Energy approach to crack growth in a fiber-reinforced brittle material modeled by an inclusion

Brittle materials randomly reinforced with a low volume fraction of strong, stiff and ductile fibers are considered, with specific reference to fiber-reinforced cements and concrete. Visible cracks in such materials are accompanied by a surrounding damage zone – together these constitute a very complex “crack system”. Enormous effort has been put into trying to understand the micromechanics of such systems. Almost all of these efforts do not deal with the “crack system” propagation behavior as a whole. The propagation process of such a “crack system” includes propagation of the visible crack and the growth of the damage zone. Propagation may take place by lengthening of the visible crack together with the concomitant lengthening of the surrounding damage zone, or simply by broadening of the damage zone while the visible crack length remains unchanged – or simultaneously by growth of both types. A phenomenological completely theoretical model (for an ideal material) is here proposed which can serve to examine the propagation process by means of energy principles, without recourse to the microscopic details of the process. An application of this theoretical approach is presented for the case of a damage zone evolving with a rectangular shape. This shape is chosen because it is expected that it will illustrate the nature of damage evolution and because the computational procedure necessary to follow the growth is the most straightforward.     

Scaling behavior of thermal shock crack patterns and tunneling cracks driven by cooling or drying

Cracks driven by shrinkage due to cooling or drying arrange themselves via mutual interaction. For parallel straight crack arrays driven by idealized transient shrinkage fields the scaling behavior in an infinite half-space is derived analytically by means of fracture mechanics bifurcation analysis with two plausible scaling assumptions. Crack spacing in thermal shock crack patterns has been found to be approximately proportional to the crack length and inversely proportional to the crack velocity. The spacing of tunneling cracks formed in a drying layer between plates scales as the 2/3rd power of layer thickness as a consequence of the specific interaction between the tunneling cracks. The difference in scaling behavior in the two cases is explained by the dimensionality of the geometrical setup determined by the boundary condition rather than by different physical processes. In either case, good agreement between theory and experiments is found.     

Meshless simulation of crack propagation in multiphase materials

The material body considered in this work consists of multiphases. Digital imaging data are taken as the input to specify the configuration and composition of the specimen. Meshless method is demonstrated as a superior numerical tool to analyze crack initiation and propagation in multiphase material. A fracture criterion, based on the ratio of the opening stress over the material toughness distributed in front of the crack tip, is proposed to determine the direction of crack propagation of mixed mode fracture problem in multiphase material. Numerical results are presented and discussed.     

Periodic cracking of films supported on compliant substrates

When a tensile strain is applied to a film supported on a compliant substrate, a pattern of parallel cracks can channel through both the film and substrate. A linear-elastic fracture-mechanics model for the phenomenon is presented to extend earlier analyses in which cracking was limited to the film. It is shown how failure of the substrate reduces the critical strain required to initiate fracture of the film. This effect is more pronounced for relatively tough films. However, there is a critical ratio of the film to substrate toughness above which stable cracks do not form in response to an applied load. Instead, catastrophic failure of the substrate occurs simultaneously with the propagation of a single channel crack. This critical toughness ratio increases with the modulus mismatch between the film and the substrate, so that periodic crack patterns are more likely to be observed with relatively stiff films. With relatively low values of modulus mismatch, even a film that is more brittle than the substrate can cause catastrophic failure of the substrate. Below the critical toughness ratio, there is a regime in which stable crack arrays can be formed in the film and substrate. The depth of these arrays increases, while the spacing decreases, as the strain is increased. Eventually, the crack array can become deep enough to cause substrate failure.     

Adiabatic decohesion in a thermoplastic craze thickening at constant or increasing rate

When a crack in a thermally non-diffusive material is impact loaded—or propagates at high speed—a cohesive process which resists slow crack extension may itself cause decohesion by adiabatic heating. By assuming that decohesion ultimately occurs by low-energy disentanglement within a melt layer of critical thickness, the fracture resistance of craze-forming crystalline polymers can be estimated quantitatively. Previous estimates used a simple, thermomechanically linear representation of craze fibril drawing. This paper presents a more physically realistic, numerical formulation, and demonstrates it for constant craze thickening rate (as imposed by an ideal full-notch tension test) and for linearly increasing thickening rate (as at the tip of an impact-loaded or rapidly propagating crack). For a linear material, the numerical formulation gives results which asymptotically approach those from analytical solutions, as craze density approaches zero. In more realistic model polymers, the enthalpy of fusion increasingly delays decohesion as impact speed increases, although the temperature distribution of an endotherm appears to have little effect. Increasing molecular weight, heuristically associated with decreasing craze density and increasing structural dimension, increases the predicted impact fracture resistance. In every case, fracture resistance passes through a minimum as impact speed increases. The conclusions encourage the use of impact fracture tests, and discourage the use of the full-notch tension test, to assess the dynamic fracture resistance of a craze-forming polymer.     

Comments on “Explicit transient solutions for a mode III crack subjected to dynamic concentrated loading in a piezoelectric material” by Yi-Shyong Ing, Mau-Jung Wang [Int. J. Solids Struct. 41 (2004) 3849–3864]

In this comment it is pointed out that the analysis of the dynamic stress intensity factor, dynamic electric displacement intensity factor and dynamic energy release rate conducted by Ing and Wang [Ing, Y.S., Wang, M.J., 2004. Explicit transient solutions for a mode III crack subjected to dynamic concentrated loading in a piezoelectric material. International Journal of Solids and Structures 41, 3849–3864] is incorrect. The correct analysis and corresponding correct plots are presented.     

Crack bridging and trapping mechanisms used to toughen brittle matrix composite

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.     

Process zone in the Single Cantilever Beam under transverse loading - Part II: Experimental

This paper describes an experimental arrangement to evaluate stress/strain fields in the process zone of asymmetric adhesively bonded joints. A transparent polycarbonate flexible beam was bonded to an aluminium alloy rigid block with an epoxy adhesive in a Single Cantilever Beam (SCB) configuration. The flexible adherend was loaded in the direction parallel to the initial crack front at constant rate. To monitor strains induced by bending and shear along the beam, electric strain gauges were attached to the upper surface of the flexible adherend. Thus strain distribution was measured above the bonded surface, which could be used to monitor crack propagation and investigate stress redistribution in the process zone. A Timoshenko beam lying on a Pasternak elastic foundation model was used for the analysis of experimental findings. Subsequently, the Digital Image Correlation technique was used to measure the flexible substrate in-plane displacement field in the vicinity of the crack front and to assess the specimen kinematics. We found that strain gauge instrumentation of the fracture mechanics specimen was a very sensitive technique for experimental analysis of crack propagation under complex loading, offering fine investigation of stress distribution in the cohesive zone.     

Crack movement in layered composites under electric field affect

The variation principle is applied for defining a crack in the solid body. The methods proposed in [G. Sih, C. Chen, Non-self-similar crack growth in elastic–plastic finite thickness plate, Theoretical and Applied Fracture Mechanics 3 (1985) 125–139] extend to presence of electromagnetic fields in material. Crack propagation in non-homogeneous media has been considered. It is shown that electromagnetic fields in the material are essentially affecting the trajectory. The crack trajectory stability has been studied as function of fracture energy, phase portraits of the trajectory in different media have been built, and various attractor types have been revealed. Different crack morphologies from single straight and oscillating crack propagation to straight double crack propagation were theoretically founded. In compliance with the experimental data of [R. Niefanger, V.-B. Pham, G. Schneider, H.-A. Bahr, H. Balke, U. Bahr, Quasi-static straight and oscillatory crack propagation in ferroelectric ceramics due to moving electric field: experiments and theory, Acta Materialia 52 (1) (2004) 117–127], it has been demonstrated that periodic electromagnetic field results in trajectory stochastization. This can be used for switching the crack over from the mode of mainline propagation into the mode of development of the field of diffused microcracks.     

A generalized Paris’ law for fatigue crack growth

An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wöhler SN curve of the material, suggesting a more general “unified law”. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Δa, the “fracture quantum”. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Δa, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture “quantum” on the applied stress range level such that the correct convergence towards the Wöhler-like regime is obtained. Hence, the final law includes both Wöhler's and Paris’ material constants, and can be seen as either a generalized Wöhler's SN curve law in the presence of a crack or a generalized Paris’ law for cracks of any size.     

Size effects on strength, toughness and fatigue crack growth of gradient elastic solids

The present study investigates the microstructural size effect on the strength of a bar under axial loading, and on the toughness and crack growth of a beam under three-point bending within the framework of strain gradient elasticity. The gradient responses have been found considerably tougher as compared to the classical theory predictions and the observed deviation increases with increasing values of the non-dimensional parameter g/L (microstructural length over structural length). Based on the analytical solution of the strain energy release rate for the three-point bending case, a new, simple and universal, strain gradient elasticity, brittle fracture criterion and a new, size adjusted fatigue crack growth law have been established. Finally, the analytical predictions of the current modeling compare well with previous experimental data, based on three-point bending tests on single-edge notched concrete beams.     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

Modern topics and challenges in dynamic fracture

The field of dynamic fracture has been enlivened over the last 5 years or so by a series of remarkable accomplishments in different fields—earthquake science, atomistic (classical and quantum) simulations, novel laboratory experiments, materials modeling, and continuum mechanics. Important concepts either discovered for the first time or elaborated in new ways reveal wider significance. Here the separate streams of the literature of this progress are reviewed comparatively to highlight commonality and contrasts in the mechanics and physics.Much of the value of the new work resides in the new questions it has raised, which suggests profitable areas for research in the next few years and beyond. From the viewpoint of fundamental science, excitement is greatest in the struggle to probe the character of dynamic fracture at the atomic scale, using Newtonian or quantum mechanics as appropriate (a qualifier to be debated!). But lively interest is also directed towards modeling and experimentation at macroscales, including the geological, where the science of fracture is pulled at once by fundamental issues, such as the curious effects of friction, and the structural, where dynamic effects are essential to proper design or certification and even in manufacture.     

Evolution of nanoscale defects to planar cracks in a brittle solid

Fracture of a solid is a highly multiscale process that associates atomic scale bond breaking with macroscopic crack propagation, and the process can be dramatically influenced by the presence of defects in materials. In a nanomaterial, defect formation energy decreases with the reduction of material size, and therefore, the role of defects in crack formation and subsequent crack growth in such materials may not be understood from the classical laws of fracture mechanism. In this study, we investigated the crack formation process of a defective (with missing atoms) nanostructured material (NaCl) using a series of molecular dynamics (MD) simulations. It was demonstrated that simple defects in the form of several missing atoms in the material could develop into a planar crack. Subsequently, MD simulations on failures of nanosized NaCl with pre-defined planar atomistic cracks of two different lengths under prescribed tensile displacement loads were performed. These failure loads were then applied on the equivalent continuum models, separately, to evaluate the associated fracture toughness values using the finite element analysis. For small cracks, the fracture toughness thus obtained is cracksize dependent and the corresponding critical energy release rate is significantly smaller than Griffith’s theoretical value. Explanation for this discrepancy between LEFM and the atomistic model was attempted.     

Incubation time fracture criterion for FEM simulations

The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes.Incubation time fracture criterion is reviewed;practical questions of its numerical implementation are extensively discussed.Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given.The examples include simulations of dynamic crack propagation and arrest,impact crater formation(i.e.fracture in initially intact media),spall fracture in plates,propagation of cracks in pipelines.Applicability of the approach to model initiation,development and arrest of dynamic fracture is claimed.     

Limitation on crack speed for a strip-craze model applied to PMMA

A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σ_ns0. When σ_ns0<60 MPa, the crack speed mm/s and the crack is basically stationary; when 60 <σ_ns0<95 MPa, then mm/s the crack is in slow propagation; when σ_ns0>95 MPa, then mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation.     

STW型生态土壤稳定剂改良工程粘性土胀缩性试验研究

根据Logvinovich独立膨胀原理发展了一种用于计算非定常通气超空泡形态的计算方法,并运用该方法对通气超空泡形态稳定性进行了数值仿真研究. 研究表明：Semenenko提出的稳定性判据可以有效判定通气超空泡形态稳定性,当超空泡处于判据的稳定区域时,超空泡表面形成的扰动波在扰动停止一段时间后消失,超空泡恢复到初始形态;当超空泡处于判据的不稳定区域时,超空泡发生自激振荡,超空泡表面形成的扰动波振幅逐渐增大,导致超空泡形态与内部压力发生周期性或准周期性振荡.