Calculation Of Stress Intensity Factors Research Articles

A new numerical approach to estimate stress intensity factors under very high cycle fatigue testing

Ultrasonic very high cycle fatigue testing finds many advantages in fatigue studies especially in very low fatigue crack growth rate investigations. In this application, the determination of the stress intensity factor has a key role and presenting a general approach to calculate stress intensity factor in reasonable time and ultimate accuracy is necessary. The present research proposes a new numerical approach (hybrid method) based on reduce order modeling (dynamic substructuring), multi-harmonic balance method, and M-integral to evaluate stress intensity factors under very high cycle fatigue testing in the most accurate and fast way possible. The verification of the hybrid method was done through a benchmark and implicit solver implemented in ABAQUS commercial software as the reference solution. Investigations proved that the presented hybrid method here could determine stress intensity factor in ultrasonic regime with the ultimate accuracy and save computational time at least 50%.

Advanced uses of Stress Intensity Factor Tables in PTS Calculations of Nuclear Power Plants

This paper introduces an approximation method developed for calculating stress intensity factor for pressure vessels in nuclear power plants. The method is based on weight functions, which has high accuracy among the methods based on crack-free stress calculations. Besides it has the advantage over the weight functions method, it corresponds to the approximation methods can be found in nuclear codes like ASME BPVC [1]. Numerical test calculations are performed to experimentally show the differences of several possible approximation methods. The results show the weighted least squares method using stress intensity factor weight functions, do have the above-mentioned advantages.

An Enhanced Virtual Crack Closure Technique for Stress Intensity Factor Calculation along Arbitrary Crack Fronts and the Application in Hydraulic Fracturing Simulation

The virtual crack closure technique (VCCT) is widely used for calculating energy release rates along crack fronts and modeling the propagation of cracks in solid materials. Although the VCCT formulation for smooth crack fronts has been sufficiently addressed in the literature, the application of VCCT to a nonsmoothed crack front with sharp corners warrants further investigation. The present study describes an enhanced VCCT to calculate energy release rates and stress intensity factors for cracks with arbitrary shapes in 3D domains discretized on structured grids. The formulations of the enhanced VCCT were developed and implemented into a multiphysics simulation environment capable of simulating crack propagation in the framework of linear elastic fracture mechanics. Comparisons with existing analytical/numerical solutions and other VCCT approaches were performed to verify the enhanced VCCT in terms of SIF calculation along nonsmoothed crack fronts. We then applied the enhanced VCCT to a hydraulically driven penny-shaped fracture problem to further demonstrate its capability to simulate nonsmoothed fracture propagation.

Analysis of Linear Elastic Fracture Mechanics for Cracked Functionally Graded Composite Plate by Enhanced Local Enriched Consecutive-interpolation Elements

This paper reports the application of consecutive-interpolation procedure into four-node quadrilateral elements for analysis of two-dimensional cracked solids made of functionally graded composite plate. Compared to standard finite element method, the recent developed consecutive-interpolation has been shown to possess many desirable features, such as higher accuracy and smooth nodal gradients it still satisfies the Kronecker-delta property and keeps the total number of degrees of freedom unchanged. The discontinuity in displacement fields along the crack faces and stress singularity around the crack tips are mathematically modeled using enrichment functions. The Heaviside function is employed to describe displacement jump, while four branch functions being developed from asymptotic stress fields are taken as basis functions to capture singularities. The interesting characteristic of functionall graded composite plate is the spatial variation of material properties which are intentionally designed to be served for particular purposes. Such variation has to be taken into account during the computation of Stress Intensity Factors (SIFs). Performance of the proposed approach is demonstrated and verified through various numerical examples, in which SIFs are compared with reference solutions derived from other methods available in literatures.

A convenient method for the strength evaluation of cracked functionally graded material plates under different loadings

As functionally graded material (FGM) plates are widely used in engineering and industrial fields, the fracture strength evaluation of the cracked FGM plate becomes increasingly important. However, due to the gradation of the mechanical properties of FGM, few analytical methods are simple and available. In this paper, a convenient strength evaluation method for the cracked FGM plates under different loadings is proposed in terms of the stress intensity factor (SIF) appearing at a crack tip. This method uses the stable relationship of singular stress fields between FGM and homogeneous material to greatly simplify the complex SIF calculation process of the cracked FGM plate. The results show that the SIFs of FGM plates under tension, bending, and three-point bending (experiment) can be obtained conveniently and accurately by using two simple formulas, and the trends of critical SIF can also be investigated directly even if the SIF solution of the homogeneous plate (reference problem) is unknown. Comparisons with the published theoretical and experimental results indicated that the present method is reliable, precise, and practical to determine SIF and perform strength prediction.

Analysis of fracture mechanics and fatigue crack growth in moderately thick plates using an efficient meshfree approach

This paper presents a robust meshfree technique for computation of moment and stress intensity factors, and analysis of fatigue crack growth in cracked plates under the application of in- and out of-plane loads; a methodology for efficient and accurate computation of parameters of fracture mechanics problems is thus developed. Although having small computational labor and few complications of formulation, the proposed method has a high accuracy and convergence rate. By adding a few nodes in the vicinity of the crack tip, instead of enriching the basis functions, the singularity of the crack-tip fields is well captured with high accuracy. Also, by employing the background decomposition method (BDM), which is an efficient method for evaluation of the domain integrals, accurate solutions are obtained with small computational labor. The stress and moment intensity factors, which are two major parameters in analysis of the crack behavior, and prediction of its growth path, are calculated using the domain form of the interaction integral. Fracture mechanics problems under static condition, as well as under fatigue condition are investigated. Applying the meshfree radial point interpolation method along with the BDM has led to not only accurate results but also small computational cost. The accuracy of the results achieved for the stress intensity factors and also fatigue life of cracked bodies under cyclic loading is assessed by comparing the computed results with those found in the literature.

Determination of complex stress intensity factors for interface cracks in bi-material specimens subjected to ununiform stresses

This paper presents the calculation of complex stress intensity factors (K) for interface cracks in commonly used bi-material specimens subjected to arbitrary ununiform stress fields. First, detailed finite element analyses were carried out for cracks in centre-cracked plate (CCP) and single edge-cracked plate (SECP) bi-material specimens of different material combinations under non-uniform stress distributions. The complex SIFs were determined for the loading cases of uniform, linear, parabolic or cubic stress distributions applied to the crack faces in both normal and shear directions. Then, general mathematical forms of the two complex crack face weight functions for interface cracks, one for normal loading, and one for shear loading, have been formulated by taking advantages of the knowledge of specific analytical complex weight functions available in the literature, and certain properties of the complex weight functions in general. The existence of the general functional forms simplifies the determination of these weight functions for specific crack geometrical configurations and bi-material combinations. The determination of a specific weight function is thus reduced to the determination of the unknown parameters of the generalized weight function functional forms. It was demonstrated these unknown parameters can be determined from reference stress intensity factors. This method was used to derive the complex weight functions for interface cracks in bi-material CCP and SECP specimens. The derived closed-form weight functions were then validated against complex stress intensity factors solutions for several non-linear normal and shear stress distributions.

Nonlinear Thermo-Mechanical Full Coupling of Aluminum Oxide Particles Transport in Electrolytic Bath Using Lattice Boltzmann Method

A three-dimensional numerical model has been developed to quantify the predominant phenomena roles on dynamics alumina particles between an electrolytic bath and the vicinity of gas bubbles. At the particle scale, the bath, regarded as turbulent flow, was modeled by a steady plane shear flow and solved using a lattice Boltzmann method. The coupling between the fluid and particle phases is carried out using an immersed boundary method to tackle the interface. This numerical scheme resolves the hydrodynamic perturbation induced by the alumina particles, and hence their interactions are described by Lagrangian particle tracking. The hydrodynamic effects combined with mechanical and thermal responses on the computation of the fluid system's stress intensity factors were investigated. An excellent convergence and accuracy were achieved for the transport and interaction of the alumina particle model.

Simulation of Quasi-Static Crack Propagation by Adaptive Finite Element Method

The finite element method (FEM) is a widely used technique in research, including but not restricted to the growth of cracks in engineering applications. However, failure to use fine meshes poses problems in modeling the singular stress field around the crack tip in the singular element region. This work aims at using the original source code program by Visual FORTRAN language to predict the crack propagation and fatigue lifetime using the adaptive dens mesh finite element method. This developed program involves the adaptive mesh generator according to the advancing front method as well as both the pre-processing and post-processing for the crack growth simulation under linear elastic fracture mechanics theory. The stress state at a crack tip is characterized by the stress intensity factor associated with the rate of crack growth. The quarter-point singular elements are constructed around the crack tip to accurately represent the singularity of this region. Under linear elastic fracture mechanics (LEFM) with an assumption in various configurations, the Paris law model was employed to evaluate mixed-mode fatigue life for two specimens under constant amplitude loading. The framework includes a progressive analysis of the stress intensity factors (SIFs), the direction of crack growth, and the estimation of fatigue life. The results of the analysis are consistent with other experimental and numerical studies in the literature for the prediction of the fatigue crack growth trajectories as well as the calculation of stress intensity factors.

Stress intensity factor computation of inclined cracked tension plate using XFEM

One of the major successes in the field of Linear Elastic Fracture Mechanics (LEFM) is the groundwork of the stress intensity factor (SIF) computation. The approaches used to carry out SIF values may be analytical, semi-analytical, experimental or numerical. Each one of the above methods has its own benefits however the use of numerical solutions has become the most frequent and popular. Numerous schemes for the numerical computation of SIF have been developed, the J-integral method being the most popular one. In this article we examine the SIFs of an edge cracked two dimensional (2-D) steel plate subjected to tensile loading. Extended finite element (XFEM) computational scheme has been employed to estimate the values of SIF. The SIF values of cracks with different lengths and inclination angles (different configurations) have been examined by utilizing the domain based interaction integral approach. The effect of crack inclination and crack position on SIFs (KI and KII) has also been studied. The results obtained in this study were compared with those from literature and theoretical values and observed that they are in close agreement.

Modeling of crack opening mode sif for a crack in a thin-walled structural channel beam

The analysis of engineering methods for determining stress intensity factors (SIF) for defective elements of open profile (channels) under bending is carried out. Mathematical models are created and dependences for calculation of SIF are deduced using two methods: using nominal stresses in net-section and using change of the inertia-moment of the profile cross-section. The obtained results are compared with the data of SIF for the crack in the channel obtained during simulation modeling using finite element method.

On the determination of first-mode stress intensity factors and T-stress in a continuous functionally graded beam using digital image correlation method

<abstract> <p>In this study, fracture parameters of epoxy/glass functionally graded composite were determined experimentally using the digital image correlation (DIC) method. A functionally graded material (FGM) with continuous variation in elastic properties was manufactured by gravity casting in vertical template. A 30% volume fraction of glass spheres was dispersed in a low viscosity resin. A single edge crack specimen was examined in a three-point bending test under mode Ⅰ loading with cracks along the gradient tendency of the material properties. The mechanical properties of FGM were calculated according to ASTM D638. The DIC technique was adopted to obtain the deformation region around the crack tip. William's series was employed to calculate stress intensity factor and T-stress. The experimental results then verified by solving the FE model using ABAQUS program. The comparison between DIC and numerical results illustrated a largely acceptable achievement.</p> </abstract>

Risk assessment based on analytical evaluation of structural integrity and life of drilling rig pipe

Risk assessment procedure based on structural integrity evaluation has been applied to oil drilling rig pipe. The new concept based on application of structural integrity evaluation to assess risk level according to probability and consequence of failure was used. Analytical expressions for surface cracks are used to calculate stress intensity factors for different crack geometries. Oil drilling rig welded pipe integrity has been evaluated analytically by simple application of the Failure Assessment Diagramme (FAD), i.e. by using the ratio of linear elastic fracture mechanics parameter, KI, and its critical value, KIc, in relation with the ratio of applied stress and its critical value, to define the point in FAD. Probability of failure is then taken according to the position of the point in the FAD, corresponding to oil drilling rig welded pipe data. The same logic is employed in the case of cyclic loading, i.e. fatigue crack growth. In that case, structural life is estimated by using Paris law to calculate crack length vs. number of cycles, to be used in risk assessment procedure and by managers to make decision about further use of damaged pipes, based on data provided by engineers.

Three‐Dimensional Stress Intensity Factor Correction Method Based on Thickness Size Effect

This paper presents the fatigue crack growth test of 7N01 aluminum alloy specimens with different thicknesses under three‐point bending. Moreover, the effect of specimen thickness on the fatigue crack growth life was analyzed. The influence mechanism of the thickness size effect on the stress intensity factor was explored. A three‐dimensional stress intensity factor calculation model based on the thickness size effect was proposed by combining the finite element method and the interaction integral method. The results show that the fatigue crack growth life of 7N01 aluminum alloy decreases with the increase of specimen thickness. The numerical solutions of the stress intensity factor (the proposed model) are higher than the analytical solutions (the traditional formula) in the steady‐state crack growth stage. The difference between numerical solutions and analytical solutions increases with the increase of crack growth length and specimen thickness. Compared with the analytical solutions, the relationship curve between crack length “a” and cycle number “N” from the numerical solutions is closer to the experimental data. This result proves that the proposed calculation model can correct the stress intensity factor with the thickness size effect.

Application of stress intensity factor superposition in residual stress fields considering crack closure

The correlation between stress intensity factor (SIF) range and fatigue crack growth is a powerful tool for fail-safe design approaches applied to lightweight structures. The key role is precise calculation of the SIFs of fatigue load cycles. Advanced material processing can shape residual stresses and makes SIF calculation a challenging task. While the consideration of tensile residual stresses is successfully tackled by SIF superposition, the treatment of compressive residual stresses needs still clarification. This work demonstrates the application of the SIF superposition principle in regions containing high compressive residual stresses leading to crack closure effects. Crack closure depends on the combined load of residual and applied stresses and is interpreted as a change of crack geometry in this work. Thus the relation between the source, i.e. the applied or residual stress, and its consequence, i.e. the corresponding SIFs, depends on the interaction of the sources, i.e. the combined load. Due to this interaction, residual stress-induced changes of the fatigue behaviour cannot be linked to the residual or applied SIF only. This work proposes two alternative definitions of applied and residual SIF, allowing a clear correlation between either residual or applied SIF to fatigue behaviour changes.

Stress intensity factors for branching cracks in space structures

One of the mechanisms of destruction of a solid is the formation and growth of “micro” and “macro” cracks. This task is especially acute for space objects. A microcrack in the body of the spacecraft practically does not affect its mechanical strength, but it can lead to depressurization of the body, which can lead to the loss of life support for the crew. Cracks can have different causes of their occurrence, but the mechanism of their growth in modern fracture mechanics is associated with the chosen criterion. For example, in the force criterion, crack growth begins when the stress intensity factors also reach a certain threshold critical value characteristic of a given material. This paper presents the results of calculating stress intensity factors for spatial branching cracks. The calculations were carried out on the basis of the original author's program, which makes it possible to determine the stress and displacement fields in a three-dimensional elastic body weakened by a system of arbitrarily oriented cracks. The program is based on the method of discontinuous displacements, implemented for three-dimensional problems of fracture mechanics in an elastic medium, implemented in C ++ codes. The main purpose of the work is to demonstrate the possibility of determining the stress intensity factors for a spatial branching crack and their dependence on the geometric parameters of the problem.

Mesh refinement for cortical and trabecular bone finite element modeling: A review

For centuries, the finite element (FE) method has been extensively used to predict the fracture performance and various method has been implemented to yield accurate results especially in healthcare industries. Bone fracture has been a critical problem since it interrupts the strength and structure of human bone. Thus, this problem will lead to bone malfunction and cause excess bleeding of surround tissues. Human bone consists of cortical and trabecular bone which serve a different amount of load sustainability before the fracture occurred. One of the most vital problems arise is the inaccuracy of the stress intensity factor related to the bone fracture. Recent studies have proven that with the implementation of appropriate meshing element produce higher accuracy results especially with the implementation of mesh refinement in the finite element model. The singularity elements suggested by Barsoum (1976) has proven that the quarter-point triangular elements give highly accurate results. Several methods for stress intensity factor calculation has been implemented by various past researchers. Among all the methods used, J-integral has proven to be the most accurate method compared to the others. The first section in your paper.

Mixed-mode stress intensity factors computation in functionally graded materials using a hypercomplex-variable finite element formulation

The hypercomplex-variable finite element method, ZFEM, is extended to compute the mode I and mode II energy release rates (ERR) for functionally graded materials. The ERR is computed using an efficient local stiffness derivative approach, L-ZFEM, that computes the derivative of the stiffness matrix at the element level using the highly accurate complex-variable sensitivity method. Mode I and II values are computed using the appropriate perturbation of the surrounding crack tip elements, i.e., perturbations in the self-similar (mode I) and perpendicular (mode II) directions. The energy release rate values are as accurate as the J-integral results. The advantage of this approach is that the derivatives are only required for a small number of elements surrounding the crack tip and no energy conservation integrals are required. In addition, derivatives of the ERR with respect to the FGM material properties are computed by combining the local stiffness derivative approach with a global complex variable formulation, G-ZFEM. This methodology was implemented into the commercial finite element software Abaqus through a combination of Abaqus intrinsic elements and a complex variable user element subroutine (UEL). Numerical results are compared against analytical solutions and other numerical approaches and demonstrate excellent accuracy.

Fatigue crack growth simulation of interacting multiple cracks in perforated plates with multiple holes using boundary cracklet method

AbstractIn this study, the recently developed boundary cracklet method (BCM) is used to model the fatigue crack propagation (FCP) in complex geometries in two‐dimensional domain. Several benchmark examples of FCP are analysed to show the effectiveness of BCM. Calculated stress intensity factors and crack paths show good agreement with reference studies. BCM is further used to simulate the multiple cracks interaction in a perforated plate with multiple holes having different cases of precracks emanating from edges of the plate and outer periphery of holes under fatigue loading. FCP is assumed to follow Paris–Erdogan law, and the maximum tangential stress criteria are used to predict the direction of propagation in each step. Moreover, to describe the computational efficiency of a numerical method in fatigue problems, a new parameter is introduced: Yavuz's fatigue computational efficiency factor (YCF), which is the number of computed million cycles per hour (CPU time).

Calculation of Stress Intensity Factor on Typical MSD Structure of Aircraft Wing

The research object of this paper is Multiple site damage (MSD) structures which are common in the service of aging aircraft. A complex function modified method is proposed to calculate the stress intensity factor of MSD cracks. On the basis of Muskhelishvili complex function method and its approximate superposition method, the concept of equivalent crack is introduced to solve the accurate stress function of MSD cracks. The stress intensity factor of MSD hole edge crack of infinite plate under far end uniform load is calculated and compared with the finite element method. The method is applied to the typical MSD structure of aircraft wing, and the stress intensity factors of cracks in three modes are compared and analyzed. This method can be used to discuss the damage tolerance of MSD structure, it has certain application value in the reliability evaluation of aircraft.