Crack Face Closure Research Articles

An improved maximum tangential stress criterion for an inclined crack in uniaxial compression considering T‐stress and crack parameter

AbstractThe rockmass in the practical engineering is often prone to compression; therefore, how to establish a fracture criterion to reflect the rockmass compression failure is vital. Take the rockmass with one inclined crack for instance, the mechanical behavior of the inclined crack face closure and friction sliding in uniaxial compression is firstly analyzed, and then the Kolosov–Muskhelishvili stress function of the cracked rockmass in uniaxial compression is established based on the complex stress functions. Next, the calculation methods of the stress intensity factor (SIF) K and three T‐stress components at or near the crack tip considering three kinds of crack parameters (e.g., geometry parameter, friction strength parameter and deformation parameter) are obtained. Thirdly, the improved maximum tangential stress (MTS) criterion is obtained considering T‐stress and three kinds of crack parameters. Finally, the test results of the wing‐crack initiation angle in uniaxial compression obtained by other researchers are adopted to verify the improved MTS criterion. Meanwhile, the effect of γ, the crack normal stiffness kn and shear stiffness ks, and the crack friction coefficient f on the wing‐crack initiation angle are discussed with the parametric sensitivity analysis.

Calibrating an adaptive cohesive zone model to simulate ductile crack propagation in structural steel under cyclic loading

AbstractA procedure is outlined for calibrating a finite element model to simulate ductile cracking that employs a continuum damage criterion for ductile fracture initiation, termed the Stress Weighted Ductile Fracture Model, with an Adaptive Cohesive Zone method to simulate crack propagation. The proposed procedure is implemented and validated with data from 44 coupon‐scale tests of an A913 structural steel. The fracture model calibration is performed in two stages to determine parameters to evaluate: (1) the continuum damage mechanics criterion and (2) ductile crack initiation and propagation. Sensitivity of the calibration to parameter uncertainty is evaluated using synthetic data, followed by calibration and validation against experimental test data. The results indicate that the computational model can accurately simulate the overall response of experimental specimens, as well as other key aspects of observed behavior, including crack tunneling and crack face closure. Guidelines are provided for practical calibration of the model components.

Crack face closure effect and opening behaviors of fatigue pre-crack treated by laser peening

The present work investigates the generation process of crack face closure under laser shock and its effect on the crack opening behavior to reveal the underlying reason for the high-level crack closure induced by laser peening (LP) on the initial fatigue crack. It is found that crack face closure generates a firm compression to the crack face, causing the significant elongation in the crack wake during the crack opening process to prevent crack faces from separating even under the high-level external load. The contribution of crack face closure to crack retardation is comparable to LP-induced residual stress.

Cyclic adaptive cohesive zone model to simulate ductile crack propagation in steel structures due to ultra‐low cycle fatigue

AbstractMicromechanics‐based continuum damage criteria have previously been developed to simulate the initiation of ductile fracture in structural steels under conditions with large‐scale plasticity where conventional fracture mechanics indices are invalid. Such models have been combined with methods to simulate ductile crack growth for monotonic loading. In this study, a micromechanics‐based adaptive cohesive zone model for simulating ductile crack propagation under monotonic loading is extended to handle cyclic loading. The proposed model adaptively modifies the cohesive traction–separation relationship for crack opening and closure, as the loading reverses between tension and compression. The approach is implemented into the finite element analysis platform WARP3D, and results of simulations that use the model are compared with data from coupon‐scale tests. The results demonstrate that the proposed model can accurately simulate the effect of crack propagation on specimen response, as well as other key aspects of observed behavior, including crack face closure and crack tunneling.

Numerical analysis of plasticity effects on fatigue growth of a short crack in a bainitic high strength bearing steel

Plasticity effects on fatigue growth were simulated for a physically short crack. The material description comprised the Drucker-Prager yield surface, non-associated flow rule and non-linear combined hardening. The simulated development of the growth limiting parameter agreed with the experimental crack behaviour with early rapid propagation followed by a transition to slow R-controlled growth. The crack was open to the tip without any crack face closure throughout all load cycles. Instead compressive residual stresses developed at the unloaded tip which supplied an explanation to the slow rate of the propagated short crack in this bainitic high strength bearing steel. The material’s strength differential effect was the key difference explaining why compressive residual stresses instead of crack face closure was responsible for the short crack effect in this material.

Propagation of physically short cracks in a bainitic high strength bearing steel due to fatigue load

Physically short cracks in a bainitic high strength bearing steel were fatigue loaded. The rapid propagation rate of early open short cracks agreed with that of long closure free cracks. After some rapid growth, the short cracks entered a transition period to the rate of growth limited long cracks. Potential drop showed that the short cracks were open to the tip throughout the growth sequence, which excluded crack face closure in the wake as the growth limiting mechanism in this material. Instead the short crack effect was related to residual stresses and other mechanisms at the crack tip. Crack manufacturing procedures were determined for straight long and short start cracks in the present material. LEFM with effective material parameters and limit compensation predicted the short crack lives.

A study of frictional contact in dynamic fracture along bimaterial interfaces

We investigate numerically the dynamic in-plane propagation of a centered crack along bimaterial interfaces using a spectral formulation of the elastodynamic boundary integral equations. Particular attention is given to the effect of contact zones at the subsonic/intersonic transition. In a single set-up, we simulate and describe the different phenomenon observed experimentally (distinct natures of contact zones, unfavorable velocity range, asymmetric crack propagation). We show that different behaviors are observed as function of the crack propagation direction, i.e., with respect to the particle displacements of the compliant material. When the crack propagates in the same direction, the propagation velocities between $$c_\mathrm{R}$$ and $$c_\mathrm{s}$$ are forbidden and the subsonic/intersonic transition occurs with the nucleation of a daughter crack in front of the main rupture. The intersonic stress field at the crack front is compressive due to the material mismatch and a contact zone appears behind the tip. In the opposite direction, a smooth subsonic/intersonic transition occurs although crack face closure (in normal direction) is observed for speeds between $$c_\mathrm{s}$$ and $$\sqrt{2}c_\mathrm{s}$$ . In this regime, a Rayleigh disturbance is generated at the crack surface causing a contact zone which detaches from the tip. Using a contact model governed by a regularized Coulomb law, we provide a quantitative evaluation of the influence of friction on the effective fracture toughness. Finally, we show the applicability of our analysis to the description of different bimaterial situations as well as the single-material set-up.

Calculation of KII in crack face contacts using X-FEM. Application to fretting fatigue

In this work, the modeling of LEFM problems that imply crack face closure and contact using the extended finite element method (X-FEM) is presented aiming at its application to fretting fatigue problems. An assessment of the accuracy in the calculation of KII is performed for two different techniques to model crack face contacts in X-FEM: one is based on the use of additional elements to establish the contact and the other on a segment-to-segment (or mortar) approach. It is concluded that only the segment-to-segment approach can lead to optimal convergence rates of the error in KII. The crack face contact modeling has also been applied to a fretting fatigue problem, where the estimation of KII under crack closure conditions plays an important role in the stage I of fatigue crack propagation. The effect of the crack face friction coefficient has been studied and its influence on the range of KII has been ascertained during loading and unloading cycles.

Determination of Stress Intensity Factors for a Cracked Shell under Bending with Improved Shell Theories

A formulation based on the linearized shallow shell theory has been developed by Delale and Erdogan to determine the stress intensity factors of a shell with a through-the-thickness crack. The drawback in the formulation is that the crack-face closure at the compressive edges when a cracked shell is subjected to a bending load is not taken into account, which results in the penetration of material at the crack faces. The present research is aimed to improve the formulation by including the effect of the crack-face closure on the stress intensity factors. Simulation of the closure is achieved by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results have shown that the crack-face closure significantly influences the magnitude of the stress intensity factors and tends to reduce the maximum stress intensity factor. The magnitude of the reduction varies with the curvatures of the shell and the ratio of the two curvatures as well.

Fracture mechanics of specially orthotropic shells containing a crack

This article presents a theoretical analysis of specially-orthotropic shells containing a crack in terms of a crack-closure theory. The formulation of Delale and Erdogan for crack problems in shells is extended to include the effect of crack-face closure. The influence of material orthotropy and shell curvatures on the closure behaviour and consequently on the stress intensity factor are studied. It is demonstrated that crack-face closure has a significant impact on the stress intensity factor and it tends to reduce the maximum stress intensity factor. The crack-face closure effect on the stress intensity factor increases with the shell radii. In flat plates, as a special case of shells when the shell radii become infinitely large, the difference of the closure stress intensity factor between the closure case and non-closure case has a maximum. The influence of material orthotropy on the closure behaviour varies with the ratio of the two shell curvatures.

Effect of crack closure in a specially orthotropic cylindrical shell containing an axial or a circumferential crack

This article presents a theoretical analysis of the crack-face closure behaviors of an axial or a circumferential crack in a specially orthotropic cylindrical shell, emphasizing the influence of material orthotropy on crack-tip stress field. The shallow shell theory developed by Delale and Erdogan is extended to incorporate the effect of crack-face closure. In the present analysis the crack-face closure is modeled by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results show that the curvature effect causes the closure behavior in cylindrical shells to differ considerably from that in flat plates. Instead of complete closure over the entire crack length in flat plates, only partial closure occurs along the crack length in shells with large curvatures. Material orthotropy is also found to strongly influence the closure behavior of an axial crack but not that of a circumferential crack. In both cases the crack closure is found to reduce the maximum stress intensity factors, which is the most pronounced for shells with large radii for a given crack length and shell thickness.

Effect of crack closure in a specially orthotropic cylindrical shell containing an axial or a circumferential crack

This article presents a theoretical analysis of the crack-face closure behaviors of an axial or a circumferential crack in a specially orthotropic cylindrical shell, emphasizing the influence of material orthotropy on crack-tip stress field. The shallow shell theory developed by Delale and Erdogan is extended to incorporate the effect of crack-face closure. In the present analysis the crack-face closure is modeled by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results show that the curvature effect causes the closure behavior in cylindrical shells to differ considerably from that in flat plates. Instead of complete closure over the entire crack length in flat plates, only partial closure occurs along the crack length in shells with large curvatures. Material orthotropy is also found to strongly influence the closure behavior of an axial crack but not that of a circumferential crack. In both cases the crack closure is found to reduce the maximum stress intensity factors, which is the most pronounced for shells with large radii for a given crack length and shell thickness.

Crack closure effect on stress intensity factors of an axially and a circumferentially cracked cylindrical shell

Crack-face closure occurs when a shell or plate containing a through-the-thickness crack is subjected to a bending load, which leads to lower stress-intensity factors than those expected from non-closure assumption. This article presents a theoretical analysis of the effect of crack-face closure on the stress intensity factors of an axially and a circumferentially cracked cylindrical shell subjected to bending moment respectively. The presented analysis extends the shallow shell theories of Delale and Erdogan by incorporating the effect of crack-face closure. In keeping consistent with the shear deformation shell theory, crack-face closure is modeled by a line contact at the compressive edges of the crack face. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, i.e. along the crack length, either the normal displacement of the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. The results show that the distribution of the contact force along the crack is generally nonuniform. Furthermore, it is found that, similar to the case of spherical shells, crack closure may occur over the full length or only some segments of the crack in cylindrical shells, depending on the geometry of the shell and the nature (direction) of applied bending load. Comparisons of the stress intensity factor ratios between the closure solutions and the non-closure solutions reveal that the crack-face closure influences significantly the magnitude of the stress intensity factors and it tends to reduce the maximum stress intensity factor. The closure effect of crack face on the stress intensity factors is highest when the shell radius becomes very large for a given crack length and shell thickness.

Crack Closure in Spherical Shells

This article presents an analytical and numerical study of the influence of crack face closure on the stress intensity factor of a crack in a spherical shell subjected to membrane force and bending moment. The formulation developed by Delale and Erdogan based on linearised shallow shell theories is extended to account for crack surface closure in cracked spherical shells, assuming a line contact at the compressive edge of the crack face. It is found that, due to the curvature effects, the closure behaviour of cracks in spherical shell differs significantly from that in flat plates. Depending on the nature of the membrane force and bending moment, crack closure may occur over the entire crack length or only some segments. In the special case of full length crack closure, the coupled integral equations reduce to a single integral equation, leading to a simpler solution. The theoretical results are compared against finite element results of cracked shells compressed between two rigid plates, indicating that the shallow shell theory is valid for a shallowness parameter up to 1/5.

Radial cracking with closure

Progressive radial cracking of a clamped plate subjected to crack-face closure is studied. The material behavior is assumed to be elastic-brittle. The cracks are assumed to be relatively long in the sense that the three-dimensional contact problem can be described via a statically equivalent two-dimensional idealization. The number of cracks is supposed large enough to permit a quasi-continuum approach rather than one involving the discussion of discrete sectors. The formulation incorporates the action of both bending and stretching as well as closure effects of the radial crack face contact. Fracture mechanics is used to explore the load-carrying capacity and the importance of the role of the crack-surface-interaction. For a given crack radius, the closure contact width is assumed to be constant. Under this condition, a closed-form solution is obtained for the case of a finite clamped plate subjected to a concentrated force. Crack growth stability considerations predict that the system of radial cracks will initiate and grow unstably over a significant portion of the plate radius. The closure stress distribution is determined exactly in the case of narrow contact widths and approximately otherwise.