Calculation Of Stress Intensity Factors Research Articles

Machine learning‐based efficient stress intensity factor calculation for aeroengine disk probabilistic risk assessment under polynomial stress fields

AbstractIn probabilistic failure risk assessment, the accuracy and efficiency of the stress intensity factor calculation are important. The universal weight function method has been widely adopted for efficiency, but this method still has some debatable parts. For accurate and efficient stress intensity factor prediction, two approaches for machine learning techniques are specially designed. Three tests are conducted for the first approach where Gaussian process regression, tree‐structure models, and artificial neural network are evaluated and compared for the ability of interpolation and extrapolation. Results show that the artificial neural network and extremely randomized trees perform better. Hybrid models in the second approach are also proposed, and results show that the accuracy of SIF calculation can be improved by 5–35% compared with the weight function. Real aeroengine disks are adopted, and the errors of machine learning methods are less than 20% in the disk life calculation.

Determination of fracture toughness for steel 22k from the results of tests of different types specimens

Nowadays, in various industries, in particular in nuclear energy, to determine the fracture toughness, along with standard tests of compact specimens, which are quite expensive and complex, methods are developed to determine these characteristics by impact tests of Charpy specimens using different correlations between Charpy impact fracture energy (CVN) and critical stress intensity factor (J-integral). The paper analyzes correlation and analytical methods, the authors of which consider them universal for a certain class of steels. Correlation methods are divided into one-stage and two-stage. One-stage methods allow to obtain the value of the critical stress intensity factor by the known fracture energy. Two-stage methods in the first stage offer the calculation of the dynamic critical stress intensity factor, in the second the temperature shift and obtaining a static critical stress intensity factor. Analytical methods according to the іmpact fracture diagram of the specimen allow to construct a J-R curve and calculate the value of the J-integral. A series of fracture tests of CT specimens made of heat-resistant steel 22K was carried out, the reference temperature T0 was determined according to the single-temperature method of the ASTM-1921 standard and the Master curve was constructed. A series of standard Charpy specimens impact tests in the temperature range -50…+100°С was performed using an instrumented drop-weight impact testing machine equipped with a high-speed registration system. According to the results of Charpy specimens impact tests, the fracture toughness were determined using different methods. It is established that both analytical and correlation methods cannot be universal and can be used to determine the fracture toughness of 22K steel. Therefore, a new exponential correlation was proposed between the fracture energy of the Charpy specimens and the critical stress intensity factor for heat-resistant steel 22K.

Modelling mode I failure at crack tip with verifications using digital image correlation

Background: Linear elastic fracture mechanics (LEFM) applies to sharp cracks, although crack sites such as holes and slots are often blunt cracks with nonzero widths. The advancement in finite element method (FEM) has enabled the calculation of stress intensity factor (SIF) for unstable crack growth prediction, regardless of crack shape and size, but the calculations often differ from contour to contour. Hence, the purpose of this work is to determine if SIFs computed using commercial FEM have experimentally verifiable advantages over the traditional stress-based modelling approaches in predicting Mode I brittle failure at blunt crack tip. Methods: Experiments and simulations were conducted on brittle Poly(methyl methacrylate) (PMMA) plastic to compare the actual and predicted strain fields and SIFs at crack tip, and the critical force at which unstable crack growth initiates. A centrally straight cracked Brazilian disc made of PMMA was subjected to purely Mode I fracture. Its strain fields were measured from deformed speckle patterns using digital image correlation software. The same disc was modelled using plane stress model in FEM. By applying the critical force, SIFs were then computed using ANSYS pre-meshed crack method at different contours away from the crack tip. The effects of element type, mesh size and crack width on the simulated SIFs were investigated. Results: It was found that the experimental critical load agreed well with LEFM prediction based on PMMA fracture toughness in published literature. Disc failure happened at the first sign of tensile yield at the crack tip in the finite element model with a triangle mesh. Digital image correlation clearly shows the occurrence of unstable crack growth at critical force. It also shows comparable far field strain responses to the FEM model. Conclusions: The computed SIFs were inconsistent, and their usefulness in predicting unstable crack growth requires further investigation.

A modified semi-weight function method for stress intensity factor calculation of a vertical crack terminating at the interface

The interfacial crack stress intensity factor (SIF) calculation plays an important role in the safety evaluation and anti-crack design for multilayer structures. The current analytical or numerical methods have difficulty of complicated auxiliary functions or special crack-tip singular elements. In this study, a modified semi-weight function method was proposed based on the submatrix method to calculate the SIFs of the crack vertical to and terminating at the interface of bimaterial (easily appears in compressed air energy storage) and verified by two calculation examples compared with the available literature results. The effects of bimaterial parameters (Ei, υi), relative crack length (a/w2) and outer integration path (r2) on the SIFs were also analyzed. Research results show that the SIFs (K1 and K2) are related to only the ratio of E2/E1 independent of the single E1 or E2, and they are increased with increase of a/w2. The reasonable range of r2 is rs < r2 < a/2 (rs is minimum finite element size). The modified semi-weight function method has advantages of unified auxiliary function for different crack sizes and external loads and simpler calculation process without any crack-tip singular elements over current methods.

Analysis of stress intensity factors in railway wheel under the influence of stress field due to heat treatment and press-fitting process

Railway transportation system is one of the main needs of the population living in industrialized countries. Many studies have been conducted by engineers due to the importance of railway wheels and railways as a major part of the train. But due to progress in railway technology, in recent years a new type of train wheel known as rim-wheels is presented that their fracture is investigated in this study. The goal of the present study is to calculate stress intensity factors numerically using the boundary element method in railway wheels based on experimental data of material behavior. For this purpose, a series of experiments were performed to determine the behavior of the railway wheel material as well as the data required for numerical analysis. The innovation of this research is that the stress intensity factor is calculated resulting from residual stress of press-fit and heat-treatment processes. Then, the stress intensity factors resulting from the two processes are superimposed in pure mode I, mode II, and mode III loading due to the same crack geometries. Also, the study includes a survey on the effect of crack length on crack propagation as one of its main effective factors. Besides, fatigue crack growth path is calculated and its propagation is also estimated and the effect of different parameters is studied on fatigue crack growth and path.

Analysis of in-plane crack problems using the localized method of fundamental solutions

In this paper, the localized method of fundamental solutions (LMFS), a recently developed meshless collocation method, is applied to the numerical solution of problems with cracks in linear elastic fracture mechanics. The main idea of the LMFS is to divide the entire computational domain into a set of overlapping sub-domains, and in each sub-domain, the classical MFS formulation and the moving least squares (MLS) technique are applied to form the corresponding local system of equations. The LMFS will finally generate a banded and sparse matrix system which makes the method very attractive for large-scale engineering applications. To deal with in-plane crack problems, an enriched LMFS approach is proposed by combining the LMFS formulation for linear elasticity problems and a set of enrichment functions which take into account the asymptotic behavior of the near-tip displacement and stress fields. The enriched LMFS can significantly improve the computational accuracy of the calculation of stress intensity factor (SIF) of the cracked materials, even with a very coarse LMFS node distribution. Several benchmark numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.

Fatigue failure of ball joint heads connected to the weight holder mechanism in railway applications

The premature causes of failure of ball joint heads attached to the weight bearing bar used on high speed trains, which were continuously under traction, have been studied, with an average load of 47.5 kN plus a cyclical load of ± 7.5 kN. Ball joint heads made of C45 (AISI 1045) carbon steel show a pearlite microstructure (80–90 %) with ferrite surrounding the prior-austenite grain boundaries. Two different external elliptical-shaped fatigue cracks of 14.5 mm and 7.7 mm nucleated in opposite positions on the cylindrical surface of the threaded shank prior to catastrophic cleavage failure. The Griffith equation applied in this study gave a value of 37 MPa for the fracture stress (σf) produced by the largest crack, which multiplied by the section of the thread is equivalent to a load of 37 kN, similar to the applied service load. In addition, the critical stress intensity factor (KIc) calculation yielded a value of 8.8 MPa m1/2, this lower KIc value was determined to be responsible for the large fatigue crack produced and the cleavage fracture causing the C45 carbon steel bolt joint failure. The pearlite/ferrite microstructure contributed to crack growth, since this type of microstructure in high carbon steels has lower strength and lower toughness than a tempered martensite microstructure. Using Paris equation, the cycles to failure were 1.5 × 105, which in service lifetime was an approximated 6 × 106 km for the piece to finally fail.

A reliability approach to fatigue crack propagation analysis of ship structures in polar regions

Fatigue is a common failure mode in ship structures. For structures with an initial crack, the fatigue crack propagation behavior needs to be considered. The purpose of this study is to establish a procedure for analysis of fatigue crack propagation of ship structures in combination with reliability methods. The stress intensity factor (SIF) and geometry correction factor are calculated by means of finite element analysis. Validation for the SIF calculation is achieved by comparing the computed results with those based on related solutions. Since fatigue damage usually occurs in weld areas, the effect of such components on the fatigue crack propagation behavior was also considered in this work. The Paris law in combination with the Monte Carlo technique are employed for the fatigue crack propagation analysis in this study. Reliability updating based on inspection for cracks is also carried out. A computer program was developed for the purpose of fatigue crack propagation analysis within the framework of reliability methods. An application example of fatigue crack propagation in relation to the hull of the icebreaker Xuelong 2 is presented. The sensitivity of the procedure to key analysis parameters (sample size, initial crack size) is also considered. Finally, the effect of low temperatures on the computed results is also analyzed.

Fracture mechanics analysis of two-dimensional cracked thin structures (from micro- to nano-scales) by an efficient boundary element analysis

In this paper, the boundary element method (BEM) based on the elasticity theory is developed for fracture analysis of cracked thin structures with the relative thickness-to-length ratio in the micro- or nano-scales. A special crack-tip element technique is employed for the direct and accurate calculation of stress intensity factors (SIFs). The nearly singular integrals, which are crucial in applying the BEM for thin-structural problems, are calculated accurately by using a nonlinear coordinate transformation method. The present BEM procedure requires no remeshing procedure regardless of the thickness of thin structure. Promising SIFs results with only a small number of boundary elements can be achieved with the relative thickness of the thin film is as small as 10−9, which is sufficient for modeling most of the thin bodies as used in, for example, smart materials and micro/nano-electro-mechanical systems.

Numerical simulation of fatigue crack growth life of single side notched specimen

Under the action of cyclic load, fatigue fracture failure often occurs in many engineering structures during their services. Fatigue cracks in engineering structures begin to propagate under cyclic loading, and eventually lead to the failure of engineering structures. The study of fatigue crack is of great significance for evaluating the service life of engineering structures under cyclic loading. The prediction of fatigue crack growth life and path is the key problem of fatigue crack research. In this paper, the numerical simulation of fatigue crack growth of single side notched specimen is carried out by using the extended finite element method. According to the calculated stress intensity factor and the generalized Paris formula, the fatigue crack growth rate of single side notched specimen is obtained and the fatigue crack growth life is predicted. The results show that this method can effectively predict the fatigue crack growth life.

Study on application range of SIF calculation method for nozzle corner crack in pressure vessel for ASME XI code

Stress intensity factors (SIF) of a nozzle corner crack in a pressure vessel subject to pressure and thermal loadings are evaluated using finite element method (FEM) and compared with the method described in ASME XI appendix G (2013 section XI). The formula in ASME XI appendix G is defined for the crack corner at a specific location of the nozzle/vessel connection which may limit the structural integrity assessment of the pressure vessel under ever changing pressures and temperatures duty loads during heat-up and cool-down phases. Using FE method SIFs at corners of similar cracks assumed at other nozzle locations are then evaluated and compared with SIFs using ASME formula to assess the degree of conservatism.

ANALYSIS OF CRACKS AT THE TORSION VALLARS CAUSED WITHOUT LOADING

Nowadays, the hull suspension systems that use torsion shafts as elastic suspension elements are fitted to the majority of modern tracked vehicles. The main type of failure in such systems is the fracture of the torsion shafts due to the formation of fatigue cracks, which leads to failure of the suspension assemblies. This work presents an analysis of fracture toughness of torsion shafts of a standard tracked chassis used to develop a family of multipurpose transport vehicles GT-TM, GT-TMS, etc. The analysis is carried out under an operating load level for a crack located on the cylindrical part of the torsion shaft, the plane of which is at an angle to the torsion shaft axis and coincides with the position of the main areas of the stress state. The calculation of fracture toughness is based on Irwin fracture criterion. The calculations of the maximum stress intensity factor along the crack front are performed using the finite element method in the ANSYS software package. The results of the analysis of fracture toughness are presented in the form of dependences of the critical depth of the crack on the ratio of the fracture half-length to its depth. The data obtained can be used to determine the residual life of torsion shafts of the tracked vehicles based on the chassis under consideration. Keywords: suspension system, fracture toughness of torsion shafts, edge crack, stress intensity factor, finite element method, Irwin fracture criterion.

Two-dimensional weight function of stress intensity factors for corner cracks emanating from a circular hole

The weight function method is adopted to calculate stress intensity factors along the corner crack front rather than at only two end points, which are pre-requisites in evaluating fatigue growth of corner cracks emanating from a circular hole. Two-dimensional weight function is derived for corner cracks emanating from a circular hole, based on reference stress intensity factors modified by Newman (2018) and corresponding accurate stress distribution on virtual crack face formulized by authors (Guo and Guo, 2019). The obtained weight function is validated against numerical results in the literature and finite element calculations and shows high accuracy. For quick fatigue crack growth prediction in engineering structures, explicit formulae are obtained for typical corner crack shapes with wide ranges of aspect ratio 0.2 ≤ a/c ≤ 2, crack depth ratio 0.1 ≤ a/B ≤ 0.95, crack front angular parameter 0.05 ≤ 2ϕ/π ≤ 0.95 and plate thickness to hole radius ratio B/R = 2. The process can be thereby extended to the estimation of stress intensity factors for corner cracks emanating from a circular hole contained in complicated structures under arbitrary stress distribution.

2D and 3D numerical simulation of fatigue crack growth path and life predictions of a linear elastic

Abstract This paper describes implementation of the finite element method (FEM) to investigate crack growth problems in linear elastic fracture mechanics and the correlation of results with experimental and numerical data. The approach involved using two different software to compute stress intensity factors (SIFs), the crack propagation trajectory, and fatigue life estimation in two and three dimensions. According to the software, crack modeling might be run in various ways. The first is a developed source code program written in the Visual Fortran language, while the second is the widely used ANSYS Mechanical APDL 19.2 software. The fatigue crack propagation trajectory and the corresponding SIFs were predicted using these two software programs. The crack direction was investigated using the maximum circumferential stress theory, and the finite element (FE) analysis for fatigue crack growth was done for both software based on Paris's law. The predicted results in both software demonstrated the influence of holes on the crack growth trajectory and all associated stresses and strains. The study's findings agree with other experimental and numerical crack propagation studies presented in the literature that reveal similar crack propagation trajectory observations.

Alternative Integration Approaches in the Weight Function Method for Crack Problems

This study proposes two alternative approaches to complement existing integration strategies used in the weight function method for linear elastic crack problems. The first approach is based on an interpolation type integration scheme and the second approach is based on Gauss quadrature. The proposed approaches enable a computationally efficient numerical integration for computing stress intensity factors in 2D fracture problems. The efficiency is gained through a comparatively low number of integration points facilitated by higher-order approximation. The integration weights only need to be computed once for a given crack length-to-width ratio and can be applied to arbitrary continuous and smooth stress distributions. The proposed approaches show excellent accuracy. In particular, the Gauss quadrature approach exhibits several orders of magnitude more accuracy compared to the most commonly used trapezoidal integration.

Determination of crack resistance of a tank with elliptical crack

The occurrence of crack-like defects is a common phenomenon in the operation of vertical steel tanks (VST). Such defects can occur both at the beginning of the operation of the tanks, which may be associated with a violation of the manufacture conditions or the installation procedures of the tank elements and during operation. Over time, such defects increase significantly and turn into cracks. Existing regulations prohibit the operation of VST with cracks. At the same time, the organization that operates the tank does not always have the opportunity to perform repairs immediately. There are cases of trouble-free operation of tanks with non-through surface cracks at the stage of sustainable growth, which are confirmed by model calculations are known from practical experience. The analysis of crack resistance of the VST-5000 tank with a semi-elliptical crack under the action of hydrostatic pressure is carried out in the work. The level of filling the tank with petroleum products is 95% of its height. The semi-elliptical crack is located on outside surface of the wall panel in lower row of cladding. Determination of crack resistance of a tank with a crack is performed on the basis of stress intensity factors (SIF). Direct and energy methods were used to SIF calculation. Determination of the stress-strain state is performed on the basis of the semi-analytical finite element method (SFEM). The SIF distribution along the crack front obtained using SFEM by both direct and energy methods almost coincides and agrees well with the values of SIF calculated by the direct method when using three-dimensional FEM. The obtained values of SIF differ along the crack front by 50%: the minimum value of SIF acquires at the point of the front, which is located on the outer surface of the tank, the maximum one - at the point of the front inside the wall that is furthest from the outer surface. The obtained results show the quite uneven SIF distribution along the crack front, so that the calculation of such problems requires the spatial setting of problem.

Crack growth models for multiaxial fatigue in a ship’s propeller shaft

A premature fatigue failure of a large intermediate propeller shaft in a shuttle tanker is discussed and analyzed. The short fatigue life consists mainly of a crack growth phase. Life predictions are carried out by crack growth modelling based on engineering fracture mechanics. The purpose of the present investigation is to identify the most likely loading modes based on the evolution of the crack propagation. A Linear Elastic Fracture Mechanics Model (LEFM) is applied with the stress intensity factor range entering the Paris law as a key parameter. Existing formulas for the geometry functions are supplemented by more detailed stress intensity factor calculations pertaining to small semi-elliptical surface cracks subjected to stress mode I. Enhanced geometry functions are proposed as a function of the relative crack depth and the crack shape aspect ratio. The ability of the fracture mechanics model to reconstruct the observed crack path and crack shape development is emphasized. Various loading modes and multi-axial stress states are applied to pursue the observed crack behavior. The observed semi-elliptical crack shapes and the shift in crack planes are included in the analysis.

Multi-patch local mesh refinement XIGA based on LR NURBS and Nitsche’s method for crack growth in complex cracked plates

The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche’s method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partition of unity, thus it is convenient in modeling evolution of crack. The locally refined non-uniform rational B-splines (LR NURBS), which have the properties of local refinement and exact description of geometry, are used to construct geometric model and taken as the shape functions in XIGA. To implement the adaptive local refinement, a method based on recovery technique by Zienkiewicz and Zhu is proposed. Based on the Mindlin–Reissner plate theory, interaction integral method is employed to calculate stress intensity factors (SIFs) and the maximum circumferential stress criterion is used to determine the crack propagation direction. Several numerical examples are carried out to demonstrate the performance of the adaptive multi-patch XIGA for simulating crack growth in complex plates.

Microstructure and fatigue damage mechanism of 6082-T6 aluminium alloy welded joint

In this paper, 6mm thick 6082-T6 high-strength aluminium alloy is taken as the research object, and CLOOS ROMAT-3500 industrial robot MIG welder is used for welding. High-cycle fatigue test is carried out on welded joint and 6082-T6 base metal. Microstructure, microhardness, tensile properties and fatigue properties are studied, and fatigue fracture is observed and analyzed. The test results show that: equiaxed crystals exist in the center of the weld. Broken equiaxed crystals are found in the weld due to stirring in the molten pool, a large number of pore and columnar crystal layers are found at the junction of the two beads. A small amount of pore and cellular dendrite are found in the fusion zone. A softening zone with a minimum hardness of 65.5HV exists in the heat affected zone(HAZ). The conditional fatigue limits for base metal and weld specimens are 77.26MPa and 48.69MPa at the set target cycle of 107 respectively. In fatigue fracture, there are a lot of cleavage fracture characteristics and ductile fracture characteristics. The crack initiation is quasi-cleavage fracture characteristic. In the past studies, I have studied the fatigue life of joints, but as the research progresses, I believe that the fatigue behavior and fatigue damage mechanism plays an important role in fatigue life. In this paper, Fatigue fracture process is analyzed by correlation calculation of stress intensity factor. Two crack initiation modes are proposed based on the welding process. The first is fatigue crack initiation caused by stress concentration at the grain boundary where hydrogen elements converged, the second is fatigue crack initiation caused by the gap between equiaxed and columnar crystals inside and outside the central pore of the weld.

Stress intensity factors for a centrally cracked Brazilian disk under non-uniformly distributed pressure

To simulate the real distribution of pressure on the specimen in the Brazilian test, non-uniform distribution is assumed to be the form of pressure distribution on the disk. The analytic solutions of the stress field for an uncracked Brazilian disk under several typical non-uniformly distributed pressures are obtained by the power series expansion method and mathematical method. Then the analytic solutions of the mode I and mode II stress intensity factors for a centrally cracked Brazilian disk under the same pressures are obtained by the weight function method. The results show that the influence of distribution form on stress intensity factors cannot be ignored for the case of large relative crack length and load distribution angle. The applicable ranges of the formulae to calculate stress intensity factors under concentrated force, uniformly and non-uniformly distributed pressure are given according to the analysis results. In addition, the loading conditions for pure mode I and II fracture are discussed when a disk with a central crack is subjected to non-uniformly distributed pressure.