Evaluation Of Stress Intensity Factors Research Articles

Reliability analysis of fatigue crack growth in shallow shell structures using the Dual Boundary Element Method

This work presents a novel methodology for fatigue life reliability analysis using a newly developed Dual Boundary Element Method-based Implicit Differentiation Method (DBEM-IDM) in shallow shell structures. The proposed DBEM formulations evaluate stress intensity factors and fatigue life sensitivities in shallow shells considering geometrical variables and curvature. The IDM formulations, obtained through direct differentiation of the shallow shell DBEM formulations, uses the First-Order Reliability Method (FORM) to assess the reliability index and probability of failure of shallow shell structures with multiple cracks. Two numerical examples were simulated to illustrate the effectiveness of the proposed methodology. The first example examines a shallow shell with a centre hole and cracks subjected to various loads. The critical crack length required to ensure structural reliability and inspectability is determined. Fatigue reliability assessment is performed for the same example, employing limit state functions expressed in terms of fatigue life. FORM results are compared with the results of Monte Carlo Simulations (MCS), and provided a maximum difference of 3.67%. Parametric analyses are conducted to identify significant variables that affect reliability, and it was found that precise determination of design parameters is necessary to reduce the probability of failure, particularly for the Paris law constants. The second example, featuring more complex geometry, involved assessing fatigue reliability in a cylindrical shallow shell structure with multiple cracks. The results of this example indicate a 3.49% maximum difference between FORM and MCS. The results exhibit a low error compared to the MCS, and the inherent efficiency of the IDM-based FORM underscores its suitability for addressing uncertainty in reliability analysis.

General point load weight function for semi-elliptical surface cracks in round bars

Offshore mooring chains are continuously subjected to cyclic environmental loadings, resulting in fatigue cracks that always develop at the surface and grow across the circular cross-sections. To analyse the fatigue crack growth in a mooring chain based on a fracture mechanics-based approach, the evaluation of stress intensity factors (SIFs) of surface cracks in the chain segments becomes essential. A general point load weight function of SIFs for semi-elliptical surface cracks in straight and curved round bars was derived in this study. Parametric three-dimensional finite element (FE) models were developed to calculate the SIF solutions for determining the unknown parameters in the weight function. The analysis matrix covered wide ranges of aspect ratios 0.1 ≤ a/c ≤ 2.0, relative crack depths 0.03 ≤ a/D ≤ 0.6 and relative bar curvatures 0.0 ≤ D/Ri ≤ 1.5. The developed weight function was verified against the solutions available in the literature and FE results, indicating good accuracy. The proposed weight function can be used in SIF calculation and remaining fatigue life prediction of surface cracked round bar components under complex stress distributions, such as chain links.

Defect induced fatigue failure behavior and life assessment of laser powder bed fused Al-Si alloy under different building directions

The influence of the building direction (0°, 45°, and 90°) on the high cycle fatigue properties of a laser powder bed fusion (LPBF) Al-Si alloy was investigated by uniaxial loading fatigue tests under a stress ratio of 0 in combination with multi-dimensional imaging and electron backscattered diffraction (EBSD) analysis. Surface/subsurface failures were induced by single irregular lack of fusion defect that originated from unmelted powder or inhomogeneous microstructure. The fatigue properties decreased with increasing building angle, which was attributed to the size difference of the original defect dominating crack nucleation and the distribution difference of melting pool boundaries deflecting crack growth. According to the stress intensity factor evaluation, the threshold value of long crack growth and the transition size of crack growth exhibited a decreasing tendency as the building angle increased. Considering the influence of building direction on defect size distribution, a fatigue index parameter-controlled crack nucleation life prediction model was established, and the prediction result was satisfactory for safety design.

Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method

This paper presents a new extended isogeometric boundary element method (XIGABEM) for the analysis of cracks in two-dimensional bimaterial interfaces. The classical NURBS approximations used in isogeometric formulations are augmented with functions based on the first two terms of the crack-tip stress and displacement series expansions. The first term is related to the complex stress intensity factor (SIF) and allows the numerical method to capture the singular and oscillatory near-tip behaviour, while the second accounts for the T-stress contribution to the solutions. The proposed enrichment strategy only introduces three additional degrees of freedom per crack tip, which are accommodated in a square linear system by a crack tip tying constraint and a novel condition on the stress parallel to the tip. These supplementary relations also cause the enrichment parameters to become proxies for the SIFs and T-stress. Therefore, the crack-tip factors can be obtained directly from the solution vector given by XIGABEM, eliminating the need for costly computational post-processing techniques. Several benchmark examples, including both straight and curved cracks, are presented to demonstrate the accuracy and convergence of the proposed method. The direct XIGABEM solutions for the SIFs and T-stress compare favourably against those from the literature.

Numerical Analysis of Fracture Behavior of Functionally Graded Materials using 3D-XFEM

Abstract This paper presents the numerical evaluation of mixed stress intensity factors (SIFs) and non-singular terms of William's series (T-stress) of functionally graded materials (FGMs) using three-dimensional extended finite element method (3D-XFEM). Four-point bending specimen with crack perpendicular to material gradation have been used in this investigation in order to study the effect of some parameters (crack position, crack size, specimen thickness) on the failure of FGMs materials. The fracture parameters (KI KII, phase angle ψ and T-stress) obtained by the present simulation are compared with available experimental and numerical results. An excellent correlation was found of the 3D-XFEM simulations with those available in the literature. From the numerical results, a fitting procedure is performed in order to propose an analytical formulation and subsequently are validated against the 3D-XFEM results.

Microstructure-based interior cracking mechanisms and life prediction of additively manufactured Ni-based superalloy with temperature effect

The localized microstructure related fatigue cracking of additively manufactured (AM) Ni-based superalloy has been attracting increasing attention. Understanding the connection between the inhomogeneous microstructure and the fatigue characteristics with small deformation is crucial. Herein, the microstructure-related high cycle fatigue and very high cycle fatigue properties of an Ni-based AM superalloy were examined. The fatigue tests were conducted with stress ratio of 0.1 at room (25 ℃) and elevated (650 ℃) temperatures. To support the modeling of the internal fatigue failure mechanism, additional studies on microstructure features and mechanical properties were carried out in conjunction with electron backscatter diffraction, energy dispersive spectrometry, and monotonic tensile tests. Results of 2D fracture surface observation showed that the interior facet-induced fatigue crack nucleated under relatively low applied stress at both temperatures, which were assisted by the interior abnormal structure. Furthermore, the interior crack nucleation region consisting many facets was formed under shear stress and strain based on 3D restructure of fracture surface. Combined with evaluation of threshold stress intensity factor, the transition lengths from small crack to long cracks for surface failure at 25 ℃ and interior failure at 650 ℃ were evaluated. Based on the above analysis, the interior failure mechanisms were summarized related with microstructure characteristics. Finally, fatigue index parameters based on different failure modes were calculated to predict the fatigue life. The anticipated and experimental data are determined to be in satisfactory agreement.

Stress intensity factor and fatigue life evaluation for important points of semi-elliptical cracks in welded pipeline by Bezier extraction based XIGA and new correlation model

NURBS-based Bezier extraction in extended isogeometric analysis (XIGA) using thermo elastic-plastic equation has been proposed for evaluating the stress intensity factor (SIF) in the various relative crack depths, aspect ratios, and important points (surface points and deepest point) of the semi-elliptical surface crack in weld line of pipelines under cyclic internal pressure. In this approach, the level set technique is used for identifying the grid points around the crack front and the crack surface. Crack in the specified domain is modeled by Heaviside and crack front enrichment functions and remeshing due to crack growth does not require. Also, new correlation models are proposed to predict SIF in these points of the crack front. Based on the proposed correlations, fatigue crack propagation, and fatigue life are investigated. Modified walker equation used for predicting fatigue crack propagation rate and fatigue life in the welded pipeline. The finite element method (FEM) analysis with a similar condition was performed and compared with XIGA and correlation models to validate the presented method. The results demonstrate good agreement. Thus, the proposed approach successfully studies the 3D crack problem with acceptable accuracy.

An efficient meshfree framework for simulation of crack tip stress fields in two-dimensional graded media subjected to thermoelastic loads

In the present work a novel framework of algorithm has been proposed for enhancing the versatility of the element-free Galerkin method for modeling of fracture in graded media subjected to thermoelastic loadings. The proposed work restructures the conventional element free Galerkin method (EFGM) at multiple level through generic MATLAB algorithms thereby developing an efficient and robust method for simulating crack tip stress fields in graded material subjected to thermoelastic loads. The proposed algorithm utilizes varying nodal density criterion in conjunction with optimum Gaussian quadrature around these nodes for numerical integration of the governing equations. The proposed algorithm also incorporates blended approximation which is effective for simulating crack tip stress fields in both convex and non-convex problem domains. Nonequilibrium formulation has been selected for evaluating stress intensity factors (SIFs) for the fracture problems in graded media. A few problems of cracked domain subjected to thermoelastic loads have been modeled and simulated to illustrate the effectiveness of proposed framework of algorithms. Further, three component level problems having non-convex domains have also been discussed to establish the robustness and modeling capabilities of the proposed work. A good agreement between the simulated results and reference data demonstrates the algorithm’s competence and robustness for modeling thermoelastic fracture in graded materials. The proposed methodology improves the computational efficiency and flexibility of the element-free Galerkin method for modeling thermoelastic fracture in graded media. Moreover, enhancement of computing speed with the proposed methodology adds to its modeling potential.

Dynamically propagating cracks in anisotropic plates subjected to hyperbolic thermal shock

ABSTRACT In this paper, dynamically propagating cracks in anisotropic plates exposed to a generalised thermal shock are investigated. Here, the governing equations are considered according to the Lord-Shulman (LS) model as a fully coupled generalised thermoelasticity theory. The crack is modelled in the context of the eXtended Finite Element Method (XFEM). To evaluate Stress Intensity Factors (SIFs), a technique based on the J integral and crack tip opening and sliding displacements, previously applied for stationary cracks, is developed for a dynamically propagating crack in orthotropic solids. Besides, a variety of functions for enriching the displacement field are derived relying on the behaviour near the tip of a dynamically propagating crack in anisotropic materials. The maximum hoop stress criterion is also modified by using the asymptotic stress field for a dynamically propagating crack. In addition, the effect of the angular variation of fracture toughness in orthotropic materials is accounted in computing the crack propagation speed. In some examples, dynamic crack growth in complex cracked orthotropic structures subjected to LS thermal shock is studied in detail. The impacts of fibre orientations and LS relaxation time are also investigated in these examples. In conclusion, applying non-Fourier thermal shock for modelling dynamically propagating cracks in orthotropic structures is recommended to obtain more realistic results. In addition, by increasing the LS relaxation time, the crack grows less oscillatory and is more aligned along the material fibres.

Evaluation of stress intensity factors in functionally graded plate under mechanical and thermal loadings

Evaluation of stress intensity factors in functionally graded plate under mechanical and thermal loadings

Comparison of crack growth rates of IPE beams made from stainless steel in three-point bending

The main focus of research dealing with a fatigue of steel components is mostly performed by mechanical testing with focus set on small-scale components. On the other hand, from a civil engineering viewpoint, the steel load-bearing structures or their elements have much larger dimension, when comparing them to laboratory specimens. Therefore, the fatigue testing took place on IPE 80 specimens made from two different stainless steels AISI 304 and AISI 316, loaded in three-point bending with data collection of crack mouth opening displacement placed in mid-span using clip-on extensometer. This presented study focuses on the comparison of crack propagation rate in linear region of well-known Paris’ law. For the assessment of material constants from Paris’ equation C and m, two steel grades of stainless steel, AISI 304 and AISI 316 were experimentally obtained. To evaluate the experimental data, a three-dimensional (3D) numerical model, representing IPE 80 geometry, in a finite element method (FEM) software Ansys Mechanical APDL was created. The generated numerical results were used to evaluate stress intensity factor values, which serves as a main input to crack propagation Paris’ law.

Improved XFEM (IXFEM): 3D dynamic crack propagation under impact loading

An improved XFEM (IXFEM) for three-dimensional non-planar crack propagation under impact loadings is developed. The proposed method couples the IXFEM (Tian and Wen, 2015; Wen and Tian, 2016) and the B-spline ruled surface method (BRSM) proposed previously by authors (Xiao, Wen and Tian (2021)). The issues of the standard XFEM for dynamic crack propagation, such as energy inconsistency, “null” critical time step size and optimal mass lumping at crack tip, are fundamentally avoided with an extra-DOF free PU approximation (Tian, 2013). The tip singularity enrichment is introduced to assure high accuracy through the extra-DOF free PU approximation. The BRSM, which is designed to solve the challenge about robust and efficient geometry representation of 3D non-planar surface crack growth, is applied to model the geometry of the 3D dynamic crack propagation in this paper. The interaction integral for 2D dynamic stress intensity factor (SIF) evaluation is extended to 3D. Efficiency of the proposed approach is demonstrated via numerical tests.

Numerical Evaluation of Stress Intensity Factors in Functionally Graded CNTRC Plates

Numerical Evaluation of Stress Intensity Factors in Functionally Graded CNTRC Plates

An enriched improved complex variable element-free Galerkin method for efficient fracture analysis of orthotropic materials

The fracture problem of orthotropic materials has been widely concerned by researchers in the fields of mechanics and engineering. The meshless method using nodes to discrete the problem domain is an effective way to analyze cracked structures. In this paper, an enriched improved complex variable moving least squares (EICVMLS) approximation, in which a group of intrinsic enrichments is introduced into the conventional ICVMLS adopting a well-defined weighted complex variable error norm, is proposed for capturing the crack-tip fields in orthotropic media accurately. Then, an enriched improved complex variable element-free Galerkin (EICVEFG) method is developed to simulate fracture behavior in orthotropic media. The visibility criterion is used to model the discontinuity behavior around cracks and the M−integral is considered to evaluate stress intensity factor (SIF). The stress field and the displacement field at the crack tip, the SIF for different crack inclinations, and different directions of orthotropy axes are investigated to verify the validity of the proposed method. In addition, the effects of linear basis functions and enriched basis functions on the results are compared in this study. The numerical results reveal that the established EICVEFG approach can achieve higher accuracy than the extended finite element method (XFEM) and traditional meshless methods such as the element-free Galerkin (EFG) method and the meshless finite volume (MFV) method. Similarly, the EICVEFG method has been proved to offer a higher convergence rate by parameter studies (including dimensionless factor dmax, integral size, and the number of integral cells in M−integral).

Advancement on optical methods in stress dead-zone characterisation and SIF evaluation

The work described in this paper is a study of the stress dead zone (SDZ) concept with advanced full-field optical methods. The SDZ is a region located around the fatigue crack flanks, adding a negligible contribution to internal stresses on the global deformation energy calculation. In the analytical modelling, this area can be removed from the structural member, resulting in a geometry simplification, and in the possibility of using analytical formulations in the Stress Intensity Factor (SIF) calculation associated to the existing fatigue crack. In a fatigue-testing program, aluminium middle tension (MT) specimens were prepared and then subjected to a cyclic fatigue loading, in order to generate different crack lengths for each specimen. Then, the fatigued specimens are monotonically tested under a uniaxial tensile loading to assess the SDZ concept.The experimental data is collected and analysed through two full-field high-resolution optical techniques with different system resolutions, Digital Image Correlation (DIC), and Electronic Speckle Pattern Interferometry (ESPI). As a result, the SDZ is geometrically characterized through a set of mathematical formulations based on the compliance function for the studied specimens, and is experimentally identified through deformation fields obtained from both DIC and ESPI techniques. The obtained results from both high-resolution methods verify the validity of the concept and demonstrate that it can be used to simplify the analysis.

3D modelling of fatigue crack growth and life predictions using ANSYS

This study uses ANSYS mechanical APDL 19.2 to predict crack propagation trajectories and fatigue crack growth at constant amplitude loading. Mixed-mode fatigue life assessment is implemented by the Paris law model for different configuration of modified compact tension specimen (MCTS) in linear elastic fracture mechanics (LEFM). The methodology includes: evaluating stress intensity factors (SIFs), a direction of crack propagation and estimating fatigue life via incremental crack growth process. Predicted crack growth path in the present analysis revealed a change in orientation of the hole proportionately affected fatigue crack life cycles. The propagation of fatigue crack is mostly attracted to the hole and the crack could either curve its path and grow towards it, or bypass the hole and propagate. The mixed-mode fatigue crack path and fatigue crack growth from this study were validated by several crack growth experimental and numerical results in literature.

High-cycle-fatigue properties of selective-laser-melted AlSi10Mg with multiple building directions

Axial loading fatigue tests with stress ratio of 0 were conducted in investigating the influence of building directions (0°, 45° and 90°) on high cycle fatigue property of a selective laser melted AlSi10Mg in combination with two-dimensional microscope observation and three-dimensional ultra-depth imaging. Results show that fatigue strength decreases with the increase of building angle due to larger defects and sparser melting pool boundaries. Two failure modes, i.e. surface and subsurface failures, are mainly induced by irregular lack of fusion whose size arises as building angle increases. Also, the roughness of crack nucleation region is mainly attributed to the plastic deformation of crack tip under tensile stress. Based on the stress intensity factor evaluation at crack tip, both long crack growth threshold value and transition size from small to long crack growth all drop as building angle increases. Based on these, the microstructure-based crack nucleation and propagation behavior is clarified, and an energy based fatigue life prediction model considering the stress concentration effect of defect is proposed. The agreement between experimental and predicted data is satisfied.

An eXtended Finite Element Method implementation in COMSOL Multiphysics: Solid Mechanics

This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software COMSOL Multiphysics for the first time. An enrichment strategy is proposed, consistent with the structure of the software. To this end, for each set of enrichment functions, an additional Solid Mechanics module is incorporated into the numerical framework, coupled with compatible modifications to the internal variables. The Linear Elastic Fracture Mechanics (LEFM) is exclusively adopted for the crack analysis. The model pre-processing, level set update, stress intensity factor calculation and crack propagation analysis are conducted by employing COMSOL’s built-in features in conjunction with external MATLAB functions through COMSOL LiveLink. All implementational aspects and suggested remedies for the treatment of enriched elements, framework setup, evaluation of stress intensity factors, and numerical integration are described in detail. The accuracy and robustness of the proposed method are examined by several numerical examples, including mixed-mode crack propagation in 2D domains as well as stationary planar fractures in 3D settings. The results represent excellent agreement with available analytical, numerical and experimental observations in the literature.

An interaction integral method coupled with special crack tip elements for evaluation of stress intensity factors

Accurate computation of stress intensity factors (SIFs) for two-dimensional cracks by an interaction integral method combined with special crack tip elements is presented in this paper. SIFs are of great importance to fracture mechanics analysis. Due to special variation of displacement around the crack tip and the singularity and near singularity of integrals in interaction integral method, the results obtained by which are affected by the radius of the closed loop. Thus, a general method for singular integrals and nearly singular integrals is applied in the paper. With the interaction integral method coupled with the proposed special crack tip element, more stable and accurate values of the SIFs can be obtained. Numerical examples have demonstrated the effectiveness of the proposed method.

Evaluating SIFs in finite orthotropic composites from experimentally determined stress coefficients

Unlike with isotropy materials, determining stress intensity factors in orthotropic composites is complicated as they can depend on constitutive properties and principal material directions. Acknowledging the above, this paper develops a novel technique to evaluate stress intensity factors in finite, plane-stressed, orthotropic composites. Upon substantiating the numerical reliability of the approach, KI is determined experimentally in a finite tensile loaded double-edge cracked [013/905/013] graphite-epoxy composite laminate from displacement-evaluated stress coefficients. Only a single DIC-measured displacement field is need. Advantages of the method include applicability beyond a laboratory environment and to other structural shapes, loads and crack configurations, wide acceptable range of stress coefficients and highly arbitrary source locations of the measured input data. Unlike purely numerical or theoretical approaches, the method does not require knowing the external loading. This is significant as loads are often unknown in practice. Results are verified independently.