Crack Propagation Speed Research Articles

Moving eccentric crack in a piezoelectric strip bonded to elastic half planes

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip which contains an eccentric crack moving at constant speed. The strip is sandwiched between two elastic half planes under combined anti-plane mechanical shear and in-plane electrical loadings. The analysis is conducted on the permeable crack condition by the integral transform approach. The field intensity factors and energy release rate are obtained in terms of a Fredholm integral equation of the second kind. Some numerical results for the dynamic stress intensity factor and the dynamic energy release rate are presented graphically to show the effects of the crack propagation speed as well as the electromechanical coupling coefficient. The initial crack branch angle for a PZT-5H piezoceramic structure is also predicted by maximum energy release rate criterion.

On the dynamic propagation of a finite crack in functionally graded materials

This article provides a comprehensive theoretical investigation of the singular behaviour of a propagating crack in a functionally graded material (FGM) with spatially varying elastic properties under plane elastic deformation. The analytical formulations are developed in terms of Fourier transforms and the solution of the resulting singular integral equations by using Chebyshev polynomials. In this study, we examine the effect of the gradient of material properties and the speed of crack propagation upon the stress intensity factors, the strain energy release rate and the crack opening displacement. The results reveal that although the singular stress field around the tip of a crack in this FGM is governed by the traditional square root singularity, significant discrepancy in the local stress field exist between it and a homogeneous solid. This indicates that the presence of a gradient in the mechanical properties affects the local stress distribution significantly and, ultimately, the fracture behaviour of the solid.

Moving eccentric crack in a piezoelectric strip bonded to elastic materials

The steady-state of a propagation eccentric crack in a piezoelectric ceramic strip bonded between two elastic materials under combined anti-plane mechanical shear and in-plane electrical loadings is considered in this paper. The analysis based on the integral transform approach is conducted on the permeable crack condition. Field intensity factors and energy release rate are obtained in terms of a Fredholm integral equation of the second kind. It is shown for this geometry that the crack propagation speed has influence on the dynamic energy release rate. The initial crack branching angle for a PZT-5H piezoceramic structure is predicted by the maximum energy release rate criterion.

Yoffe-type moving edge crack in a piezoelectric block

We consider an anti-plane edge moving crack problem with the constant velocity in a piezoelectric ceramic block. The far-field anti-plane shear mechanical and in-plane electrical loads are applied to the piezoelectric block. It is expressed to a Fredholm integral equation of the second kind. Expressions for the dynamic field intensity factors and the dynamic energy release rate are obtained. The dynamic stress intensity factor and the dynamic energy release rate depend on the crack propagation speed. Numerical results for several piezoelectric materials are also presented.

Kinetics of adherence of a rigid truncated cone on an elastic half-space (unfilled natural rubber)

The equilibrium contact of a rigid flat-ended cone, applied against the flat and smooth surface of a soft elastomer sample (unfilled natural rubber), is studied with the help of fracture mechanics concepts, which can be easily introduced in this class of problems by using Sneddon's solution (Int. J. Eng. Sci. 3 (1965) 47) of Boussinesq's problem extended to all axisymmetric adhesive punches with a convex profile. The kinetics of adherence is measured when an imposed tensile force is applied in order to disturb the size of the contact area. Variations of the strain energy release rate G and of the associated dissipation function Φ=( G− w)/ w, where w is the Dupré energy of adhesion, are studied as a function of the crack propagation speed V at the interface between a truncated cone made of PMMA and the rubber sample (the limit of the contact is considered as a crack tip). As expected, a master curve Φ( V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established by Barquins et al. in adherence of a perfect cone and flat-ended spheres in pull-off/push-on tests, adherence and rolling of cylinders experiments and rebound of balls tests, with the same elastic rubber-like material.

球状黒鉛鋳鉄の疲労き裂進展特性に及ぼす試験片板厚の影響

In order to clarify the influence of the thickness of specimen on the fatigue crack propagation properties in spherical graphite cast iron, fatigue crack propagation test was carried. Spherical graphite cast iron (FCD450) was used as specimen material. Therefore, this material was conducted two kind of heat treatment process. One is the austemper treatment (ADI) and another is quenching and tempering (QT). As-cast material is added to those, and three kinds of materials are used for the experiment. The fatigue crack propagation test is carried out on the stress ratio R at 0.05 in the room temperature. The specimen is used 1CT type fatigue specimen, which followed ASTM Standard. The thickness of specimens are 12.5mm, 8mm and 4mm·And, it is investigated the correlation between the fatigue crack propagation and measured crack closure of each specimen. The obtained results are as follows:(1) The influence of the thickness specimen is caused from threshold stress intensity factor range, ΔKth to II a stage. The crack propagation speed increase, as the thickness of specimen is less, and ΔKth is lowers.(2) The results of various thickness of specimen agree well in da/dN-ΔKeff curve. Therefore, the influence of the thickness of specimen is mainly depended on the crack closure. The difference of crack closure with thickness is not depended on graphite or fracture surface roughness. It is influenced by the presence of the oxide on fracture surface.(3) It will be cosidered that crack tip shape is influenced on the thickness of specimen.

Adhésion et cinétique de décollement d'un cône rigide tronqué en contact avec un élastomère souple

The equilibrium contact and the kinetics of adherence, at an imposed applied load, of a rigid flat-ended cone in contact with the flat and smooth surface of a soft elastomer sample (unfilled natural rubber) are examined with the help of fracture mechanics concepts. The variation of the dissipation function Φ=( G− w)/ w, where G is the strain energy release rate and w the Dupré energy of adhesion, is studied as a function of the crack propagation speed V at the interface between the flat-ended rigid cone and the elastic solid. As expected, a master curve Φ( V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established by Barquins et al. in adherence experiments, with the same rubber-like material. To cite this article: S. Bouissou, M. Barquins, C. R. Physique 3 (2002) 239–245.

Adhesive contact and kinetics of adherence of a rigid conical punch on an elastic half-space (natural rubber)

The equilibrium contact of a rigid conical punch, applied against the flat and smooth surface of a soft elastomer sample (unfilled natural rubber), is studied with the help of fracture mechanics concepts which can be easily introduced in this class of problems by using Sneddon's solution (Int. J. Eng. Sci. 3 (1965) p.47) of Boussinesq's problem extended to all axisymmetric adhesive punches with a convex profile as a cone. The kinetics of adherence is measured when an imposed tensile force is applied in order to disturb the size of the contact area. Variations of the strain energy release rate G and of the associated dissipation function Φ=( G− w)/ w, where w is the Dupré energy of adhesion, are studied as a function of the crack propagation speed V at the interface between a cone made of plexiglass (PMMA) and the rubber sample (the limit of the contact is considered as a crack tip). As expected, a master curve Φ( V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established by Barquins et al. in adherence of flat-ended spheres in pull-off/push-on tests, adherence and rolling of cylinders experiments and rebound of balls tests, with the same elastic rubber-like material.

Constant moving crack in a piezoelectric block: anti-plane problem

The problem of an anti-plane Griffith moving crack in a rectangular piezoelectric ceramic block is solved by integral transform technique under the condition of continuous permeable electric crack faces. The far-field anti-plane shear mechanical and in-plane electrical loads are applied to the piezoelectric block. It is expressed as a Fredholm integral equation of the second kind. Expressions for the dynamic field intensity factors and the dynamic energy release rate are obtained. The dynamic stress intensity factor and the dynamic energy release rate depend on the crack propagation speed. Based on the criterion of maximum energy release rate, the propagation orientation of a crack moving at constant speed is predicted. Numerical results for PZT-5H piezoelectric ceramic are also presented by graphical representations.

Thermomechanical Behavior of Thermoviscoelastic Solid during Dynamic Crack Propagation

The constitutive relations of the thermoviscoelasticity are rigorously formulated, and the corresponding finite-element equations are derived. Due to the second law of thermodynamics, a nonlinear term, which appears in both the energy equation and the Clausius-Duhem inequality, is incorporated in the finite-element equations. This work is focused on the effect of this dissipative energy term on the stress and temperature field of an isotropic thermoviscoelastic solid during dynamic crack propagation through a finite-element analysis. The numerical solutions clearly demonstrate that the temperature elevates on the cracked surface in the wake of the advancing crack tip. This is the consequence of truthfully incorporating the second law of thermodynamics in the analysis of the dynamic process for materials that possess viscosity. Meanwhile, the effect of different crack propagation speeds on the stress and temperature distributions is also investigated.

Adhesive Contact And Kinetics Of Adherence Of A Rigid Conical Punch On An Elastic Half-space (natural Rubber)

Abstract The equilibrium contact of a rigid conical punch, applied against the flat and smooth surface of a soft elastomer sample (unfilled natural rubber), is studied with the help of fracture mechanics concepts which can be easily introduced in this class of problems by using Sneddon's solution (Int. J. Eng. Sci. 3 (1965) p.47) of Boussinesq's problem extended to all axisymmetric adhesive punches with a convex profile as a cone. The kinetics of adherence is measured when an imposed tensile force is applied in order to disturb the size of the contact area. Variations of the strain energy release rate G and of the associated dissipation function Φ =( G − w )/ w , where w is the Dupre energy of adhesion, are studied as a function of the crack propagation speed V at the interface between a cone made of plexiglass (PMMA) and the rubber sample (the limit of the contact is considered as a crack tip). As expected, a master curve Φ ( V ) is found, confirming the variation of Φ as the 0.55 power function of V , as recently established by Barquins et al. in adherence of flat-ended spheres in pull-off/push-on tests, adherence and rolling of cylinders experiments and rebound of balls tests, with the same elastic rubber-like material.

Dynamic delamination fracture toughness in unidirectional polymeric composites

A modified end-notched flexure (ENF) specimen was used to determine Mode-II-dominated dynamic delamination fracture toughness of fiber composites at high crack propagation speeds. A strip of FM-73 adhesive film was placed at the tip of the interlaminar crack created during laminate lay-up. This adhesive film with its greater toughness delayed the onset of crack extension and produced crack propagation at high speeds. Dynamic delamination experiments were performed on these ENF specimens made of unidirectional S2/8553 glass/epoxy and AS4/3501-6 carbon/epoxy composites. Crack speed was measured by means of conductive aluminum lines created by the vapor deposition technique. A finite-element numerical simulation based on the measured crack speed history was performed and the dynamic energy release rate calculated. The results showed that the dynamic fracture toughness is basically equal to the static fracture toughness and is not significantly affected by crack speeds up to 1100 m/s.

Observations of transonic crack velocity at a metal/ceramic interface

A system for measuring the interface crack velocity is presented, and applied to photolithographically-generated 90–100 μm long cracks between a thin (1 μm) Nb strip of 60 μm width and a sapphire substrate. The cracks were loaded using a laser-generated stress wave. The duration of crack advance used for determining the average crack velocity was taken as the time during which the interface tensile stress exceeded that needed for crack initiation. This was numerically calculated using the interferometrically-measured free surface velocity of the sapphire as an input. Equi-spaced Al lines of 200 Å thickness were deposited in front of the crack tip using photolithography and used as markers to determine the total crack advance by viewing the shock-loaded samples in a scanning electron microscope. The maximum crack propagation speed of 11,346 m/s was determined which is close to the dilatational wave speed of 11,090 m/s in the stiffer sapphire along its basal plane axis. These observations are the first report of crack speeds approaching the dilatational wave speed of the stiffer bimaterial component.

Multimillion Atom Simulations of Nanostructured Materials on Parallel Computers

Multiresolution molecular-dynamics approach for multimillion atom simulations has been used to investigate structural properties, mechanical failure in ceramic materials, and atomic-level stresses in nanoscale semiconductor/ceramic mesas (Si/Si3N4). Crack propagation and fracture in silicon nitride, silicon carbide, gallium arsenide, and nanophase ceramics are investigated. We observe a crossover from slow to rapid fracture and a correlation between the speed of crack propagation and morphology of fracture surface. A 100 million atom simulation is carried out to study crack propagation in GaAs. Mechanical failure in the Si/Si3N4 interface is studied by applying tensile strain parallel to the interface. Ten million atom molecular dynamics simulations are performed to determine atomic-level stress distributions in a 54 nm nanopixel on a 0.1 µm silicon substrate. Multimillion atom simulations of oxidation of aluminum nanoclusters and nanoindentation in silicon nitride are also discussed.

Kinetics of adherence of a rigid flat-ended sphere in contact on a soft rubber-like material surface

The equilibrium contact of flat-ended spheres applied against the flat and smooth surface of a soft elastomer sample (unfilled natural rubber) is examined as a function of the size of the flat. As previously shown by Maugis and Barquins, the elastic adherence force increases as the radius of the flat is enlarged. New results on the kinetics of adherence at imposed normal load are presented. They consist of a study of variations of the strain energy release rate G and of the associate dissipation function Φ=( G− w)/ w, where w is the Dupré energy of adhesion, as a function of the crack propagation speed V at the interface between the flat-ended sphere, with global radius R and flat radius a m, and the elastic solid. As expected, a master curve Φ( V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established by Barquins et al. in adherence and rolling of cylinders experiments and rebound of balls tests, with the same rubber-like material.

Cinétique de décollement d'une sphère rigide coupée en contact avec un élastomère souple

The equilibrium contact and the kinetics of adherence of flat-ended spheres, under an imposed applied load, in contact with the flat and smooth surface of a soft elastomer sample (natural rubber) are examined with the help of concepts from fracture mechanics. The variation of the dissipation function Φ = (G − w)/w, where G is the strain energy release rate and w is the Dupré energy of adhesion, is studied as a function of the crack propagation speed V at the interface between the flat-ended sphere and the elastic solid. As expected, a master curve Φ(V) is found, confirming the variation of Φ as the 0.55 power function of V, which Barquins and Charmet established recently in adherence experiments with the same rubber-like material.

État d'équilibre et cinétique de décollement d'un cylindre rigide en contact avec un élastomère souple

The equilibrium contact of a rigid cylinder applied against the flat and smooth surface of a soft elastomer sample (natural rubber) is examined and a method is proposed for evaluating both the Young's modulus E of the rubber-like material tested and the Dupré energy of adhesion w using a presentation of results similar to that recently described by Chaudhury et al. from the previous work of Barquins. New results on the kinetics of adherence at imposed normal load are presented. They consist of a study of variations of the strain energy release rate G and of the associate dissipation function Φ = ( G - w)/w as a function of the crack propagation speed V at the interface between the rigid cylinder and the elastic solid. As expected, a master curve Φ(V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established in rolling and rebound experiments by Barquins and Charmer with the same rubber-like material.

Dynamic Mode-I crack-propagation in a carbon/epoxy composite

A modified DCB specimen has been used to study the dynamic Mode-I delamination fracture toughness of an AS4/3501-6 carbon/epoxy composite at high crack-propagation speeds. A strip of FM-73 adhesive film was placed at the tip of a pre-crack created during laminate lay-up. The adhesive strip substantially increased the crack-initiation toughness so that after initiation an unstable crack-propagation was produced and high crack-propagation speeds were achieved. Specimens were loaded at a constant displacement rate of 0·1mms−1 on an MTS machine. Crack extension was monitored by means of a conductive circuit placed along the path of the propagating crack. Continuous records were obtained for the load, deflection and crack extension. The strain-energy release rate was calculated by using plate finite elements based on the crack-propagation data. It was found that the critical dynamic strain-energy release rate for crack speeds up to 200ms−1 is a constant and is equal to the critical static strain-energy release rate.

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.

Adhesive contact and kinetics of adherence between a rigid cylinder and an elastomeric solid

The equilibrium contact of a rigid cylinder applied against the flat and smooth surface of a soft elastomer sample (natural rubber) is examined, and a method is proposed for evaluating both the Young modulus E of the rubber-like material tested and the Dupré energy of adhesion w using a results similar to that recently proposed by Chaudhury et al. from the previous work of Barquins. New results on the kinetics of adherence at imposed normal load are presented. They comprise a study on variations of the strain energy release rate G and of the associate dissipation function Φ=( G− w)/ w as a function of the crack propagation speed V at the interface between the rigid cylinder and the elastic solid. As expected, a master curve Φ( V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established in rolling and rebound experiments with the same rubber-like material (natural rubber).