Accurate Stress Intensity Factors Research Articles

Multi-domain wavelet boundary element method for calculating two-dimensional stress intensity factors

In order to improve the accuracy of stress intensity factors (SIFs) calculated by traditional boundary element methods (BEM), the multi-domain wavelet boundary element method (WBEM) is proposed. Firstly, by adjusting the nodes of the B-spline wavelet element on the interval, crack-tip elements are constructed. Since B-spline wavelet on the interval (BSWI) has excellent compact support characteristics and is particularly suitable for describing solution domains with large gradient changes, the constructed crack-tip can reduce the numerical oscillation effect near the crack tip. Secondly, the crack-tip elements are implemented into WBEM. And the combination of WBEM and multi-domain technology can effectively handle interface cracks. Thirdly, the crack problem solving strategy based on multi-domain WBEM can directly evaluate the SIFs of cracks. Finally, several numerical examples involving homogeneous media and bi-material models are given to verify that the proposed method is simple and highly accurate.

SIF formula based on exact SIF distribution for semi‐elliptical surface cracks subjected to mode I, II, III uniform loading

AbstractThe stress intensity factor (SIF) distribution of a semi‐elliptical surface crack is often used for evaluating the fatigue strength of structures. Virtually exact distributions of SIFs can be provided along the crack front by solving the hypersingular integral equation of the body force method. In this paper, to create a very accurate SIF variation formula, the elliptical crack SIF solutions , , are used and the SIF ratios , , are mainly focused. Paying attention to the corner point singularity, by applying the least squares method to the ratio , in the whole range of parametric angle , and formulas can be proposed. Instead, formula can be proposed by applying the method of least squares to the ratio of in the range but applying directly to in the range . In this way, all of formulas proposed in this paper provide the SIFs with better than 1.0% accuracy.

Improved XFEM for 3D interfacial crack modeling

The conventional extended finite element method (XFEM) usually suffers from the crack tip enrichment for removing the blending elements. This may be inconvenient when treating the three dimensional (3D) and curved crack modeling since the crack tip enrichment is usually defined in the local coordinate system depending on the crack front. To avoid these shortcomings of the XFEM, an improved enrichment scheme is proposed for the 3D interfacial crack modeling. The proposed enrichment scheme removes the crack tip enrichment and two weight functions are introduced to capture the strong and weak discontinuities in the element including the crack front. The new enrichment scheme has advantages for the 3D curved interfacial cracks since all the enrichment functions are defined in the global system and it is unnecessary to introduce additional coordinate systems. Several benchmark problems including the mixed mode stress intensity factors (SIFs), anti-plane load and curved cracks are analyzed by the proposed method with the local refinement technology. Numerical results demonstrate that the proposed method can obtain accurate 3D energy release rate and SIFs. In addition, the proposed method enhances the applications of XFEM and has the potential abilities to the multiple-fields coupling and interfacial crack growth phenomena due to the fact that compatible enrichment functions are utilized.

Role of crack offset and loading condition on fracture behavior of wire specimen

Accurate stress intensity factor (SIF) solutions for cylindrical specimens with varied wire aspect ratios, crack aspect ratio, relative crack depth and crack offset are required to evaluate the fracture toughness of high strength yet brittle rods, cables, fibres and wire specimens. The mode I geometric factor (GF) solutions of various crack configurations in a cylindrical fracture specimen in tension have been determined using linear elastic fracture mechanics in earlier studies. In the present study, finite element analysis (FEA) was used to compute these as a function crack offset and wire aspect ratios for two different boundary conditions-constrained and unconstrained. In constrained loading condition, the GF was seen to decrease significantly with crack offset for wires at lower aspect ratio in all the 3 crack curvatures – concave, straight and convex. GF stabilized as the wire aspect ratio was increased beyond 40. In unconstrained loading the GF values were independent of the wire aspect ratio and crack offset for the 3 crack curvatures.

Enriched physics-informed neural networks for 2D in-plane crack analysis: Theory and MATLAB code

In this paper, a method based on the physics-informed neural networks (PINNs) is presented to analyze 2D in-plane crack problems in the linear elastic fracture mechanics. Instead of using a discretizing mesh, the PINNs-based method is meshless and can be trained on batches of discretely sampled collocation points. In order to capture the asymptotic behavior of the near-tip displacement and stress fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the local behavior in the crack-tip region can be modeled accurately without a nodal refinement. The trainable parameters of the enriched PINNs are learned to satisfy the governing partial differential equations of the cracked elastic solid and the corresponding boundary conditions. It is found that the incorporation of the crack-tip enrichment functions in the PINNs is substantially simpler and more feasible than in the conventional finite element method (FEM) or boundary element method (BEM). The present PINNs-based algorithm is tested and verified by several representative benchmark examples for different loading and crack-mode types. Numerical results show that the present PINNs-based method can provide highly accurate stress intensity factors (SIFs) with only few degrees of freedom. For interested readers, a self-contained MATLAB code and data-sets supplementing this paper are also provided in the Supplementary material.

A new multiscale XFEM with projection method for interaction between macrocrack and microcracks

Crack develops through the accumulation and development of microcracks near its crack tip. In the present study, a new multiscale XFEM was proposed to simulate the interaction between macrocrack and microcracks. In the proposed method, a multiscale projection method is used to construct the discontinuous multiscale base functions, since the enrichment schemes at macroscale and microscale differ. These multiscale base functions can correctly and conveniently deliver the discontinuous information between the macroscale and microscale. The strategy provides a new approach to address the deficiency that the traditional coarse elements in multiscale finite element method (MsFEM) cannot well characterize the displacement jump on the boundary of the unit cell, therefore enables extended finite element method (XFEM) to be employed at both scales. The feasibility of the proposed method is demonstrated using three numerical examples: a bending beam containing a mixed mode crack, a macro crack interacting with two symmetrical micro cracks, and a macrocrack interacting with multiple micro cracks. The proposed method can provide detailed displacement field and accurate stress intensity factor results with high computational efficiency.

Stress intensity factor assessment for reactor pressure vessel nozzles containing postulated corner cracks

Due to the structural discontinuity of geometry having higher stress concentration, the nozzles may dominate the structural integrity of reactor pressure vessel (RPV) system, even the material radiation embrittlement is insignificant. The nonmandatory Appendix G in Section XI of the ASME Boiler and Pressure Vessel code provides a fracture mechanics-based methodology using magnification factors to calculate the stress intensity factor of reference crack tips as long as the stress distribution through the nozzle section is available. This paper establishes various three-dimensional finite element models of Taiwan domestic RPV nozzles to conduct a series of stress and linear elastic fracture mechanics analyses to estimate the stress intensity factors. The circular and elliptical reference corner cracks with depths of one-fourth and one-tenth thickness of the vessel wall along the 45° path are considered. Two evaluation results using the ASME method and the finite element linear elastic fracture mechanics analysis are compared. It is found that the ASME method produces conservative values of stress intensity factor at crack tips of circular corner cracks but underestimates the elliptical corner cracks. Finally, an adjusted magnification factor formula is proposed to obtain more accurate stress intensity factors for elliptical-shaped nozzle corner cracks.

Fatigue characterization analysis of a submerged fishing farm platform through spectral-based fracture mechanics

This study proposes a general direct calculation approach for fatigue crack growth evaluation and life predictions through a spectral-based fracture mechanics method. First, equivalent damage accumulation rates are introduced to describe the crack propagation characteristics under short-term sea states, integrating wave spectrum and fracture mechanics. Subsequently, a general fatigue crack growth program is integrated to realize automatic crack growth, accurate stress intensity factor (SIF) calculation and reliable fatigue life prediction through coupling analysis of meter-scale structures and millimeter-scale cracks. Finally, a parameter study is implemented to explore the influence of wave direction and initial crack size/shape on the fatigue performance of the fishing farm platform. Results indicate that the remaining fatigue life is evidently longer under 90° wave direction than that under 0 and 45°, which can be well characterized through SIF transfer functions. Critical fatigue life decreases with the increase of crack size and aspect ratio with the shortest duration of 12.8 years, demonstrating that residual fatigue life is closely associated with initial crack state. Fatigue failure is more predominant at lower tubular joints with the critical fatigue life ranging from 15 to 30 years, indicating the self-developed program possesses good universality and applicability in dealing with fatigue issues.

Stress-intensity factors solutions for straight through cracks in C-sections

This work details a new stress-intensity factor (SIF) solution for a through-thickness edge crack in a structural member with a cross-section idealized as a generic C-section. This solution employs the methodology by Herrmann and co-workers (Herrmann and Sosa, 1986; Kienzler and Herrmann, 1986) that relates notch widening in structural sections to crack advance in the cross-section. Here, we calibrate an additional correction factor using a response surface methodology informed by results from finite element analyses. This approach results in an accurate SIF solution over the design space that is suitable for fatigue crack growth (FCG) analyses. Additional analyses performed in this work show the impact of changing the geometric ratios, loading, and restraint conditions on the SIF solutions.

Stress intensity factor prediction on offshore pipelines using surrogate modeling techniques

This study aims to predict the accurate stress intensity factor (SIF) of a crack propagating in offshore piping, which is one of the crucial factors used to assess the remaining fatigue life (RFL) of offshore pipelines. Four soft computing techniques are examined and evaluated in the modeling of SIF of a crack propagating in topside piping, as an inexpensive alternative to the finite element methods (FEM). In the training and testing stages, developed models of Functional Network (FN), Emotional Neural Network (ENN), Relevance Vector Machine (RVM), and minimax probability machine regression (MPMR) for SIF prediction were used and compared. Also, a comparative study was conducted for the developed models with the Adaptive Gaussian Process Regression Model (AGPRM). The load, crack depth, and half crack length have been adopted as input variables of the models, and the output variable is the SIF. All variables were simulated and determined based on the flat-plate FEM model. The analysis confirms that the RVM and MPMR models are superior to FN and ENN models for SIF prediction in the training and testing stages. In addition, the RVM and MPMR models show better than AGPRM for the prediction of pipe SIF in the testing stage. The MPMR accurately outperforms all models within 1.31% prediction error, and the majority of its error values at 99% confidence level fall within ±29.64 MPamm.

A new path-independent interaction integral for dynamic stress intensity factors of cracked structures

A new interaction integral derived from the path-independent Ĵ integral is proposed for the computation of stress intensity factors (SIFs) in both cracked homogeneous and non-homogeneous materials under the dynamic loading. The new interaction integral is theoretically proven to be path-independent and does not contain any derivatives of material properties by introducing the incompatibility auxiliary fields. In addition, the local refinement technique is introduced to the SIFs analysis in the framework of the extended finite element method (XFEM), where the initially generated mesh around the crack tip is refined and the variable-node element (VNE) is used to connect the refined elements and the adjacent elements. Several numerical examples determining the SIFs of cracked structures of homogeneous and non-homogeneous materials in static, dynamic and crack propagation are analyzed to test the accuracy of the proposed new interaction integral and more accurate SIFs can be obtained than those by the traditional ones.

Weight function method and stress intensity factor for two unsymmetric through-thickness and quarter-elliptical corner cracks at circular hole

Two unsymmetric through and quarter-elliptical corner cracks at a circular hole are frequently encountered in aircraft structures. Stress intensity factors for these crack geometries are the prerequisite for aircraft damage tolerance analysis. However, compared to single and symmetric double crack(s) case, the present two unsymmetric through and corner cracks at a hole is much more complicated because more geometric variables are involved. In the present article, the two-dimensional displacement-based weight function method is extended to derive the weight functions of two unsymmetric hole-edge cracks. Accurate and wide-range weight functions and stress intensity factors are obtained. The two-dimensional weight function for the hole-edge cracks is further used in the slice synthesis weight function method to compute stress intensity factors for two unsymmetric quarter-elliptical corner cracks at a circular hole. The solution accuracy is extensively verified through comparisons to stress intensity factors obtained using finite element analysis. Compared to 3D finite element method, the present slice synthesis weight function method is 500 times faster, and therefore can provide accurate and very efficient tool for fatigue and fracture analysis of structures containing through and quarter-elliptical corner hole-edge cracks.

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.

A displacement correlation method for stress intensity factor extraction from 3D fractures in anisotropic materials

A numerical method to extract stress intensity factors (SIFs) from 3D fractures in anisotropic materials is presented. The formulation of a displacement correlation method that is valid for linear elastic materials with arbitrary symmetry in their elastic properties is given in detail. An algorithm for the numerical implementation of the method is also given. The methodology can take an approximate displacement field from any numerical method as input to the extraction process. However, to return accurate stress intensity factors an accurate numerical displacement field is required. In this work, this is provided by a Generalized Finite Element Method. Several verification problems show that the anisotropic displacement correlation method is robust and can extract accurate SIFs. The methodology is used in a parametric study of crack–crack interactions in a high-strength aluminum alloy to demonstrate a practical application. More than 200 simulations are run using the Generalized Finite Element Method, which are largely able to be scripted and ran without user intervention after one simulation is set up.

Accurate stress intensity factors for kinked interface crack in bonded dissimilar half-plane

In this study, the stress intensity factor (SIF) of an interface kinked crack is analyzed by the singular integral equation of the body force method. The problem can be expressed by distributing the body force doublets of the tension and shear types along all the boundaries of the kinked and interface crack parts. The SIFs can be obtained directly from the densities of the body force doublets at the crack tips. Although the problem has already been calculated using the crack connection model, the accuracy of the analysis has not been clarified. From the analysis results in this study, it can be seen that the SIFs calculated by the crack connection model have a nonnegligible error, and the present method gives more accurate results. The advantage of the present method is that the SIFs of the kinked and the interface crack tips can be obtained at the same time with high accuracy.

Convenient and accurate formulas for stress intensity factor distribution of semi-elliptical surface crack

In this paper, the stress intensity factor (SIF) formula [Formula: see text] along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution [Formula: see text] is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio [Formula: see text]/[Formula: see text] is focused considering the exact solution [Formula: see text] of an elliptical crack. By applying the least squares method to the ratio [Formula: see text]/[Formula: see text], accurate and convenient formula is proposed. The proposed formulas may provide the accurate SIF distributions for the aspect ratio [Formula: see text]–4 better than 0.2% accuracy.

A novel method for characterizing the fatigue crack propagation of steel via the weak magnetic effect

Generally, the fatigue failure of reinforced concrete beams under the coupled action of fatigue and corrosion is mainly controlled by the brittle fracture of the steel bar, confirming the significance of the fatigue crack growth (FCG) behavior of the steel bar. In this regard, FCG tests of opening mode I were conducted based on standard compact specimens manufactured from HRB400E steel bar. Meanwhile, the weak magnetic field, including the piezomagnetic field throughout the FCG process and the residual magnetic field (RMF) at certain crack lengths were both recorded. Piezomagnetic hysteretic curves and RMF distribution were analyzed separately, and the characteristic parameters of them were both determined. The evolution mechanism of the weak magnetic field was then comprehensively explored. Finally, the quantitative relationships between the FCG parameters and the characteristic parameters of weak magnetic field were separately established. The proposed relationships were applied in a prediction model of crack length, FCG rate and the FCG life, which were validated through the experimental results. The results showed that the prediction accuracy of stress intensity factor using PE method, and the prediction accuracy of crack length using PE and MMM methods all reached 90%. The errors between the FCG life predicted by PE and MMM methods and the experimental results were both within 20%.

Study on the stress intensity factor and the double-degeneracy mechanism in the BEM/BIEM for anti-plane shear problems

The crack and the rigid-line inclusion problems under the anti-plane shear are the special case of the elliptic hole and elliptic rigid inclusion, respectively. We revisit this kind of problem by using the degenerate kernels in terms of the elliptic coordinates. The stress intensity factor (SIF) is also addressed. Three ways are employed to determine the SIF. One is the extrapolation approach for the boundary or interior displacement near the tip. Another is the extrapolation approach for the boundary stress or interior stress near the tip. The other is the J-integral enclosing the crack tip. It is interesting to find that a rigid-line inclusion case yields a singular influence matrix due to the degenerate scale of length four in the log kernel. However, double-degeneracy including degenerate scale and degenerate boundary may still result in a singular matrix even though the dual BEM/BIEM is employed. The mechanism is well explained thanks to the introduction of degenerate kernel. Without the introduction of degenerate kernel, the mechanism of the double-degeneracy problem in the BIEM can’t be clearly examined. By using the degenerate kernel, the SIF can be easily determined for the crack or the rigid-line inclusion under the anti-plane shear. The path independence of the J-integral can be derived analytically. The reciprocal relation for the SIF between a crack and a rigid-line inclusion with respect to opposite loading is also addressed. In the numerical implementation, the SIF can be determined using the dual BEM. It is worth noting that BEM shows the advantage that the obtained boundary displacement or boundary stress can be directly used to obtain the more accurate SIF for the crack or the rigid inclusion, respectively.

High-order stable generalized/eXtended finite element approximations for accurate stress intensity factors

This paper investigates the accuracy and robustness of stress intensity factor (SIF) extraction using the p-Hierarchical Discontinuous Interpolant Stable Generalized Finite Element Method (pFEM-DSGFEM). This method is well-conditioned and optimally convergent for fracture mechanics problems if a proper enrichment strategy and mesh refinement are used. The method performs well when calculating global quantities such as strain energy, but its ability to capture local quantities such as SIFs has not yet been explored. pFEM-DSGFEM spaces are used to solve a variety of fracture mechanics problems and their solutions are used to extract SIFs with the Displacement Correlation Method (DCM). These numerical experiments show that pFEM-DSGFEM spaces provide highly accurate SIFs, even better than standard GFEM spaces, while being well-conditioned.

A modified three-dimensional virtual crack closure technique for calculating stress intensity factors with arbitrarily shaped finite element mesh arrangements across the crack front

To obtain accurate stress intensity factors (SIFs) with arbitrarily shaped finite element mesh arrangements across the crack front, a modified three-dimensional virtual crack closure technique (modified 3D-VCCT) is proposed in this paper. This method is based on three-dimensional virtual crack closure technique (3D-VCCT) and finite element method. To increase the SIFs calculation accuracy for the crack with arbitrary shape, the length and shape of finite element meshes across the crack front are considered in this method. Then the SIFs with arbitrarily shaped finite element mesh arrangements across the crack front are calculated by three different methods, the modified 3D-VCCT in this paper, the extension of virtual crack closure-integral method proposed by Okada and the 3D-VCCT. The solutions of SIFs obtained by three methods are compared and the comparison results show the modified 3D-VCCT has better accuracy with arbitrarily shaped finite element mesh arrangements across the crack front. In addition, the simulations of fatigue crack growth are carried out by using the modified 3D-VCCT. Then the simulation results are compared with the test results, which shows good agreement.