Results For Stress Intensity Factors Research Articles

Transient thermal fracture investigation of a cracked functionally graded layer via Guyer-Krumhansl model

Recent experimental evidence proves the Guyer-Krumhansl (G-K) model’s capability of predicting the nonclassical transient heat transfer process in heterogeneous composites. The objective of this article is to explore the dynamic thermal and fracture behaviors of a cracked orthotropic functionally graded material (FGM) layer subject to abrupt thermal shocks via the G-K equation. The thermal and elastic governing equations determined by the G-K model are transformed into the singular integral equations, which are calculated numerically to assess the non-Fourier transient temperatures and the resultant dynamic thermal stress intensity factors. Parametric comparisons are carried out for the effects of the non-Fourier thermal lagging time and thermal nonlocal length on the transient thermoelastic responses. The findings would benefit the applications of unconventional heat conduction theories and shed light on the scientific understanding of FGM’s fracture behaviors.

Transient thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method

To model fracture in functionally graded materials (FGMs), the scaled boundary finite element method (SBFEM) is extended to examine the effects of fully coupled transient thermoelasticity. Previously developed SBFEM supplementary shape functions are utilized to model thermal stresses. The spatial variation of thermal and mechanical properties of FGMs are approximated by polynomial functions facilitating the semi-analytical evaluation of coefficient matrices. The dynamic stress intensity factors (SIFs) are also evaluated semi-analytically from their definitions without the need for additional post-processing. Scaled boundary polygon elements are employed to facilitate the meshing of complex crack geometries. Both isotropic and orthotropic materials with different material gradation functions are considered. To study the transient effects of thermoelasticity on fracture parameters, several numerical examples with different crack configurations and boundary conditions are considered. The current approach is validated by comparing the results of dynamic SIFs with available reference solutions.

Three-dimensional X-FEM modeling of crack coalescence phenomena in the Smart CutTM technology

A new 3D X-FEM approach is proposed to model crack coalescence phenomena in the Smart Cut TM technology. An adaptive mesh is developed based on a 3D fractal mesh allowing a significant gain in computing time compared to regular meshes. In order to calculate stress intensity factors (SIFs), the term corresponding to internal pressure, that is normal loading on crack faces has been determined, added to the interaction integral and the results of SIFs in mode I have been compared to their analytical values with mean error less than 1%. An implicit algorithm is implemented to predict the evolution of the internal pressure for growing cracks of any shape; a constitutive law in pressure correlated with the equation of state of ideal gases has therefore been used. Compared to the analytical solution, numerically evaluated pressure is accurate with maximum errors less than 1% for relevant convergence tolerance. Finally, the coalescence of two cracks is taken into account in the model. Qualitative local stress analysis makes it possible to explain some phenomena experimentally observed in the Smart Cut TM such as neighboring effects of growing cracks, the outgrowth of nearby cracks or influence of the presence of concave areas at a front on growth. • A 3D X-FEM model has been proposed to model crack coalescence phenomena under variable pressure (Smart Cut TM process). • The interaction integral has been adapted to take into account the internal pressure when computing 3D stress intensity factors. • Prediction of the internal pressure of propagating cracks whatever are their shapes. • Analysis of neighboring effects by stress analysis on a two penny-shape crack coalescence model.

Fracture analysis of single edge notched specimen using phase field approach

For the damage tolerant design of cracked structural components, two important parameters namely, residual strength and remaining life are very important. To evaluate these, a reliable fracture parameter such as stress intensity factor (SIF) is to be determined. Phase field (PF) based finite element formulation for a brittle fracture to determine crack propagation trajectory is presented in this paper. PF methodologies have been formulated by coupling partial differential equations (PDEs) after minimizing the total potential energy, which includes elastic strain energy and fracture energy, with respect to the displacement field and PF variable. Solutions of these PDEs for PF variable resulted in identifying crack path geometry, while PDEs displacement field obtained near the crack field is used to determine SIF. In the present study, extending PF formulation to fracture analysis of a structural component is first of its kind. To simulate PF phenomena, a four noded 2-D bilinear quadrilateral element with three degrees of freedom (DOF) at each node (two translations and one for phase field) has been developed to analyze single edge notched (SEN) specimen under tensile and shear loading. By combining the displacement results of PF method with displacement extrapolation technique, SIF has been determined for various crack lengths representing crack propagation in SEN specimens. It is then compared with the analytical SIF solution available in Handbook, and also with the contour integral method SIF results. It is found that the SIF obtained by PF method is in good agreement (±10%) with the other solutions.

Three-Dimensional analysis of mixed mode Compact-Tension-Shear (CTS) Specimens: Stress intensity Factors, T-stresses and crack initiation angles

In order to characterize the crack tip stress field in three-dimensional fatigue and fracture problems, stress intensity factor and T-stress solutions are usually necessary. In this paper, extensive three-dimensional (3D) finite element models are constructed for Compact-Tension-Shear (CTS) specimen, which is one of the most widely used specimens for fatigue and fracture tests under mixed-mode I&II loading. In-plane and out-of-plane geometric dimensions including varying crack depths ratios (a/W = 0.3, 0.5 and 0.7) and thicknesses ratios (B/W = 0.1, 0.3 and 0.5) are considered under different loading angles (β = 0°, 15°, 30°, 45°, 60°, 75° and 90°). The results of stress intensity factors (KI,KII and KIII) and T-stresses (T11 and T33) along the crack front are computed and analyzed. The combined effects of geometric dimensions and loading angles on these fracture parameters have been illustrated. The solutions of the parameters are then described using empirical formulae by fitting numerical results with the least-squares method. Solutions obtained have been used to predict the crack initiation angles for CTS specimens based on mixed-mode fracture criteria including the maximum tangential stress (MTS) criterion, the generalized MTS (GMTS) criterion, the strain energy density (SED) criterion and the generalized SED (GSED) criterion. Solutions are useful for fracture and fatigue problems of mixed-mode I&II, such as analysis of the constraint effects on fracture toughness and propagation path of fatigue crack.

An Elastic Half Space with a Moving Punch

The dynamic problem of a punch with rounded tips moving in an elastic half-space in a fixed direction has been considered. The static problem of determining stress component under the contact region of a punch has also been solved. Fourier integral transform has been employed to reduce the problems in solving dual integral equations. These integral equations have been solved using Cooke’s [1] result (1970) to obtain the stress component. Finally, exact expressions for stress components under the punch and the normal displacement component in the region outside the punch have been derived. Numerical results for stress intensity factor at the punch end and torque applied over the contact region have been presented in the form of graph.

A Numerical Investigation of an Abnormal Phenomenon of Stress Intensity Factor (SIF) in a Cracked T-Butt Joint Accounting for Welding Effect

Industry design standards such as BS 7910 deployed some empirical formulas for the prediction of stress intensity factor (SIF) based on simulation results from traditional finite element method (FEM). However, such FEM simulation occasionally failed to convince people due to the large discrepancies compared with engineering practice. As a consequence, inaccuracy predictions via such formulas in engineering standards inevitably occur, which will compromise the safety of structures. In our previous research work, an abnormal phenomenon of SIF in a cracked T-butt joint accounting for welding effect has been observed. Compared with BS 7910, the calculation results of SIF at the surface points of welded specimens cannot be well predicted, with a large discrepancy appearing. In order to explore such problem with an abnormal increase at the surface points of cracked welded specimens, a numerical investigation in terms of SIF among BS 7910, XFEM, and FEM is performed in this paper. Numerical models on both a simple cracked plate without welding effect and a cracked T-butt joint with welding effect are developed through ABAQUS. Parametric studies in terms of the effects of varied crack depth to thickness ratio (a/T) and the effects of crack depth to crack half-length ratio (a/c) are carried out. Empirical solutions from BS 7910 are used for comparison. It is found that the XFEM can provide predictions of SIF at both the crack deepest point and crack surface point of a simple cracked plate as accurate as FEM. For a T-butt joint with a transverse stiffener, a large discrepancy in terms of the weld magnification factors (Mk) occurs at the crack surface point compared with empirical predictions. An exceptional increase of von Mises stress gradient in regions close to the weld-toe is found through the simulation of FEM, whereas a constant stress gradient is obtained through XFEM. The comparison results indicate an inappropriate prediction of SIF by the utilization of the empirical formulas in BS 7910. A more reasonable prediction of the SIF at the surface point of a crack is obtained by the XFEM. Therefore, further updating of the empirical solutions in BS 7910 for SIF accounting for welding effect is recommended.

Numerical study of fatigue crack growth considering out-of-phase mixed-modes in laminar composites

In this work, the effects of out-of-phase fracture modes are investigated in the fatigue propagation of a crack located in an weak interface between layers of a laminar composite. Elastic and elastic-plastic constitutive equations are adopted for the layers. Mode II loading is delayed from mode I by a phase angle. A plane strain model is used in the simulations. Fracture propagation process is taken into account by an irreversible cyclic cohesive zone model. The present work shows that a resultant stress intensity factor controls the crack propagation in elastic specimens. In elastic-plastic specimens, propagation also depends on the energy dissipated in the volume. It was possible to conclude that most of the dissipation occurs due to closure of the cohesive zone during unloading of the mode I. The phenomenon is related to the rotation of the plastic zone around the crack tip and it is controlled by the phase angle between fracture modes.

The effects of thermal stress on the crack propagation in AP1000 reactor pressure vessel

In this paper, the effects of thermal stress on AP1000 reactor pressure vessel (RPV) is analyzed, and the elliptical corner crack propagation at the nozzle-cylinder intersection is investigated. The corner crack stress intensity factor (SIF) is computed under static pressure and combination (static pressure plus thermal stress) loadings and crack propagation. The analysis reveals that with an increase degree of the surface corner crack in the longitudinal section of in-let nozzle, SIF will decrease gradually; Due to the influence of thermal stress, the crack growth length is shorter, the growth rate is slower and the SIF is smaller. The numerical results of SIF for a wide range of crack propagation are provided as a reference for the fracture mechanics design of the RPV.

Mode-I pressurized axisymmetric penny-shaped crack in graded interfacial zone with variable modulus and Poisson’s ratio

This paper presents an analytical treatment to the fracture problem of a Mode-I pressurized penny-shaped crack in a graded interfacial zone or FGMs interlayer with variable shear modulus and Poisson’s ratio. An efficient multilayered model is proposed to address the general form of material inhomogeneity. The mixed boundary value problem is reduced to a Fredhom integral equation of the second kind. The solution procedure is also extended to address the Leonov-Panasyuk-Dugdale plastic crack. Analytical solutions in explicit form are derived for the full stress fields at the crack plane, Mode-I stress intensity factor (SIF), crack opening displacement (COD), T-Stress and plastic zone in terms of the solution of the integral equations. Numerical results of SIF, elastic stress fields, COD, T-Stress and length of plastic zone are presented to quantitively explore the effects of material inhomogeneity on the fracture response. It is demonstrated that the graded Poisson’s ratio has non-negligible influences on COD and T-Stress under certain condition. The present solutions can be used to advanced fracture analysis of pressurized crack in engineering composite material.

Interaction between a screw dislocation and a completely coated semi‐infinite anticrack

AbstractWe use complex variable methods to derive analytic solutions to the problem associated with the interaction between a screw dislocation and a completely coated semi‐infinite anticrack. The two sides of the anticrack or rigid line inclusion are perfectly bonded to the surrounding coating, which is also perfectly bonded to its neighboring matrix. The screw dislocation can be located anywhere in the composite structure. We obtain explicit expressions for the resultant stress intensity factor characterizing the square root singularity in the stress distribution at the anticrack tip, the resultant anticrack contraction force, which is always negative, and the image force acting on the screw dislocation.

The effect of crack length on the fracture parameters of an edge crack parallel to the material variation in a rectangular FGM plate

In this study, the extended element free Galerkin method (XEFG) is used for crack analysis an edge crack parallel to the material variation in a rectangular functionally graded material (FGM) plate under traction loading. For the first time, the effective parameters of XEFGM are employed such as the sub-triangulation term for numerical integration, suitable influence domain, and enrichment functions for discontinues locations in the fracture analysis of different crack positions of an edge cracked FGM plate. In addition, the incompatible formulation is adopted to extract the stress intensity factors (SIFs). Good data and results are observed about the relationship between the crack lengths and SIFs with good verification during changing XEFG parameters. There is good agreement and stability in the results of SIFs through the sizes of J-integral rJ equal to 0.4 -0.8. In addition, the acceptance results for the size of the support domain are bound between dmax=1.52 to 2.

A new integral equation method for calculating interacting stress intensity factor of multiple crack-hole problem

In this paper, a new integral equation method is proposed based on elementary solutions and superposition principle to study multiple crack-hole problem under both remote and surface stresses. Several typical crack-hole problems are solved in order to compare the calculation results of interacting stress intensity factors (SIFs) obtained by the newly proposed method with those obtained by Green’s function method, dislocation density method, finite element method and digital photo-elasticity method, and further to investigate the effect of loading conditions and crack-hole geometric parameters on SIFs. Research results show that there exists a neutral inclination angle α0 of the crack (with x-axis) for eliminating the crack-hole interaction when σx∞ ≥ σy∞. Increase of σx∞ is helpful for cracking arrest and the compressive stresses on crack and hole surfaces are helpful for crack propagation. In addition, the normal stress (p) on the crack surface only affects KI and α0 of KI, while the normal stress (n) on the hole surface affects both KI and α0 of KI, and KII and α0 of KII. The hole radius (R) and the crack-hole spacing distance (t) have little effect on α0 of KI and KII. The new integral equation method not only has almost the same calculation results of SIFs as the Green’s function, dislocation density and finite element methods, but also has advantage of simplicity and wide applicability over Green’s function and dislocation density methods in calculating the interacting SIFs of the cracks under both remote and surface stresses.

Effect of aspect ratio on dynamic fracture toughness of particulate polymer composite using artificial neural network

The present study discusses about the effect of the aspect ratio of the fillers on the fracture toughness of the glass-filled epoxy composites under impact loading. Three different kinds of fillers (spheres, flakes and rods) were used with different volume fractions (5%, 10% and 15%). Experimental results for Stress Intensity Factor (SIF) were obtained using a gas gun setup and a high speed camera. Further experimental investigation was done using fractographs obtained from Scanning Electron Microscope (SEM). Then the potential of using Artificial Neural Network (ANN) in predicting the effect of filler shape on the fracture behavior is studied. The framework of Multi-Layer Perceptron (MLP) feed forward network was used to predict the SIF history using four input parameters viz. time, dynamic elastic modulus, aspect ratio and volume fraction of the glass fillers. Experimental results of fracture test under impact loading were fed to train the ANN network and later the predicted results were compared with the experimental ones. Owing to the fact that predicted values had an accuracy of 91%, crack initiation toughness was predicted corresponding to the intermediate values of aspect ratio for which the experiments were not performed. Among the four input parameters, aspect ratio (largest/shortest dimension) was found to be the most important parameter in the prediction of SIF after time, followed by the dynamic modulus and volume fraction. The significance of aspect ratio lies in increasing the surface area to volume ratio which is responsible for the interfacial strength between the matrix and the filler and hence affects the fracture toughness of the overall composite material.

Combined influence of pin-hole interference and additional hole on the stress intensity factor for a pin loaded finite plate

This paper presents the results of Stress Intensity Factors (SIFs) for a crack emanating from a finite width plate with pin loaded cracked hole, through a 2-D plane stress Finite Element analysis using ANSYS®. The effect of pin-hole interference and additional stress relieving holes in the plate is investigated. Initial studies were performed on the pin-loaded plate with various crack sizes at the center of the plate, with different interference levels, typical of industrial components. Later, parametric studies were conducted by inserting an additional hole of different diameters placed at a distance from the central cracked hole that acts as stress reliever. The synergistic effect of interference and additional hole in reducing the SIF has been analyzed and the most beneficial interference level, diameter of additional hole and its position has been identified.

Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

Elastic interaction between a semi-infinite debonded anticrack and a screw dislocation

We study the elastic interaction between a semi-infinite debonded anticrack lying on the negative real axis and a screw dislocation under the assumption of anti-plane mechanical loading. The lower side of the anticrack (or rigid line inclusion) is perfectly bonded to the surrounding material in contrast to its upper side which is fully debonded. A simple closed-form solution to this interaction problem is developed by means of conformal mapping and the method of images. Specifically, we obtain expressions for the image force acting on the screw dislocation, the two resultant stress intensity factors respectively characterizing the r−3/4 and r−1/4 type singularities at the tip of the debonded anticrack and the resultant material force on the debonded anticrack. The dislocation emission criterion from the debonded anticrack in terms of two critical stress intensity factors is also established.

Interaction between a completely coated semi-infinite insulating crack and a piezoelectric screw dislocation

We derive analytic solutions to the problem of a completely coated semi-infinite insulating crack interacting with a screw dislocation under the assumption of anti-plane mechanical and in-plane electrical loading in a piezoelectric composite. The screw dislocation can be located either in the piezoelectric matrix or in the piezoelectric coating itself. We obtain explicit expressions for the resultant stress and electric displacement intensity factors, the resultant crack extension force and the image force acting on the screw dislocation. By employing orthogonality relations for two corresponding eigenvectors, we avoid tedious matrix operations in the development of the final expressions for the resultant field intensity factors, resultant crack extension force and image force.

Adaptive extended isogeometric analysis based on PHT-splines for thin cracked plates and shells with Kirchhoff–Love theory

• We implement an extended isogeometric analysis based on PHT-splines for thin-walled structures fracture problems. • C 1 -continuity is guaranteed by high smoothness of PHT-splines thus preventing hinge effects in Kirchhoff–Love theory. • We present a stress recovery-based posteriori error estimator technique to drive the adaptive procedure in cracked thin structures. • Results obtained using the adaptive XIGA-PHT demonstrate efficiency and accuracy compared with available literature solutions. In this paper, a posteriori error estimation and mesh adaptation approach for thin plate and shell structures of through-the-thickness crack is presented. This method uses the extended isogeometric analysis (XIGA) based on PHT-splines (Polynomial splines over Hierarchical T-meshes), which is abbreviated as XIGA-PHT. In XIGA-PHT, the isogeometric displacement approximation is locally enriched with enrichment functions, which efficiently capture the displacement discontinuity across the crack face as well as the stress singularity in the vicinity of the crack tip. On the one hand, the rotational degrees of freedom (RDOFs) are not required in Kirchhoff–Love theory, which drastically reduces the complexity of enrichment mode and computational scale for crack analysis. On the other hand, the PHT-splines basis functions can automatically satisfy the requirement of C 1 -continuity for the Kirchhoff–Love theory. Moreover, the PHT-splines facilitate the local refinement, which is the deficiency of NURBS-based isogeometric formulations. The local refinement is highly suitable for adaptive analysis. The stress recovery-based posteriori error estimator combined with the superconvergent patch recovery (SPR) technique is used to evaluate the approximate local discretization error. A new strategy for selecting enriched recovered functions in the enriched areas was proposed. Special functions extracted from the asymptotic stress solutions are applied to obtain the recovered stress field in the enriched area. The results of stress intensity factors or J-integral values obtained by the adaptive XIGA-PHT are compared with reference solutions. Several thin plate and shell illustrative examples demonstrate the effectiveness and accuracy of the proposed adaptive XIGA-PHT.

Interaction between a completely coated semi-infinite crack and a screw dislocation

Using complex variable methods, we derive analytic solutions to the problem of a screw dislocation interacting with a completely coated semi-infinite mode III crack. The crack and the parabolic coating–matrix interface have a common focus. The screw dislocation can be located either in the surrounding matrix or in the coating itself. Explicit expressions for the resultant stress intensity factor at the crack tip and the image force acting on the screw dislocation are obtained. Several special cases are discussed in detail to demonstrate the solutions and also to validate their correctness.