Crack Velocity Research Articles

Experimental Research on Explosively Driven Crack Initiation and Propagation from Flaws of Various Geometry

Abstract The aim of this study is to explore the fracture dynamic properties of defect bodies under explosion loading by using the system of digital laser dynamic caustics test. The propagation of directional cracks and the fracture process of defect bodies have been observed by high-speed camera, as well as analyzed for the changing rules of speed and stress intensity factors when the directional crack was close to defect. Experimental results found that the defect has an inhibitory effect on the spreading of cracks when the detonation crack is extended toward the defect. With the decrease of the curvature of the elliptical defect, the energy accumulation rate decreases with the decrease of the curvature in the process of the generation of the cracks at the endpoints of wings, and its fracture toughness increases with the decrease of the curvature, and when the curvature is reduced to a certain extent, the wing crack cannot crack. The dynamic stress intensity factor of the crack tip has a positive correlation with the velocity of cracking, within a certain range. The fracture toughness of the crack at the time it begins is larger than during its spreading.

Damage and fracture of gun barrel under wear-fatigue interaction

Gun, projectile and propellant are three fundamental components of a launching system. Generally, a barrel has to be condemned after a number of rounds have been fired. During the total useful life of gun barrel, it bears severe damage induced from erosion by high pressure and high temperature propellant combustion gas, and wear due to high speed friction between projectile and gun bore. Meanwhile, the gun barrel undergoes a dynamic loading of gas pressure, mechanical stress and thermal stress when firing a round. Thousands of firing cycles lead to gun barrel fatigue. Interaction of wear, including erosion, and fatigue damages the gun barrel and eventually the gun will become inaccurate because of wearing away gun bore materials. However, a gun barrel will fracture in a sudden manner because of fatigue. It is found that microcracks form on the bore surface after only a few rounds have been fired, which lays the foundation for growth and propagation of cracks under fatigue loading. In this paper, laboratory hydraulic fatigue tests were carried out on a tube with pre-machined crack on its inner surface by using an MTS 809. Strain gauges were adhered to the outer surface of the tube to monitor strain during testing process. The hydraulic oil pressure was measured by a pressure sensor. The experimental results show that there are three stages of outer surface strain variation, namely stable increase, fast increase and abrupt increase, which corresponds to the history of crack evolution. Crack grew stably in the initial stage under cycle of loading and a major crack is gradually formed. When the major crack size reaches a certain value, the propagation velocity of crack is accelerated fast and the critical size is reached in a short time. Eventually the tube fractured suddenly. The experimental findings will help us to gain new insight into the physical mechanism of fatigue and fracture of gun barrel and provide a possible method to evaluate health of gun barrel in service.

Contribution of steel fiber on the dynamic tensile properties of hybrid fiber ultra high toughness cementitious composites using Brazilian test

A series of quasi-static and dynamic Brazilian tests were conducted in this study to investigate the influence of steel fiber (SF) on the dynamic tensile behavior of hybrid fiber ultra-high toughness cementitious composites (UHTCCs). Four different kinds of hybrid fiber UHTCCs were prepared with different SF content, but the polyvinyl alcohol (PVA) fiber content remained as 2%. Under quasi-static tensile loading, the composites with 0.5% SF exhibited the highest energy dissipation approximately 2.9 times that of the composites with 1.5% SF. However, the composites with 1.5% SF was recommended to resist the dynamic tensile loading with the highest dynamic tensile strength and energy dissipation among the four composites. The increase in SF content improved the dynamic tensile strength and energy dissipation of hybrid fiber UHTCC, and their contribution was influenced by the strain rate. Based on the high speed image investigation, the crack velocity in the UHTCC increased with the strain rate, which led to the strain rate effect on the various micromechanical parameters of the fiber tension and pullout. By comparing the dynamic tensile behavior of hybrid fiber UHTCC and ultra-high performance concrete (UHPC), it was found that the dynamic energy dissipation of UHTCC were similar with that of UHPC under the same impact loading, although their dynamic tensile strength was 59%–73% of UHPC.

Analysis of rapid crack arrestability enhancement by structural factors in cross-joint components using a transparent elastic solid

This study investigates the effect of structural factors on rapid crack arrestability by simulating cross-joint components made of polymethyl methacrylate (PMMA). Three types of specimens were designed for double cantilever beam-type crack arrest tests; one of them was without a hole and others were with holes of different sizes. The experimental results demonstrated a significant improvement in the crack arrestability due to the larger hole at the joint part. The changes in the crack front shapes were captured successfully using a high-speed camera. The observation results indicated that the crack velocity histories were affected significantly by the change in the crack front shapes. Numerical simulations based on the extended finite element method (XFEM) were then performed on these captured crack-front-shape transitions to discuss the effectiveness of the enhancement of crack arrestability by structural factors. The numerical results revealed the same values of the stress intensity factor (KI) at the crack-arrested locations in all the tests. KI in the test using the specimen with the larger hole exhibited a steeper decrease at the flange. Consequently, KI decreased by 35% in the test using the specimen with the largest hole, whose width was 46% of the upper-web thickness. This enhancement effect was equivalent to that using materials with 54% higher crack arrest toughness in terms of the stress intensity factor. Focusing on the design of structural factors could drastically enhance the rapid crack arrestability of joint components.

A study of the fracture behavior of ballistic gelatin based on wire-cutting tests

The present study explores fracture properties of ballistic gelatin at different loading rates. Wire-cutting fracture tests were undertaken, and a new analysis method was proposed, in order to delineate the fracture force from the total cutting force. The new method was proved to be effective in obtaining the fracture toughness of ballistic gelatin at different cutting rates. It was found that the fracture toughness of 10% ballistic gelatin at 4°C increases almost linearly from 3.1 N/m at a cracking velocity of 10 mm/min to 19.4 N/m at 200 mm/min.

Experimental determination of crack velocities in steel

One of the little-studied problems of modern mechanics and the physics of fracture is the branching of the crack, which is observed in materials of a different nature. To experimentally determine the rate of crack branching velocity in steels, a series of tests were carried out on the fracture by internal pressure of steel thin-walled cylindrical shells (vessels) with measuring of the crack velocity by the method of breaking the conductive strips. A measurement setup was created on the basis of a precision converter “Tercon” signals of resistance thermometers and thermocouples, connected to a computer. Velocity measurements showed that in the case of straight-line propagation, the crack velocity is 350-541 m/s, and when crack branching, the crack velocity is 679-746 m/s. The results show that the crack branching velocity is a critical (limiting) crack propagation velocity, and the energy entering the top of a moving crack is not spent on increasing the crack velocity, but on creating new cracks by branching.

Instabilities encountered in the dynamic crack propagation process under impact loading as a natural consequence of the dynamic fracture discreetness

Dependence of stress intensity factor (SIF) on crack velocity (KI−ȧ dependence) in Homalite-100 specimens subjected to pulse loading was numerically studied. The numerical scheme is based on finite element method and incubation time fracture criterion. Experimental results from works by Ravi-Chandar and Knauss (1984a,b,c) were used. Experimentally obtained KI−ȧ dependence is characterized by considerable scatter of the SIF values.Application of the incubation time based approach made it possible to qualitatively describe scattering of the SIF values since the used fracture condition does not rely neither on critical SIF value, nor on a a priori given KI−ȧ dependence.

Experimental and numerical investigation of the interaction between blast wave and precrack in a defected material.

This study uses a cracked medium to study the interaction mechanism between blast waves and the precrack. The experimental results show that the compressive phase of the dilatational wave would cause the opened precrack to close with a negative sign of stress intensity factor $K_{\rm I}^d$KId, while the tensile phase of the dilatational wave attributes to the precrack opening and increases the crack velocity. However, the shear wave tends to make crack initiation at mixed-mode I/II fracturing by increasing the dynamic stress intensity factor $K_{\rm II}^d$KIId. As a dynamic crack approaches the precrack, the precrack initiated and finally formed an interlocking fracture shape between the precrack and dynamic crack. Besides, the shading effect of the precrack on blast waves is investigated numerically.

Experimental Study of Crack Branching Velocity in Polymers

One of the little-studied problems of modern mechanics and the physics of destruction is crack branching, which is observed in materials of varying nature. In order to study this phenomenon, the criteria and mechanisms for crack branching are analyzed. Studies of crack branching in polymers and steel, as well as fractographic studies of the fracture surface, are considered. It is found that the crack at branching in brittle plastics reaches the limiting propagation velocity V* = 500–800 m/s. Tensile tests of flat samples made of polymethyl methacrylate (PMMA) at temperatures of +20 and –60°C are carried out with measurement of crack velocity by the method of rupture of conductive strips. A measuring device based on a TERCON precision converter of signals of resistance thermometers and thermocouples connected to a computer is created. Crack velocity is measured for (i) rectilinear crack propagation in the mirror, matte, and feather zones of PMMA fracture surface, (ii) single branching of the crack, and (iii) multiple crack branching with parallel movement of the front of several cracks. A hypothesis for the physical mechanism of crack branching is proposed.

Crack velocity- and strain rate- dependent dynamic compressive responses in brittle solids

Crack velocity and strain rate have an important influence on the dynamic fracture in brittle solids. However, the correspondence between crack velocity- and strain rate- dependent dynamic compressive responses is hardly established. In this study, a dynamic compression-based model triggered by microcrack growth of brittle solids is proposed. This dynamic model consists of the improved model of wing crack extension containing crack inclination effect, the correlation of crack velocity and strain rate, and the crack velocity-related dynamic fracture toughness. This correlation of crack velocity and strain rate is obtained by the time derivative of crack extension relating to axial strain. Crack extension relating to axial strain is obtained by use of correlation of damage relating to crack and strain. The whole variations of strain rate- (or crack velocity-) dependent stress-strain constitutive relationships from low strain rate (or crack velocity) to high strain rate (or crack velocity) are studied. The micro-mechanisms corresponding to the dynamic stress-strain curves also are explained. Moreover, a unified conclusion revealing the sensitivities of strain rate on peak axial strain ε1peak appearing at peak strength and initial tangent modulus Eini of stress-strain curves is proposed. Influences of crack velocity and strain rate on crack initiation stress and dynamic strength are analyzed in compression. Effects of the size, inclination and friction of microcracks on dynamic strength also are illustrated. The reasonability of these proposed theoretical results is verified via the published experimental results.

Analysis of self-similar rate-dependent interfacial crack propagation in mode II

The present study analyzes the fundamental properties of a rate-dependent cohesive model applied to the description of dynamic mode-II crack propagation. To make a semi-analytical treatment possible, the idealised problem of a crack along the interface between a semi-infinite elastic layer and a rigid substrate is considered. Solutions corresponding to the propagation of the crack tip at a constant speed are constructed. Using asymptotic properties of the solution far from the crack tip allows obtaining the complete solution of the boundary value problem by direct integration without iterations, using a specific form of the shooting method. By conversion of the problem to dimensionless variables, the behavior of the system for all possible crack velocities and arbitrary combinations of material and geometric parameters can be characterized. The dependence of fracture energy and other important characteristics on model parameters and the crack speed can then be analyzed. Even if the approach is applied to a specific form of damage rate dependence and motivated by the analysis of delamination propagation, the same technique could be used for other classes of interfacial cohesive rate-dependent models.

On the energetics of dynamic cohesive crack formation

AbstractDynamic fracture under static loading, as it takes place in the absence of a perfect pre‐crack, is studied from simple 1D and 2D examples. Special emphasis is placed on the cohesive fracture energy which gives rise to a finite duration of the fracture process and – in conjunction with the material's tensile strength – introduces a material specific length scale.In case of the 2D problem (plate with hole under remote tension/compression), a (quasi‐)spontaneous formation of the finite crack increment, as predicted by FFM, can only be identified for compressive loading (stable crack growth). For tensile loading (unstable crack growth), a non‐monotonic dependence of the crack velocity on the hole radius was observed, attributed to a competition between the effects of crack initiation under higher overall stress for smaller holes and a comparatively larger process zone w.r.t. the hole radius.

Dynamic localized shear failure influenced by changing rates in brittle solids containing initial microcracks

Dynamic microcracks growth has a great influence on macroscopic dynamic mechanical properties under impact loadings in brittle solids containing numerous initial microcracks. Confining pressure plays an important part in shear failure along with shear bands in brittle solids. However, the theoretical micro-macro relationship between shear failure and microcracks growth subjected to impact loadings is rarely proposed. Furthermore, evaluations of changing rates-dependent dynamic mechanical properties have a great meaning for engineering applications. In this study, a micro-macro dynamic localized shear failure model is proposed to explain the effects of changing rates on stress-deformation constitutive curves. A dramatic dynamic failure criterion is proposed by calculating zero crack velocity (ZCV) under constant strain rate during continuous deformation. The formulation of this micro-macro model is based on Ashby and Sammis's crack model, dynamic crack fracture propagation toughness law, a suggested physical correlation of the microcrack and deformation rates, and a deformation path function of changing rates. This suggested rate correlation of microcrack and deformation explains a unified correspondence of crack velocity, axial strain rate and shear velocity with increasing crack length, axial strain and shear displacement, which is established by unifying crack damage and deformation damage. The deformation path function of changing rates describes the step variation of crack velocity, strain rate and shear velocity with ascending crack length, axial strain, and shear displacement, respectively. Effects of parameters in this path function of changing rates on axial stress-crack curve, axial stress-strain, and shear stress-displacement curve are discussed. Rationality of the proposed model is verified by comparing with the published results. The theoretical results will provide an important help for evaluating the mechanical behaviors of applied brittle solids materials in engineering.

Rate effects on fiber–matrix interfacial transverse debonding behavior

The rate effect of fiber–matrix interfacial debonding behavior of SC-15 epoxy with S-2 glass and aramid fiber reinforcements was studied via in-situ visualization of the transverse debonding event. In this study, the debonding force history, debonding initiation, debonding crack velocity, and crack geometry were characterized using a quasi-static load frame and a modified tension Kolsky bar at loading velocities of 0.25 mm/s and 2.5 m/s. Cruciform-shaped specimens were used for interfacial transverse debonding between SC-15 epoxy matrix and two types of fiber reinforcements. The load history and high-speed images of the debonding event were simultaneously recorded. A major increase was observed for the average peak debonding force and a minor increase was observed for the average crack velocity with increasing loading velocity. The crack geometry of the cruciform specimens under both loading velocities was also tracked. Scanning electron microscopy of the recovered specimens revealed the debonding direction along the fiber–matrix interface through angled patterns on the failure surface.

Experimental study on a Mach cone and trailing Rayleigh waves in a stress wave chasing running crack problem

This paper focuses on a blast-induced Mach cone followed by trailing Rayleigh waves during blast stress waves chasing a running crack in an epoxy plate, using the photoelasticity method and high-speed photography. A Mach cone and trailing Rayleigh waves were visualized and interpreted based on isochromatic fringes, agreeing well with theoretical wave paths. The Mach cone was the coalescence of shear wavelets generated by P waves on crack surfaces, which was verified by the half-cone angle, equal to arcsin (CS/CP). Effects of the Mach cone and trailing Rayleigh waves on the running crack were evaluated by measuring crack velocity and dynamic stress intensity factors (SIFs) of the crack tip. It was found that the Mach cone decreased both crack velocity and SIFs, while trailing Rayleigh waves had the opposite effect. Finally, because of similarities, the findings in our experiments were discussed with those in the supershear rupture. In particular, effects of the Mach cone and trailing Rayleigh waves on the running crack were consistent with particle motion near the fault in the supershear rupture.

Crack propagation resistance of slide-ring gels

The crack propagation behavior of pre-cut slide-ring (SR) gels with movable cross-links is investigated and compared to that of fixed cross-link (FC) gels under uniaxial stretching at a constant speed. Two fracture stages with 20-fold difference in crack velocity are observed for both SR and FC gels. At the beginning, the crack propagates slowly, and the crack propagation resistance is in good accordance with the evaluation based on tearing modulus Tr, the initial slope of J-integral – crack tip opening displacement (CTOD) curve. Higher Tr and slower crack velocity are observed in SR gels compared to FC gels with similar modulus. Moreover, Tr decreases and crack velocity increases with increasing modulus (cross-linking density) for FC gels, whilst both parameters are modulus-independent for SR gels. This means that the slow mode crack propagation resistance of SR gels is dominated by the sliding movement of cross-links instead of the cross-linking density. However, as the strain energy input exceeds a critical value, crack accelerates abruptly and overtakes the sliding dynamics of the cross-links, thus the fracture behavior of SR gels resembles that of FC gels. Our results have revealed the strong correlation between the cross-link mobility and crack propagation resistance of SR gels.

Theoretical modeling of the dynamic tensile response of Laurentian granite using the dominant crack algorithm

Dominant crack algorithm (DCA) is a statistical micromechanics model for the dynamic tensile response of brittle materials. In the DCA model, both microscopic and macroscopic material parameters are included to construct the constitutive relation, and the damage evolution is described by the growth of the dominant crack. In this study, the sensitivity analysis of the microscopic parameters (i.e. the characteristic volume size a, the initial crack size c0, and the crack velocity related parameter m) in the DCA model is conducted. The results demonstrate that the dynamic tensile strength is sensitive to the value of c0/a. Compared with the influence of the c0/a on the dynamic tensile strength, the dynamic tensile strength is less sensitive to the variation of the characteristic volume size a or the variation of the crack velocity related parameter m. Furthermore, the DCA model is applied to predict the dynamic tensile response of Laurentian granite (LG). A nonlinear regression method - Particle Swarm Optimization (PSO) - is utilized to optimize the values of the microscopic parameters. The results indicate that the dynamic tensile response of LG predicted by the DCA modeling has a good agreement with that obtained from the experiments. Therefore, the DCA modeling is valid and applicable to describe the dynamic tensile response and predict the dynamic tensile strength of rock-like materials.

Multi-crack propagation in PMMA plates under dynamic out-of-plane impact

In this paper, the multi-crack propagation within polymethyl methacrylate (PMMA) plates under out-of-plane impact is experimentally investigated. First, the dynamic propagation behaviors of in-plane radial and circular cracks are directly recorded using a non-contact optical measurement platform in which a high-speed imaging system is combined with a low-speed impact loading device. Second, the dynamic energy release rates and crack velocities of multiple cracks are studied using caustics, and the effects of impact speed and plate thickness are studied. Finally, a mathematical model of dynamic energy release rate which is related to the radial crack length is established based on the principle of energy conservation. The fracture mechanism of multi-crack propagation in PMMA plates is quantitatively analyzed.

Peridynamic investigation of dynamic brittle fracture

AbstractIn this study, we investigate the dynamic fracture process in amorphous brittle materials using 3D peridynamic analyses of dynamic crack propagation in PMMA plates subjected to quasi‐static loads. This loading condition allows one to assume, that the crack will accelerate to a steady‐state velocity and will continue propagating straight forward at a constant velocity. Dynamic crack instability and its effect on the fracture surface creation as well as the dissipated energy is analyzed numerically for cracks propagating at different velocities. Simulations reproduce many salient features of experimental observations, such as instabilities occurring at the crack tip for cracks propagating above a certain critical velocity. It is shown from the simulations, that increasing crack velocity results in excessively repeated micro‐branching. An increased energy dissipation is also observed at higher crack velocities in the simulations, which correspond to the well known velocity toughening effect. Simulations also reproduce a limiting crack speed, which is below the theoretical limit, i.e. the Rayleigh wave speed.

Cohesive-zone analyses with stochastic effects, illustrated by an example of kinetic crack growth

Cohesive-zone models of fracture are traditionally implemented using a deterministic failure criterion, with crack advance occurring when the work done against crack-tip tractions reaches a critical level. There are, however, many physical phenomena where crack growth is controlled by stochastic events ahead of the crack. These can include kinetic crack growth, stress-corrosion cracking, and void nucleation. In this paper, we show how a cohesive-zone model might be adapted to describe such stochastic phenomena. In particular, we have chosen to model kinetic crack growth by assuming that the probability of local failure, or bond rupture, depends on the difference between the level of local work done against the cohesive tractions and the equilibrium toughness of the interface. We have shown that if the cohesive parameters are within a range appropriate for linear-elastic fracture mechanics (LEFM), and the possibility of failure is limited to the crack tip, then the model accurately reproduces a classical analytical model for kinetic crack growth, with the crack velocity having an exponential relationship with respect to the level of the energy-release rate above a threshold. As with all cohesive-zone models, a transition between toughness-controlled fracture and strength-controlled fracture occurs as the cohesive length is increased. However, it is further noted that if failure is not limited to the crack tip, but is allowed to occur anywhere ahead of the crack tip, then the length scale controlling the crack velocity changes from the mesh size to the cohesive length. This mesh-independent result is associated with diffuse damage ahead of the crack tip. From a physical perspective, such a damage zone could correspond to a situation with a low activation energy for bond rupture, or to one where the a crack grows in response to spatially diffuse stochastic process in a damage zone such as void nucleation, crazing or micro-cracking.