of the prediction was in good agreement with the experimental findings.     

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N ₁(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.     

FRACTURE MODELLING OF BRITTLE-MATRIX COMPOSITES WITH SPATIALLY DEPENDENT CRACK BRIDGING

Abstract In brittle-matrix composites cracking of the matrix is often accompanied by bridging of the crack surfaces. The bridging will reduce the net stress intensity factor at the crack tip and consequently increase the toughness of the composite material. The bridging mechanism is due to for example unbroken whiskers, fibres, ductile particles or interlocking grains. Analysis of the bridging mechanism in cracked structures is conveniently carried out using the concept of cohesive zone modelling. In this case the action of the bridging elements is replaced by a distribution of forces, so called cohesive forces trying to close the crack. The commonly used approach in such modelling has been to replace the action from individual bridging elements by a continuous spatially independent distribution of closing tractions whose magnitude is a function of the crack opening displacement only. In this paper the influence of the spatial distribution of bridging elements is considered for plane crack problems. The cross section of the bridging elements is assumed to be circular and the distance between the different bridging elements is determined by the volume fraction, the radius and the geometrical distribution of the bridging elements. Damage resistance curves have been calculated for typical whiskers-reinforced ceramic composites, and the results from the present spatially dependent models are compared with results from calculations with spatially independent models. The influence of the radius of the bridging element, the volume fraction of whiskers and the material properties are illustrated and the use of spatially independent models is discussed.     

Stress-strain relations in elastoplastic solids with Dugdale-type cracks

Mechanical behavior of a two-dimensional elastoplastic solid with rectilinear cracks is investigated. Plastic strip model is used to reduce plasticity problem to the equivalent linear elasticity formulation. Two realizations of the mixed mode plastic strip model are considered: in-line plastic strips as proposed by Becker and Gross [Int. J. Fract. 37 (1988) 163], and inclined plastic strips of Panasyuk and Savruk [Appl. Mech. Rev. 47 (1994) 151]. The effective mechanical response predictions are based on the procedure presented in Kachanov et al., [Appl. Mech. Rev. 47 (1994) 151]. Stress-strain relations are obtained for parallel and randomly oriented non-interacting cracks. Results are compared with known elastic solutions.     

Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals

A planar double slip crystal plasticity model is applied to the evaluation of crack tip opening (CTOD) and sliding (CTSD) displacements for microstructurally small stationary cracks under monotonic loading for a material with nominal stress-strain behavior that is representative of a relatively high strength helicopter rotor hub material. Two-dimensional plane strain finite element calculations are presented for CTSD and CTOD of microstructurally small transgranular surface cracks in a polycrystal subjected to monotonic loading. The effects of crack length relative to grain size, orientation distribution of nearest neighbor grains, stress state and stress level are considered for nominal stress levels below the macroscopic yield strength. The CTOD and CTSD are computed for stationary crystallographic surface cracks with various realizations of crystallographic orientations of surrounding grains. It is found that (i) the opening displacement is dominant for remote tension even for crystallographic cracks oriented along the maximum shear plane in the first surface grain, (ii) there is a strong dependence of the CTOD on the proximity to grain boundaries, but lesser dependence of the CTSD, and (iii) that the elastic solutions for CTOD and CTSD are valid below about 30% of the 0.2% offset-defined yield strength.     

The role of porosity in the phase composition evolution and texture formation at the friction surface of partially stabilized tetragonal zirconia ceramics

The influence of porosity on the phase composition evolution and texture formation at the friction surface of yttria-partially-stabilized tetragonal zirconia polycrystalline (Y-TZP) ceramics (ZrO₂ + 3 mol % Y₂O₃) in contact with steel was studied. The Y-TZP ceramic samples with a porosity of P = 0.33 and 3.3% were tested in a rod-on-disk configuration. The sample of higher porosity exhibited a much lower degree of wear. The friction wear was accompanied by irreversible phase transformations from the cubic to tetragonal and from the tetragonal to monoclinic structure. It is suggested that such irreversible phase transformations in porous ceramics favor the development of compressive stresses at the friction surface, which account for the observed behavior.     

Particle modeling of random crack patterns in epoxy plates

This paper employs particle modeling for simulation of dynamic fragmentation in (elastic–brittle) epoxy plates (8.25 cm×33.02 cm), containing non-uniformly distributed circular holes [Al-Ostaz A, Jasiuk I. Crack initiation and propagation in materials with randomly distributed holes. Eng Fract Mech 1997;58:395–420]. Since the experiments on nominally identical specimens resulted in a range of different crack patterns, the model focuses on matching the most dominant experimentally observed cracks. Indeed, this is achieved with lattices having several different mesh resolutions. Next, by introducing very weak, microscale perturbations in the material properties, it is found that the stiffness has a stronger effect on the deviation from the dominant crack pattern than does the tensile strength.