Estimation Of Stress Intensity Factors Research Articles

Stress singularity evaluation for three-dimensional cracks using characteristic tensor method

The Characteristic tensor method (CTM) is a new method to evaluate the singular stress field with a characteristic tensor (CT) which is calculated by averaging the stress in an infinitesimal volume at a crack tip. The CT has a linear relation with the stress intensity factor (SIF), which characterizes the singular stress field around a crack tip in an isotropic homogeneous elastic body. Even under mixed-mode loading conditions, the SIFs of each mode can be easily and efficiently estimated using CT. For the practical use in industries, the evaluation of the CTM for a three-dimensional crack under general three-dimensional stress state is necessary. In this study, the reliability and accuracy of CTM is investigated by estimating SIFs in several representative types of three-dimensional cracks where stress states are calculated by the finite element method. The results show that the SIFs estimated by the CTM have high accuracy even for mixed-mode conditions. It was, thus, demonstrated that CTM provides a practical and reliable approach for the efficient estimation of SIFs of three-dimensional cracks.

Estimation of Stress Intensity Factor of Multiple Inclined Centre Cracks under Biaxial Loading

All mechanical components are usually subjected to several manufacturing operations such as primary processing, machining, and finishing operations. During these operations, it is possible for the flaws to be introduced in the component either internally or on the external surface. In this situation, the reliability and safety assessment of the component in the presence of flaws can be achieved using fracture mechanics tool. This tool aids in analysing the severity of crack situation and its stability for the given loading conditions using certain fracture parameters. In this work, the stress intensity factor (SIF) analysis of a 2D rectangular plate with a centre crack (through the thickness) subjected to biaxial loading is performed through simulation. The numerical model is validated using analytical results available in the literature. The influence of parameters such as biaxial loading factor, ratio of crack length to width of the plate, inclination of crack, number of cracks on the SIFs is investigated.

Fatigue crack growth of Al 5083-H111 subjected to mixed-mode loading

Fatigue is a major cause of failure in several industries, and in many practical cases, local mixed-mode conditions prevail at the crack front. The effect of plane mode mixity on the crack growth rate and crack growth direction has been investigated. Fatigue crack growth experiments have been conducted on aluminum alloy Al5083-H111 for several mode mixities. A fixture was manufactured in order to apply the different combinations of mode I and II by changing loading angle. Afterward, three-dimensional simulations have been implemented using the Zencrack software. Based on numerical simulations, new relations are proposed to estimate stress intensity factors for compact tension shear geometry by modifying Richard’s equations [1].

Extraction formulas of stress intensity factors for the biharmonic equations containing crack singularities

We derive formulas extracting stress intensity factors of the biharmonic equations on cracked domains with clamped (or simply supported or free) boundary conditions along the crack faces. Each of these formulas can be written in terms of the integral of the given source function multiplied by the cut-off dual singularity and the integral of the unknown true solution multiplied by the cut-off dual singularity over the unit disk. The unknown true solution in the extraction formulas is calculated by either the Implicitly Enriched Galerkin Method or the Iteration Methods. The former was developed by the authors (Kim, Oh, Palta, Kim) and the latter proposed in this paper is the sum of the solution of a regular biharmonic equation and singular functions with iteratively estimated stress intensity factors as coefficients. We show the Iteration Methods quickly converge and the proposed Enrichment Method yields highly accurate stress intensity factors. We also demonstrate that for a known true solution, the extraction formulas yield exact stress intensity factors.

Mode-I, Mode-II, and Mode-III Stress Intensity Factor Estimation of Regular- and Irregular-Shaped Surface Cracks in Circular Pipes

Stress intensity factor (SIF) of surface cracks (semi-circular, semi-elliptical, and irregular shapes) located on a circular pipe (hollow) has been determined using numerical method. The irregular-shaped crack geometry was considered in the present work in order to simulate the cracks that are generally developed during service condition. The interaction behavior of multiple cracks on SIF calculation has also been investigated. Crack aspect ratios [a/c; “a” is the crack depth and where “c” is semi-major axis of elliptical crack] ranging between 0.6 and 1.0 and crack depth ratios [(a/d); where “d” diameter of the pipe] ranging between 0.1 and 0.4 were considered. Irregular-shaped cracks were modeled by keeping the crack depth (a) constant. For a regular profile semi-elliptic crack [(a/c) = 0.6], higher SIF was observed at crack middle region [(S/S0) = 0]. In contrast, higher SIF was observed at crack surface region [(S/S0) = ± 1] for semi-circular crack. Asymmetric spreading of SIF was noticed because of added effect of mode-II and mode-III fracture. In addition, the leading mode of fracture at short crack depth [(a/d) ≤ 0.1] was mode-II (in-plane shear) and mode-III (out of plane shear) fractures whereas at deep crack depths [(a/d) ≥ 0.4], the leading mode of fracture was mode-I fracture which is crack opening mode. Marginal influence of crack aspect ratio was noticed at crack surface region [(S/S0) = ± 1] and the effect is significant at crack middle region [(S/S0) = 0]. For a constant crack depth, higher SIF was obtained at the middle region [(S/S0) = 0] compared to regular profile crack. When comparing the observations of regular semi-elliptic crack, higher influence of mode-II and mode-III fracture was observed for irregular-shaped semi-circular crack which may leads to additional crack growth. Thus, approximating the standard crack geometry may over/under predict the SIF values. It is also inferred that the presence of adjacent cracks significantly affects the SIF of middle crack due to interaction effect. The interaction behavior was observed to be more pronounced when multiple cracks are located at closer interval. The interaction effect reduces gradually when the distance between crack centers increases. The improved SIF solutions obtained with consideration of additional fracture modes will be useful during the residual life determination.

Analysis of stress intensity factor for fatigue crack using bootstrap S-version finite element model

PurposeFailure of the materials occurs once the stress intensity factor (SIF) overtakes the material fracture toughness. At this level, the crack will grow rapidly resulting in unstable crack growth until a complete fracture happens. The SIF calculation of the materials can be conducted by experimental, theoretical and numerical techniques. Prediction of SIF is crucial to ensure safety life from the material failure. The aim of the simulation study is to evaluate the accuracy of SIF prediction using finite element analysis.Design/methodology/approachThe bootstrap resampling method is employed in S-version finite element model (S-FEM) to generate the random variables in this simulation analysis. The SIF analysis studies are promoted by bootstrap S-version Finite Element Model (BootstrapS-FEM). Virtual crack closure-integral method (VCCM) is an important concept to compute the energy release rate and SIF. The semielliptical crack shape is applied with different crack shape aspect ratio in this simulation analysis. The BootstrapS-FEM produces the prediction of SIFs for tension model.FindingsThe mean of BootstrapS-FEM is calculated from 100 samples by the resampling method. The bounds are computed based on the lower and upper bounds of the hundred samples of BootstrapS-FEM. The prediction of SIFs is validated with Newman–Raju solution and deterministic S-FEM within 95 percent confidence bounds. All possible values of SIF estimation by BootstrapS-FEM are plotted in a graph. The mean of the BootstrapS-FEM is referred to as point estimation. The Newman–Raju solution and deterministic S-FEM values are within the 95 percent confidence bounds. Thus, the BootstrapS-FEM is considered valid for the prediction with less than 6 percent of percentage error.Originality/valueThe bootstrap resampling method is employed in S-FEM to generate the random variables in this simulation analysis.

Generalized displacement correlation method for mechanical and thermal fracture of FGM

The main objective of this work is to present a numerical modeling of mixed-mode fracture in isotropic functionally graded materials (FGMs), under mechanical and thermal loading conditions. In this paper, the displacement-based method, termed the generalized displacement correlation (GDC) method, is investigated for estimating stress intensity factor (SIF). Using the ANSYS Parametric Design Language (APDL), the continuous variations of the material properties are incorporated by specified parameters at the centroid of each element. This paper presents various numerical examples in which the accuracy of the present method is verified. Comparisons have been made between the SIFs predicted by the GDC method and the available reference solutions in the current literature. A good agreement is achieved between the results of the GDC method and the reference solutions.

Study of the biaxial fatigue behaviour and overloads on S355 low carbon steel

This work aimed to study the fatigue behaviour of S355 low carbon steel under uniaxial and biaxial loading conditions and to measure the overload effects under both types of loads. The analysis is performed with a local strain approach and with damage tolerance approach. Local strain based investigation was based on Fatemi-Socie critical plane model. This allows the life reduction caused by growing the crack from a stress raiser to be quantified. The fatigue life reduction caused by applying simultaneously torsional and tension loads was also evaluated with Fatemi-Socie model. In addition, the crack opening displacement (COD) and the effective stress intensity factor (SIF) were evaluated experimentally via full-field technique of digital image correlation (DIC). Both COD and SIF have been useful to understand the transient effects caused by a 40% overload under the two types of load. In addition, COD measurements allowed the offset compliance method for evaluating the opening load to be applied on a cylindrical specimen subjected to tension load. SIF estimation was also useful to quantify the mode mixity (I + II) developed during the experiment under the two types of load.

Theoretical study for estimation of the dynamic stress intensity factor from results of an experimental measurement

The aim of this contribution is a theoretical study for the estimation of the dynamic stress intensity factor (DSIF) using results from an experimental measurement. Using optical methods, it is possible to determine individual displacements of crack surfaces in multiple distances from the crack tip. Based on the theoretical distribution of displacements in the crack front, the DSIF can be estimated using the displacement extrapolation method at each time step. The main motivation for this methodology is the difficulty of estimation DSIF in real structures. The described approach is consequently compared with conventional numerical methods and the applicability is evaluated.

Estimation of stress intensity factors from crack flank displacements

In the present numerical investigation, the efficacy of a recently proposed displacement based method for estimation of mixed mode (I/II) stress intensity factors of 2D configurations are demonstrated using additional benchmark examples. The proposed displacement based technique is simple, efficient and robust and can be used for the fatigue crack growth simulations. This technique uses the crack opening and crack sliding displacements obtained from the finite element analysis to determine the mode I, mode II and mixed mode (I/II) stress intensity factors (SIFs). This technique can provide the sign of the mode II stress intensity factors which enables it to be used for the fatigue crack growth simulations involving numerous computational steps. Quarter point elements (QPEs) are employed around the crack tip. Convergence of the present method is studied and the performance is assessed by comparing the extracted SIFs using other methods such as displacement extrapolation, J-integral and interaction integral techniques. The present study indicates that very accurate values of SIFs can be computed using the proposed technique and the accuracy of the SIF solutions are of the order of the path independent integrals

Characteristic Tensor for Evaluation of Singular Stress Field under Mixed-mode Loadings

A characteristic tensor is defined using stress tensor averaged in a small circular domain at the crack tip and multiplied by the root of domain radius. It possesses the original stress tensor characteristics and has a simple relationship with conventional fracture-mechanics parameters. Therefore, it can be used to estimate stress intensity factors (SIFs) for cracks of arbitrary shape subjected to multiaxial stress loads. A characteristic tensor can also be used to estimate SIFs for kinked cracks. This study examines the relation between a characteristic tensor and SIFs to demonstrate the correlation between the characteristic tensor and fracture-mechanics parameters. Consequently, a single straight crack and a kinked crack of finite length existing in a twodimensional, infinite isotropic elastic body in a plane stress state, were considered to investigate the properties of the characteristic tensor under mixed-mode loadings. To demonstrate the practical utility of the characteristic tensor, the stress distribution obtained through finite element analysis (FEA) was used to estimate mixed-mode SIFs, and the values of estimated SIFs were compared with those obtained using an analytical solution. Results demonstrate that SIFs estimated under mixed-mode loadings exhibit a good agreement with the analytical values. This indicates that the proposed characteristictensor-based approach is effective in extracting features of singular stress fields at crack tips, and can be employed to estimate values of fracture-mechanics parameters, such as SIFs. Owing to its simplicity, the proposed approach can be easily incorporated in commercial FE codes for practical applications to simulate the crack-growth problem under both static and dynamic loading scenarios. The excellent applicability of the characteristic tensor greatly contributes to efficiency of the design process in industries.

A wavelet multiresolution interpolation Galerkin method with effective treatments for discontinuity for crack growth analyses

A wavelet multiresolution interpolation Galerkin method (WMIGM) with effective algorithm for treatments on the discontinuity of cracks is developed to handle the growth of cracks. In our WMIGM, two robust nodal refining models of multiresolution enhancement are proposed to effectively control the generation of local nodes around the crack tips for capturing the singular stress fields. With our local multiresolution refinement algorithm, these local nodes are automatically generated and/or moved with ease, which will not affect the other nodes. The formulation of the proposed WMIGM is presented in detailed. Several problems of both stationary and growing cracks are studied to validate the present method. Results demonstrate that the present WMIGM possesses an excellent accuracy in both estimating stress intensity factors and tracing crack growth paths, as well as a strong stability against irregular nodal distribution with extremely large ratio of the maximum grid size to the minimum in the problem domain.

Thermo-electro-mechanical fatigue crack growth simulation in piezoelectric solids using XFEM approach

Cracks and multiple voids resulting from manufacturing processes interact with each other and severely affect the fracture phenomenon of piezoelectric components. These geometrical discontinuities degrade the service performance and lower the reliability of the piezoelectric devices. Therefore, the present work predicts fatigue-cracking behavior of piezo-electric structures in existence of multiple geometrical discontinuities under cyclic thermal-electrical-mechanical loads using extended finite element method (XFEM). Thermal interaction integrals approach and Stroh formalism are applied for estimating stress intensity factors (SIFs). Modified hoop SIF criterion has been utilized to predict crack growth direction under quasi-static fatigue loading conditions.

Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials.

Comprehensive Comparisons of Two-and Three-Dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis

This paper presents a comprehensive comparison of two finite element software in two and three dimensions. The first is a two-dimensional crack growth simulation program developed as source code by using Visual Fortran Language whereas the second is ANSYS mechanical program (3D structural analysis for fracture mechanic analysis). The procedure consists of computing stress intensity factors (SIFs), the crack growth path and the stresses and strain distributions via an incremental analysis of the crack extension, considering two and three-dimensional analysis. Comparisons between these two software were performed for different case studies for stress intensity factors as well as crack growth trajectory. This source code includes the mesh generator based on the advancing front method as well as all the pre and post process for the crack growth simulation under linear elastic fracture mechanics theory with a user-friendly interface. The maximum circumferential stress criterion was used for prediction of the crack growth in isotropic materials under mixed-mode loading. Furthermore, the equivalent domain integral method has been used for calculating the stress intensity factors values during crack growth. Verification of the predicted crack path and stress intensity factors values were validated with relevant experimental data and numerical results obtained by other researchers with a good agreement.

In situ through-thickness analysis of crack tip fields with synchrotron X-ray diffraction

In this work a novel approach to estimate in situ the stress intensity factor (SIF) through the thickness of metal specimens is presented. It is based on a hybrid methodology that combines powerful synchrotron X-ray diffraction data with an elastic analytical model describing the strain field around the crack tip. A sensitivity analysis is conducted to understand the largest sources of error and their impact on the estimated SIF values. The accuracy in locating the crack tip position was found to affect the quality of the SIF estimation. Accordingly a procedure is developed to help locate the crack tip position. The methodology is tested on ultra-fine grained aluminium alloy 5091 and on a bainitic steel. It is recommended that an area of interest having a size at least 3 times larger than the plane strain plastic zone is mapped, providing good SIF estimations (within 8%) for all cases studied.

Effect of shape factor on structural reliability analysis of a surface cracked pipeline-parametric study

The variation of crack shape factor (a/c) during propagation has an important role on calculation of the stress intensity factor (SIF), where imprecise estimation of this latter can lead us to an inaccurate prediction of failure probabilities. For the case of external cracked surface pipeline carried oil and gas products, such estimation can results undesired fault decisions like excessive repairs action or inspection planning. In this paper, the structural integrity analysis of pipeline with semi elliptical crack on the external surface is evaluated. Reliability calculations expressed in term of reliability index β are carried out based on Monte Carlo simulation and First Order reliability Method (FORM). The crack shape factors are varied to cover a variety of geometries from shallow to deep cracks while fatigue crack growth is assumed in depth direction. For SIF estimation, surface and deep point are considered. Results of the analysis indicate that for a constant crack depth a/t, the reliability index is strongly affected by a/c ratio and the trend is not similar in deep and surface point for different crack shapes.

Mixed-Mode Stress Intensity Factor Estimation of Inclined Cracks in an Unnotched Round Bar

The extent on mixed-mode stress intensity factor (SIF) of inclined multiple cracks in an unnotched bar has been investigated numerically. Opposite cracks with various crack depth ratios (a/d), crack aspect ratios (a/c) and inclination angles (θ) were considered. The geometry correction factor (Y) was calculated by considering the effect of mode-II and mode-III fracture. It was observed that, for short cracks [(a/d) = 0.1], as the inclination angle increases, SIF of mode-I decreases and conversely mode-III SIF increases. For short cracks in crack-2, as the inclination angle increases, the mode-I SIF decreases similar to crack-1, but the SIF of mode-III decreases as well. The mode-III contributes to a significant amount of SIF owing to the inclination of the crack. Regardless of the inclination angle, with an increase in the aspect ratio [a/c], the mode-I and mode-III SIF for both crack-1 and crack-2 decreases.

Numerical simulation of SIF in Es-Salam research reactor vessel

Abstract During NPP operation the reactor vessel will be affected by degradation mechanizms, such as thermal aging, irradiation embrittlement, corrosion and fatigue. These degradation mechanisms may significantly impact component integrity. When the metal is aging under certain conditions, the crack can appear and this finally could lead to the failure of components. The stress intensity factor (SIF) as fracture criterion are used to evaluate the resistance to fracture of the components with cracks. In the case of complex structures the estimation of stress intensity factor it is complicated by applying only the analytical formulas. The Es-Salam research reactor vessel is a complex 3D structure with high level safety requirements. As a result, sophisticated methods are necessary for the fracture analysis of critical components. In this manuscript the proposed methodology for the numerical simulation of the stress intensity factor in Es-Salam research reactor vessel by finite element method using software ANSYS is presented. The validation of the proposed methodology was performed by analytical analysis (according ASME requirement and R6 method (SACC software)). Additionally this methodology was validated by applying a finite element method using software ABAQUS. The comparison of these results shows a good coincidence, and the deviation does not exceed 9%. According to this, the proposed methodology can be used for numerical simulation of the stress intensity factor in Es-Salam research reactor vessel.

Numerical estimation of stress intensity factors in cracked functionally graded piezoelectric materials – A scaled boundary finite element approach

Abstract The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis of functionally graded piezoelectric materials is developed. The formulation is linearly complete for uncracked polygons and can capture crack tip singularity for cracked polygons. These salient features enable the computation of the fracture parameters directly from their definition. Numerical examples involving cracks in FGPMs show the accuracy and efficiency of the proposed technique.