Running Crack Research Articles

Scattering of antiplane shear wave by a propagating crack at the interface of two dissimilar elastic media

An analysis of the scattering of horizontally polarized shear wave by a semi-infinite crack running with uniform velocity along the interface of two dissimilar semi-infinite elastic media has been carried out. The mixed boundary value problem has been solved completely by the Wiener-Hopf technique. The effect of different values of the material parameter, the angle of incidence of incident wave and the crack propagation velocity on the stress intensity factor have been illustrated graphically.

Mechanics of dynamic debonding

Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined. Emphasis is placed on extending an established frame work for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response. For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity. This simplifies the problem, rendering the Stroh techniques applicable. In general, the singularity oscillates, similar to quasi-static cracks. The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds. In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed. Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials. Implications on crack branching and substrate cracking are discussed. Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol’dshtein and Dugdale problems. Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed.

Specimen size effects on dynamic crack propagation and arrest in DCB specimens

In this study, high-speed photographs of caustic patterns for dynamically propagating cracks were taken by a laser caustic method which can be quickly synchronized to the initiation of a brittle fracture event. The dynamic stress intensity factors were evaluated on the basis of a theory of caustics for mixed-mode fast running cracks, which was previously developed by the present authors. Influences of the length of double cantilever beam (DCB) specimens were thoroughly investigated by changing the specimen length systematically. It was found that the crack arrest toughness K IA values in shorter specimens were larger than those in longer specimens. Therefore, sufficiently long specimens should be used to obtain conservative K IA values.

A theory of caustics for mixed-mode fast running cracks

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. Completely analytical expressions were derived for the caustic curves as well as for the initial curves for fast running cracks under inplane mixed-mode conditions. The effects of crack velocity and mixed-mode condition on the caustic pattern and the initial curve were investigated. New procedures were also proposed for the evaluation of the dynamic stress intensity factors K I and K II using the overall dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.

Dynamic caustics and its applications

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 Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K d I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.

The experimental and numerical studies on arrest process of a running crack

The arrest process of a running crack meeting a small hole or arrest cylinder was studied by means of experimental and numerical methods. The results showed that velocity of the running crack increased when the crack approached a hole, but the velocity decreased rapidly when the running crack approached the arrest cylinder. Whether the running crack passes through the hole or arrest cylinder depends on the dynamic stress intensity factor and the notch toughness of the hole or the dynamic fracture toughness of the arrest cylinder.

Determination of mixed-mode dynamic stress intensity factors in a fast curving fracture test using a laser caustic method.

In order to investigate the mechanism governing elastodynamic crack curving, a series of fast curving fracture tests were carried out. In the present experiments, high-speed photographs of the caustic patterns for dynamically curving cracks were taken by a laser caustic method which can be quickly synchronized to the initiation of brittle fracture event. The mixed-mode dynamic stress intensity factors were evaluated on the basis of a theory of tics for mixed-mode fast running cracks, which was developed by some of the authors. It found that the magnitude of the mode II stress. intensity factor is closely related to the dynamic crack curving.

A theory of caustics for mixed-mode fast running cracks. (2nd report. General mixed-mode theory).

In the previous paper, a theory of caustics was developed for elastodynamically propagating cracks under an inplane mixed-mode condition. A new procedure was also proposed for the evaluation of the dynamic stress intensity factors. In this paper, the theory of caustics was also extended for dynamically propagating cracks under general mixed-mode conditions including modes I, II and III. Complex potentials for the general solutions of the near-tip field which have been previously derived by the authors were used in this theoretical development. The effects of crack velocity and the mixed-mode condition on the caustic pattern and the initial curve were investigated. It was found that even a small magnitude of the mode III loading influences the shape of the caustic pattern. The deformed surface around a crack tip under the above condition was also clarified.

A study on fast crack propagation and arrest. (2nd report. Geometry dependence of the behavior).

The dynamic stress intensity factors are presented for the fast running crack of the double-cantilever beam type specimens with various heights machined from the model material PMMA. The dynamic stress intensity factors decrease at the beginning of the crack propagation phase, remain almost unchanged in the next stage, and then increase in all specimens. After this period the behavior of the stress intensity factors varies with the specimen geometry. The values of the stress intensity factors at three characteristic points in the stress intensity factor-crack extension curve are discussed with relation to the crack arrest.

Temperature fields near a running crack tip

Near a running crack tip, the plastic work rate is high. According to the theory of irreversible thermodynamics, the plastic work will be almost completely converted into heat which may lead to high temperature rise at the running crack tip. The plastic zone is regarded as the zone of the heat source, and the plastic work rate as the strength of the heat source. In this paper, the plastic work rate is derived from the solution of stress and strain fields obtained by Chitaley and McClintock[1] for a steady state crack growth under anti-plane shear in an elastic perfectly-plastic material. The dependence of the thermal conductivity on temperature has been considered and a non-linear model for temperature fields has been proposed. The numerical results for glass have been given and compared with other papers.

MICRO-MECHANISM OF DYNAMIC CRACK PROPAGATION IN BRITTLE MATERIALS

Micro-mechanism of dynamic crack propagation is experimentally studied. A running crack experiment in brittle PMMA plates is conducted under constant velocity condition by the use of a fixed grip apparatus. The fracture surface is microscopically observed. Analysis of parabolic patterns on the fracture surface shows the process of micro-crack initiations, propagations and their coalescences to the global crack propagation. The condition of the micro-crack initiation at the nuclei is obtained from the examination of the patterns and the dynamic stress analysis.

A theory of caustics for mixed-mode fast running cracks. 1st Report. Inplane mixed-mode theory.

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. The effects of crack velocity and the mixed-mode condition on the caustic pattern and intial curve were investigated. A new procedure was also proposed for the evaluation of the dynamic stress intensity factors KI and KII using appropriate dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.

A study on fast crack propagation and arrest. 1st report. Method of experiment and calculation.

This paper is concerned with the problem of fast crack propagation and arrest. The crack tip position versus time is measured by the ladder gages for the double-cantilever beam specimens machined from the model material, polymethylmethacrylate. Using this data, the dynamic stress intensity factor of the running crack is calculated by an improved finite difference method. In this FDM, the stress at a node adjacent to the crack tip is gradually relaxed depending on the crack tip location between nodes. The solutions of the equations of motion obtained by the central difference approximation are corrected by the trapezoidal rule. With these techniques, the crack propagation processes are simulated more accurately by an explicit time-step algorithm with little computing time required.

Pulsations of damage during a fast running crack

Pulsations of damage during a fast running crack

Ductile Instability of Long Arrested Crack under R-Curve Concept

To prevent the catastrophic failure of a large storage tank, it is necessary to ensure not only that the long brittle crack will be arrested by the material toughness, but also that the arrested crack will subsequently be stable. After the long and fast running crack is arrested, the bulging force applied to the crack flanks will grow and re-initiate the unstable ductile crack.R-curve concept combined with J-integral is adopted as a theoretical tool and wide plate tests are carried out to estimate the fracture resistance of a material for LPG storage tanks. The tested material is the 34 mm thickness 2 1/2% Ni steel plate manufactured by the special thermomechanical process, SHT-DAC. The specimens are 3 m in width and 4. 6 m in length so as to reproduce long arrested cracks in storage tanks. The specimens were loaded in the 10, 000 tonf test rig under the room temperature and as the ductile crack extended, they were unloaded in less than 10% for measuring the crack growth.The applied driving force is calculated from J-integral, the Battelle's equation on the bulging effect.The ductile resistance of the test material is 200 N/mm2 as dR/da for long arrested cracks. For a large LPG storage tank of 40 m in diameter, the strake height should be limited under 3. 2 m to avoid the ductile instability of the long arrested crack.

Diffraction of transient horizontal shear waves by a running crack at the interface of two bonded dissimilar elastic solids.

This paper deals with the problem of diffraction of horizontally polarized shear waves of arbitrary profile by a running crack located at the interface of two-bonded dissimilar elastic solids. A set of moving coordinate systems attached at the center of the running crack and a new time parameter are employed to obtain the basic equations of motion for two dissimilar elastic half spaces. By the use of Laplace and Fourier transforms we reduce the problem to a pair of dual integral equations. The solution to the dual integral equations is expressed in terms of a pair of Fredholm integral equations of the second kind having the kernel of a finite integration. Dynamic stress intensity factor for an incident wave with a step function profile is obtained as a function of the speed of crack propagation, the angle of incidence, the material properties, and time, and is shown graphically.

Microscopic observation of the tips of fast running cracks in PMMA

Although various theoretical models exist, little experimental data is available on the material behaviour in the ultimate vicinity of the tip of fast running cracks. Using a microscope coupled image converter camera, the tips of cracks running in PMMA (polymethylmethacrylate) at speeds between 250 m s −1 and 680 m s −1 were photographed. Due to the high aperture of the optical set-up, shadow optical effects could be greatly reduced. Thus it was possible to observe the contour of the crack flanks up to the crack tip, revealing the existence of fibrils in between the flanks. Seemingly the appearance of these fibrils is connected with the onset of crack branching. Having the crack pass a microlattice, which had been vapor deposited onto the specimen surface, the displacements around the crack tip could be determined. The recorded plastic zone is of triangular shape. Experimental results are compared with theoretical predictions.

Crack propagation due to indentation with constant speed

This paper is concerned with the propagation of a surface crack in a brittle solid induced by the indentation of a sharp wedge into the crack under constant speed. The analysis is based on a double-cantilever-beam model. Only the shear deformation of the cantilever is considered. Griffith concept of the balance of energy is used as the fracture criterion. It is found that crack propagation begins when the shear wave front is at the tip of the initial crack. During crack propagation, the crack speed remains constant with finite jumps at those moments when the shear wave front reaches the tip of the running crack. The results obtained by the dynamic analysis agree approximately with those derived from a quasi-static analysis.

Crack-propagation trajectories under biaxial loading, based on fracture criteria

A procedure based on either of the fracture criteria, i.e. the two-term S 2-criterion ( S 2) and the T-criterion ( T), is proposed to simulate crack initiation and propagation from an initially inclined crack. According to this model the running crack, during its initial stage, follows a strongly zig-zag trajectory, forming successive kinks. Then, after a certain number of steps, the crack path is stabilized in a straight line, until complete fracture of the plate occurs. The directions of the successive kinks are essentially the same as those given by the two-term S 2- criterion for brittle materials and the T-criterion for ductile materials.

Dynamic studies of running half-plane and cruciform cracks

The dynamic problems of a crack running perpendicularly into a half-plane surface and a cruciform crack running in an unbounded solid under the action of moving point forces are analyzed. The cracks are treated as dislocations distributed w.r.t. Speed, so that the problems reduce to singular integral equations with Dirac functions as non-homogeneous terms. By extracting physically significant limit cases with analytical solutions, the terms are removed, and the resulting equations solved numerically by a standard technique. Dynamic stress intensity factor and crack opening data are presented. For the cruciform crack, this data is compared with that for the plane crack limit case.