Effect of reflected stress waves on the stress intensity factor of an anti-plane strain edge crack during crack propagation and after crack arrest

Current theories of dynamic fracture are based on elastodynamic analyses of mathematically sharp plane cracks and as such do not explain the observed terminal velocities or the phenomenon of crack branching satisfactorily. The present investigation addresses the above problems by using both microscopic and macroscopic interpretations. The experimental scheme that is used in this investigation is the configuration of a pressure loaded semi-infinite crack in an infinite medium. The loading is achieved through an electromagnetic device which provides highly repeatable loading. The method of caustics is used in conjunction with a high speed camera to obtain the time histories of the crack tip stress intensity factor and the crack position. The problems of crack initiation and crack arrest are explored. The stress intensity factor at initiation is found to be independent of the rate of applied loading when the latter is below about 104MPA/sec, but the initiation stress intensity factor increases considerably when the loading rate is increased further. Crack arrest is obtained in large specimen by using very low energy loading pulses. It was found that the stress intensity factor at crack arrest was constant and also that, within the time resolution of the high speed camera (5 μsec), the crack comes to a stop abruptly. The crack propagation and branching aspects were investigated first using post-mortem analysis of the fracture surfaces and high speed photomicrography to get an idea of the microscopic processes that occur in the fracure process. From this investigation, it was found that crack propagation involving high stress intensity factor and high velocity situations takes place by the growth and interaction of microcracks, due to the voids present in the material. A surprising result of this investigation was that cracks propagated at a constant velocity, although the stress intensity factor varied. Current theories of dynamic fracture cannot explain such behaviour. The crack branching process was found to be a continuous process arising out of propagation along a straight line. High speed photomicrographs of the branching process indicated the presence of a number of part-through attempted branches that interact with one another and finally the successful emergence of a few full fledged branches. The microscopic observations on the crack propagation and branching process leads to a new interpretation of dynamic fracture that attempts to qualitatively explain the constancy of the velocity of propagation, the terminal velocity and crack branching. The crack branching mechanism is a logical continuation of the mechanism for crack propagation.

Characterizing dynamic crack-tip stress distribution and evolution under blast gases and reflected stress waves by caustics method

In this paper, the problem of a functionally graded piezoelectric material (FGPM) with a constant–velocity Yoffe–type moving crack is considered. The strip is assumed to be under an anti–plane mechanical loading and an in–plane electric loading and its material properties, such as the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density, are assumed to vary continuously along the thickness of the strip. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. The closed forms of the singular stress, electric field and electric displacement are obtained from the asymptotic expansion of the stresses and electric fields around the crack tip. Different from the case of a stationary crack in an FGPM, it is found that at the tip of the crack the electric field also exhibits the singularity of the inverse square root, along with the stress and electric displacement singularities. It is also observed that increasing the gradient of the material properties can reduce the magnitudes of the stress and electric displacement intensity factors but it has little effect on the electric field intensity factor. When the crack moving velocity increases, both the stress and the electric displacement intensity factors decrease but the electric field intensity factor increases.

In order to seek a more reasonable dynamic theory for fast fracture and crack arrest, the authors carried out a dynamic fracture mechanics analysis with the use of finite difference method and revealed that the method is a useful tool to analyze the crack propagation and arrest as reported in the previous paper.This report describes the results of an experimental investigation using polymethylmethacrylate (PMMA) and is a preliminary report on the study of dynamic aspects of brittle crack propagation and arrest in structural steels. Using dynamically measured data in the experiment as the boundary condition for finite difference method, mechanism of fast crack propagation and arrest in PMMA was analyzed by energetics considerations. As one of the most interesting results, a particular relation between dynamic fracture toughness and crack velocity was obtained, i. e. crack acceleration and crack deceleration followed two different curves and the crack arrest stress intensity factor was found to be substantially lower than the critical stress intensity factor for crack initiation.Further studies on the crack arrest phenomenon in structural steels using the procedure described in this paper should be conducted in the near future.

Mechanics of crack initiation, propagation and crack grain boundary interaction in bicrystal silicon using near-tip localized stress calculation

This paper presents the roles of slanted cracks on the stress intensity factors (SIF) under mode I tension and bending loading. Based on the literature survey, lack of solution of SIFs of slanted cracks in plain strain plates are available. In this work, the cracks are modelled numerically using ANSYS finite element program. There are two important parameters such as slanted angles and relative crack length. SIFs at the crack tips are calculated according to domain integral method. Before the model is further used, it is validated with the existing model. It is found that the present model is well agreed with the previous model. According to finite element analysis, there are not only mode I SIFs produced but also mode II. As expected the SIFs increased as the relative crack length increased. However, when slanted angles are introduced (slightly higher than normal crack), the SIFs increased. Once the angles are further increased, the SIFs decreased gradually however they are still higher than the SIFs of normal cracks. For mode II SIFs, higher the slanted angels higher the SIFs. This is due to the fact that when the cracks are slanted, the cracked plates are not only failed due to mode I but a combination between both modes I and II.

Effects of vertical and horizontal reflected blast stress waves on running cracks by caustics method

A model for simulating brittle crack propagation and arrest in steel plates is presented. The model considers the influence of shear lips formed on a fracture surface acting as a crack closure force and the influence of the loss of the plane-strain condition at a propagating crack tip with an increasing dynamic stress intensity factor. The shear lips are assumed not to fracture during the test, so they will yield and provide a crack closure force. The crack closure effect depends on not only the stress intensity factor but also the crack velocity. The model was applied to temperature-gradient crack-arrest tests and ultrawide duplex crack-arrest tests. The model successfully explained anomalous crack-arrest toughness under excessively high applied stress in the temperature-gradient tests and crack arrest at a stress intensity factor far above the cleavage crack-arrest toughness in the ultrawide duplex tests.

Axisymmetric Slipless Indentation of an Infinite, Elastic Cylinder

Design and analysis procedures which include dynamic crack propagation and crack arrest are currently under development in order to assure the safety of such structures as nuclear pressure vessels. This type of design and analysis procedure requires a knowledge of the relationship of stress intensity factor (K) as a function of crack speed (å). The minimum value of stress intensity factor (designated as KIm) on the K versus å relationship is of particular importance because crack arrest will occur if the stress intensity factor falls below this minimum value. Direct determination of the K versus å relationship and of the value of KIm for pressure vessel grade steels is an extremely difficult and complex task. For this reason methods have been developed to approximate KIm values. One such method was developed by Battelle Columbus Laboratory (BCL) and another by Materials Research Laboratory in Chicago. One difficulty involved in an analysis of dynamic crack propagation and arrest is the interaction of the specimen and loading system, and its effect on crack behavior. This paper describes a series of experiments conducted to determine the influence of loading system on crack jump length and stress intensity as a function of velocity. Rectangular double-cantilever models made from Homalite 100, a birefringent polymer, were tested with two different wedge loading systems. One system used steel loading pins and aluminum wedge. The second system used both plastic pins and plastic wedge. A Cranz-Schardin high speed camera was used to photograph isochromatic fringe patterns associated with propagating and arrested cracks. Dynamic stress intensity factors were determined from the isochromatic fringe loops using a three-parameter Westergaard stress function. The high speed photographs also were used to determine crack length as a function of time. From this relationship the crack velocity was determined. The results were compared with the predictions of a one dimensional finite difference computer code written by BCL. The crack jump for the models loaded with the plastic pins and wedge was found to be about twice the crack jump for the models loaded by metal pins and wedge for the same initial pin displacement. The amount of energy stored in pin contact stress was computed and when this additional energy was added to the computer input it was found that the proper crack length as a function of time was predicted by the BCL code.

Influence of compressive stress on stress intensity factor of hole-edge crack by high strain rate laser shock processing

Stress intensity factors for asymmetric branched cracks in plane extension by using crack-tip displacement discontinuity elements

An unresolved question in fracture mechanics is whether the variations in the size or aspect-ratio of cracked plates or structures have a significant effect on the stress intensity factor (SIF) at the crack tip. Indeed, there are significant numerical data showing the effect of specimen aspect-ratio on SIF. There is also experimental evidence supporting the existence of the size effect on fatigue and fracture behavior. However, there is no analytical formula to capture such a size effect on the stress intensity factor for standard fracture mechanics crack configurations. In this study, a novel net-section-based approach is used to develop simple and approximate SIF expressions for center and edge cracks in tension plates of various aspect ratios. Expressions have been derived for both uniform stress as well as uniform displacement boundary conditions. Comparisons are made with the available numerical stress intensity factor data. A remarkable agreement of the net-section-based SIF expressions with the numerical data (complex potential, finite element, and variational approaches) is found. For the clamped-end condition, the net-section approach leads to Rice's limiting SIF for a semi-infinite crack in an infinitely wide strip, validating the analysis. Additionally, the SIF expressions developed here also highlight some discrepancies in numerical data. The study provides simple SIF expressions that can be readily used to analyze specimen size or aspect-ratio effects on critical values of stress intensity factors for cracks in materials and structures under tension loading.

The objective of the present research is to build a modeling method for delayed hydride cracking (DHC) of zirconium alloys. DHC tests were carried out on Zircaloy-2 cladding tubes in the chamber of a scanning electron microscope to directly observe the crack propagation and measure the crack velocity in the radial direction. These in situ observations showed that a sharply tipped crack propagated at a relatively high rate, while the velocity decreased when the crack tip was blunted, supporting the occurrence of intermittent crack propagation that could be expected from the DHC mechanism. V-KI curves or diagrams of crack velocity, V, versus stress intensity factor at a crack tip, KI, were obtained as a function of 0.2 % offset yield stress, hydride orientation, and pre-crack depth. The steady state crack velocity and the threshold stress intensity factor for the onset of the crack propagation tended to increase or decrease, respectively, with an increase in the 0.2 % offset yield stress. Analyses of stress distribution and hydrogen diffusion around a crack tip were made using a finite element computer code. The analyses showed that a strong hydrostatic pressure field was generated concentrically around the crack tip and hydrogen diffused towards the crack tip according to the hydrostatic pressure gradient. The crack velocity was estimated from the calculated hydrogen flux rate assuming the critical hydrogen quantity for the crack propagation. There was good agreement between the experiments and the calculations regarding the crack velocity and its dependency on KI. Calculations showed that the increase in the 0.2 % offset yield stress would accelerate the crack propagation by increasing the hydrostatic pressure at the crack tip.

The objective of the present research is to build a modeling method for delayed hydride cracking (DHC) of zirconium alloys. DHC tests were carried out on Zircaloy-2 cladding tubes in the chamber of a scanning electron microscope to directly observe the crack propagation and measure the crack velocity in the radial direction. These in situ observations showed that a sharply tipped crack propagated at a relatively high rate, while the velocity decreased when the crack tip was blunted, supporting the occur-rence of intermittent crack propagation that could be expected from the DHC mechanism. V-KI curves or diagrams of crack velocity, V, versus stress intensity factor at a crack tip, KI, were obtained as a function of 0.2 % offset yield stress, hydride orientation, and pre-crack depth. The steady state crack velocity and the threshold stress intensity factor for the onset of the crack propagation tended to increase or decrease, respectively, with an increase in the 0.2 % offset yield stress. Analyses of stress distribution and hydrogen diffusion around a crack tip were made using a finite element computer code. The analyses showed that a strong hydrostatic pressure field was generated concentrically around the crack tip and hydrogen diffused towards the crack tip according to the hydrostatic pressure gradient. The crack velocity was estimated from the calculated hydrogen flux rate assuming the critical hydrogen quantity for the crack propagation. There was good agreement between the experiments and the calculations regarding the crack velocity and its dependency on KI. Calculations showed that the increase in the 0.2 % offset yield stress would accelerate the crack propagation by increasing the hydro-static pressure at the crack tip.