Crack initiation in brittle solids under multiaxial compression

Experiments combined with numerical simulations were used to study crack initiation in brittle materials under biaxial static compression with particular attention to the frictional resistance of the cracks. A new methodology has been developed to prepare specimens with a central crack where crack surfaces are in contact and with the desired friction coefficient: two pieces of Homalite-100 (a brittle polymer) were bonded except for a central region that served as a crack. The measured failure load for cracks with different orientation angles and surface roughness was in close agreement with theoretical predictions for compressive failure. In situ photoelastic fringes were obtained and compared with numerical results enabling the determination of stress distribution along crack faces, as well as the identification of slip and stick regions.     

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.     

Microcrack nucleation and growth in elastic lamellar solids

The nucleation and growth of microcracks in elastic lamellar microstructures is studied numerically. The analyses are carried out within a framework where the continuum is characterized by two constitutive relations: one relating the stress and strain in the bulk material and the other relating the traction and separation across a specified set of cohesive surfaces. In such a framework, fracture initiation and crack growth, including micro-crack nucleation ahead of the main crack, arise naturally as a consequence of the imposed loading, without any additional assumptions concerning criteria for crack growth, crack path selection or micro-crack nucleation. Full transient analyses are carried out and plane strain conditions are assumed. The specific problem analyzed is a compact tension specimen with two regions of differing lamellar orientation separated by a fracture resistant layer of finite width d, which is small compared to the physical dimensions of the specimen. An initial crack, normal to the applied loading, is assumed to exist in the first region whose lamellar orientation is fixed. The lamellar orientation of the second region, , is varied, as is the thickness of the fracture resistant layer. It is found that microcrack nucleation in the second region is highly sensitive to the lamellar orientation in that region for small values of d. However, microcrack nucleation becomes rather insensitive to with increasing d. It is also shown that a linear elastic fracture mechanics model with one adjustable parameter gives good agreement with the numerical results for fracture initiation.     

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.     

Atomically sharp cracks in brittle solids: an electron microscopy study

The issue of bond rupture versus microplasticity as an essential mechanism of crack propagation in brittle solids is addressed. A detailed survey of existing theoretical and experimental evidence relating to this issue highlights the need for direct observations of events within the crack-tip process zone, at a level approaching 10 nm. Transmission electron microscopy is accordingly used to study arrested cracks about sharp-contact (Vickers indentation and particle impact) sites in Si, Ge, SiC and Al₂O₃. The nature of the deformation which accommodates the irreversible contact impression is first investigated, in the light of Marsh's proposal of an equivalence between indentation and crack-tip zone processes. Interfacial and tip regions of the surrounding cracks are then examined for any trace of a plasticity-controlled fracture process. Dislocation-like images are indeed evident at the crack planes, but these are shown to be totally inconsistent with any conventional slip mechanism. The close connection between the dislocation patterns and moiré fringe systems along the cracks points to lattice mismatch contrast in association with a partial closure and healing operation at the interface. Analysis of all other details in the crack patterns, e.g. the presence of a crack-front contrast band indicative of a residual strain field and the disposition of interfacial fracture steps relative to the dislocation/moiré system, reinforces this interpretation. It is concluded that the concept of an atomically sharp crack provides a sound basis for the theory of fracture of brittle solids.     

Instability of microcracks in molybdenum in heating under conditions of uniaxial compression

Strength of Materials -     

Slip and fracture in brittle solids

The conclusion is reached that the condition for slip and fracture in a solid must be expressed by an inequality rather than an equation to meet the requirements imposed by general stress distributions. A general condition for slip and fracture is proposed and it is found that a special case of this condition suffices to explain the slight deviations of the planes of slip and fracture from the planes of maximum shearing stress which are sometimes observed in ordinary tension and compression tests on flat plates. Defining a perfectly brittle body as one in which slip and fracture will occur without plastic deformation, it is shown that a slip discontinuity will be propagated in such bodies with the velocity of a longitudinal wave and the velocity of a crack will be equal to the velocity of a shear wave in the strained medium. The more realistic case where plastic deformation precedes the occurrence of fracture has not been discussed specifically; however, it is surmised from the results of one of our earlier papers that the velocity of propagation of a crack in the presence of plastic deformation will be less than the velocity of a shear wave and will depend on the rate of energy release which is considered to be one of the characteristic features of the fracture process.     

Endurance of brittle solids under cyclic loads with local overheating

This article describes a method of calculating the endurance of brittle solids under cyclic loads with local over-heating of the material at the crack tips when no spontaneous heating of the material takes place during fracture. The method is applicable when the number of cycles to fracture is sufficiently large and when the loading frequency is relatively high so that other manifestations of the relaxation phenomena may be neglected. The method was used to carry out an approximate calculation of the endurance of polymethylmethacrylate under loading conditions corresponding to experimental data.     

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 numerical study of ductile void growth under dynamic loading conditions

A numerical study of void growth at differing global strain rates in the range 149 s^–1–2240 s^–1 and at start temperatures between 173 K and 573 K has been carried out for a material containing a three-dimensional periodic array of equally spaced, initially spherical voids. To take account of the effect of strain rate and temperature on the flow stress under dynamic adiabatic conditions, the well-established Zerilli-Armstrong constitutive relations for pure copper and iron have been employed. An instability criterion based on the maximum mean tensile stress has been used to identify the point at which unstable void growth occurs. For both materials, the strain at instability has been found to be dependent on stress triaxiality and start temperature but only weakly affected by strain-rate     

A three-dimensional micromechanics model for the damage of brittle materials based on the growth and unilateral effect of elliptic microcracks

Based on the analysis of a representative elliptic microcrack embedded in a RVE, the additional compliance tensor induced by an embedded opening/closed microcrack is derived, and that corresponding to the kinked growth of a closed elliptic microcrack is also derived by making use of its approximately equivalent simplification. The effect of the microcracks is analyzed with the Taylor’s scheme by introducing an appropriate probability density function. A three-dimensional micromechanics damage model is obtained for brittle materials, assuming numerous randomly distributed elliptic microcracks and taking into account their deformation, frictional sliding, growth and kinked growth.     

Dislocation nucleation and propagation during thin film deposition under compression

In this paper, we study the nucleation of dislocations and their subsequent propagation, during thin film deposition, using the three-dimensional (3D) molecular dynamics (MD) method. Aiming to reveal the generic mechanisms, the case of tungsten on a substrate of the same material is investigated. The substrate is under uniaxial compression along the [1 1 1] direction, with the thermodynamically favored surface being horizontal. The simulation results indicate that the nucleation starts with a surface step where an atom is squeezed to the layer above, generating a half-dislocation loop at the surface. It may then either propagate into the film or become the bottom of a sessile dislocation loop. In the first case, the dislocation loop, having a Burgers vector on a (1 0 1) glide plane, propagates along the direction on the surface, and extends to about two atomic layers along the [1 1 1] direction. In the second case, the missing layer propagates along the [1 0 0] direction on the surface, extending to about four atomic layers along the [1 1 1] direction. In this case, the sessile dislocation has a Burgers vector on the plane (0 1 1).     

Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression

Uniaxial compression experiments were carried out for the marble samples (located in the eastern ground of China) with different pre-existing flaws in non-overlapping geometry by the rock mechanics servo-controlled testing system. Based on the experimental results of complete axial stress-axial strain curves, the effect of flaw geometry on the strength and deformation behavior of marble samples is made a detailed analysis. Compared with the intact marble sample, the marble samples with different pre-existing flaws show the localization deformation failure. The uniaxial compressive strength (UCS), elastic modulus and peak axial strain of marble samples with pre-existing flaws are all lower than that of intact marble sample, and the reduction extent is closely related to the geometry of pre-existing flaws. The crack coalescence were observed and characterized from internal tips of different pre-existing flaws in brittle marble sample. Eight different crack types were identified based on their geometry and crack propagation mechanism (tensile, shear and compressive) for two pre-existing flaws, which can be used to analyze the failure mode and cracking process of marble sample containing different flaws in uniaxial compression. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle marble sample is analyzed under uniaxial compression. The present research provides increased understanding of the fundamental nature of rock failure under uniaxial compression.