Crack Opening Profiles Research Articles

Fatigue crack-growth behavior of materials in viscous fluid environments

The potent effect of the hydrodynamic pressure developed in the wake of a crack growing under cyclic loads in a viscous fluid environment is considered. While existing semi-analytical solutions provide an estimate of the hydrodynamic pressure effect, they are inherently restricted by the assumption of specific crack opening profiles. To correct this limitation and to extend the study to a complete range of materials and fluid environments, a fully consistent numerical approach was developed. A self-consistent fracture mechanics solution procedure is derived initially for atomistically sharp cracks in brittle materials, and then extended to include the effect of crack tip blunting in more ductile materials. Three important dimensionless parameters are identified through which effects of various physical properties on crack-growth behavior can be examined. These include specimen geometry, material properties, fluid viscosity and cyclic loading conditions. General plots are constructed spanning wide ranges of these dimensionless parameters so that the hydrodynamic pressure contribution to crack-growth rates can easily be estimated for a complete range of materials, fluid environments and loading parameters.

Effect of viscous grain bridging on cyclic fatigue-crack growth in monolithic ceramics at elevated temperatures

The bridging tractions developed behind a crack tip are considered for a stationary crack under cyclic loading conditions at elevated temperatures in high-toughness, monolithic ceramics. Assuming a temperature range where the grain-boundary phases are sufficiently soft such that bridging can occur due to a viscous layer in the boundary, a viscoelastic model is developed in which bridging forces associated with the shear resistance of the grain-boundary phase are transmitted across the surfaces of a crack. Throughout the work, cyclic and static damage mechanisms which may be operating ahead of the crack tip (e.g. creep cavitation) are ignored in order to focus exclusively on the role of viscous grain bridging. A primary goal is to incorporate microstructural details like grain shape, grain-boundary thickness, and glass viscosity, as well as the effects of external variables such as loading rate and temperature. A fully self-consistent numerical approach is adopted, which does not require any prescribed assumptions as to the shape of the crack-opening profile. The self-consistent solution is compared to an analytical solution for a simplified parabolic approximation of the crack-flank opening displacements. The model is applicable to a wide range of ceramic materials at elevated temperatures, and rationalizes the frequency and temperature sensitivity not generally observed in ceramics at room temperature. Solutions identify a non-dimensional group associated with microstructure and external loading conditions, and solutions are presented over a range of this parameter.

Bridging stress distribution in center-cracked fiber reinforced metal laminates: modeling and experiment

A theoretical model for the distribution of the bridging stress in center-cracked fiber reinforced metal laminates (FRMLs) was developed based upon fracture mechanics analysis, and a test method presented. The model includes the effect of the delamination shape and size, the saw-cut size and the shear deformation of the adhesive. Moiré technique was employed for measuring the crack opening profiles in the test method. The bridging stresses in CCT specimens of 2/1 GLARE were tested. The results of the bridging stress calculated by the present model were compared with test results, and good agreement was achieved. Based on the present model, the factors affecting the distribution of the bridging stress in FRMLs were analyzed. Delamination shape and size, and the saw-cut size were identified as the main factors.

Modeling crack development in reinforced concrete structures under service loading

Reinforced and partially prestressed concrete structures are generally designed to allow cracking under service loading. Accurate modeling of crack formation and propagation at lower load levels is therefore important, especially in severe environments where structural durability is a concern. Here, a spring-network approach is used to study cracking in scaled models of reinforced concrete bridge piers, which are subjected to eccentric loading. An energetic fracture mechanics approach is used to model tension softening of developing cracks. Numerical results for cracking loads, crack opening profiles, and global load–displacement response agree well with experimentally measured values. In contrast, a brittle fracture model significantly underestimates the load level of crack formation, provides unrealistic crack opening profiles at low load levels, and indicates a mechanism for structural failure different from that witnessed in the test program.

Stable crack growth along a brittle\\ductile interface—II. Small scale yielding solutions and interfacial toughness predictions

The problem of a crack growing steadily and quasi-statically along a brittle\\ductile interface under plane strain, mixed mode, and small scale yielding conditions is considered. The ductile material is assumed to be characterized by the J 2-flow theory of plasticity with linear strain hardening, while the brittle material is assumed to be linear elastic. A displacement-based finite element method, exploiting the convective nature of the problem, is utilized to solve the relevant boundary value problem. In Part I of this work, the corresponding asymptotic problem was solved. This paper addresses the full-field problem in order to validate the asymptotic solutions, and to explore the physical implications of the results. The numerical full-field results are found to be in good agreement with the analytical asymptotic solutions. In particular, the full-field results strongly suggest that the stress fields in the vicinity of the crack tip are variable-separable of the power singular type; and also that the mode mix of the near-tip stress fields is, to a large extent, independent of the applied elastic mode mix. The amplitude (the plastic stress intensity factor) and the regions of validity of the asymptotic fields are estimated from the full-field results, and are observed to be strongly dependent on the applied mode mix. The remote elastic loading fields appear to influence the near-tip fields, primarily, through the plastic stress intensity factor. The present work also explores the suggestion made by Bose and Ponte Castaneda, 1992 that the solutions to the small scale yielding problem may be used in the context of a standard crack growth criterion, requiring that continued growth take place with a fixed near-tip crack opening profile, to obtain theoretical predictions for the dependence of interfacial toughness on the applied mode mix. Based on the numerical results, predictions for mixed mode toughness of the brittle\\ductile interface are reported. The results, which are in qualitative agreement with available experimental data and also with some recent theoretical results, predict a strong dependence of interfacial toughness on mode mix. This suggests that ductility provides the main operating mechanism for explaining the dependence of interfacial toughness on the mode mix of the applied loading fields, during steady crack growth.

Transverse matrix cracks in cross-ply laminates: Stress transfer, stiffness reduction and crack opening profiles

Cross-ply laminates with transverse plies containing through-width matrix cracks across the thickness of the transverse plies are studied using an energy-based approach,complementary to that of Hashin. An upper bound on the effective axial stiffness of the cracked laminates with a uniform distribution of transverse cracks is derived. The equations governing the field variables in a typical RVE are derived using thelayerwise laminate theory of Reddy and are solved using the finite element method. The predicted reduction in the effective axial modulus is in good agreement with experimental results, and it approaches a fixed value with increase in crack density for laminates with bothstaggered andnon-staggered cracking. Laminates with staggered cracks showed a greater reduction in effective modulus at lower crack densities. The stress distribution and mechanics of load transfer is examined in detail, at two crack densities including the characteristic damage state. The crack opening profile has been normalized in a special way in terms of the crack density, layup parameters and material properties.

The Mode Conversion of a Guided Wave by a Part-Circumferential Notch in a Pipe

A study of the reflection of mode-converted guided waves from notches in pipes has been carried out. Measurements were made on a 76-mm bore diameter (nominal 3-inch), 5.5-mm wall thickness pipe with circumferentially oriented through-thickness notches of various lengths. In parallel, a finite element model was used to simulate the experiments. The axially symmetric L(0, 2) mode was incident on the notches and the L(0, 2), F(1, 3), and F(2, 3) modes were received in reflection. The results showed excellent agreement between the measurements and the predictions for all three modes. They also showed that the F(1, 3) mode reflects as strongly as the L(0, 2) mode when the notch length is short. Finally, it has been shown that a very simple analysis based on an assumed crack-opening profile may be used to make accurate predictions of the mode conversion.

Crack tip shielding in elastic particulate composites undergoing damage

A simple rate-independent phenomenological constitutive model is used to model fracture behavior in elastic particulate composites undergoing damage. The constitutive model consists of two damage functions that govern the degradation of the bulk and the shear moduli. The elastic modulus is assumed to reach a saturation level under uniaxial conditions. Using the path independence of the J-integral and the concept of cracktip shielding, the remote or the applied stress intensity K ∞ is related to the cracktip stress intensity factor K t. The results from the model are used to predict the cracktip conditions in particulate composites undergoing damage. The model compares well with experimental results in predicting the crack opening profile as well as the displacement field in the vicinity of a cracktip.

An element free Galerkin formulation for stable crack growth in an elastic solid

The discrete formulation for stable crack growth in an elastic solid using the Element Free Galerkin (EFG) method based on the moving least-squares approximations has been established. The EFG method provides the ability to successfully model steep gradients, such as those that exist at a crack tip, through the introduction of an additional distribution of nodal points. In this formulation, the inertia force term in the momentum equation is converted into a spatial gradient term by employing the steady state conditions. A convective domain is employed to account for the analysis domain moving at the same speed as the crack front. A number of stable crack growth problems are examined and comparisons between the numerical predictions and analytical solutions are made for the near-tip fields, the crack opening profiles, as well as the global control parameters such as stress intensity factor K and energy release rate G.

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Crack Projection Method has been proposed for the crack opening measurement of rocks, using the 3-dimensional data of the linear absorption coefficient given by the X-rays Computerized Tomography. This is a promising method to measure the crack opening from the X-rays projection normal to the crack surface. The fundamental formulae for the crack opening measurement have been firstly described as well as the necessary regional averaging technique and the data processing for measurement of accuracy to micron meters, and subsequently the crack model experiments using a couple of half-moon aluminum plates has been conducted to examine the accuracy and reliability of the method. As a case example of the Crack Projection Method, the Short Rod testing has been presented and discussed,that is a suggested testing method of the International Society for Rock Mechanics for determining the fracture toughness of rock. Crack growth characteristics with pull-loading has been described by showing the 2-dimensional images of the X-rays Computerized Tomography. The permanent opening displacement of the extended crack has been successfully examined by the subtraction of the crack opening profiles measured before and after the Short Rod testing, and the elastic opening of the extended crack has been also examined by analyzing the change of the crack opening profile by reloading. Moreover, the dimension of the fracture process zone has been estimated as well as the permanent strain in this zone.

Experiments and Simulations of Directionally dependent Fracture along Copper/Sapphire Interfaces

AbstractTo test the hypothesis that the brittleness and ductility of crystalline materials are controlled by a competition between dislocation nucleation and cleavage failure at a crack tip, Riceet al.[1] designed a four-point bend copper/sapphire bicrystal which has two cracks that propagate along the interface in opposing directions. They predicted, on the basis of the Rice-Thomson model [2], that the specimen would exhibit a directionally dependent fracture behavior; that is, one crack would propagate more readily than the other. Beltz and Wang [3] carried out the experiments and reported that the specimen exhibits a directionally dependent fracture behavior in accordance with the predictions. In the present work, these experiments are repeated independently and it is shown thatthe orientation of the experimentally observed directionally dependent behavior is opposite that of the predicted orientation.Furthermore, we show that Beltz and Wang incorrectly measured the orientation of the directional dependence in their experimental results. A correct interpretation of their results is consistent with the present work.Taking advantage of the transparent sapphire, the normal crack opening displacement (NCOD) profile of both cracks is measured with optical interferometry. The measurements show that, away from the very tip of the crack, the NCOD takes the form of a constant angle, irrespective of load level. The opening angle of the apparently brittle crack is smaller than that of the apparently ductile crack. Complementary measurements of the very tip of the crack with Atomic Force Microscopy show that the near-tip crack opening profiles of the brittle and ductile cracks differ significantly.The specimen is analyzed with the Finite Element Method, taking into account the elastic and plastic properties of the single crystal constituents. Since the very essence of the observed phenomenon is one of crack growth, the two cracks are simulated as they grow quasistatically along the interface. The asymptotic deformation fields, characteristic of single crystals, of the growing interfacial cracks are identified. The stress and strain fields, as well as the NCOD, are calculated. We present a plausible explanation of the directional dependence of fracture on the basis of the continuum plastic fields surrounding the quasistatically growing cracks.

On the quantification of bridging tractions during subcritical crack growth under monotonic and cyclic fatigue loading in a grain-bridging silicon carbide ceramic

The mechanisms of cyclic fatigue-crack propagation in a grain-bridging ceramic, namely an in situ toughened, monolithic silicon carbide, is examined. The primary goal is to directly quantify the bridging stresses as a function of cyclic loading. To investigate the effect of the number of loading cycles on the strength of the wake bridging zone, crack-opening profiles of cracks grown at high velocity near the K c instability (to simulate behavior on the R-curve) and at low velocity near the fatigue threshold (to simulate the cyclically-loaded crack) were measured in situ in the scanning electron microscope at a fixed applied stress intensity. Differences between the measured profiles and those computed for elastic traction-free cracks permit the estimation of the traction distributions. These are then used to simulate resistance curve and fatigue-crack growth rate date. Predictions are found to be in close agreement with experimental measurements on disc-shaped compact-tension specimens. The results provide direct, quantitative evidence that bridging tractions are indeed progressively diminished due to cyclic loading during fatigue-crack propagation in a grain-bridging ceramic.

SUBCRITICAL CRACK GROWTH IN GLASSES UNDER CYCLIC LOADS: EFFECT OF HYDRODYNAMIC PRESSURE IN AQUEOUS ENVIRONMENTS

The effect of hydrodynamic pressure developed in the wake of a crack growing in a brittle material under cyclic loads in an aqueous environment is considered. The pressure acts in opposition to the movement of the crack faces, thus shielding the crack tip from the applied loads. A general hydrodynamic fluid pressure relation based on a one-dimensional Reynolds equation, which is applicable to a crack with an arbitrary crack opening profile, is developed. The model is modified to account for side flow through the thickness of the sample and cavitation near the crack tip. Both effects significantly modify the hydrodynamic pressure distribution. Finally, the resulting hydrodynamic pressure relations are combined with a fracture mechanics model to account for the change in the near-tip stress intensity. Resulting predictions of the cyclic crack-growth rate are found to be in good agreement with measured values for a borosilicate glass tested at various frequencies in a water environment. © 1997 Acta Metallurgica Inc.

Stiffness Loss of Composite Laminates with Transverse Cracks under Mode I and Mode III Loading

In this paper, the stiffness loss of general composite laminates with transverse cracks under mixed-mode loading is analyzed. The effective stiffnesses of the laminates are assumed to be functions of the nonlinear internal state variables (ISVs), which are dependent on crack densities, ply constraints, and crack opening profiles. The ISV corresponding to Mode I cracking is obtained from a series of finite element analysis. The ISV corresponding to Mode III cracking can be related to the Mode I ISV by considering geometrical constraints arising from the layup, for a laminate under tensile loading. Theoretical predictions of stiffness loss of glass/epoxy and graphite/epoxy composite laminates with transverse cracks are compared with experimental data available from published sources, for crossply, angleply, and quasi-isotropic laminates. In addition, the model enables the contributions from respective modes to the overall stiffness reduction to be determined. Results of analyses have shown good and excellent agreement with published experimental data from other researchers.

Experimental and numerical studies in model composites Part I: Experimental results

Results on strength, apparent toughness, fatigue crack growth and fiber debonding on specially made composite materials are reported. The compact tension composite specimen used consisted of an epoxy matrix and layers of long aligned glass or kevlar fibers that were equally spaced. The experimental data on crack initiation strength showed that for a range of fiber spacing λ, the composite's strength δ A , scaled with the fiber spacing in the form of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaaieGacaWFbbaabeaakmaakaaabaGaeq4UdWgaleqaaOGaeyyp% a0JaeqOUdSgaaa!3EB5!\[\sigma _A \sqrt \lambda = \kappa \]. The apparent toughness of the composite specimens increased with a decrease in fiber spacing. Two sets of fatigue crack propagation experiments were performed. The first one was on specimens with the same fiber spacing and under different applied loads. The second set was on specimens with different fiber diameter and the same loading conditions. While crack arrest was observed in the first set, crack arrest was seen in the second set for the relatively large diameter fibers and specimen fracture for the relatively thin fibers. A method, based on fracture mechanics principles and crack opening displacements, for evaluating bridging tractions is outlined. Using this method, simulations for the bridging tractions and stress intensity factor were carried out using a linear crack opening profile. The total stress intensity factor was found to decrease with crack length. The debonding in the bridging zone, on specimens with different fiber spacing, was evaluated using a one dimensional debonding analysis. The model was calibrated with the debonding on the first fiber and consequently used to describe debonding on the bridging zone of specimens with different fiber spacing. In spite of the assumptions adopted in the present studies, the model seems to describe debonding well.

A finite element analysis of plane strain dynamic crack growth at a ductile-brittle interface

In this work, steady, dynamic crack growth under plane strain, small-scale yielding conditions along a ductile-brittle interface is analysed using a finite element procedure. The ductile solid is taken to obey the $J_2$ flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behaviour. The objectives of this work are to establish the validity of an asymptotic solution for this problem which has been derived recently [12], and to examine the effect of changing the remote (elastic) mode-mixity on the near-tip fields. Also, the influence of crack speed on the stress fields and crack opening profiles near the propagating interface crack tip is assessed for various bi-material combinations. Finally, theoretical predictions are made for the variation of the dynamic fracture toughness with crack speed for crack growth under a predominantly tensile mode along ductile-brittle interfaces. Attention is focused on the effect of mismatch in stiffness and density of the constituent phases on the above aspects.

Fatigue crack tip opening behavior in particulate reinforced Al-alloy composites

Behavior of fatigue crack growth was examined in an Al2O3 particulate reinforced Al-Cu matrix composite and its matrix alloy, heat-treated to peak-aged and overaged conditions. The fatigue crack growth resistance of the composite was much better, especially at low growth rates, and depended on aging condition. Measurements of crack opening profiles have shown that crack tip in the composite remained closed at fairly high stress intensities and was opened to a much smaller displacement compared to the crack tip opening in the matrix alloy at the same stress intensity. Correlation of the fatigue crack growth rate with crack tip opening displacement (CTOD) revealed that both the composite and the matrix alloy obey the same fundamental relationship that the fatigue crack growth rate scales with the square of the CTOD.

Elastic solutions for corner cracks undergoing uniform displacement-controlled loading

To understand the behavior of corner cracks involving displacement-controlled loading, the mode-I stress intensity factors and crack face displacements are determined for a quarter-elliptical corner crack undergoing uniform end displacement. A 3-D weight function method is used for the analysis. Various crack aspect ratios and crack-length-to-plate-height ratios are considered. The results show that the stress intensity factor and the crack opening profile for the uniform displacement-controlled loading can be significantly different from those for the uniform-stress controlled loading.

Determination of Bridging Stresses in Reinforced Al2O3

The determination of bridging stresses by evaluation of crack opening profiles is outlined for a whisker‐reinforced alumina. The application of the fracture mechanics weight function procedure results in an integral equation between bridging stresses and crack opening displacements. Its solution provides the bridging stress relation.

Evaluation of Fiber-Bridging Effect on Model I Interlaminar Fracture Toughness of Unidirectional CFRP Based on Measurements of Crack Opening Profiles.

For evaluating the mode I crack-tip stress intensity factor, KItip, of cracks with fiber bridging in fiber-reinforced plastics, a method based on measurements of crack opening profiles is proposed. The values of KItip and the bridging stress intensity factor, KI bridge, can be separately determined with good accuracy by the boundary element calculation based on measured crack opening profiles. This method was applied to the growth of interlaminar cracks in unidirectional carbon/epoxy laminates, Toray T800H/# 3631, under mode I monotonic loading. The measured value of the crack opening displacement of interlaminar cracks with fiber bridging was smaller than that without fiber bridging. The critical value of the applied stress intensity factor, KI ap, c, increased with crack extension, while the critical value of KI tip obtained from the proposed method took a constant value, KI tip, c, during crack growth. Therefore, KI tip is the true crack-driving force and the true resistance of crack growth is given by a material constant, KI tip, c for the laminates with fiber bridging.