Crack Tip Velocity Research Articles

Sudden deceleration or acceleration of an intersonic shear crack

Sudden jumps in the crack tip velocity were revealed by numerical simulation (in both continuum/cohesive element and molecular dynamics approaches) and experiments for rapid shear cracking. The cracking velocity may accelerate from a sub-Rayleigh speed to the intersonic range, or from an intersonic speed to a higher one, when the reflected impact wave reloads the crack tip. On the other hand, the cracking velocity may decelerate from an intersonic speed to a lower one or recede to the sub-Rayleigh range when the fracture driving force declines. The velocity change encountered during intersonic cracking plays a different role from that in the acceleration or deceleration of a subsonic crack. A crack propagating at an intersonic speed would leave a shear wave trailing behind. When the crack decelerates or accelerates, the effect of the trailing wave will lead to a transition period from one steady-state solution of crack tip singularity to another. This investigation aims at quantifying these processes. The full field solution of an intersonic mode II crack whose speed changed suddenly from one velocity (intersonic or subsonic) to another (intersonic or subsonic) is given in closed form. The solution is facilitated via superposing a series of propagating crack problems that are loaded by dislocations to seal the unwanted crack-face sliding or by concentrated forces moving at various speeds to negate the crack-face traction. In contrast to the subsonic solution, the results in the intersonic case indicate that the elastic fields around the crack tip depend on the deceleration or acceleration history that is traced back over a long time. Singularity matching dictates the jump that may actually take place.

Role of plasticity in heat generation during high rate deformation and fracture of polycarbonate

Abstract The role of plastic deformation in generating heat during dynamic compression and fracture of polycarbonate was examined in a combined experimental and numerical investigation. Split Hopkinson pressure bar (SHPB) experiments and opening mode dynamic fracture experiments were performed to measure the thermomechanical response of polycarbonate at various loading conditions. A companion set of dynamic, thermomechanically coupled explicit finite element simulations of the tested geometries was performed to isolate the temperature increase of the polymer due to plasticity effects only, and these were then compared to the experiments to identify the role of plasticity in the overall heating of the polymer. Temperature measurements during the experiments were made with a remote sensing technique that utilizes the detection of infrared radiation. Polycarbonate was observed to have a rate dependent yield and plastic deformation response under uniaxial compression. For the strain rates tested in the SHPB experiments (400 to 3000 s−1), the fraction of plastic work rate converted to heat was found to be approximately 0.5. The dynamic fracture experiments indicated that the maximum temperature increase in the region surrounding the propagating crack was over 100 K, and the crack tip velocity was limited to approximately 60% of the Rayleigh wave speed. The numerical simulations used the plastic behavior of polycarbonate observed during the compression SHPB experiments as inputs for an incremental plasticity model that uses a rate dependent Mises yield surface and isotropic hardening. Plastic deformation was the only source of material heating in the simulations. Good agreement between the SHPB experiments and the numerical simulations was seen for both stress and temperature during the compression event. Crack growth during the dynamic fracture simulations was imposed by a manual node release technique that duplicated the crack growth speed observed in the experiments. The dynamic fracture simulations which only included the thermoplastic effect significantly under-predicted the temperature increase in the region surrounding the propagating crack. The results indicate that plastic deformation is not the dominating source of heat generation during the dynamic fracture of polycarbonate, it only accounts for about 8% of the measured heating. Additional effects, such as thermofracture coupling, must be considered in the simulations if a more accurate comparison is to be made with experiments.

On the intersonic crack propagation in an orthotropic medium

Motivaded by recent theoretical studies the elastodynamic response of an orthotropic material with a semi-infinite line crack, which propagates intersonically. is revisited through an approach which differs from those used in previous studies. The near tip stress and displacement fields are obtained for Mode I and Mode II of steady state crack propagation. The strain energy release rate analysis confirms that the Mode I is physically impossible due to the order of stress singularity, which is larger then one half. For Model II the order of stress is less than one half and it is shown that a steady state intersonic propagation is allowed only for a particular crack tip velocity which is a function of the material orthotropy.

Intersonic Crack Propagation—Part I: The Fundamental Solution

Recent experiments of Rosakis et al. have clearly shown that the crack-tip velocity can exceed the shear wave speed for a crack tip propagating between two weakly bonded, identical and isotropic solids under shear-dominated loading. This has motivated recent theoretical and numerical studies on intersonic crack propagation. We have obtained analytically the fundamental solution for mode-II intersonic crack propagation in this paper. This fundamental solution can provide the general solutions for intersonic crack propagation under arbitrarily initial equilibrium fields. We have also developed a cohesive zone model to determine the crack-tip energy release for an intersonic shear crack.

Cessation of environmentally-assisted cracking in a low-alloy steel: experimental results

The presence of dissolved metallurgical sulfides in pressure vessel and piping steels has been linked to environmentally-assisted cracking (EAC), a phenomenon observed in laboratory tests that results in fatigue crack growth rates as high as 100 times that in air. Previous experimental and analytical work based on diffusion as the mass transport process has shown that surface cracks that are initially clean of sulfides will not initiate EAC in most applications. This is because the average crack tip velocity would not be sufficiently high to expose enough metallurgical sulfides per unit time and produce the sulfide concentration required for EAC. However, there is a potential concern for the case of a relatively large embedded crack breaking through to the wetted surface. Such a crack would not be initially clean of sulfides, and EAC could initiate. Previous experiments have suggested that under some conditions, EAC could be persistent. This paper presents the results of a series of experiments conducted on two heats of an EAC susceptible, high-sulfur, low-alloy steel in 243°C low-oxygen water to further study the phenomenon of EAC persistence at low crack tip velocities. A load cycle profile that incorporated a significant load dwell period at minimum load was used. Experiments using compact tension specimens with various initial precrack depths were employed to simulate the breakthrough of embedded cracks. The results showed that EAC ceased after several hundred hours of cycling. This indicates that significant dwell periods can allow sufficient time for sulfur diffusion to turn off EAC provided that the initial crack tip velocities are not unusually high.

Acoustic emission and dynamic energy release rate for steady growth of a tunneling crack in a plate in tension

The dynamic steady state growth of tunneling cracks in membrane loaded isotropic Kirchhoff plates is considered. Explicit solutions for the asymptotic displacement and velocity fields are presented. It is shown that the asymptotic fields are inversely proportional to the square root of distance from the crack tip, and that a wake may or may not develop behind the crack tip depending on the static membrane state. If the crack tip velocity is smaller than a certain critical velocity, the asymptotic solution will completely vanish. An explicit solution for the dynamic energy release rate is also presented. Due to elastic waves radiated from the crack tip, the dynamic energy release rate will generally be smaller than the corresponding static energy release rate.

Crack propagation in solids and crack-surface roughness

It is seen from extensive computer simulation results and some experimental observations that for inhomogenous solids with moving cracks, the surface roughness exponent ζ crosses over from a low value ζ∼0.42 to a higher value ζ∼0.8, as the crack-tip velocity increases above a certain threshold. In this paper we extend a simple phenomenological model and a scaling analysis for the growth of crack surfaces in inhomogenous solids by introducing explicitly the effects of the stress rate. We find that the stress rate is indeed a relevant parameter and its consideration leads to a qualitative understanding of the phenomena described above.

Analysis of intersonic crack growth in unidirectional fiber-reinforced composites

Recent experiments on dynamic fracture of unidirectional fiber-reinforced graphite/epoxy composite materials showed that, in Mode I, the crack tip velocity could never exceed the shear wave speed, while the crack tip velocity in Mode II not only exceeded the shear wave speed but also approached a stable velocity at which the crack grew for a substantial period of time in experiments. The experimentally obtained fringe patterns also clearly showed the existence of shear shock waves when the crack tip velocity exceeded the shear wave speed. In the present study, we have obtained the asymptotic fields near an intersonically propagating crack tip. It is shown that Mode-I intersonic crack propagation is impossible because the crack tip energy release rate supplied by the elastic asymptotic field is negative and unbounded, which is physically unacceptable since a propagating crack tip cannot radiate out energy. For Mode II, however, it is established that there exists a single crack tip velocity (higher than the shear wave speed) that gives a finite and positive crack tip energy release rate. At all other intersonic crack tip speeds the energy release rate supplied by the elastic asymptotic field is identically zero. This critical crack tip velocity agrees well with the stable crack tip velocity observed in experiments. The synthetically obtained fringe patterns based on the asymptotic field also agree with experimentally obtained fringe patterns, particularly on the existence of the shock waves.

Fracture of polymers

I present a model study of brittle fracture of polymers. I show that the relation v=v(F) between the crack-tip velocity v and the driving force F exhibit discontinuous transitions and hysteresis. For short polymers, at the onset of crack propagation the polymer chains separate by pulling out the molecular chains, while a discontinuous transition to a new state of rapid crack motion occurs at higher driving force, where the polymer chains break. In contrast to earlier atomistic studies of crack motion involving brittle materials such as silicon, for short polymers we find (at zero temperature) that the onset of crack motion is continuous, i.e., the crack-tip velocity v increases continuously from zero when F is increased above the critical value Fc necessary for starting crack motion. The difference is attributed to inertia, which is less important during pull-out of the molecular chains, than in models where the crack motion involves breaking strong short-ranged bonds. I also present a detailed study of the polymer chain pull-out process.

Model Study of Brittle Fracture of Polymers

I present a model study of brittle fracture of polymers. I show that the relation $v\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}v(F)$ between the crack-tip velocity $v$ and the driving force $F$ exhibits discontinuous transitions and hysteresis. For short polymers, at the onset of crack propagation, the polymer chains separate by pulling out the molecular chains, while a discontinuous transition to a new state of rapid crack motion occurs at a higher driving force, where the polymer chains break.

Opening-mode dominated crack growth along inclined interfaces: Experimental observations

This experimental study investigates the dynamic decohesion of inclined interfaces between aluminum and a polymeric material PSM-1. Two lead azide explosive charges are detonated to initiate dynamic loading in a specially designed bimaterial specimen. The dynamic loading results in crack initiation, propagation and arrest in the same experiment. Photoelasticity, in conjunction with high-speed photography, is used to observe the dynamic event. Dynamic complex stress intensity factor and the energy release rate histories are obtained using the available steady-state singular stress field equations. The dependence of the dynamic initiation and arrest toughness on the mixity under dynamic loading is also investigated. Mixity at crack initiation is controlled by the inclination of the interface. The results show that the initiation toughness is higher than the arrest toughness by about 21%. Based on the experimental observations, a dynamic fracture criterion for subsonic crack growth along the bimaterial interfaces is proposed. According to this criterion, the displacement at a point behind the crack tip varies exponentially with the crack-tip velocity (0 < v < cs; where cs is the shear wave speed of the compliant material). This criterion establishes a generalized relationship between the dynamic energy release rate and the instantaneous crack-tip velocity.

Intersonic crack propagation along interfaces: Experimental observations and analysis

The isochromatic fringe patterns surrounding an intersonically propagating interface crack are developed and characterized using the recently developed stress field equations. A parametric investigation is conducted to study the influence of various parameters such as the crack-tip velocity and the contact coefficient on the isochromatic fringe patterns. It has been observed that the crack-tip velocity has a significant effect on the size and shape of isochromatic fringe patterns. The contact coefficient, on the other hand, does not affect the fringe pattern significantly. The paper also presents a numerical scheme to extract various parameters of interest such as the series coefficients of the stress field, the contact coefficient and the dissipation energy. The results show that the crack growth is highly unstable in the intersonic regime, and the energy dissipation decreases monotonically with increasing crack-tip velocity. The experimental data fit well with the recently proposed fracture criterion for intersonic interfacial fracture.

Dynamic Fracture Criteria for Crack Growth Along Bimaterial Interfaces

Dynamic fracture criteria based on experimental observations are proposed for subsonic crack growth along bimaterial interfaces. These criteria are based on the premise that the crack-face displacements at a point behind the crack tip increase exponentially with the instantaneous crack-tip velocity. This assumption establishes a generalized relationship between the dynamic energy release rate and the instanta-neous crack-tip velocity. Experiments are performed on PSM-1/aluminum bimaterial systems for both shear dominated and opening-mode dominated crack growth to verify the proposed criteria. Two different bimaterial specimen geometries are employed to obtain the complete range of crack-tip speeds in the subsonic regime. The dynamic loading is achieved either by detonating two explosive charges on the specimen or by impacting the specimen in one-point bend configuration. Dynamic photoelasticity in conjunction with high-speed photography is used to analyze the fracture event. Explosive loading of the interface crack results in crack propagation speeds on the order of 65 percent of the shear wave speed of PSM-1 and the crack growth is observed to be stable and opening-mode dominated. In contrast, the impact loading results in very high crack propagation speeds on the order of shear wave speed of PSM-1 and the crack growth is observed to be shear dominated.

Identifying failure mechanisms of composite structures under compressive load

Various failure mechanisms involving both local and global deformation mechanisms of layered structures, consisting of differently oriented orthotropic laminae, are investigated with a large deformation finite element analysis. Under large compressive loads, fiber-reinforced composite structures can fail by buckling, kink band formation and/or delamination growth. Our aim is to identify the dominant mode which leads to the structural failure under a given boundary condition and geometrical shape. It is assumed that these structures contain initial interlaminar flaws represented by embedded delaminations. Such flaws can play a significant role in defining overall structural integrity and deformation mechanisms. Our study considers two structures with distinguished shapes, both consisting of four layer laminae. The first structure is a flat panel under compressive load and the second structure is a cylindrical shell subjected to external pressure. In both cases, the energy release rate and mixed-mode stress intensity factors are computed to quantify the crack driving force and used to measure likelihood of delamination growth. In the flat panel model, two buckling modes, a global and a local, are observed under quasi-static loading conditions. Depending upon the delamination length and laminate stacking orientations, the interaction of these two modes can produce an unstable post-buckling behavior. It is found that the energy release rate exceeds experimentally estimated fracture toughness values only after buckling occurs. In the cylindrical shell study, lower critical buckling loads are observed for models with longer interlaminar delamination as in the flat panel model. However, unlike the flat panel case, the energy release rate surpasses the critical toughness well before the applied pressure reaches the buckling load of the flawed cylindrical shell. This behavior implies that a shell containing an embedded defect along an interface can fail by delamination growth and therefore has a failure load lower than its critical buckling load. Also, for thicker cylindrical shells, the compressive internal stress exceeds the predicted stress required for kink band formation prior to structural buckling. The competition among these failure modes, buckling, delamination growth and compressive kinking in fiber-reinforced composite structures, is studied and a design diagram is introduced here. This diagram predicts a likely dominant failure mode for given structural dimensions and material properties. In addition, unstable delamination growth along the lamina interface under dynamic loading conditions is simulated using an iterative computational procedure. The results predict that the crack tip velocity can reach a fraction of the material wave speed leading to total structural failure in a very short time. For the cylindrical shell, the inertial effect on the pressure-deformation relation is investigated by comparing it with the static results.

Crack dynamics and crack surfaces in elastic beam lattices

The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as ${t}^{1/7}.$ At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a ``mirror-mist-mirror'' crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the ``mirror-mist-hackle''--type interface typical in many experimental situations.

Plane Stress Crack Tip Field Around a Rapidly Growing Ductile/Rigid Interface Crack

Plane stress dynamic crack growth along a ductile/rigid interface is investigated. The ductile material is taken to be ideally plastic and obey the J2 flow theory of plasticity. Under steady-state conditions, the asymptotic structure of the crack-tip stress, velocity and strain fields has been obtained. The study reveals that two types of crack-tip sectors exist, namely uniform and nonuniform plastic sectors and that the stress, strain and velocity fields are bounded (nonsingular) in all sectors. In a uniform sector, the rectangular Cartesian components of the stress, strain and velocity fields are constant, and there is no plastic strain accumulation. In a nonuniform sector, the stress, strain and velocity components at a point depend on the angular position of the point in the crack-tip polar coordinate system and are governed by a system of simultaneous ordinary differential equations. This is a sector plastic strains can accumulate. A general crack-tip sector assembly is obtained for a practical range of crack growth speeds. Several nontrivial families of admissible solutions of the crack-tip fields based on this general assembly of uniform and nonuniform crack-tip sectors are presented and discussed.

Numerical simulations of a dynamically propagating crack with a nonlinear cohesive zone

Numerical solutions of a dynamic crack propagation problem are presented. Specifically, a mode III semi-infinite crack is assumed to be moving in an unbounded homogeneous linear elastic continuum while the crack tip consists of a nonlinear cohesive (or failure) zone. The numerical results are obtained via a novel semi-analytical technique based on complex variables and integral transforms. The relation between the properties of the failure zone and the resulting crack growth regime are investigated for several rate independent as well as rate dependent cohesive zone models. Based on obtained results, an hypothesis is formulated to explain the origin of the crack tip velocity periodic fluctuations that have been detected in recent dynamic crack propagation experiments.

A study of dynamic crack growth in elastic materials using a cohesive zone model

The problem of a semi-infinite mode III crack dynamically propagating in a two-dimensional linear elastic infinite body is considered. The crack tip is assumed to be a cohesive zone whose (finite) size is determined so as to cancel the classical crack tip stress singularity caused by the applied loads. The cohesive zone behavior is assumed rate dependent and is characterized by a thermodynamically based constitutive equation. A new semi-analytical solution method has been formulated to solve the resulting initial value problem. The proposed solution method offers the capability to analyze the entire crack growth phenomenon (acceleration-steady state-arrest), without requiring special assumptions, neither on the crack propagation mode (e.g. steady state or assigned crack tip velocity), nor on the space-time discretization, so to obtain solutions that are not affected by grid size effects. Several solutions, corresponding to various values of the initial and boundary conditions as well as cohesive zone constitutive properties, are presented and analyzed.

A FINITE ELEMENT TECHNIQUE TO SIMULATE THE STABLE SHAPE EVOLUTION OF PLANAR CRACKS WITH AN APPLICATION TO A SEMI-ELLIPTICAL SURFACE CRACK IN A BIMATERIAL FINITE SOLID

This paper describes a numerical procedure to model the crack front evolution of initially arbitrary shaped planar cracks in a three-dimensional solid. The influence of a bimaterial interface on the fracture path of a semi-elliptical surface crack in a three-dimensional structure is examined. The analysis is based on the assumption that fracture is controlled by small-scale yielding and linear elastic fracture mechanics. The finite element method and the crack-tip contour J-integral in a volume domain representation are utilized to calculate the crack front energy release rate. The computed values of the energy release rate are used with a crack-tip velocity growth law to model crack growth increment. The progress of the crack growth evolution is brought forward by successive iterations. Examples of computed crack evolution are given for an embedded circular crack, a semi-elliptical surface crack in a finite plate, and a configuration that defines an isotropic homogeneous material layer with a surface crack located between two material layers. © 1997 by John Wiley & Sons, Ltd.

Elastodynamic parameters for dynamic interface fracture mechanics

Dynamic extension of cracks running along curvilinear interfaces of brittle bimaterials subjected to mechanical crack surface loads and superimposed thermal strains acting along the ligament is considered. This paper especially addresses the provision and discussion of elastodynamic interface parameters in order to assess quantitatively the bimaterial fracture in view of the governing physical features: applied mechanical and thermal strain loading, existence of an interface, crack-tip velocity and curvature of the interface contour. By utilizing the linear theory of thermoelasticity and adopting Stroh's method of generalized complex potentials, from the corresponding boundary and continuity conditions vectorial Hilbert problems are derived. It is shown that the parameters of the eigenvalues and of the eigenvectors of the Hilbert problems can be interpreted as elastodynamic interface mechanics parameters reading (β,vp, β Hf , μ Hf ). Generalized Dundurs parameters of dynamics (α, β) and consequently an associated generalized Dundurs diagram of dynamics are proposed. While the aforementioned elastodynamic interface parameters (α, β,vp, β Hf , μ Hf ) do not assume the interface to be damaged, interfaces with running interface cracks generally cause two additional interface parameters, denoted as bimaterial constants (e, α Hf ), where the latter is specific to the curvature of the interface in conjunction with the velocity of the interface crack. However, the bimaterial constants (e, α Hf ) can be traced back to interface parameters for an uncracked bimaterial, namely to (β, β Hf ).