Young's modulus of porous brittle solids

A new equationE =E ₀ (1 –aP) ⁿ whereE andE ₀ are the Young's moduli at porosity,P, and zero, respectively, a andn are material constants, has been derived semi-empirically for describing the porosity dependence of Young's modulus of brittle solids. The equation satisfies quite well the exact theoretical solution for the values of Young's moduli at different porosities for model systems with ideal and non-ideal packing geometry. The equation shows excellent agreement with the data On- and-alumina over a wide range of porosity. Unlike the existing porosity-elastic modulus equations, the proposed equation satisfies the boundary conditions and is inherently capable of treating isometric closed pores as well as non-isometric interconnected pores. The parameters a and n provide information about the packing geometry and pore structure of the material.     

Compressive failure of microcracked porous brittle solids

Constitutive equations for porous, brittle solids are developed based on the damage mechanics of elastic materials containing cavities and microcracks. For homogeneous deformation modes, microcrack growth from pores causes changes in the average elastic compliance of the material. Failure criteria in terms of bifurcations of the constitutive paths are established by examining the properties of the evolving tangent stiffness tensor. Limit points as well as localized shear band failure modes are addressed. The influence of moderate levels of lateral stresses is studied for biaxial stress states.     

Modeling of compression-induced splitting failure in heterogeneous brittle porous solids

Brittle solids, such as rock or concrete, may contain numerous randomly distributed micro-flaws (e.g. cracks, pores or weak inclusions). When they are loaded in compression, cracks may nucleate from these flaws. These cracks then continue to grow in a stable manner with the increasing axial compression, curving toward an orientation parallel to the direction of axial compression. Their propagation and interaction may lead to the collapse of the solid in a splitting mode. With a newly developed numerical code, MFPA^2D (material failure process analysis), heterogeneous solids containing pre-existing single, triple and multi-pore-like flaws are numerically tested to study the mechanisms of compression-induced axial splitting. The interaction of growing cracks with the surfaces of the specimen and with each other in terms of stress field and failure modes is numerically analyzed in detail. Under uniaxial compressions, specimens containing holes in a diagonal array are more conducive to interaction than specimens containing holes arranged either in a horizontal or vertical array. Various parameters, such as hole diameter, specimen width, and the geometrical arrangement of hole locations, that characterize the growth process are quantified. Numerical results mimic the phenomena of experimentally observed splitting failure in brittle solids such as rocks in a realistic way.     

A model for deformation and fragmentation in crushable brittle solids

A unified framework of continuum elasticity, inelasticity, damage mechanics, and fragmentation in crushable solid materials is presented. A free energy function accounts for thermodynamics of elastic deformation and damage, and thermodynamically admissible kinetic relations are given for inelastic rates (i.e., irreversible strain and damage evolution). The model is further specialized to study concrete subjected to ballistic loading. Numerical implementation proceeds within a finite element context in which standard continuum elements represent the intact solid and particle methods capture eroded material. The impact of a metallic, spherical projectile upon a planar concrete target and the subsequent motion of the resulting cloud of concrete debris are simulated. Favorable quantitative comparisons are made between the results of simulations and experiments regarding residual velocity of the penetrator, mass of destroyed material, and crater and hole sizes in the target. The model qualitatively predicts aspects of the fragment cloud observed in high-speed photographs of the impact experiment, including features of the size and velocity distributions of the fragments. Additionally, two distinct methods are evaluated for quantitatively characterizing the mass and velocity distributions of the debris field, with one method based upon a local energy balance and the second based upon global entropy maximization. Finally, the model is used to predict distributions of fragment masses produced during impact crushing of a concrete sphere, with modest quantitative agreement observed between results of simulation and experiment.     

A fiber-bundle model for the continuum deformation of brittle material

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.     

Measuring hardness of brittle solids

A method for determining the hardness of brittle solids under high loads is proposed. Using this technique, the hardness of inorganic glasses has been measured in a broad range of loads (1–300 N).     

Discretized peridynamics for brittle and ductile solids

Peridynamics is a theory of continuum mechanics expressed in forms of integral equations rather than partial differential equations. In this paper, a peridynamics code is implemented using a graphics processing unit for highly parallel computation, and numerical studies are conducted to investigate the responses of brittle and ductile material models. Stress–strain behavior with different grid sizes and horizons is studied for a brittle material model. A comparison of stresses and strains between finite element analysis (FEA) and peridynamic solutions is performed for a ductile material. By applying the proposed procedure to bridge the material model defined for peridynamic bonds and the corresponding macroscale material model for FEA, peridynamics and FEA show good agreements as regards the stresses and strains. Copyright © 2011 John Wiley & Sons, Ltd.     

Shock-wave compression of brittle solids

Extensive experimental investigation in the form of large-amplitude, nonlinear wave-profile measurements which manifest the shock strength and equation-of-state properties of brittle solids has been performed. Brittle materials for which a base of dynamic property data is available include Al₂O₃, AlN, B₄C, CaCO₃, SiC, Si₃N₄, SiO₂ (quartz and glass), TiB₂, WC and ZrO₂. Planar impact methods and velocity interferometry diagnostics have been used exclusively to provide the high-resolution shock-profile data. These wave-profile data are providing engineering dynamic strength and equation-of-state properties as well as controlled, shock-induced motion histories for the validation of theoretical and computational models. Of equal importance, such data are providing a window into the physics of a newly emerging understanding of the compression and deformation behavior of high-strength brittle solids. When considered along with a rich assortment of strength and deformation data in the literature, a systematic assessment of this shock-wave data lends strong support for failure waves and concomitant high-confinement dilatancy as a general mechanism of inelastic deformation in the shock compression of ceramics. Phase transformation in selected brittle solids appears to be a critical state phenomenon strongly controlled by kinetics. The risetime and structure of deformation shock waves in brittle solids are controlled by viscous effects which at present are still poorly understood. The shock-wave data also suggest that both crystalline plasticity and brittle fracture may play important and interconnected roles in the dynamic failure process.     

An adaptive material point method coupled with a phase-field fracture model for brittle materials

In this study, a new adaptive method for crack propagation analysis is developed by using the material point method coupled with a phase-field fracture model for brittle materials. A background grid of material particles is adaptively refined based on the amount of material damage to resolve the length scale in the phase-field evolution equation. A division process of the material particles associated with the refined background cells is also performed to increase the resolution of solutions near the crack tip. The effectiveness and validity of the proposed method is assessed through several numerical examples for crack propagation in brittle materials.     

On estimating the Weibull modulus for a brittle material

Common methods of estimating the Weibull modulus are surveyed. Computer simulation is used to obtain the statistical properties of different estimators. Most estimators are shown to be biased and their respective adjustment factors, for a range of experimentally feasible sample sizes, are given.     

Preliminary compression of a material as a factor in changing the brittle fracture mechanism for BCC metals

We have investigated the effect of preliminary plastic compression on the characteristics of brittle fracture in bcc metals using 15Kh2MFA pearlitic steel as an example. We have experimentally established that preliminary plastic compression of the material leads to a change in the mechanism of brittle fracture from transcrystallite to intercrystallite. We have shown that the critical stress for brittle fracture is significantly lower for the intercrystallite mechanism than for the transcrystallite mechanism. We suggest mechanisms for embrittlement of material as a result of its preliminary plastic compression. We present schemes for the transition from intercrystallite fracture to transcrystallite, depending on the thermal and mechanical loading conditions for the precompressed material.Translated from Problemy Prochnosti, No. 4, pp. 5–18, April, 1996.     

Phonon theory of brittle fracture of solids

In this article we outline the basic principles of a new approach to the solution of the problem of brittle fracture of solids. The kinetic theory of long-time strength formulated by S. N. Zhurkov et al. is analyzed and generalized.