Porosity dependence of strength in brittle solids

The effect of pore size and pore volume fraction on strength in brittle solids is evaluated. The analysis considers that the strength degradaton of a solid containing a large number of spherical pores is due to a strong effect of porosity on Young's modulus. Each pore is assumed to possess radial or annular flaws emanating from the pore surface whose lengths are considered to be independent of pore size. The effect of stress concentration induced by the presence of the pore is included in the equation for strength through the Young's modulus dependence of porosity originally developed using the concept of crack opening displacement. It is shown that the strength of a solid containing spherical pores is controlled by the pore size, pore volume fracton and the radial (or annular) crack size to pore size ratio. Predicted variation of strength with pore volume fraction is tested against experimental data for glass and polycrystalline alumina.     

Fracture-mode map of brittle coatings: Theoretical development and experimental verification

Brittle coatings, upon sufficiently high indentation load, tend to fracture through either ring cracking or radial cracking. In this paper, we systematically study the factors determining the fracture modes of bilayer material under indentation. By analyzing the stress field developed in a coating/substrate bilayer under indentation in combination with the application of the maximum-tensile-stress fracture criterion, we show that the fracture mode of brittle coatings due to indentation is determined synergistically by two dimensionless parameters being functions of the mechanical properties of coating and substrate, coating thickness and indenter tip radius. Such dependence can be graphically depicted by a diagram called ‘fracture-mode map’, whereby the fracture modes can be directly predicated based on these two dimensionless parameters. Experimental verification of the fracture-mode map is carried out by examining the fracture modes of fused quartz/cement bilayer materials under indentation. The experimental observation exhibits good agreement with the prediction by the fracture-mode map. Our finding in this paper may not only shed light on the mechanics accounting for the fracture modes of brittle coatings in bilayer structures but also pave a new avenue to combating catastrophic damage through fracture mode control.     

Multiple fractures produced by the bending of brittle beams

This paper describes experiments where the bending of beams results in two or more fractures being formed, apparently simultaneously. This is explained in terms of the stress waves emitted by the initial fracture process. It is shown that three separate types of secondary fracture may occur as a result of the interaction between the stress pulses produced by the initial fracture and the loading stresses already present in the beam. In treating these problems it has been found helpful to use an analytical solution for the bending wave propagated when a semi-infinite beam, which is subjected to a constant bending moment, is suddenly unloaded at the free end. In modelling the longitudinal stress pulse produced by the fracture we have used a simplified model which assumes that the forcing function on the fracture plane is a force field equal to the resultant force acting on the unbroken portion of the fracture surface prior to the onset of fracture.     

Simulation of spallation in brittle solids

A new model of dynamic fracture for brittle materials based on Perzyna's[1] idea and Seaman's experimental results[2] is developed. Numerical simulations of metal uranium[3] spalling process in its impact tests are carried out with the model. Fair agreement between the computation and experimental data has been obtained.     

Deformation of cylindrical containers and ceramic powders by explosive compaction

Experiments on explosive compaction of an oxide powder layer in a cylindrical container by sliding detonation of ammonite are performed with various thicknesses of the HE and the container and for various materials of the container and the powder. With increase in the loading rate, stepped irregularities appeared and increased in amplitude on the boundaries between the metal and the compacted ceramic layer. The ceramics layer in this case cracked into pieces, which were shifted relative to each other and pressed into the metal surface. The results obtained are explained by features of the compaction of the powder in the container by sliding loading. The strength of the ceramics turned out to be higher than that of the metal of the container, and the ceramics that formed immediately behind the incident shock wave in the powder experienced additional strain. Design-Technological Institute of Hydroimpulse Engineering, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 159–166, November–December, 1998.     

Static and dynamic compaction of ceramic powders

The static and dynamic compaction of ceramic powders was investigated experimentally using a high-pressure friction-compensated press to achieve static stresses of 1.6 GPa and with a novel gas gun setup to stresses of 5.9 GPa for a tungsten carbide powder. Experiments were performed in the partial compaction region to nearly full compaction. The effects of variables including initial density, particle size distribution, particle morphology, and loading path were investigated in the static experiments. Only particle morphology was found to significantly affect the compaction response. Post-test examination of the powder reveals fracture of the grains as well as breaking at particle edges. In dynamic experiments, steady structured compaction waves traveling at very low velocities were observed. The strain rate within the compaction waves was found to scale nearly linearly with the shock stress, in contrast with many fully dense materials where strain rate scales with stress to the fourth power. Similar scaling is found for data from the literature on TiO₂ powder. The dynamic response of WC powder is found to be significantly stiffer than the static response, probably because deformation in the dynamic case is confined to the relatively narrow compaction wave front. Comparison of new static powder compaction results with shock data from the literature for SiO₂ also reveals a stiffer dynamic response.     

An experimental investigation into modeling solids friction for fluidized dense-phase pneumatic transport of powders

Results are presented of an ongoing investigation into modeling friction in fluidized dense-phase pneumatic transport of bulk solids. Many popular modeling methods of the solids friction use the dimensionless solids loading ratio and Froude number. When evaluated under proper scale-up conditions of pipe diameter and length, many of these models have resulted in significant inaccuracy. A technique for modeling solids friction has been developed using a new combination of dimensionless numbers, volumetric loading ratio and the ratio of particle free settling velocity to superficial conveying air velocity, to replace the solids loading ratio and Froude number. The models developed using the new formalism were evaluated for accuracy and stability under significant scale-up conditions for four different products conveyed through four different test rigs (subject to diameter and length scale-up conditions). The new model considerably improves predictions compared with those obtained using the existing model, especially in the dense-phase region. Whereas the latter yields absolute average relative errors varying between 10% and 86%, the former yielded results with errors from 4% to 20% for a wide range of scale-up conditions. This represents a more reliable and narrower range of prediction that is suitable for industrial scale-up requirements.     

Computational modeling of the cold compaction of ceramic powders

A finite-element model of the cold compaction of ceramic powders by uniaxial pressing is developed and validated by comparison with experimental data. The mechanical behavior of processing powders is assumed according to the modified Drucker-Prager cap model. The frictional effects and the mechanical behavior of tools involved in the process are taken into account. The proposed model allows evaluation of the density distribution into the processed part, as well as stress and strain fields. Variations of the density distribution due to the unloading and the ejection of the part are evaluated Published in Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 135–143, October 2006.     

Photoelasto-plastic studies on brittle fracture of high-polymer solids

The mechanism of brittle fracture of high-polymer solids is experimentally investigated under one-or two-dimensional stress states by a new photoelastoplastic method suggested by the author. The application of the photoelasto-plastic method on the brittle-fracture problem is based on the principle that breaking stress can be computed in brittle fracture by the measurement of the fringe orderN _B of isochromatic lines at fracture point. Bending under three-point and four-point loads, and the plane problems, some having stress concentration and others being under contacting load, are examined by using rigid polyester cast resin containing styrol as a model specimen; and, in conclusion, the brittle fracture of high-polymer solids under one- or two-dimensional stress states is decided by the constant tensile stress, whose magnitude depends only upon the material used as a model specimen, and is larger than its ultimate tensile strength. Many kinds of factors in fracture are defined, and stress-concentration factors in fracture are compared with stress-concentration factors in elasticity. A new photoelasto-plastic simple method for the determination of stress-concentration factors in elasticity is suggested by utilization of the experimental results on this brittle fracture of high-polymer solids and is examined on the perforated plane problem having finite width under tension in comparison with theoretical analysis and the experimental results by other measuring methods.     

Kinematics of the flow of dry powders and bulk solids

Summary Although qualitative pictures of the flow pattern in moving powders and bulk solids have been published, there is no quantitative evidence on the velocity profiles. This was needed in developing an energy theorem determining flow rates (Brown, Nature, 1961, 191, 458–461) and the experiments described here were undertaken to test various suppositions made at that time. It is shown that the assumptions made were correct.The gravity flow of dry powders and bulk solids through apertures cannot begin until the powder has dilated. The friction caused by the motion then determines the flow pattern.In this paper only those materials that flow freely under gravity are considered. In such materials cohesive forces between the grains are inappreciable. The results are expected to apply to all bulk solids that do not contain large quantities of finely-divided powders in the range of sizes below 20 to 30 microns, and to closely graded powders with particles larger than about 100 microns. In all cases it is assumed that the moisture content is in equilibrium with the ambient air.Measurements of the voidage in a single layer of ballbearings flowing down an inclined plate show that dilatant waves pass upward through the bed. Below the aperture the emergent stream forms a vena contracta. At the aperture there is a statistically empty space adjacent to the edges, through which few balls pass. The existence of a free-fall arch at the aperture is demonstrated, below which the grains fall freely under gravity.By fixing a flowing system in wax it is shown that the flow just above the free-fall arch is radial, converging to an apex below the aperture, and that the flowing region is bounded by the surfaces of sliding that separate flowing from non-flowing material.By observing the flow of powder through a transparent end face, the angle to the vertical ( degrees) of the surface of sliding at the aperture has been measured for (a) flow through a central slot (_c ^o), (b) flow through an edge slot adjacent to a vertical wall (_E ^o). A different method was used to determine the inclination of the surface of sliding through a central circular aperture (₃ ^o). It was found that ₃ ^o < _c ^o _E ^o.The surfaces of sliding are steeper than the drained angle of repose of a conical heap.Paper presented at a meeting of the British Society of Rheology, University of Nottingham, April 6–8, 1965.     

Phase field modeling of fracture in anisotropic brittle solids

A phase field model of fracture that accounts for anisotropic material behavior at small and large deformations is outlined within this work. Most existing fracture phase field models assume crack evolution within isotropic solids, which is not a meaningful assumption for many natural as well as engineered materials that exhibit orientation-dependent behavior. The incorporation of anisotropy into fracture phase field models is for example necessary to properly describe the typical sawtooth crack patterns in strongly anisotropic materials. In the present contribution, anisotropy is incorporated in fracture phase field models in several ways: (i) Within a pure geometrical approach, the crack surface density function is adopted by a rigorous application of the theory of tensor invariants leading to the definition of structural tensors of second and fourth order. In this work we employ structural tensors to describe transverse isotropy, orthotropy and cubic anisotropy. Latter makes the incorporation of second gradients of the crack phase field necessary, which is treated within the finite element context by a nonconforming Morley triangle. Practically, such a geometric approach manifests itself in the definition of anisotropic effective fracture length scales. (ii) By use of structural tensors, energetic and stress-like failure criteria are modified to account for inherent anisotropies. These failure criteria influence the crack driving force, which enters the crack phase field evolution equation and allows to set up a modular structure. We demonstrate the performance of the proposed anisotropic fracture phase field model by means of representative numerical examples at small and large deformations.     

Uniqueness and minimum theorems for a multifield model of brittle solids

Some minimum theorems potentially useful to construct numerical schemes related to quasi-static evolution of damage in brittle elastic solids are proposed. The approach is that of multifield theories, with a second-order damage tensor describing the microcrack density. The use of damage entropy flux and damage pseudo-potential are both investigated.     

Analysis of shear band instabilities in compaction of powders

A model for metal powder compaction is proposed as an interpolation between well-known models corresponding to a high level of porosity with low inter-particle cohesive strength or a low level of porosity with high cohesion. A simple model for analysis of shear band development in uniformly strained solids is used to study the possibility of flow localization during metal powder compaction. It is found that the material model predicts localization when the porosity is high and the cohesion is low, and localization is also predicted at intermediate levels of porosity, but not at low porosity levels where full cohesion applies.     

土体爆炸压密的原理及试验研究

针对目前土体爆炸压密理论研究不够深入、施工中主要依靠工程经验确定爆炸参数的现状,建立了基于塑性力学和爆炸力学的土体爆炸压密模型,推得压密效果(压密范围、压密程度)与爆炸参数之间的关系式,并通过室外试验进行验证.在孔径为48 mm的炮孔中进行了不耦合系数分别为2.000、1.714、1.500、1.333、1.200、1...     

Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method

Mechanism of quasi-static crack branching in brittle solids has been analyzed by a modified displacement discontinuity method. It has been assumed that the pre-existing cracks in brittle solids may propagate at the crack tips due to the initiation and propagation of the kink (or wing) cracks. The originated wing cracks will act as new cracks and can be further propagated from their tips according to the linear elastic fracture mechanics (LEFM) theory. The kink displacement discontinuity formulations (considering the linear and quadratic interpolation functions) are specially developed to calculate the displacement discontinuities for the left and right sides of a kink point so that the first and second mode kink stress intensity factors can be estimated. The crack tips are also treated by boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. The propagating direction of the secondary cracks can be predicted by using the maximum tangential stress criterion. An iterative algorithm is used to predict the crack propagating path assuming an incremental increase of the crack length in the predicted direction (straight and curved cracks have been treated). The same approach has been used for estimating the crack propagating direction and path of the original and wing cracks considering the special crack tip elements. Some example problems are numerically solved assuming quasi-static conditions. These results are compared with the corresponding experimental and numerical results given in the literature. This comparison validates the accuracy and applicability of the proposed method.     

脆性材料动态强度应变率效应

通过求解波动方程,结合有限结构-时间破坏准则,得到了动态载荷下脆性材料单轴拉伸强度应变 率效应的解析表达式。分析结果表明:材料动态强度的应变率效应具有明显的结构响应特征,即材料动态强 度除与应变率和静态参数相关外,还显著地依赖于外载荷结构及其与材料间的相互作用,因而动态强度不是 表征材料动态破坏的内禀材料性质;此外,由于在不同的外载荷条件下材料将表现出不同的动态强度,这是导 致实验结果离散性大的内在因素。     

Numerical simulation of density distribution during compaction of iron powders

Summary The compaction process of iron powder is considered. Due to negligible elastic strains the rigid-plastic model is applied. A yield condition containing the first stress invariant is used. All material functions depend on the relative density of the powder, which changes during the compaction process. Siebel friction law is applied, and the friction factor is considered to be depending on the relative density. Various material functions are applied in the numerical simulation, and the results are compared with experimentally obtained data. The best fitting material functions and friction factors are obtained. Accepted for publication 18 July 1996