Mechanodestruction of minerals at the crack tip (overview): 2. Theory

Journal of Physics and Chemistry of Solids, 1987

This article first presents introductory material which should make it possible for the person unfamiliar with fracture to read the papers of this series. Then material of a basic physical nature regarding cracks in materials is presented. Emphasis is placed on the effects of chemical attack of bonds at a crack tip, and on the basic physical cause for a material to exhibit a tough (desirable) or a brittle (undesirable) overall aspect.

Journal of Materials Science, 1987

A new picture of environmentally-enhanced fracture in highly brittle solids is presented. It is asserted that the fundamental relations for crack growth are uniquely expressible in terms of the surface force functions that govern the interactions between separating walls in an intrusive medium. These functions are the same, in principle, as those measured directly in the newest submolecular-precision microbalance devices. A fracture mechanics model, based on a modification of the Barenblatt cohesive zone concept, provides the necessary framework for formalizing this link between crack relations and surface force functions. The essence of the modification is the incorporation of an element of discreteness into the surface force function, to allow for geometrical constraints associated with the accommodation of intruding molecules at the crack walls. The model accounts naturally for the existence of zero-velocity thresholds; further, it explains observed shifts in these thresholds in cyclic load-unload-reload experiments, specifically the reduction in applied loading needed to propagate cracks through healed as compared to virgin interfaces. The threshold configurations emerge as thermodynamic equilibrium states, definable in terms of interfacial surface energies. Crack velocity data for cyclic loading in mica, fused silica and sapphire are presented in support of the model. Detailed considerations of the theoretical crack profiles in these three materials, with particular attention to the atomic structure of the "lattice" (elastic sphere approximation) at the interfaces, shows that intruding molecules must encounter significant diffusion barriers as they penetrate toward the tip region. It is concluded that such diffusion barriers control the fracture kinetics at low driving forces. At threshold the barriers become so large that the molecules can no longer penetrate to the tip region. This leads to a crucial prediction of our thesis, that the cohesive Zone consists of two distinct parts: a "protected" primary zone adjacent to the tip, where intrinsic binding forces operate without influence from environmental influences; and a "reactive" secondary zone more remote from the tip, where extrinsic interactions with intruding chemical species are confined. The prevailing view of chemically enhanced brittle fracture, that crack velocity relations are determined by a concerted reaction with reactive species at a single line of crack-tip bonds, is seen as a limiting case of our model, operative at driving forces well above the threshold level. The new description offers the potential for using brittle fracture as a tool for investigating surface forces themselves.

MRS Bulletin, 2001

Mechanical Engineering Series, 2011

International Journal of Fracture, 2015

Any fracture process ultimately involves the rupture of atomic bonds. Processes at the atomic scale therefore critically influence the toughness and overall fracture behavior of materials. Atomistic simulation methods including large-scale molecular dynamics simulations with classical potentials, density functional theory calculations and advanced concurrent multiscale methods have led to new insights e.g. on the role of bond trapping, dynamic effects, crackmicrostructure interactions and chemical aspects on the fracture toughness and crack propagation patterns in

Journal of the American Chemical Society, 1993

A fundamental understanding of the atomic mechanisms responsible for the stress-induced bond failure of solid-state materials will facilitate the synthesis of materials with desired mechanical properties. Outside of a small group of network solids and polymers, no such understanding is available. By adopting an appropriate model for solid-state bonding, based on features of the total charge density, it is possible to apply chemical reaction theory to an investigation of this process. First-principle local-density-functional techniques were used to model the transgranular fracture of two alloys with the same crystal structure but different mechanical properties, a hitherto unexplained observation. It was found that the transition state for decohesion occurs earlier in the reaction path for the brittle than for the ductile alloy. This observation is argued to be the result of a comparatively flat charge density at a few special points within the alloy. The success found in the application of reaction theory toward an understanding of decohesion suggests that reaction theory might be profitably employed in more complex and technologically important investigations of mechanical properties of solids.

Physical Review E, 2004

Europhysics Letters (EPL), 2004

A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with respect to the control parameter (reduced stress) exhibits a singular behaviour. Our results are nevertheless compatible with previous experimental findings, if one restricts the comparison to the (limited) range accessible in the experiment. A power-law avalanche distribution is also found with an exponent close to the experimental values. PACS numbers: 46.50.+a, 62.20.Mk, 05.70.Ln Fractures are very complex phenomena which involve a wide range of spatial and sometimes temporal scales. Accordingly, the development of a general theory is quite an ambitious goal, since it is not even clear whether a continuous coarse-grained description makes sense; additionally, for the very same reason, realistic simulations are almost unfeasible. However, such difficulties have not prevented making progress on several aspects of fracture dynamics such as propagation velocity, roughness, or the failure time under a constant stress [1, 2, 3]. In this paper we are interested in studying the development of the socalled precursors, microcracks preceding the macroscopic fracture in a brittle disordered environment. Some recent experiments suggest that we are in the presence of a critical phenomenon, although the accuracy is not yet high enough not only to discuss its universality properties, but also to assess the order of the transition.

Modelling and Simulation in Materials Science and Engineering, 1998

As our title implies, we consider materials failure at the fundamental level of atomic bond breaking and motion. Using computational molecular dynamics, scalable parallel computers and visualization, we are studying the failure of notched solids under tension using in excess of 10 8 atoms. In rapid brittle fracture, two of the most intriguing features are the roughening of a crack's surface with increasing speed and the terminal crack speed which is much less than the theoretical prediction. Our two-dimensional simulations show conclusively that a dynamic instability of the crack motion occurs as it approaches one-third of the surface sound speed. This discovery provides an explanation for the crack's surface roughening and limiting speed. For three-dimensional slabs, we find that an intrinsically ductile FCC crystal can experience brittle failure for certain crack orientations. A dynamic instability also occurs, but brittle failure is not maintained. The instability is immediately followed by a brittle-to-ductile transition and plasticity. Hyperelasticity, or the elasticity near failure, governs many of the failure processes observed in our simulations and its many roles are elucidated.

Experimental Chaos, 2004

We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous materials. We first compare the dynamic behavior of "standard" brittle materials (e.g. glass) with the corresponding features observed in "model" materials, polyacrylamide gels, in which the relevant sound speeds can be reduced by 2-3 orders of magnitude. The results of this comparison indicate universality in many aspects of dynamic fracture in which these highly different types of materials exhibit identical behavior. Observed characteristic features include the existence of a critical velocity beyond which frustrated crack branching occurs 1, 2 and the profile of the micro-branches formed. We then go on to examine the behavior of the leading edge of the propagating crack, when this 1D "crack front" is locally perturbed by either an externally introduced inclusion or, dynamically, by the generation of a micro-branch. Comparison of the behavior of the excited fronts in both gels and in soda-lime glass reveals that, once again, many aspects of the dynamics of these excited fronts in both materials are identical. These include both the appearance and character of crack front inertia and the generation of "Front Waves", which are coherent localized waves 3-6 which propagate along the crack front. Crack front inertia is embodied by the appearance of a "memory" of the crack front 7,8 , which is absent in standard 2D descriptions of fracture. The universality of these unexpected inertial effects suggests that a qualitatively new 3D description of the fracture process is needed, when the translational invariance of an unperturbed crack front is broken.