Michal Kotoul

Crack bridging and trapping mechanisms used to toughen brittle matrix composite

Abstract Two basic mechanisms of toughening brittle solids are presented. They involve crack-tip shielding from crack deformation and/or crack bridging by introducing ductile particles in the crack wake region. The crack opening displacement is realized from the constant volume plastic flow of the particles according to the model in [J. Dominguez, C.A. Brebbia, (Eds.), Proceedings of Computational Methods in Contact Mechanics V, WIT Press, Boston, 2001, p. 87; A.T. Yokobori, R.O. Ritchie, K. Ravi-Chandar, B.L. Karihaloo, (Eds.), Proceedings of ICF10, Elsevier, Oxford, 2001, p. 348]. The second mechanism involves arresting the crack ductile phase such that it can only renucleate on the other side. As a result of trapping the crack, the material is toughened intrinsically. Energy considerations are made to estimate the extent of particle/matrix debonding. A perturbation analysis [A.T. Yokobori, R.O. Ritchie, K. Ravi-Chandar, B.L. Karihaloo, (Eds.), Proceedings of ICF10, Elsevier, Oxford, 2001, p. 348] is used to account for the configuration of the front of a planar crack trapped by a periodic array of closely spaced bridges. Debonding of the particle/matrix interface controls is associated with the two aforementioned mechanisms. Comparison of analytical results with some experimental observations is provided.

A Comparison of Two Direct Methods of Generalized Stress Intensity Factor Calculations of Bi-Material Notches

The study of bi-material notches is becoming a topical problem as they can model geometrical or material discontinuities efficiently. Assessing the conditions for crack initiation in bimaterial notches makes it necessary to calculate the generalized stress intensity factors H. In contrast to the determination of the K factor for a crack in an isotropic homogeneous medium, for the ascertainment of a generalized stress intensity factor (GSIF) there is no procedure incorporated in the calculation systems. The calculation of these fracture mechanics parameters is not trivial and requires certain experience. Nevertheless, the accuracy of the H-factor calculation directly influences the reliability of the assessment of the singular stress concentrators. Direct methods of the estimation of H factors usually require choosing the length parameter entering into the calculation. Two types of direct methods of calculating the GSIFs are presented, tested and mutually compared. Recommendations for reliable estimation of H factors are suggested.

Study of the Stress Distribution Around an Orthotropic Bi-Material Notch Tip

Knowledge of the stress distribution is the first and necessary step for the reliable assessment of construction with a geometrical or material discontinuity. General geometry and orthotropic material characteristics of both material components lead to singular stress distribution with general stress singularity exponents different from ½. For the final stress field determination both analytical and numerical approaches are utilised. The results of the theoretical approaches are compared to results from finite element method.

Crack resistance curve in glass matrix composite reinforced by long Nicalon® fibres

Theoretical micromechanical analysis of bridged crack development at chevron-notch tip of three-point bend specimens has been applied to determine the crack resistance curve for a composite made of a glass matrix reinforced by continuous Nicalon® fibres. Fracture toughness (KIC) values were determined using the chevron-notch technique at room temperature. The theoretical predictions were based on micromechanical analysis exploiting weight functions. Detailed FEM analysis using the ANSYS package was applied to determine numerically the weight functions for orthotropic materials. Appropriate bridging models for the theoretical prediction of the R-curve behaviour typical of the investigated composite were applied together with the weight functions. Experimental observations confirmed the theoretical calculations.

Constitutive modeling of ratcheting of metal particulate-reinforced ceramic matrix composites

Abstract Brittle solids fail in compression by a process of progressive microfracture. If subjected to cyclic loading beyond the elastic range with non-zero mean stress, usually there is a cycle by cycle accumulation of inelastic strain related to microfracturing in the direction of mean stress similarly like an accumulation of plastic strain in steels or other metals. This phenomenon is called cyclic creep or ratcheting. In cyclic plasticity there are several models capable to describe ratcheting, among others Armstrong–Frederick model (AF), Chaboche, Ohno/Wang and/or Jiang model. AF model, however, in most situations, overpredicts ratcheting. Within the context of brittle composites reinforced by ductile inclusions one can apply these models for describing the cyclic plasticity of inclusions while matrix remains macroscopically elastic. Using a suitable composite approach a response of representative volume element of composite may be modeled. But even with the AF model we do not get any ratcheting which contradicts to experimental observations. This is due to a strong constraint exerted by matrix on inclusions. It is proposed that the weakening constraint power of the matrix caused by microfracture damage around inclusions can reconcile the model predictions with experiment. It can be easily shown that even under compression loading a local tensile stress field develops around a softer inclusion. The treatment of local stresses makes possible to introduce a microfracture damage by an approximative, self-consistent method. The microfracture damage is closely coupled with the plasticity of inclusions and provides additional inelastic strains. The effect of lateral pressures under multiaxial loading can be straightforwardly included. Numerical results are presented and compared with experimental data.

Effective toughness for bridged crack interacting with an arbitrary oriented and located microcrack

Abstract The fracture problem for a brittle matrix reinforced by ductile particles is considered. As a crack propagates through the brittle matrix, it circumvents ductile particles which are left to form isolated bridges capable of supporting tractions across the crack faces and thus improve the fracture toughness of the matrix. The stress induced microcracking, which can provide another important toughening mechanism, is assumed to also take place. More specifically, a single microcrack arbitrary oriented and located ahead of the main crack tip is considered and the resulting combined toughening effect of crack bridging and crack–microcrack interaction is investigated. To make the problem mathematically tractable the restraining effect of bridging discrete forces is approximated by a continuum with an effective yield stress acting over a specified multiligament zone behind the crack tip. This zone is further simulated by an unknown continuous distribution of edge dislocations. The present work then proposes a self-consistent scheme, which relies on using a point-source representation for the microcrack and a simultaneous solution of integral equation for the unknown dislocation distribution. Both, the stress intensity factor (SIF) and crack opening displacement (COD) are derived for general orientation and position of microcrack and an effective fracture toughness of composite is assessed. This approximative solution is further tested using the exact solution for a collinear microcrack.

Shielding model of fracture in WC-Co

Abstract A shielding model of fracture in WC-Co alloys, aiming to explain an unexpectedly frequent occurrence of the binder phase on the crack surface, is presented. The shielding of the crack tip is caused by the multiligament zone formed by ductile binder ligaments behind the crack tip. The shielding leads to a decrease of the crack tip opening displacement and the plastic zone size ahead of a blunting crack tip. Consequently, normal stresses build up and, as a result, the cleavage of matrix is facilitated even under a lower local intensity factor perceived by crack tip. The co-operation of the cleavage of the matrix and the tearing of binder ligaments results in a meandering path of crack with a surprisingly high ligament area fraction. The partition between carbide and binder phase related fracture is predicted. The composite toughness is linked to the mechanical and microstructural parameters of WC-Co composite by a simple relationship.

On the stability of cracks with bridged kinks

Abstract Crack extension in composites consisting of brittle matrix reinforced by ductile particles is analyzed under conditions of mixed in-plane loading. The applied loading is characterized in terms of the nominal stress intensity factors, k I N and k II N . Mixed mode loading leads to crack kinking and the local state of stress ahead of crack tip is described by the local stress intensity factors, K I loc and K II loc . Contrary to previous work, the kink is subjected to bridging load generated by isolated ductile ligaments. After calculation of K I loc and K II loc and the crack opening displacement at the deflection point, appropriate fracture criteria are suggested. The brittle matrix is assumed to fail by maximum tensile stress criterion, which is equivalent to the first-order to K II loc =0 condition while K I loc reaches the fracture toughness of the matrix. Further, a critical value of the crack opening displacement, Δ c , determines the ligament rupture. Both criterions have to be fulfilled for further crack extension. Solving these criteria for k I N and k II N provides us with a set of fracture loci in the k I N – k II N plane.

Applicability of the Critical Energy Release Rate for Predicting the Growth of a Crack in Nanoscale Materials Applying the Strain Gradient Elasticity Theory

The paper investigates the limits of applicability of the critical energy release rate for predicting the growth of a crack in nanoscale materials applying the strain gradient elasticity theory (SGET) capable to capture size effects, nonlocal material point interactions and surface effects in the form of (phenomenological) higher-order stress/strain gradients.

Validity of the Finite Fracture Mechanics Based Asymptotic Analysis for Predictions of Crack Deflection in Thin Layers of Ceramic Laminates

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection occurs is only one order higher than the crack extension lengths considered within the solution. A purely FEM based calculation of the energy and stress conditions, necessary for the crack propagation, serves as the reference solution to the problem. The asymptotic analysis is used after for calculations of the same quantities (especially of energy release rate – ERR). This concept enables semi-analytical calculations of ERR or changes in potential energy induced by the crack extensions of different lengths and directions. Such approach can save a large amount of simulations and time compared with the pure FEM based calculations. It was found that the asymptotic analysis provides a good agreement for investigations of the crack increments enough far from the adjacent interfaces but for longer extensions (of length above 1/5-1/10 of the distance from the interface) starts more significantly to deviate from the correct solution. Involvement of the higher order terms in the asymptotic solution or other improvement of the model is thus advisable.