Flexural Properties of Brittle Multilayer Materials: I, Modeling

Multilayer systems comprising brittle materials can exhibit substantially different behaviors under flexural and tensile loadings. The present article addresses the origins of such differences, with emphasis on the modeling of the flexural stress–strain response. Systems with both a deterministic tensile strength and a distribution in strengths (characterized by Weibull statistics) are considered. The model predictions show that both the ultimate strength and strain-to-failure in flexure exceed the corresponding values in uniaxial tension. In addition, systems comprising alternating layers of two different materials are examined, and disparities in the flexural and tensile behaviors addressed.     

Flexural Strength by Fractography in Modern Brittle Materials

Thin components made from advanced brittle glasses or ceramics are becoming increasingly important due to the widespread adoption of portable consumer products as well as other modern electronic and medical devices. The strength of these brittle materials is traditionally estimated from empirical relationships relating the stress at failure to characteristic lengths derived from the fracture surface's topography. One example is Orr's relationship, σ_f?R_m^1/2 = A_m, which correlates the material strength, σ_f, to the radius of the “mirror‐mist boundary region,” R_m, through the empirical constant, A_m. Although various studies have shown that, for flexural fractures (failed in bending), A_m depends on the specimen's geometry, this effect has been generally neglected by arguing that the magnitude of A_m is almost constant for thicker specimens. However, we show that this argument cannot be applied to thin geometries, and that by not accounting for the thickness of the sample, the flexural strength will be grossly underestimated. In this work, we introduce an expression based on an iterative fracture mechanics algorithm which yields more accurate estimates of flexural strength for thin brittle components in bending. The accuracy of the model is validated both through flexural strength tests on glass and by comparing our predictions to an extensive literature survey of experimental results.     

High-Temperature Mechanical Properties of Ceramic Materials: II, Beta-Eucryptite

High stresses arise in sintered β-eucryptite (Li₂O. Al₂O₂-2SiO₂) during cooling from the firing temperature because of its extreme anisotropy of thermal expansion. These stresses cause extensive fracturing of the crystals, resulting in abnormally low mechanical property values at room temperature. During reheating, many fractures recombine, causing increase in strength and in elastic modulus with increasing temperature. Beta-eucryptite creeps under load at room temperature because of additional fracturing and the propagation of fractures. Equations are presented for calculating internal stresses in sintered single-phase aggregates of anisotropic crystals.     

PE/多层石墨导热复合材料的制备与性能

PE、GPE为基材,多层石墨、石墨为填料,采用机械混炼法制备高导热塑料复合材料。SEM分析表明PE/多层石墨比GPE/多层石墨复合材料的插层效果更好。研究填料对复合材料的热导率和热稳定性的影响。结果表明:导热复合材料的热导率随填料填充量的增大而增大,多层石墨的填充量达到100%时,热导率为4.15 W.m-1.k-1。并且在相同填充量下PE/多层石墨较之GPE/多层石墨、PE/石墨、GPE/石墨的导热率更高。TGA分析表明:填充多层石墨、石墨的导热塑料复合材料热稳定性高于未填充的PE。经研究提出,形状比(径厚比)大和导热率高的导热填料更易形成导热网链;为了不影响导热填料的分散性,可先使基体材料与填料先混合均匀再增加其韧性、黏度等。     

Mechanics of Transformation-Toughening in Brittle Materials

Particles which undergo a stress-induced martensitic transformation are known to toughen certain brittle materials. The enhanced toughness can be considered to originate from the residual strain fields which develop following transformation and tend to limit the crack opening. The increased toughness can estimated from the crack-tip stress-intensity change induced by the transformation of a volume of material near the crack tip. It is found that the initial zone, prior to crackgrowth, provides no change in stress intensity. As the crack grows, the zone (associated with a positive transformation strain) induces a stress-intensity reduction that rises to a maximum level after some crack propagation. The influence of particle-size distribution on the stress-intensity reduction is also discussed.     

Crack-Growth Resistance of Microcracking Brittle Materials

A mechanics model of microcrack toughening is presented. The model predicts the magnitude of microcrack toughening as well as the existence of R -curve effects. The toughening is predicated on both the elastic modulus diminution in the microcrack process zone and the dilatation induced by microcracking. The modulus effect is relatively small and process-zone-size-independent. The dilatational effect is potentially more substantial, as well as being the primary source of the R curve. The dilatational contribution is also zone-size-dependent. The analysis demonstrates that microcrack toughening is less potent than transformation toughening.     

Elastic-Plastic Indentation of Hard, Brittle Materials with Spherical Indenters

A method was developed at the U.S. Bureau of Mines to measure the plastic deformation of hard, brittle materials with low values of elastic modulus to hardness ( E/H ). The method involves indenting the hard materials with spherical indenters and measuring the resulting contact diameter and depth. Subsequent analysis separates the plastic deformation from the elastic deformation. The analysis is an extension of a theoretical study of the indentation of ductile materials by spherical indenters. The analysis is based on Meyer's law and the results include the distribution of the contact pressure and the profile of the deformed surface. Measurements were made on alumina and WC–Co.     

Statistics of Flaw Interaction in Brittle Materials

The problem of elastic interaction of an array of microcracks is considered. The solution is based on an efficient surface integral method using distribution of edge dislocations to represent the microcracks in the mathematical model. From the analysis of the interaction between two identical cracks, it is seen that interaction is most likely to produce a slight enhancement in the stress intensity factor. By performing computer experiments on a random array of microcracks, the effect of crack interaction is studied statistically as a function of the density of the microcracks. The significance of the interaction effects for fracture in ceramics is discussed.     

Uniaxial Strength Behavior of Brittle Cellular Materials

Two types of brittle reticulated materials were evaluated under uniaxial tensile and compressive loading and analyzed in terms of the Gibson and Ashby model for brittle open-cell solids. The samples consisted of an open-cell alumina–mullite material which was tested as a function of density at a constant cell size and a reticulated vitreous carbon tested at one density and two cell sizes. The samples were mounted such that only the loading direction was varied in the tests. A combination of video photography and acoustic emission was critical to interpreting the results. The model assumes that identical deformation modes, bending failure of the struts, are responsible for failure of the bulk foam in tension and compression. The results of this work indicate a significant difference between the density dependence in tension and compression. Tensile failure in both materials appeared to be characterized by the catastrophic propagation of a single crack. Compressive failure was significantly different between the alumina and glassy carbon foams. The alumina foam failed by a damage accumulation process, whereas the carbon foam failed by the catastrophic collapse of a band of cells perpendicular to the loading direction.     

Reliability of Brittle Materials in Thermal Shock

The fracture-of alumina disks subjected to thermal shock is predicted from Weibull parameters derived from isothermal three-point-bend tests. Both the shear-insensitive Batdorf model and the principle of independent action model are used to compare results from three-point-benr1 and isothermal biaxial strength tests to results from thermal fracture tests. It is found that the shear-insensitive Batdorf model gives good agreement between mechanical tests and fracture of the thermally shocked disks.     

Model for Strength of Brittle Porous Materials

Many porous bodies form by the growth and joining of individual solid particles into a network-like structure. Assuming that the distribution of particles in the porous body is random, the relation between strength and porosity was derived and compared with commonly used empirical relations.     

Rationalized Load and Lifetime of Brittle Materials

The design and testing of structural parts from materials which exhibit subcritical crack growth can be improved by introducing auxiliary quantities into the classical concepts of fracture mechanics. The equivalent static stress, equivalent loading time, standardized loading time, and standardized lifetime, as well as the decrease in lifetime and residual lifetime, are defined, with examples of their application.     

Model of Transformation Toughening in Brittle Materials

Assuming that the energy dissipation decreases inversely with distance from the crack tip, the increase in steady-state toughness of a transformation-toughened ceramic is estimated to be δ J = (δ J ₀/ω) In (1 +ω), where (i) δ J ₀ denotes the toughness increment which would be expected for a given zone height h ₀ assuming full transformation throughout the zone, and (ii) ω is a nondimensional parameter giving the ratio of the inelastic transformation strain (for full transformation) to the initial elastic strain at the onset of transformation. This estimate extends the earlier result of McMeeking and Evans (1982) in two significant respects: (i) the transformation strain may include a shear component, instead of being purely dilatational, and (ii) the range of ω is now unrestricted, whereas the McMeeking and Evans approach strictly applies only in the weak transformation limit, ω« 1. The height of the inner zone h _i within which transformation has proceeded to completion (or saturation) is estimated to be h _i= h ₀/(1 +ω). Experimental data of Mg-PSZ and Ce-TZP can be quantitatively accounted for using this approximate model, which is also in very good agreement with the rigorous finite-element results of Budiansky, Hutchinson, and Lambropoulos in the special case of subcritical dilatational transformation.     

A Statistical, Micromechanical Theory of the Compressive Strength of Brittle Materials

A general theory of the compressive strength of brittle materials is presented. This theory proposes that failure is brought about by structural weakening from accumulated crack damage which increases with the stress level. The statistics of the flaw distribution and the mechanism of crack initiation and extension are important. A sample calculation using the theory is given to demonstrate its application.     

Use of the Blister Test to Study the Adhesion of Brittle Materials. Part II. Application

Using a modified form of the blister test, where the adhesive layer was between the substrate and a massive base, instead of as a continuous sheet on top of the substrate, we determined the interfacial fracture energy F for a series of interfaces where a brittle material (ice) was adhering to various substrates. Fracture energies obtained were compared with work of adhesion values measured for water on the same substrates. Fracture energy, which contains within it both a reversible contribution due to intermolecular interactions across the interface (work of adhesion) and an irreversible contribution due to collective dissipative processes, was found to rise rapidly with modest increases in work of adhesion. The observed relation suggests that the irreversible contribution to fracture energy is influenced strongly by the intermolecular interactions at the interface.     

Use of the Blister Test to Study the Adhesion of Brittle Materials. Part II. Application

Using a modified form of the blister test, where the adhesive layer was between the substrate and a massive base, instead of as a continuous sheet on top of the substrate, we determined the interfacial fracture energy F for a series of interfaces where a brittle material (ice) was adhering to various substrates. Fracture energies obtained were compared with work of adhesion values measured for water on the same substrates. Fracture energy, which contains within it both a reversible contribution due to intermolecular interactions across the interface (work of adhesion) and an irreversible contribution due to collective dissipative processes, was found to rise rapidly with modest increases in work of adhesion. The observed relation suggests that the irreversible contribution to fracture energy is influenced strongly by the intermolecular interactions at the interface.     

Direct Measurement of Fracture Energies of Brittle Heterogeneous Materials

A noncatastrophic fracture was shown to exist in the three-point bending test with a "hard-beam" machine when an artificially cracked or notched specimen was used. In this mode of fracture the energy produced by external work was transformed completely into the effective surface energy (fracture energy) of the specimen. The energy was measured from the load-time curve for the test. The fracture energies obtained by this method for plate glass were in the range 3 to 6 × 10³ ergs cm⁻², in good agreement with results obtained by other methods. The effective fracture energies of firebrick were about one order of magnitude larger than those of glass.