An experimental investigation of dynamic crack growth past a stiff inclusion

The mechanics of transient crack growth past stiff inclusions embedded in a relatively compliant matrix are studied optically under stress wave dominant loading conditions. An ultra high-speed rotating mirror-type CCD digital camera is used to record gray scales in the crack–inclusion vicinity at rates of up to 300,000 frames per second and 1000 × 1000 pixel resolution in real time. By analyzing the images before and after deformations, crack-tip deformation histories from the time of impact up to complete fracture are mapped and fracture parameters are extracted. The effects of inclusion–matrix adhesion strengths (weak and strong) and eccentricity of the inclusion relative to the crack path in the crack-tip vicinity are examined. A weakly bonded inclusion attracts and traps a dynamically growing mode-I crack momentarily whereas the same is deflected away by the inclusion if it is bonded strongly to the matrix. As a result, significantly higher re-initiation crack velocities are seen in weakly bonded inclusion cases upon re-initiation when compared to the strongly bonded counterparts. The effective stress intensity factor histories extracted from measured full-field displacements show a spike in values corresponding to higher crack velocities. Further, crack-tip mode-mixities correlate well with crack attraction and deflection mechanisms. The measured surface roughness is found to be consistently higher for weakly bonded inclusion specimens compared to the strongly bonded ones.     

Measurement of transient deformations using digital image correlation method and high-speed photography: application to dynamic fracture

The digital image correlation method is extended to the study of transient deformations such as the one associated with a rapid growth of cracks in materials. A newly introduced rotating mirror type, multichannel digital high-speed camera is used in the investigation. Details of calibrating the imaging system are first described, and the methodology to estimate and correct inherent misalignments in the optical channels are outlined. A series of benchmark experiments are used to determined the accuracy of the measured displacements. A 2%-6% pixel accuracy in displacement measurements is achieved. Subsequently, the method is used to study crack growth in edge cracked beams subjected to impact loading. Decorated speckle patterns in the crack tip vicinity at rates of 225,000 frames per second are registered. Two sets of images are recorded, one before the impact and another after the impact. Using the image correlation algorithms developed for this work, the entire crack tip deformation history, from the time of impact to complete fracture, is mapped. The crack opening displacements are then analyzed to obtain the history of failure characterization parameter, namely, the dynamic stress intensity factor. The measurements are independently verified successfully by a complementary numerical analysis of the problem.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.     

An Experimental Study on the Elastic–Plastic Fracture in a Ductile Material under Mixed-Mode Loading

Abstract:  Stereo vision was used to measure the crack-tip parameters, such as J integral, plastic mixity and elastic mixity of mixed-mode fracture specimens, and to study the applicability of the Shih's plane strain solution to the mixed-mode crack-tip fields. The fracture specimen used in this study was a compact tension shear (CTS) specimen made of 2024-O aluminum. The in-plane strain and stress fields near the mixed-mode crack tip of the CTS specimen were determined using the deformation field measured by the stereo vision. It is observed that the J integral values computed along rectangular contours surrounding the mixed-mode crack-tip approach constant values after r / h  > 0.5. The in-plane strains determined experimentally at several points near the crack tip and at several radial lines emerging from the crack tip are compared with the values calculated using Shih's plane-strain solution and the HRR slope, named after the investigations of Hutchinson, Rice and Rosengren respectively. It is found that the measured values follow the trends of the Shih's plane-strain solution. The elastic mixity evaluated using the measured crack-tip stress fields is close to that obtained from analytical solution. However, the evaluated plastic mixity deviates from the analytical solution.     

Dynamic fracture of graphite/epoxy composites stiffened by buffer strips: An experimental study

Fracture responses of unidirectional graphite/epoxy composite coupons enhanced by buffer strips are investigated under impact loading conditions using digital image correlation technique and high-speed photography. Composite coupons made of phenylethynyl terminated imide oligomer (PETI-5) as matrix and IM7 graphite fiber as reinforcement are studied. Buffer strips are made of the same material but with a different stacking sequence to attain quasi-isotropy. Edge-notched coupons are subjected to impact loading along the axis of symmetry. The effectiveness of methods used for attaching the buffer strip, namely, co-curing at elevated temperatures and adhesive bonding at room temperature, are also examined. The optically measured stress intensity factor histories reveal that both methods provide nearly identical fracture responses. However, the crack initiates much later in coupons stiffened using adhesive bonding method than its co-cured counterpart and thus shows higher stress intensity factor at initiation. The residual stresses are shown to be responsible for the difference in the fracture responses.     

INTERFACIAL CRACK INITIATION UNDER QUASI-STATIC AND DYNAMIC LOADING CONDITIONS: AN EXPERIMENTAL STUDY

Abstract— Interfacial fracture parameters under quasi-static and dynamic loading are examined in a large elastic mismatch bimatenal system. A wide range of remote field loading ratios of shear and tension are considered. The crack tip fields are mapped using the optical method of coherent gradient sensing or CGS and fracture parameters are quantified. Distinctly different crack initiation responses are observed for positive and negative shear stresses acting on the interface. Also, low velocity impact loading experiments are conducted to study the influence of dynamic loading on crack initiation parameters. Dynamic interfacial crack tip fields are recorded using high speed photography and fracture parameters for dynamically loaded stationary cracks are obtained. Measurements suggest significant crack initiation toughness reduction under dynamic loading conditions.     

Determination of crack surface displacements for cracks emanating from a circular hole using weight function method

Cracks emanating from a circular hole are of significant engineering importance, especially in aerospace industry. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue life predictions. The purpose of this paper is to provide an efficient and accurate closed‐form weight function approach to the calculation of crack surface displacements for radial crack(s) emanating from a circular hole in an infinite and finite‐width plate. Results were presented for two loading conditions: remote applied stress and uniform stress segment applied to crack surfaces, and extensively compared to recent studies using other methods in the literature. Both single and double radial cracks were considered, and also the effect of finite plate width on crack surface displacements has been investigated. A brief assessment was made on an engineering estimation of displacements based on a correction of stress intensity factor ratio. It has been demonstrated that the Wu‐Carlsson closed‐form weight functions are very efficient, accurate and easy‐to‐use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

The fracture of wood under impact loading

High speed motion picture photography was used to study the fracture, under impact loading, of wood beams. Photographs were taken at the rate of 500 frames per second, which permitted the crack development during the fracture event to be monitored. Load vs. time data during the test were also recorded. This paper presents a photographic record of the crack patterns which developed when the beams were tested in an instrumented impact machine.     

Resistance Against the Intrinsic Rate of Fracture Mechanics Parameters for Polymeric Materials Under Moderate Impact Loading

This study contributes towards understanding crack toughness as resistance against the intrinsic rate of fracture mechanics parameters. Up to now only few investigations have been done under moderate impact loading conditions. Based on experimental investigations using the crack resistance (R) concept, it has been shown that the stop block method combined with the multiple-specimen technique is a unique method for polymers under impact loading conditions in comparison with different R-curve methods. Other methods for the determination of R curve such as the low-blow technique are normally not applicable for polymers due to their time-dependent mechanical properties. The crack-tip opening displacement (CTOD) rate is a measurement of the rate sensibility of stable fracture process depending on the type of deformation, which can provide deep insights into the micromechanics and activation mechanisms during the fracture processes. In the polymeric materials mostly investigated, one can understand the stable crack propagation with three-stage processes; crack-tip blunting/crack initiation, non-stationary stable crack growth and steady-state stable crack growth (an equilibrium state). In this stable crack propagation, the values of normalized CTOD rate converge rapidly to a ‘matrix’-specific threshold. The stop block method in the multiple-specimen technique assures the criteria of the time-independent strain field around the crack tip and constant crack speed therewith and the J-integral is a valid toughness parameter.     

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

Axisymmetric boundary integral equation analysis of interface cracks between dissimilar materials

The numerical boundary integral equation (BIE) method with quadratic quarter-point crack-tip singular elements is used to analyse interface cracks between dissimilar material in axisymmetry. Such crack problems present modelling difficulties using conventional procedures for obtaining the stress intensity factors. This is because of the oscillatorily singular nature of the stresses in the vicinity of the bimaterial interface crack-tip. Analytical expressions for the direct evaluation of the fracture characterising parameters from the BIE numerical results of displacements or tractions are derived. Three different crack problems are investigated, two of which have known solutions in the literature. Excellent agreement between the BIE results and these other established solutions are obtained even with relatively coarse mesh discretisations. The present study illustrates the ease with which the BIE method may be used in the fracture analysis of both straight and curved binaterial interface cracks.     

Fracture mechanics parameters for cracks on a slightly undulating interface

Typical bimaterial interfaces are non-planar due to surface facets or roughness. Crack-tip stress fields of an interface crack must be influenced by non-planarity of the interface. Consequently, interface toughness is affected. In this paper, the crack-tip fields of a finite crack on an elastic/rigid interface with periodic undulation are studied. Particular emphasis is given to the fracture mechanics parameters, such as the stress intensity factors, crack-tip energy release rate, and crack-tip mode mixity. When the amplitude of interface undulation is very small relative to the crack length (which is the case for rough interfaces), asymptotic analysis is used to convert the non-planarity effects into distributed dislocations located on the planar interface. Then, the resulting stress fields near the crack tip are obtained by using the Fourier integral transform method. It is found that the stress fields at the crack tip are strongly influenced by non-planarity of the interface. Generally speaking, non-planarity of the interface tends to shield the crack tip by reducing the crack-tip stress concentration.     

Approximation of curved cracks under mixed-mode loading

The calculation of stress intensity factors or mechanical energy release rate for non-straight cracks can be complicated. Approximation to equivalent crack shapes can simplify calculations considerably, but this requires an understanding of the influence of key shape parameters on crack-tip stresses. A simple analytical model has been developed, based on the concept of a relaxed volume, to predict mechanical energy release rate and deflection angle for a range of crack shapes under mixed-mode loading. Results from this model compared well with those obtained from finite element (FE) simulations, and with predictions from previous analytical models. It was found that the crack length and orientation of the crack-tip with respect to loading direction are the key influences on fracture parameters, whilst curvature near the crack-tip can also affect results.     

Procedure for accurate calculation of the J-integral from digital volume correlation displacement data

The application of digital image and volume correlation techniques to obtain displacement fields from images has become ubiquitous in experimental fracture mechanics. In this paper, a procedure to extract the J-integral (J) from three-dimensional displacement fields obtained using digital volume correlation is presented. The procedure has been specially adapted to allow for experimental noise and errors, such as poorly defined crack front displacements, smearing of the displacement field across the crack faces, and knowledge of the imprecise crack front location. The implementation is verified using analytical crack-tip fields perturbed with synthetic image correlation errors to characterise the response of J. The method is then applied to experimental results using a Magnesium alloy WE43 loaded elastically in mixed mode. The steps outlined are intended as a guideline for the application of the volume integral from displacement fields to allow for accurate calculation of J along a crack front embedded within the volume.     

Some experimental observations on crack closure and crack-tip plasticity

This study presents a methodology for evaluating crack closure and the effect of crack-tip plasticity on stress intensity. Full-field displacement maps obtained by digital image correlation are used to obtain the mixed-mode, crack-driving force. The methodology allows the quantification of the effect of a range of contact phenomena: effects arising from interlocking, plastic deformation of crack face asperities and wedging generated as a consequence of sliding displacements of fatigue cracks have been identified. By evaluating the effective crack-tip stress intensity factor, crack opening levels can be quantified for both mode I and mode II. Moreover, the approach can take into account plasticity effects local to the crack in determining the stress intensity factor. All the information can be extracted in a non-contacting fashion with equipment that can be easily incorporated into industrial environments.     

Full‐field characterisation of crack tip deformation and fatigue crack growth using digital image correlation—a review

In recent years, digital image correlation has been widely used in the analysis of crack problems. This review will examine digital image correlation, as a full‐field measurement technique, in the studies of crack tip mechanical behaviour under cyclic loading conditions. In particular, topics including determination of fracture mechanics parameters and evaluation of crack closure will be discussed. Micromechanical aspects of crack growth under cyclic loading will also be explored in crack driving and attenuation effects.     

On the mechanics of fracture in monoliths and multilayers from low-velocity impact by sharp or blunt-tip projectiles

The propagation of cracks in layered glass from low-velocity impact of sharp or spherical tip projectiles is observed using high-speed photography. Tests are also carried out to determine the threshold impact energy for chipping in glass blocks and subsurface crack instability in an edge-supported glass plates. The results identify the median and subsurface radial crack systems as the prime damage sources in such applications.     

Three-dimensional stress intensity factor analysis of a surface crack in a high-speed bearing

The boundary element method is applied to calculate the stress intensity factors of a surface crack in the rotating inner raceway of a high-speed roller bearing. The three-dimensional model consists of an axially stressed surface cracked plate subjected to a moving Hertzian contact loading. A multi-domain formulation and singular crack-tip elements were employed to calculate the stress intensity factors accurately and efficiently for a wide range of configuration parameters. The results can provide the basis for crack growth calculations and fatigue life predictions of high performance rolling element bearings that are used in aircraft engines.     

Experimental investigation of the mixed-mode crack propagation in ZrO2/NiCr functionally graded materials

Mixed-mode fracture response of ZrO₂/NiCr functionally graded materials (FGMs) is investigated using fracture test, digital image correlation technique and extended finite element method. It is found that: (1) prior to crack initiation, the increasing elastic modulus ahead of crack-tip can enhance the mode mixity of crack-tip; (2) the crack with the increasing elastic modulus ahead of crack-tip kinks less than the one with the decreasing elastic modulus, which is caused by the elastic gradient and the local fracture toughness; (3) the heterogeneity of microstructure can cause the local perturbation but has no obvious effect on the overall crack propagation path.