Including Stress Intensity Factor Research Articles

A study of Griffith crack in nonlocal infinite magneto-elastic media

The main objective of this article is to study how a finite crack interacts with horizontally polarized shear (SH) waves in a nonlocal isotropic medium when a magnetic field is present. The study aims to understand the effects of various parameters, including the magnetic field, non-locality, frequency of SH waves, on the behavior of the crack. Here, we are concerned with Griffith’s theory of a brittle fracture crack mechanism. The article starts by formulating the governing equations for the propagation of SH waves in the given medium. These equations are converted into dual integral equations using Fourier transformation. Subsequently, an Abel transformation is applied to obtain a Fredholm integral equation of the second kind. Daubechies wavelet family has been used to find an approximate solution for the integral equation. The article aims to determine specific physical quantities including stress intensity factor (SIF), shear stress, and crack energy related to the behavior of the crack. These parameters are essential in understanding how the crack responds to the external conditions. The application of Daubechies wavelets in this context is a relatively new and innovative approach. The study performed a comprehensive analysis of the effects of various factors on the crack behavior. The findings are presented in graphical form to help illustrate the conclusions. To assess the accuracy of the proposed method, the obtained results are compared with known results from the literature for local media. This is an important step in demonstrating the reliability and effectiveness of the proposed approach.

Analysis of mixed-mode Compact-Tension-Shear (CTS) specimens with slanted propagating cracks

Compact-Tension-Shear (CTS) specimen with its loading device has been widely used in mixed-mode I&II fatigue crack growth (FCG) experiments. To accurately describe the FCG behavior of materials, it is necessary to determine both the crack length and the parameters that represent crack driving force or crack front stress field in real-time. However, the relevant solutions are currently incomplete or insufficient. In this paper, for CTS specimen with slanted propagating crack, the variations of stress field parameters including stress intensity factors (SIFs) and T-stresses, as well as crack-mouth-opening-displacement (CMOD) compliance were investigated through finite element (FE) analysis. The results show that KI, KII and T11 are greatly influenced by the initial crack length ratio, the slanted propagating crack length ratio and the loading angle, but rarely by the specimen thickness among the considered range of geometries; T33 as an out-of-plane constraint parameter, however, is subject to the coupling effects of in-plane geometries, out-of-plane geometries and the mixed-mode loading. Moreover, it is shown that the measurement span has an effect on CMOD-compliance results for CTS specimens under mixed-mode loading, which is only negligible within the recommended range of D/W∈(0.02, 0.16]. Finally, the accuracy of the developed CMOD-compliance equations was validated through FCG experiments. The conclusions obtained in the current work will provide usable constraint-related crack front stress field parameter solutions for the analysis of FCG behavior in mixed fracture mode, and also give a reliable non-visual method for the determination of fatigue propagating crack length in CTS experiments.

Interaction integral method for thermal fracture of nonhomogeneous magneto-electro-elastic materials

This paper focuses on the thermal fracture performance of magneto-electro-elastic (MEE) materials and proposes a new interaction integral (I-integral) method for extracting the key fracture parameters, including stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF). After introducing the integrals along the interfaces with mismatched thermal properties, the I-integral is strictly proved to be independent of the integration domain size. This domain-independence is numerically validated for nonhomogeneous and discontinuous MEE materials (relative deviation <1%). Through the combination with the extended finite element method (XFEM), the developed I-integral method is employed to study thermal crack problems of MEE materials. The results show that the I-integral can achieve high numerical accuracy in determining the intensity factors. The thermal boundary condition of crack surface affects the intensity factors significantly. Finally, this paper focuses on the thermal fracture of laminated and fiber reinforced MEE composites. As for MEE composites (BaTiO3/CoFe2O4), the SIFs increase as the volume fraction of PM (CoFe2O4). Reducing the percentage of piezomagnetic phase can enhance the fracture resistance of MEE multiphase composites. At the identical volume fraction of components, the fracture resistance of fiber-reinforced MEE composites is generally better than that of laminated MEE composites and the PE-fiber composite exhibits greater fracture resistance than the PM-fiber composite.

Direct Computation of 3-D Stress Intensity Factors of Straight and Curved Planar Cracks with the P-Version Finite Element Method and Contour Integral Method.

This paper presents direct computations of 3-D fracture parameters including stress intensity factors (SIFs) and T-stress for straight and curved planar cracks with the p-version finite element method (P-FEM) and contour integral method (CIM). No excessive singular element or enrichment function is required for the computation. To demonstrate the accuracy and efficiency of the proposed approaches, several benchmark numerical models of 3-D planar straight and curved cracks with single and mixed-mode fractures are considered and analyzed: a through thickness edge straight crack in a homogeneous material, a through thickness inclined straight crack, a penny-shaped crack embedded in a cube and a central ellipse shaped crack in a homogeneous cube. Numerical results are analyzed and compared with analytical solutions and those reported by the extended finite element method (XFEM) and the scaled boundary finite element method (SBFEM) in the available literature. Numerical experiments show the accuracy, robustness and effectiveness of the present method.

Finite element analysis of road structure containing top-down crack within asphalt concrete layer

In this paper, a four-layered road structure containing a top-down crack is investigated by performing finite element analyses in ABAQUS. In this study, in addition to the vertical load of a vehicle wheel, the horizontal load as well as its position with respect to the crack is also considered in the analyses, and the crack tip parameters including stress intensity factors (SIFs) and T-stress are then calculated. Moreover, influence of elastic modulus and thickness of the pavement layers on the crack tip parameters is studied. Results show that the horizontal and vertical loads along with their position with respect to the crack, elastic modulus and thickness of the road layers influence the crack tip parameters (KI, KII and T-stress) significantly. It was also found that for the cases that the vehicle wheel is positioned near the crack plane, only the shear deformation mode is observed at the crack tip; while, for the vehicle wheel positions far from the crack, only the opening mode is observed, and between these positions, both the opening and shear deformation modes (i.e., mixed mode I/II) are observed at the crack tip.

A Hamiltonian‐based analytical method for fracture analysis of linear thermo‐viscoelastic media

AbstractA Hamiltonian‐based methodology is presented to study the fracture behaviors of the thermo‐viscoelastic materials based on the Laplace transform. The governing equations and associated boundary conditions are rebuilt in a Hamiltonian form by using the symplectic mathematics in the frequency domain (s‐domain). The fundamental unknown vector composed of both displacements and stresses variables is expanded in terms of the symplectic eigensolutions. The corresponding unknown coefficients of the symplectic series are determined from the outer boundary conditions. Thus, the main unknowns are obtained and transformed into the time domain (t‐domain). The fracture parameters including stress intensity factors (SIFs) and J‐integrals are derived simultaneously. Numerical examples as well as convergence studies are given and are found to be in good agreement with the ANSYS results. A parametric study of thermo‐viscoelastic parameters is included also.

Influence of the Anisotropy of Materials on the Distribution of Stresses Near Parabolic Notches

We consider the problems of distribution of stresses in an infinite anisotropic plane containing a parabolic notch for three main types of deformation in the case where the asymptotics of the stress field is specified at infinity (including stress intensity factors at the tip of the corresponding semiinfinite crack). The solutions of these problems are obtained with the help of the limit transition from the known analytic solutions obtained for an elliptic hole in the anisotropic plane for three types of loading at infinity (symmetric tension, transverse and longitudinal shear). These results generalize the well-known data on the distribution of stresses near narrow rounded notches in the isotropic plane and reflect the influence of anisotropy of the material on the stress concentration.

Evaluation of crack-tip fields from DIC data: A parametric study

In the past two decades, crack-tip mechanics has been studied increasingly using full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), crack opening displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, the position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF by using Williams’ model. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation around the crack-tip has been examined. The comparison between nominal and experimental values of KI showed that the effect of subset size on the measured KI is negligible compared to the effect of the field of view and the position of the area of interest.

Computation of three-dimensional fracture parameters at interface cracks and notches by the scaled boundary finite element method

This paper presents the computations of fracture parameters including stress intensity factors and T-stress of three-dimensional cracks and notches by the scaled boundary finite element method. The singular stress field along the crack front is approximated by a singularity at a point through a semi-analytical solution. The solution is expressed as a matrix power function which allows direct extraction of the fracture parameters based on their definitions. No singular element or asymptotic solution is required for the extraction process. The numerical examples presented which include bimaterial interface cracks and V-notches illustrate the accuracy and versatility of the proposed approach.

Some experimental observations of crack-tip mechanics with displacement data

In the past two decades, crack-tip mechanics has been increasingly studied with full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), Crack Opening Displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, size of the images, position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF and T-stress by using Williams’ model. The concept of determination of the K-dominance zone from experimental data has also explored. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation ahead of the crack tip has been examined. The comparison between theoretical and experimental values of KI showed that the effect of subset size on the measured KI is negligible compared to the effect of size of the image.

An analytical approach for the mixed-mode crack in linear viscoelastic media

Abstract In this paper, an analytical approach is developed for the fracture analysis of linear viscoelastic media. By the Laplace transform, the governing equations for the time domain ( t -domain) are changed into frequency domain ( s -domain). Then, a Hamiltonian system is established by introducing the dual variables of displacements and energy variational principle. In the framework of symplectic mathematics, the unknown vector consisting of displacements and stresses is expanded in terms of symplectic eigensolutions whose coefficients can be determined from the outer boundary conditions. Then t -domain solution is finally obtained by inverse Laplace transform and exact forms of fracture parameters including stress intensity factor (SIF) and J -integral are derived simultaneously. Numerical examples are provided to verify the validity of the present method. A parametric study of viscoelastic parameters and outer boundary conditions is carried out also.

Effect of filler shape, volume fraction and loading rate on dynamic fracture behavior of glass-filled epoxy

The effect of filler shape and filler volume fraction on the dynamic fracture behavior of particulate polymer composites (PPC) has been studied. Mode-I dynamic fracture experiments were carried out on pre-notched glass-filled epoxy. An experimental setup comprising of a gas-gun and a long-bar was used to deliver one-point impact loading to unconstrained specimens. Pulse shapers were utilized to control the loading rate during impact loading. The dynamic crack initiation and propagation events were captured using high-speed photography (∼300,000 frames per second). Digital Image Correlation (DIC) method was utilized to measure in-plane displacement fields around the crack-tip and extract fracture parameters including stress intensity factor histories to examine the filler shape, volume fraction and loading rate effects. The results showed a pronounced improvement in crack initiation toughness for rod-shaped fillers producing ∼145% increase over unfilled epoxy at 15% Vf with flakes and spherical fillers showing ∼97% and ∼67% improvement, respectively. For all three different volume fractions – 5%, 10%, and 15% – considered, the rod-shaped fillers produced the highest crack initiation toughness as well as post-initiation stress intensity factors followed by flakes and spheres, respectively. A linear relationship between crack initiation toughness and log of filler aspect ratio was also recorded. In addition, for 10% Vf rod-shaped filler case, the effect of loading rate on dynamic fracture behavior has been examined. The loading rate study showed ∼113% and ∼50% increase in crack initiation toughness for the lowest and the highest loading rate cases, respectively, compared to that of neat epoxy.

A domain-independent interaction integral for magneto-electro-elastic materials

Magneto-electro-elastic (MEE) materials usually consist of piezoelectric (PE) and piezomagnetic (PM) phases. Between different constituent phases, there exist lots of interfaces with discontinuous MEE properties. Complex interface distribution brings a great difficulty to the fracture analysis of MEE materials since the present fracture mechanics methods can hardly solve the fracture parameters efficiently of a crack surrounded by complex interfaces. This paper develops a new domain formulation of the interaction integral for the computation of the fracture parameters including stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF) for linear MEE materials. The formulation derived here does not involve any derivatives of material properties and moreover, it can be proved that an arbitrary interface in the integral domain does not affect the validity and the value of the interaction integral. Namely, the interaction integral is domain-independent for material interfaces and thus, its application does not require material parameters to be continuous. Due to this advantage, the interaction integral becomes an effective approach for extracting the fracture parameters of MEE materials with complex interfaces. Combined with the extended finite element method (XFEM), the interaction integral is employed to solve several representative problems to verify its accuracy and domain-independence. Good results show the effectiveness of the present method in the fracture analysis of MEE materials with continuous and discontinuous properties. Finally, the particulate MEE composites composed of PE and PM phases are considered and four schemes of different property-homogenization level are proposed for comparing their effectiveness.

Thermal response of a partially insulated interface crack in a graded coating-substrate structure under thermo-mechanical disturbance: Energy release and density

Consider the thermal fracture problem of a functionally graded coating-substrate structure of finite thickness with a partially insulated interface crack subjected to thermal-mechanical supply. A new model is proposed that the heat conduction through the crack region occurs and the temperature drop across the crack surfaces is the result of the thermal resistance. For the first time, real fundamental solutions are derived for the fracture analysis of functionally graded materials. The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically. The asymptotic expressions with higher order terms for the singular integral kernels are considered to improve the accuracy and efficiency of the numerical integration. Explicit expressions of various failure modes including stress intensity factors, energy release rate and strain energy density, are provided. Numerical results are presented to illustrate the effects of non-homogeneity parameters and the dimensionless thermal resistance on the temperature distribution along the crack surfaces and extended crack line, the thermal stress intensity factors and minimum strain energy density.

Short fatigue crack growth from a blunt notch in plate specimens

Short crack growth behavior from a notch including crack closure and load ratio effects was investigated. Experiments and analyses were carried out using four-point bending specimens made of SAE 1045 steel, using a blunt notch keyhole specimen geometry. The lower the load ratio, the more notch effect on short crack growth behavior was observed. Short cracks in the notch affected zone had higher growth rates than long cracks. After the crack grew out of the notch effect field, short crack growth rates merged with the long crack growth rates. Several parameters were used to correlate the short crack growth rates including stress intensity factor range, effective stress intensity factor range, and stress intensity factor range based on notch root stress.

Elastodynamic Crack Analysis by Boundary Element Method Using Numerical Inversion of Laplace Transform.

In the present study, an alternative strategy for elasto-dynamic crack problems using boundary element method is discussed. The Laplace transformation is applied to time variation in the formulation. Since the numerical solutions are obtained in the Laplace-transformed domain, the numerical-inverse Laplace transformation is adopted to obtain time histories of the solutions. In the present method, the distributions of the displacement and traction in the vicinity of the crack tip are expressed as the superposition of singular terms and regular ones. The singular terms are the analytical solutions including stress intensity factors of Modes I and II, while the regular terms are approximated by the discrete polynomial functions in general BEM formulations. Additionally, the ligament side is discretized by singular-type crack elements in order to increase the accuracy of the traction near the crack tip. It is shown that the dynamic stress intensity factors (DSIFs) of Modes I and II are determined directly without supplementary procedures such as extrapolation or J-integral scheme. The validity of the present method is confirmed through the analysis of mixed mode dynamic problems of crack.

A multiparameter approach to the prediction of fatigue crack growth in metallic materials

A multiparameter approach is proposed for the characterization of fatigue crack growth in metallic materials. The model assesses the combined effects of identifiable multiple variables that can contribute to fatigue crack growth. Mathematical expressions are presented for the determination of fatigue crack growth rates, da/dN, as functions of multiple variables, including stress intensity factor range, ΔK, stress ratio, R, crack closure stress intensity factor, Kcl , the maximum stress intensity factor Kmax , nominal specimen thickness, t, frequency, Ω, and temperature, T. A generalized empirical methodology is proposed for the estimation of fatigue crack growth rates as a function of these variables. The validity of the methodology is then verified by making appropriate comparisons between predicted and measured fatigue crack growth data obtained from experiments on Ti–6Al–4V. The effects of stress ratio and specimen thickness on fatigue crack growth rates are then rationalized by crack closure considerations. The multiparameter model is also shown to provide a good fit to experimental data obtained for HY‐80 steel, Inconel 718 polycrystal and Inconel 718 single crystal. Finally, the implications of the results are discussed for the prediction of fatigue crack growth and fatigue life.

Application of complex path-independent integrals to problems of bending of thin elastic plates

Complex path-independent integrals have been already widely applied to problems of plane and antiplane elasticity for the determination of a variety of quantities of interest including stress intensity factors, loading intensities and the positions of geometrical characteristic lengths of singularities in the elastic field (like cracks, holes and inclusions). In this paper, we show that the same results apply also to the case of problems of thin isotropic elastic plates under bending where the complex-variable formulation is also valid. We make reference to the experimental methods which are appropriate for these integrals in an engineering environment and, finally, we apply this approach to the location of a circular hole in the problem of bending of a thin plate. Numerical results are also presented.