Defect kinetics in crack instabilities

ABSTRACT. A mechanical model for simulating intergranular crack propagation is presented. In order to understand fracture mechanics and processes that occur in a polycrystalline body it is necessary to accommodate a large number of parameters, including the macroscopic effects of load together with stress state and component geometry. A dislocation analysis based on the boundary element method is introduced to model crack growth through microstructures.

Selected Papers from the 11th International Conference on Fracture, Turin, Italy, March 20-25, 2005, 2007

In this seminar we will review several experimental and theoretical aspects of two very important problems of material failure: crack precursors and crack prediction. We will summarize the results of several experiments and numerical simulations that we have performed in order to give new insight on these two important problems. Specifically the acoustic emission of fracture precursors, and the failure time of samples made of heterogeneous materials (wood, fiberglass) are studied as a function of the load features and geometry . The accurate study of the localization and of the statistics of acoustic emission is indeed very important in order to compare the experimental results with those of percolation and critical models for crack formation. A typical example of microcrack localization in a large cylindrical sample is described in Once the microcracks have been localized we study the statistics of the time interval δt between events (precursors) and the acoustic energy ε of each event. We find that they are power law distributed and that the exponents of these power laws depend on the load history and on the material. An example is shown in , 2, 3, 4] When the sample failure is produced by an imposed stress (see ) the cumulative acoustic energy E, that is the integral of ε as a function of time, presents a critical divergence near the failure time τ , which is

International Journal of Fracture, 2010

Crack propagation in a linear elastic material with weakly inhomogeneous failure properties is analyzed. An equation of motion for the crack is derived in the limit of slow velocity. Predictions of this equation on both the average crack growth velocity and its fluctuations are compared with recent experimental results performed on brittle heterogeneous materials (Ponson in Phys Rev Lett, 103, 055501; Måløy et al. in Phys Rev Lett, 96, 045501). They are found to reproduce quantitatively the main features of crack propagation in disordered systems. This theoretical framework provides new tools to predict life time and fracture energy of materials from their properties at the micro-scale.

International Journal of Solids and Structures, 2009

In this study, the growth of a short edge crack during more than 14 000 cycles of fatigue loading is investigated in detail. An edge crack, in a semi-infinite body with no pre-existing obstacles present, is modelled in a boundary element approach by a distribution of dislocation dipoles. The fatigue cycles are fully reversed ðR ¼ À1Þ, and the load range is well below the threshold for long fatigue cracks. The developing local plasticity consists of discrete edge dislocations that are emitted from the crack tip. The movements of discrete dislocations are restricted to slip along preferred slip planes. The present model is restricted to a 2D plane strain problem with a through-thickness crack, assuming no 3D irregularities. A remote load is applied perpendicular to the crack extension line, and the material parameters are those of a BCC crystal structure. The competition between influence of the global loading on and local shielding of the crack tip governs the crack growth. The growth rate increases in discrete steps with short periods of retardation, from approximately the size of Burgers vector, b, up to 25 b per cycle as the length of the crack is tripled. The plastic zone changes from having an elongated, slender form to include a low angle grain boundary, which, eventually, divides into two parts. The crack growth is found to change from constant acceleration to constant growth rate as the event of the low-angle grain boundary split is approached. The results are compared to long crack characteristics, for which linear elastic fracture mechanics and Paris law can be used to predict fatigue crack growth. The exponent in Paris law varies between 1 and 0 in the present study, i.e. smaller than typical values for ductile BCC materials. The ratio between static and cyclic plastic zone sizes is found to increase during crack growth, and the angle of the general plastic zone direction increases, showing a tendency towards long crack values. The characteristics of the simulated crack growth, found in the present study, are typical for below-threshold growth, with slow acceleration, constant growth rate, and, eventually, either arrest or transition to long crack growth behaviour, as reported in the literature.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005

The influence of the material texture (substructure) on the force driving the crack tip in complex materials admitting Ginzburg-Landau-like energies is analyzed in a three-dimensional continuum setting. The theory proposed accounts for finite deformations and general coarse-grained order parameters. A modified expression of the J-integral is obtained together with other path-integrals which are necessary to treat cases where the process zone around the tip has finite size. The results can be applied to a wide class of material substructures. As examples, cracks in ferroelectrics and in materials with strain-gradient effects are discussed: in these cases the specializations of the general results fit reasonably experimental data.

Acta Metallurgica, 1986

Crack trajectories under different loading conditions and material microstructural features play an important role when the conditions of crack initiation and crack growth under fatigue loading have to be evaluated. Unavoidable inhomogeneities in the material microstructure tend to affect the crack propagation pattern, especially in the short crack regime. Several crack extension criteria have been proposed in the past decades to describe crack paths under mixed mode loading conditions. In the present paper, both the Sih criterion (maximum principal stress criterion) and the R-criterion (minimum extension of the core plastic zone) are adopted in order to predict the crack path at the microscopic scale level by taking into account microstress fluctuations due to material inhomogeneities. Even in the simple case of an elastic behaviour under uniaxial remote stress, microstress field is multiaxial and highly non-uniform. It is herein shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks.

Physical Review Letters, 2001

We address the role of material heterogeneities on the propagation of a slow rupture at laboratory scale. With a high speed camera, we follow an in-plane crack front during its propagation through a transparent heterogeneous Plexiglas block. We obtain two major results. First, the slip along the interface is strongly correlated over scales much larger than the asperity sizes. Second, the dynamics is scale dependent. Locally, mechanical instabilities are triggered during asperity depinning and propagate along the front. The intermittent behavior at the asperity scale is in contrast with the large scale smooth creeping evolution of the average crack position. The dynamics is described on the basis of a Family-Vicsek scaling.

Journal of the Mechanics and Physics of Solids, 1992

DISLOCATION nucleation from a stressed crack tip is analyzed based on the Peierls concept. A periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip. This allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability is developed via the J-integral for the case when the crack and slip planes coincide, and an approximate solution is given when they do not. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The leveJ of applied stress intensity factors required for dislocation nucleation is shown to be proportional to x/)'u,, where 7,,., the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of ~,~j are summarized and the results are used to evaluate brittle vs ductile response in fcc and bcc metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The predictions seem compatible with known behavior and also show that in many cases solids which are predicted to first cleave under pure mode I loading should instead first emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis in this paper also reveals a feature of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, as is of interest for thermal activation.

The intrinsic lattice resistance to dislocation motion, or Peierls stress, depends on the core structure of the dislocation and is one essential feature controlling plastic anisotropy in materials such as HCP Zn, Mg, and Ti. Here, we implement an anisotropic Peierls model as a friction stress within a 2d discrete dislocation (DD) plasticity model and investigate the role of plastic anisotropy on the crack tip stress fields, crack growth, toughening, and micro-cracking. First, tension tests for a pure single crystal with no obstacles to dislocation motion are carried out to capture the general flow behavior in pure HCP-like materials having slip on basal and pyramidal planes. Then Mode-I crack growth in such a single crystal of the HCP material is analyzed using the 2d-DD model. Results show that the fracture toughness scales inversely with the tensile yield stress, largely independent of the plastic anisotropy, so that increasing Peierls stress on the pyramidal planes gives decreasing resistance to crack growth, consistent with recent experiments on Zn. Analyzing the results within the framework of Stress Gradient Plasticity concepts shows that the equilibrium dislocation dipole spacing serves as an internal material length scale for controlling fracture toughness. Furthermore, the fracture toughness of materials with flow stress controlled by a Peierls stress (this work) and of materials with flow stress controlled by dislocation obstacles (prior literature) is unified through the Stress Gradient Plasticity concept. Finally, the DD simulations show that local stress concentrations exist sporadically along the pyramidal plane(s) that emanate from the current crack tip, suggesting an origin for experimentally observed basal-plane microcracking near the tip of large cracks.