Notch Stress Intensity Factors Research Articles

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Residual Stress Prediction during TIG and MIG Welding Process of Steel - A Review

In this study, a forensic review of residual stress predictions and its impact on welded joints especially the steel pipes during the Tungsten inert gas welding and metal inert gas welding processes were reviewed. It was established that in the case of MIG welding, the effect of residual stress can be reduced after treatment. In the case of TIG welding process, increase in current will lead to deformation and residual stresses. Estimating the residual stress is a challenging task. It is common to predict residual stress using a notch stress intensity factor, a numerical simulation approach coupled with a thermal-mechanical finite element model. Thus, adequate design in welding parameters will help in the optimization of the process to achieve a safe and reliable welded joint during TIG and MIG welding process.

Determination of notch stress intensity factors for V-notched specimens under mode I loading using the 3D-Digital image correlation and strain energy approach

In this paper, the fracture behaviour of Single Edge Notched Tension Specimen (SENT) is investigated by using the three-dimensional digital image correlation (3D-DIC) method and the mode I notch stress intensity factors (NSIFs) for the SENT specimen is derived. Initially, the concept of NSIFs and different experimental methods are reviewed. This is followed by a review of the theory of the DIC method. Then, the step-by-step process for setting up a 3D-DIC full-field experimental system for the SENT specimens tested is described. In the experiments, the SENT specimens were tested with pinned and clamped boundary conditions (BCs) and different notch initial opening angles. Furthermore, the analytical stress fields around the sharp V-notches are presented. Combining with the strain energy approach (SEA), the experimental strain fields are analysed to calculate the mode I NSIFs. Moreover, the presented numerical mode I NSIF values for the SENT model are validated by the available results in the literature. Finally, the experimental results obtained from the 3D-DIC method are compared with the numerical results from finite element analysis (FEA) to verify the feasibility and accuracy of the 3D-DIC method. The effect of different BCs of pinned and clamped ends is discussed.

Determination of notch stress intensity factors under mode I loading using the 3D-DIC and finite element over-deterministic methods

In this paper, the fracture behaviour of Single Edge Notched Tension Specimens (SENT) is investigated experimentally and numerically using the three-dimensional digital image correlation (3D-DIC) experimental method and the Finite Element Analysis (FEA) technique, respectively. The mode I notch stress intensity factors (NSIFs) for the SENT specimens are derived from the measured and simulated displacement fields using the Finite Element Over-Deterministic (FEOD) method. The step-by-step process of a 3D-DIC experimental system for the SENT specimens is described. The SENT specimens were tested with pinned and clamped boundary conditions (BCs) and different notch initial opening angles. There are three main contributions of the paper: (1) the derivation of the NSIFs under Mode I Loading for thin plates subjected not only to the common pinned BCs, but also to the rare, clamped BCs; (2) the application of the FEOD method to derive the NSIFs from the displacement fields measured using the 3D DIC technique and predicted using FEA; (3) the validation of the NSIFs derived numerically via experimentally-determined NSIFs for notched thin plates subjected to both pinned and clamped BCs. Thus, four sets of NSIF data are provided in the paper and enable confident application of the NSIF values for the conservative (pinned BCs) and light-weight (clamped BCs) design of notched thin plates.

Fatigue strength assessment of aluminium welded joints under variable amplitude loading using the Peak Stress Method

One of the simplest and most efficient ways to design lightweight structural components is the combination of welding and aluminum alloys. However, welded joints are extremely sensitive to fatigue failure and making accurate lifetime predictions is still challenging when Variable Amplitude (VA) loading conditions are involved. Among all design criteria available in the literature, the present investigation focuses on the Peak Stress Method (PSM), an engineering finite element (FE)-based approach to rapidly assess the fatigue strength of welded joints. In more detail, the PSM suggests modelling both weld toe and weld root as sharp V-notches having null tip radius and correlates their fatigue strength using the intensity of the local linear elastic asymptotic stress distributions described by the Notch Stress Intensity Factors (NSIFs). The theoretical formulation of the PSM for the fatigue strength assessment of welded joints subjected to VA loadings has been recently proposed by combining its Constant Amplitude (CA) formulation with the Palmgren-Miner's cumulative linear damage rule. Such VA formulation has been successfully validated against a large bulk of experimental fatigue results generated by testing welded joints made of structural steels under uniaxial as well as multiaxial loadings. In the present investigation, the VA formulation of the PSM has been further validated against experimental data relevant to welded joints made of aluminium alloy under VA loadings.

Fatigue assessment of steel tube-to-flange welded joints with reinforcement ribs subjected to multiaxial loads according to the Peak Stress Method

In fatigue design of welded structures, the Peak Stress Method (PSM) is a FE-oriented tool to estimate the Notch Stress Intensity Factors (NSIFs). In compliance with proper fatigue design curves validated against more than 1300 experimental data, the PSM allows to estimate the fatigue lifetime of welded structures made of either aluminium alloys or structural steels and subjected to uniaxial and multiaxial loadings. Moreover, an interactive analysis tool has also been developed in Ansys® Mechanical to automate PSM application on welded structures and support the FE analyst. In this work, the fatigue strength of complex steel tube-to-flange welded joints with reinforcement ribs has been experimentally investigated under pure bending, pure torsion and in-phase as well as out-of-phase combined bending-torsion loadings. The tested joint consists of a steel SHS tube having 6.3 mm thickness, which is joined at both ends to a 15-mm-thick flange. In addition, tube and flanges are joined by fillet welding to 6-mm-thick steel reinforcement ribs. A test rig has been designed in order to perform the experimental fatigue tests, taking advantage of two hydraulic actuators. The experimental fatigue results have been compared with fatigue lifetime estimations performed using the automated PSM tool.

Fatigue lifetime assessment of weld ends with idealized or real geometry in steel joints for off-road vehicles using the Peak Stress Method

The Notch Stress Intensity Factors (NSIFs) for the fatigue analysis of welded structures can be rapidly estimated by FEM by applying the Peak Stress Method (PSM). Two steel welded joint geometries adopted for off-road vehicles and containing four intermittent fillet welds were tested under uniaxial loading. To apply the PSM, an idealized as well as the real 3D scanned geometry of the weld ends were implemented in the numerical analyses. The PSM properly anticipated where cracks initiated and estimated the fatigue lives in fairly good agreement with the outcomes of the fatigue tests.

An analytical approach for evaluation of linear elastic stress fields around sharp V-shaped notches in plates

In the context of the theory of elasticity, the stress state at a sharp notch is singular, and the degree of stress singularity depends on the notch opening angle. Most existing analytical approaches for evaluating asymptotic linear elastic stress fields ahead of V-notches rely on notch stress intensity factors (N-SIFs). This paper presents an alternative analytical approach for evaluating notch stress fields by taking advantage of traction-based structural stress and Williams’ eigenfunction methods. To better represent notch stress fields, the first order and higher order terms of eigenfunction are included in the present study. The analytical solutions are then compared to the stress fields resulting from finite element analysis for validation purposes. The stress contours evaluated by the analytical approach are nearly identical to the numerical results corresponding to three distinguishing notch opening angles under pure Mode I loading, which signifies the effectiveness and robustness of the analytical solution methodology developed in the present study. Subsequently, the approach is extended to accommodate Mode II loading by introducing a skew-symmetric term in the stress function. The generalized method is then applied on a welded cruciform joint, which precisely captures the notch fields compared to FEA results.

Loading rate effect on mixed-mode I + II fracture of V-notched Brazilian disc rock specimen under impact loads

Dynamic failure processes of rock masses containing numerous discontinuities including pores, cracks and notches have been the major issues in structural safeties of underground buildings subjected to impact loads, such as earthquake, blast and vehicle vibration. At present, most of the studies are focused on the dynamic fracture behaviors of rocks containing crack-like defects, while the studies on rocks containing notch-type defects are very rare, especially under mixed-mode loading conditions. This paper aims to study the effects of loading rate on mixed-mode I + II fracture characteristics of flattened V-notched Brazilian disc rock specimen under impact loads by means of an split Hopkinson pressure bar (SHPB) system combined with a high-speed camera. Dynamic fracture tests were performed on a total of 125 groups of V-notched rock specimens with different notch angles (0°, 30°, 45°, 60°, and 90°) and loading angles (0°, 30°, 45°, 60°, and 90°) at different air pressures (0.16 MPa, 0.18 MPa, 0.20 MPa, 0.22 MPa, and 0.24 MPa). Based on dimensional analysis, a numerical method was proposed to establish the relationship between mixed-mode notch stress intensity factor (NSIF) at the V-notch tip and external axial load. The dynamic notch fracture toughness values of flattened V-notched Brazilian disc rock specimens were calculated from the maximum values of dynamic force in the SHPB tests according to the proposed numerical method. The effects of loading rate, notch angle, and loading angle on the mixed-mode I + II notch fracture toughness value and crack initiation angle were quantitatively analyzed, which were verified using a modified maximum tangential stress (MTS) criterion by considering the loading rate effect. It is found that the loading rate has a significantly positive effect on the notch fracture toughness value, but has a negative effect on the crack initiation angle due to the inertial effect under dynamic impact loads. Generally, pure mode I fracture occurs for the loading angle of 0° or 90°, pure mode II fracture occurs for the loading angle varying from 35° to 45°, and mixed-mode fracture occurs for other loading angles. Good consistencies of the mixed-mode I + II notch fracture toughness values and crack initiation angles of the V-notched rock specimens are observed between the modified MTS criterion prediction and experimental results. This work may improve the understanding of the dynamic fracture behaviors of rock masses containing notch-type defects during tunnel excavation and underground construction process.

Fracture assessment of U-notched diagonally loaded square plates additively manufactured from ABS with different raster orientations

This paper investigates the fracture behavior of 3D-printed notched specimens under various combinations of mode I and mode II loadings, including pure mode I and pure mode II loadings. The study employs fused deposition modeling (FDM) to fabricate U-notched diagonally loaded square plate (UNDLSP) specimens using Acrylonitrile Butadiene Styrene (ABS) filaments. To experimentally measure the fracture load and fracture initiation angles, 120 UNDLSP specimens are 3D printed with different notch tip radii, notch orientation angles, and [0, 90], [45, −45] raster orientations. Tensile characteristics and translaminar fracture toughness of ABS plates with [0, 90] and [45, −45] raster orientations are obtained using dog-bone and cracked DLSP samples, respectively. Considering the layered nature and anisotropy of the material, the virtual isotropic material concept (VIMC) is utilized along with two well-known stress-based brittle fracture models: the maximum tangential stress (MTS) and the mean stress (MS) criteria. The test results are predicted using the fracture limit curves and fracture initiation angle curves developed for these fracture models in terms of the notch stress intensity factors (NSIFs). Furthermore, a general equation is established to estimate the fracture initiation angle of U-notched ABS specimens under mixed mode I/II loading, irrespective of geometry, raster orientation, and notch tip radius, based on the curves obtained from the MTS and MS criteria. The fracture surfaces of the UNDLSP specimens are examined using scanning electron microscopy (SEM) to study the micro-mechanisms involved in the fracture process. The findings indicate that both the VIMC-UMTS and VIMC-UMS criteria accurately predict the experimentally achieved fracture loads. Additionally, it is observed that the fracture initiation angle curves for both criteria are nearly identical and accurate. The significance of this research is not only providing numerous new experimental results on mixed mode I/II fracture of notched 3D-printed ABS plates, but also providing simple, fast, accurate, and robust criteria for predicting the critical loads of such plates, without the need for conducting layer-by-layer failure analysis using progressive damage models.

Utilization of Quarter-Point Elements in Computation of Notch Stress Intensity Factors

Utilization of Quarter-Point Elements in Computation of Notch Stress Intensity Factors

Fatigue failure investigation of thick plate butt‐welded joints with incomplete penetration effect

AbstractThe objective of this paper was to investigate the fatigue performance of the thick plate structural steel butt‐welded joints influenced by its geometrical factors, such as the notch angles, incomplete penetration length, and plate thickness. Utilizing experimental tests, finite element calculations, and analytical models, the fatigue behavior of various weld joint shapes and dimensions was analyzed, and the discrepancy of fatigue strength for different incomplete penetration lengths was evaluated using the nominal stress method. Meanwhile, the local approaches, including notch stress intensity factor (NSIF), averaged strain energy density (SED), effective notch stress (ENS) method, peak stress method (PSM), and implicit gradient effective stress (IGES) method, are employed to assess the fatigue life of thick plate welded joints. According to the results, incomplete penetration ratios in butt‐welded joints led to a decrease in fatigue strength. The analytical solutions of butt‐welded joints in high cycle regime based on SED results were obtained to estimate the fatigue characteristic values for different plate thickness and incomplete penetration ratios. The proposed equations could illustrate the relationship between the nominal stress and local SED dealing with the variations of incomplete penetration length and geometrical dimensions. Moreover, the results obtained by the analysis of ENS, PSM, and IGES could be deduced by the analytical models to determine the fatigue life of welded joints.

Study of Local Fatigue Methods (TCD, N-SIF, and ESED) on Notches and Defects Related to Numerical Efficiency

The fatigue strength of structural components is strongly affected by notches and imperfections. Both can be treated similarly, as local notch fatigue strength methods can also be applied to interior defects. Even though Murakami’s √area approach is commonly used in the threshold-based fatigue design of single imperfections, advanced concepts such as the Theory of Critical Distances (TCD), Notch Stress Intensity Factors (N-SIF), or Elastic Strain Energy Density (ESED) methods provide additional insight into the local fatigue strength distribution of irregularly shaped defects under varying uniaxial load vectors. The latter methods are based on the evaluation of the elastic stress field in the vicinity of the notch for each single load vector. Thus, this work provides numerically efficient methods to assess the local fatigue strength by means of TCD, N-SIF, and ESED, targeting the minimization of the required load case count, optimization of stress field evaluation data points, and utilization of multi-processing. Furthermore, the Peak Stress Method (PSM) is adapted for large opening angles, as in the case of globular defects. In detail, two numerical strategies are devised and comprehensively evaluated, either using a sub-case-based stress evaluation of the defect vicinity with an unchanged mesh pattern and varying load vector on the exterior model region with optimized load angle stepping or by the invocation of stress and strain tensor transformation equations to derive load angle-dependent result superposition while leaving the initial mesh unaltered. Both methods provide numerically efficient fatigue post-processing, as the mesh in the evaluated defect region is retained for varying load vectors. The key functions of the fatigue strength assessment, such as the evaluation of appropriate planar notch radius and determination of notch opening angle for the discretized imperfections, are presented. Although the presented numerical methods apply to planar simulation studies, the basic methodology can be easily expanded toward spatial fatigue assessment.

Semi-empirical formulas on notch stress field and SIF of orthotropic V-shaped thin plate with initial crack under tensile-bending loads

For orthotropic materials, the solution of notch stress field and stress intensity factor (SIF) is not only related to crack opening angle, crack depth, notch length, geometric parameters, but also obviously influenced by material characteristics and constitutive relation. On the basis of isotropic notch stress field and SIF theoretical formula, a series of multi-parameter models of orthotropic materials were constructed and fitted. The effects of notch depth, crack length, the ratio of notch depth to plate width, opening angle and mechanical properties of composite materials on geometric correction coefficient YI are systematically analyzed. On this basis, a semi-empirical formula of YI is put forward by combining stress field analysis and multi-parameter fitting. The semi-empirical formula is further verified with finite element method, traditional formula and various composite materials. The numerical results show that the simple formula proposed in this paper has higher prediction accuracy. Finally, the proposed formula is extended to the solution of notch stress field and geometric correction coefficient for V-notch-cracked plate under bending load, tension-bending complex loads.

A finite element simulation for notch stress intensity factors of sharp center V-notched tensile configuration using strain gauge technique

A finite element simulation for notch stress intensity factors of sharp center V-notched tensile configuration using strain gauge technique

A finite element simulation for notch stress intensity factors of sharp center V-notched tensile configuration using strain gage technique

A finite element simulation for notch stress intensity factors of sharp center V-notched tensile configuration using strain gage technique

Analytical expressions to estimate rapidly the notch stress intensity factors at V‐notch tips using the Peak Stress Method

AbstractThe Peak Stress Method (PSM) enables a rapid estimation of the notch stress intensity factors (NSIFs) for the fatigue strength assessment of sharp V‐notches and notably welded joints. It takes advantage of the linear elastic peak stresses calculated at the V‐notch tip using coarse finite element (FE) mesh patterns, thanks to properly calibrated coefficients depending on the V‐notch opening angle, FE type, formulation, and FE mesh pattern typical of the employed FE code. The original calibration was performed only for few master values of opening angle; therefore, in the present study, the coefficients have been calibrated by using Ansys® FE code for the full range of notch opening angles to generalize the PSM. In particular, polynomial expressions have been fitted on the results of FE analyses and implemented in a tool that automates the application of the PSM. Two case studies have been analyzed highlighting the benefits of the new polynomial expressions.

Notch effect in 20% short carbon fibre-PA reinforced composites under quasi-static tensile loads

In this work the static behaviour of notched specimens made of a polyamide-6 thermoplastic material reinforced with 20% of short carbon fibres was investigated. In more details, U and V-shaped notched specimens were manufactured by a wire cutting process from injected plates and tested under tensile quasi static loadings. All in all, 42 new experimental data have been provided, related to different notch root radii and notch opening angles, investigating the effect of the local geometry on the notch strength. Taking advantage of the scanning electron microscopy, a detailed damage analysis was also carried out on the fractured specimens, identifying the main damaging mechanisms occurring in the highly stressed regions close to the notch tip. Eventually, all the experimental data from the notched specimens have been reconverted in terms Generalised Notch Stress Intensity Factors, GSIFs, and summarised in a single scatter band.

Some useful expressions and a proof of the validity of the volume free procedure for the SED method application

This work provides some useful expressions for the application of the strain energy density method to component having sharp V-notches under mixed loading conditions. The strain energy density method is characterized by showing a low sensitivity to the mech refinement; however, both the conventional procedure for the application of this method and the volume free procedure result in unavoidable approximation of the theoretical control volume integration domain. The analytical expressions for the parameters e1, e2 and e3, useful to evaluate the averaged strain energy density value in the control volume starting from the notch stress intensity factors values have been obtained. The theoretical difference, obtained by approximating the control volume shape according to both the conventional and the volume free procedure, has been assessed and the mesh size, below whose value the approximation of the control volume shape results in negligible difference with respect to the SED value that should be obtained theoretically, has been found as a function of R0. It has been found that for the conventional procedure, a mesh size equal to or lower than R0/3 ensures having an absolute difference lower than 4% while as regards the volume free procedure a mesh size equal to or lower than R0/7 is required regardless of the mode mixity and the Poisson ratio.

Singularity analysis of linear hardening V-notch by asymptotic expansion coupled BEM

In this paper, a general numerical method by the asymptotic expansion coupled the boundary element method (CBEM), considering the singular term and the higher order terms, is developed to analyze the complete singular stress field of linear hardening elastic–plastic material with a V-notch. The method firstly transforms the singularity analysis for the governing equation of the V-notch tip into an ordinary differential eigenvalue equation, which is then solved by the interpolating matrix method. Then, the complete singular stress field and the notch stress intensity factors (SIFs) can be obtained by coupling the asymptotic expansion of the elastic–plastic singular stresses at the V-notch tip with the conventional boundary elements method for the remaining region of the structure. Two types of examples are analyzed for the V-notch problem of linear hardening material. It is shown that the elastic–plastic singular stress field can be evaluated by the equivalent Young’s modulus and Poisson’s ratio. The proposed new approach is found to be accurate and effective in evaluating singular stress fields in a V-notch structure with linear hardening material.