Mixed Mode SIFs Research Articles

Mixed-mode fracture analysis of FGMs using [formula omitted]-integral: Formulation and FE implementation

This paper introduces a computational method based on the Jk-integral for mixed-mode fracture analysis of isotropic functionally graded materials (FGMs), subjected to mixed-mode loading. The present development is implemented by means of the finite element method (FEM), by couplingofAnsys and Matlabsoftware’s. The continuous variations in the material parameters of the functionally graded medium are treated by specifying the material properties at the centroid of each finite element. The Jk-integral implementation is validated numerically by considering two different problems, the edge-cracked FGM plate and the four-point bending specimen with crack parallel to material gradation. The presented results illustrate the influences of material property gradation and crack geometry on the mixed-mode SIFs. The comparisons reported by available reference solutions indicate also that the numerical results obtained by present method have a high precision and that the expanded form of the Jk-integral is independent of the domain.

Accurate and efficient method for analyzing mixed-mode SIFs for inclined surface cracks in semi-infinite bodies by using numerical influence function method

An effective technique to compute mixed-mode stress intensity factors (MM-SIFs) for inclined surface cracks in semi-infinite bodies under arbitrary stress fields is proposed and validated. The proposed technique in this study is accurate and handiness for calculating MM-SIFs of different crack angles by using only one non-inclined cracked model. The benefit of this technique is achieved by using the influence function method (IFM) to evaluate MM-SIFs. A fully-automated influence coefficient database (ICDB) calculation system is developed based on the IFM. The interaction integral method (IIM) including the crack face traction (CFT) integral, which can improve the accuracy of SIF solutions, is employed in the developed ICDB. Once the ICDB for unit distributed load (UDL) is established for a target finite element (FE) model, MM-SIFs under arbitrary stress distributions of different crack angles can be calculated accurately in a short time. The developed ICDB is validated by comparing mode-I and MM-SIF solutions obtained by IFM with well-established reference solutions for different crack angles and Poisson’s ratios. The effect of Poisson’s ratio on MM-SIFs is also discussed based on the SIF solutions.

Comprehensive study on the crack tip parameters of two types of disc specimens under combined confining pressure and diametric concentrated forces

Stress intensity factors and T-stress of centrally cracked circular disc (CCCD) and hollow central cracked disc (HCCD) specimens with different geometric parameters under the combined diametric concentrated forces and confining pressure were calculated using Finite Element Method. The influence of crack length, crack inclination angle, aperture ratios and confining pressure on the mixed mode SIFs, T-stress and biaxiality ratio of CCCD and HCCD specimens is investigated in this paper. Compared with the HCCD specimens, CCCD specimens can more easily transform pure mode I loading to pure mode II loading. The results obtained in this paper are helpful to understand the mechanical mechanism of rock fracture under combined confining pressure and diametric concentrated forces.

A novel approach to evaluate mixed-mode SIFs for a through-thickness crack in a welding residual stress field using an effective welding simulation method

This paper accurately evaluates mixed-mode SIFs (MM-SIFs) for cracks in welding residual stress (WRS) fields using a novel approach based on finite element method (FEM). For this reason, the interaction integral method (IIM) available in WARP3D, an open source code, was developed to include normal and shear stress components in MM-SIF solutions. The effectiveness of the developed WARP3D-IIM was verified based on the superposition method and by means of well-established analytical and numerical reference solutions using an inclined through-thickness cracked FE model. After validating the adequacy of the developed WARP3D-IIM, different welding simulations were conducted using JWRIAN (Joining and Welding Research Institute ANalysis). JWRIAN, a sophisticated welding simulation in-house code, was adopted as a welding simulation tool to predict WRS. Different weld line (WL) orientations, as well as different perpendicular distances between WLs, were performed to investigate their influence on the behavior of MM-SIFs. The developed WARP3D-IIM and superposition method were thereafter employed to evaluate MM-SIF solutions for an inclined through-thickness crack in the simulated WRS fields. Different crack angles were also employed to examine the effect of the induced WRS on calculated MM-SIFs. SIF solutions resulting from WRS were validated with analytical reference solutions. Results showed that WRS has a considerable influence on the behavior of MM-SIFs. Moreover, WL orientation as well as the perpendicular distance between WLs revealed a significant influence on the induced WRS and thus MM-SIF solutions. On the other hand, the crack angle showed a remarkable effect on the behavior of MM-SIFs. MM-SIFs calculated at through-thickness crack fronts were influenced by the induced WRS distribution as well as crack angle.

Steady State Thermo XFEM Fracture Analysis of Isotropic and an Isotropic FG Plate with Inclined Center Crack

The extended-finite element method (X-FEM) is usedfor crack analysis of orthotropic and isotropic functionally graded composite material (FGCM) plate with a slanted crackunder thermal loadings. The enrichments functions ofdiscontinuity are implemented. Mixed-mode SIFs arecalculated in isotropic and orthotropic FGMs. Gaussiantechnique (Q4) has been applied in the numerical calculation ofinteraction of solution. Thermal effects, fundamentalequations, the interaction integral of non-homogeneous cases(M-integral), and proposal numerical integration rule is set tosimulate and to debate the accuracy of the present work resultsin comparing with the results of the references available inthe literature. In addition, the effect of the size of crack is studiedto discuss the values of energy release rate and stress intensityfactors with different crack angles. The present study isimplemented by using MATLAB program to present steady-state thermo XFEM fracture analysis of isotropic and anisotropic FG plate with inclined center crack.

Stochastic investigation of the facture problem in functionally graded materials with uncertain mechanical properties and an arbitrarily oriented crack

The macro and micro analysis methods of the fracture mechanics are adopted to investigate the fracture mechanics problem of functionally graded materials (FGMs) with uncertain mechanical properties and an arbitrarily oriented crack. In this paper, the piecewise-exponential model and the Mori-Tanaka model are combined to solve the mixed-mode crack problem for every sample analytically. Then according to the probability theory, the mixed-mode SIFs for the samples are obtained. So the probabilistic attributes of the mixed-mode SIFs in FGMs can be obtained. As a result, the probabilistic density function of SIFs can be provided by means of the graphic method. The method based on macro and micro mechanics can be efficiently applied to carry out the related research of the influences of the crack angles and lengths on the stochastic characteristics of the mixed-mode SIFs.

Probabilistic fracture investigation of symmetric angle ply laminated composite plates using displacement correlation method

AbstractThe second order statistics of mixed mode stress intensity factors (MSIF) of single edge V-notched angle ply laminated composite plate subjected to uniaxial tensile load with uncertinity in the system properties using displacement correlation method (DCM) is evaluated. The random system properties such as material properties, crack opening and crack length are modelled as combined uncorrelated and correlated random system variables. A C0 finite element method (FEM) based on higher order shear deformation plate theory (HSDT) is used for basic formulation. The Taylor series based first order perturbation technique (FOPT), second order perturbation technique (SOPT) are used and direct Monte Carlo simulation (MCS) is performed to evaluate the statistics (mean and coefficient of variance) of the mixed mode SIFs. The present work signifies the accurate analysis of frature behaviour by influence of different random variables and fibre orientations on the fracture behaviour in angle ply laminates.

Mixed mode stress intensity factors for elliptical subsurface cracks in an elastic half‐space subjected to a uniform normal loading

ABSTRACTAn elliptical subsurface crack under normal loading may experience mixed fracture modes due to the non‐symmetrical geometry. This paper investigates the coupling of the modes of elliptical subsurface cracks subjected to a uniform normal loading. First, a three‐dimensional finite element model of a crack in an infinite space has been developed and validated. Then, by moving the crack close to surface, mixed mode SIFs have been calculated for a wide range of elliptical subsurface cracks under uniform normal loading. Cracks with aspect ratios of 0.2–1.0 and ratios of crack depth to crack length from 0.05 to infinity have been investigated through 50 finite element analyses. In this range, KII/KI and KIII/KI ratios increase up to 68.9% and 9.4%, respectively. Three equations for mode I, II and III SIFs have been obtained by fitting to the finite element results. These equations can be used efficiently as reference SIFs for extracting the weight functions.