TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

Dynamic fracture mechanics—A scientific tool for the prevention of catastrophic failure

The major area of research in dynamic fracture has been the extension of the concept of static fracture toughness to predict crack arrest for a propagating crack. In this work crack propagation due to a ductile (microvoid) mechanism and cleavage (brittle) mechanism, as well as transition from one mode to another, has been analysed theoretically. Dynamic fracture toughness as a function of crack velocity has been determined. Temperature distribution near a propagating crack tip has been predicted for plane stress condition. The effect of reflected stress wave in a single edge notch specimen under transient crack growth conditions has also been analysed.     

Nanoscale void nucleation and growth and crack tip stress evolution ahead of a growing crack in a single crystal

A constrained three-dimensional atomistic model of a cracked aluminum single crystal has been employed to investigate the growth behavior of a nanoscale crack in a single crystal using molecular dynamics simulations with the EAM potential. This study is focused on the stress field around the crack tip and its evolution during fast crack growth. Simulation results of the observed nanoscale fracture behavior are presented in terms of atomistic stresses. Major findings from the simulation results are the following: (a) crack growth is in the form of void nucleation, growth and coalescence ahead of the crack tip, thus resembling that of ductile fracture at the continuum scale; (b) void nucleation occurs at a certain distance ahead of the current crack tip or the forward edge of the leading void ahead of the crack tip; (c) just before void nucleation the mean atomic stress (or equivalently its ratio to the von Mises effective stress, which is called the stress constraint or triaxiality) has a high concentration at the site of void nucleation; and (d) the stress field ahead of the current crack tip or the forward edge of the leading void is more or less self-similar (so that the forward edge of the leading void can be viewed as the effective crack tip).     

Conditions for crack kinking under stress-wave loading

Kinking of a crack in a prestressed body under the influence of incident stress waves is investigated on the basis of the balance of rates of energies. It is assumed that the crack tip will choose to propagate at a time, in a direction, and at a speed for which the energy flux into the propagating crack tip attains a maximum value with respect to variation of the kinking angle. It is shown that the balance of rates of energies implies that the crack tip speed is zero at the onset of fracture. Consequently, the conditions for the onset of crack kinking and for the computation of the kinking time and kinking angle are completely defined by the elastodynamic field around the original crack tip. Examples of the incidence of step stress waves on a semiinfinite crack in a prestressed body have been investigated. It is shown that for an incident antiplane wave with Mode III fracture, kinking is generally not possible. For an incident inplane wave with mixed Mode I–II fracture, kinking may happen. For that case curves are presented which relate the kinking time and the kinking angle to the state of prestress and to the parameters of the incident wave.     

Numerical analysis of dynamic crack propagation in rubber

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.     

Inclined pileup of screw dislocations at the crack tip with a dislocation-free zone

A single pileup of screw dislocations extending from the crack tip along an inclined direction has been observed in experiments. It is often associated with dislocation emission mechanisms at the crack tip. This linear pileup is a microplastic slipline emanating from the crack tip. A region near the crack tip is often free from dislocations because of a finite resistance value for the crack tip to emit dislocations. The mathematical problem is solved in this paper by applying the extended Wiener-Hopf method. The condition of finite stress at the end of the plastic zone, the crack opening displacement, and the stress distribution along the slipline are obtained in analytical expressions. Numerical values are calculated and the results can be used to discuss brittle versus ductile fracture for metals as treated in previous studies. A method to approximately calculate the corresponding results for edge dislocations is suggested.     

Closed-Form Solutions for the Mode ii Crack tip Plastic Zone Shape

Analytical closed-form solutions for the Mode II crack tip plastic zone shape have been derived for a semi-infinite crack in an isotropic elastic-plastic solid under both plane stress and plane strain conditions. Two yield criteria have been applied: the Von Mises and Tresca yield criteria. The results indicate that the Tresca zone is larger in size than the Von Mises zone. The results also reveal an intricate dependence on Poisson's ratio in plane strain conditions.     

Failure prediction in toughened epoxy resins

In order to improve the damage tolerance of composites and the performance of adhesives, one of the methods being considered is toughened or modified epoxy resins. The modifiers which are commonly used are CTBN rubber and inorganic fillers. A major toughening mechanism causing the increased toughness is the shear deformation process occurring near the crack tip. The effect of such a deformation process is to blunt the crack tip and increase the size of the plastic zone. Several models are available to predict the toughness on the basis of plastic zone size, crack tip opening displacement or crack tip radius, but these are only applicable to Mode I crack extension. Also, most of these approaches use only one stress component which is normal to the crack plane to predict the fracture toughness. The present paper reviews the existing models and suggests a criterion based on the phenomenological approach to failure in order to study the yielding and fracture toughness behavior of both unmodified and modified epoxies. The proposed yield and fracture criteria give predictions in good agreement with experimental results.     

Experimental study of crack propagation in polymethyl methacrylate material with double holes under the directional controlled blasting

The crack propagation behaviours of polymethyl methacrylate material with double holes under the directional controlled blasting are studied using dynamic caustic method. A series of dynamic caustic patterns at the propagating crack tip under the explosive loading are recorded using the digital high‐speed camera. Some important dynamic fracture characterizations and parameters about two main cracks are determined including the crack path, the propagating speed and the crack tip stress intensity factors. The fracture mechanisms of the double blasting holes are analysed. The results provide the important experimental basis for evaluating and designing the directional controlled blasting for the rock tunnel and the rock face excavation.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

Transient analyses of dislocation emission in the three modes of fracture

Exact transient solutions for a micromechanical process of dislocation emission from stationary cracks in each of the three Modes of fracture are assembled. Each process involves a possible slip mechanism for the Mode, and the loading in each case is due to plane wave diffraction.

The solutions are examined in view of an emissions criterion similar to one developed for quasi-static studies on the basis of standard dislocation force concepts. Among the results are formulas for three parameters: emission time, distance traveled by an emitted dislocation prior to arrest, and the time of arrest. The formulas involve material properties such as yield stress and surface energy, as well as a dimensionless variable parameter governing the size of a zone of dislocation attraction at the crack edge.

The parameters themselves exhibit dislocation speed-dependent dynamic effects, but, on the other hand, the Mode I and Mode III cases achieve minimum emission times for the zero-speed limit. The effect of crack blunting serves to raise the emission time required. Order-of-magnitude estimates of the parameters indicate that they are definitely on a micromechanical scale, suggesting that emission may depend only on the region very near the crack edge.     

Elastodynamic forms of caustics for running cracks under constant velocity

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I, which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating under Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I, evaluated.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

Dynamic fields near a crack tip growing in an elastic-perfectly-plastic solid

A complete asymptotic solution is given for the fields in the neighborhood of the tip of a steadily advancing crack in an incompressible elastic-perfectly-plastic solid.For Mode I crack growth in the plane strain condition, the following noteworthy results are revealed: (1) The entire crack tip in steady crack growth is surrounded by a plastic region, and no elastic unloading is predicted by the complete dynamic asymptotic solution. Thus, the elastic unloading region predicted by the result of neglecting the important influence of the inertia terms in the equations of motion. (2) Unlike the quasi-static solution, the dynamic solution yields strain fields with a logarithmic singularity everywhere near the crack tip. (3) The stress field varies throughout the entire crack tip neighborhood, but does display behavior which can be approximated by a constant field followed by an essentially centered-fan field and then by another constant field, especially for small crack growth speeds. Indeed, the stress field reduces to that for the stationary crack, as the crack tip velocity - measured by the Mach number, M - reduces to zero; the strain field, however, does not reduce to that for the static solution, as M vanishes. (4) There are two shock fronts emanating from the crack tip across which certain stress and strain components undergo jump discontinuities. The location of the shock fronts and the magnitude of the jumps depend on the crack growth speed. The stress jump vanishes while the strain jump becomes unbounded, as the crack tip speed goes to zero.Finally, the Mode III steady-state crack growth is reviewed and, on the basis of Mode I and Mode III results, it is concluded that ductile fracture criteria for nonstationary cracks must be based on solutions which include the inertia effects, and that for this purpose, quasi-static solutions may be inadequate. Then, a possible ductile fracture criterion is suggested and discussed.One interesting feature of the complete dynamic asymptotic solution is that, unlike the quasi-static solution, it yields the same strain singularity for all three fracture modes.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

On stress field near a stationary crack tip

It is well known that the stress and elastic-plastic deformation fields near a crack tip have important roles in the corresponding fracture process. For elastic-perfectly-plastic solids, different solutions are given in the literature. In this work we examine and compare several of these solutions for Mode I (tension), Mode II (shear), and mixed Modes I and II loading conditions in plane strain. By consideration of the dynamic solution, it is shown that the assumption that the material is yielding all around a crack tip may not be reasonable in all cases. By admitting the existence of some elastic sectors, we obtain continuous stress fields even for mixed Modes I and II.     

Plane stress crack-line fields for crack growth in an elastic perfectly-plastic material

Mode-I crack growth in an elastic perfectly-plastic material under conditions of generalized plane stress has been investigated. In the plastic loading zone, near the plane of the crack, the stresses and strains have been expanded in powers of the distance, $\text{y}$, to the crack line. Substitution of the expansions in the equilibrium equations, the yield condition and the constitutive equations yields a system of simple ordinary differential equations for the coefficients of the expansions. This system is solvable if it is assumed that the cleavage stress is uniform on the crack line. By matching the relevant stress components and particle velocities to the dominant terms of appropriate elastic fields at the elastic-plastic boundary, a complete solution has been obtained for ?_y in the plane of the crack. The solution depends on crack-line position and time, and applies from the propagating crack tip up to the moving elastic-plastic boundary. Numerical results are presented for the edge crack geometry.     

Dynamic fracture mechanics analysis of failure mode transitions along weakened interfaces in elastic solids

Dynamic fracture mechanics theory was employed to analyze the crack deflection behavior of dynamic mode-I cracks propagating towards inclined weak planes/interfaces in otherwise homogenous elastic solids. When the incident mode-I crack reached the weak interface, it kinked out of its original plane and continued to propagate along the weak interface. The dynamic stress intensity factors and the non-singular T-stresses of the incident cracks were fitted, and then dynamic fracture mechanics concepts were used to obtain the stress intensity factors of the kinked cracks as functions of kinking angles and crack tip speeds. The T-stress of the incident crack has a small positive value but the crack path was quite stable. In order to validate fracture mechanics predictions, the theoretical photoelasticity fringe patterns of the kinked cracks were compared with the recorded experimental fringes. Moreover, the mode mixity of the kinked crack was found to depend on the kinking angle and the crack tip speed. A weak interface will lead to a high mode-II component and a fast crack tip speed of the kinked mixed-mode crack.     

Quasi-sudden brittle fracture at both edges of a finite crack

The diffraction of a plane horizontally polarized shear wave by a crack of finite length is analyzed and the extension of both crack edges prior to the arrival of the first diffracted waves, i.e. quasi-sudden fracture, is studied. In light of an energy rate balance criterion it is found that for an incident step-stress pulse, quasi-sudden fracture may occur but always at both crack edges, often initiating at the trailing edge first. For an incident wave whose stress vanishes at the wavefront, however, quasi-sudden fracture may occur only at the leading crack edge, or if at both edges, at the leading edge first. For both waveforms, the rate of crack extension is non-constant and increases rapidly so that crack branching may be expected. Finally instantaneous crack extension at a uniform rate is possible only if the incident wave stress possesses a square-root sinularity at the wavefront. This result agrees with earlier work by Achenbach.     

Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs’ parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs’ parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.