Experimental and numerical investigations on stress concentration factors of concrete filled steel tube X-joints.

An SHS-CFSHS X-joint is fabricated by welding two square hollow section (SHS) braces to a concrete-filled square hollow section (CFSHS) chord. In this paper, the stress concentration factors (SCFs) of SHS-CFSHS X-joints are investigated through experimental tests and finite element analysis (FEA), with the hot spot stress method serving as the analytical approach. Eight specimens are designed and manufactured, with FE models built in software ANSYS. These FE models are validated against the test results. The specimens are tested under brace axial tension to determine the SCFs of the X-joints. It shows that the concrete filled in the chord effectively reduces the SCFs of the X-joints. To further explore various load conditions and the influence of the parameters, FEA is carried out and a total of 64 FE models are built. Based on the FEA results, multiple regression analysis is used to obtain the SCF formulae of SHS-CFSHS X-joints under axial tension load and in-plane bending load in the brace, respectively. Comparison and analysis of the SCF results obtained from experimental tests, the proposed formulae, and FE simulations reveal that the formulae presented in this study are both conservative and suitable for predicting SCFs.

Effective Computational Model for Determining the Geometry of the Transition Zone of End Coils of Machined Springs, Enabling Efficient Use of the Spring Material.

This paper presents an analysis of the effect of the geometry of the end-coil transition zone on the material stress state of a machined compression spring with a rectangular wire cross-section. The literature relationships for determining the stresses in rectangular wire compression springs neglect the effects associated with the geometry of this zone. A series of non-linear numerical analyses were carried out for models of machined compression springs with a wide range of variation in geometrical parameters. The results of these analyses were used to develop a computational model to estimate the minimum value of the rounding radius ρmin, which ensures that the stresses in this zone are reduced to the level of the maximum coil stresses. The model is simple to apply, and allows the radius ρmin to be estimated for springs with a spring index between 2.5 and 10, a helix angle between 1° and 15°, and a proportion of the sides of the wire section between 0.4 and 5.

Stress Concentration Factors for Non-Load-Carrying Welded Cruciform Joints Subjected to Tension, Bending, and Shear.

This paper deals with the problem of stress concentration at the weld toe of non-load-carrying-type plate cruciform joints under tension, bending, and shear. Theoretical stress concentration factors were derived using the finite element method. Five of the most important geometrical parameters: the thickness of the main plate and the attachments, the weld throat thickness, the weld toe radius, and the weld face inclination angle were treated as independent variables. For each loading mode-tension, bending, and shear-parametric expression of high accuracy was obtained, covering the range used in real structures for cruciform connections. The maximum percentage error was lower than 2.5% as compared to numerical values. The presented solutions proved to be valid for the toe radius ρ tending to zero.

Stress Concentration on PDMS: An evaluation of three numerical constitutive models using digital image correlation.

The examination of hyperelastic materials' behavior, such as polydimethylsiloxane (PDMS), is crucial for applications in areas as biomedicine and electronics. However, the limitations of hyperelastic models for specific stress scenarios, with stress concentration, are not well explored on the literature. To address this, firstly, three constitutive models were evaluated (Neo-Hookean, Mooney-Rivlin, and Ogden) using numerical simulations and Digital Image Correlation (DIC) analysis during a uniaxial tensile test. The samples were made of PDMS with stress concentration geometries (center holes, shoulder fillets, and edge notches). Results of ANOVA analysis showed that any of the three models can be chosen for numerical analysis of PDMS since no significant differences in suitability were found. Finally, the Ogen model was chosen to obtain the stress concentration factors for these geometries, a property which characterize how discontinuities change the maximum stress supported by an element. Our study provides new values for variables needed to analyze and design hyperelastic elements and produce a foundation for understanding PDMS stress-strain behavior.

Stress Distribution Prediction of Circular Hollow Section Tube in Flexible High-Neck Flange Joints Based on the Hybrid Machine Learning Model.

The flexible high-neck flange is connected to the circular hollow section (CHS) tube through welding, and the placement of the weld seam and corresponding stress concentration factor (SCF) are crucial determinants of the joint's fatigue performance. In this study, three hybrid models combining ant colony optimization (ACO), a genetic algorithm (GA), and grey wolf optimization (GWO) with a random forest (RF) model were developed to predict the stress distribution on the inner and outer walls of the CHS tube under different flange parameter combinations. To achieve this, an automated finite element (FE) analysis program for flexible high-neck flange joints was initially developed based on ABAQUS 2020 software. Parameter combinations were randomly selected within a reasonable range to simulate the nonlinear mechanical behavior of the joint under uniform tension, generating a dataset comprising 5417 sets of data. The accuracy of the FE model was validated through experimental data from the literature. Based on this, feature importance analysis was conducted to reveal the influence of different variable parameters on the stress distribution in the tube of the joint. The flange parameters and tube stress distribution are considered as inputs and outputs, respectively. Three hybrid RF models, specifically ant colony optimization-based random forest (ACO-RF), genetic algorithm-based random forest (GA-RF), and grey wolf optimization-based random forest (GWO-RF), are trained for regression prediction. The results demonstrate that the three hybrid models outperform the original machine learning model in predictive accuracy. The ACO-RF model achieved the highest accuracy with average coefficients of determination (Rmean2) of 0.9983 and 0.9865 on the testing and training sets, respectively. Building upon this foundation, the study developed a corresponding open-source graphical user interface (GUI) as a tool for facilitating computations and visualizing results. Finally, a case study on fatigue damage assessment of a flexible high-neck flange joint in a wind-turbine tower is presented to demonstrate the application of the proposed model in this study.

Effect of Welding Defects on Fatigue Properties of SWA490BW Steel Cruciform Welded Joints.

Welding is prone to several defects. To test the fatigue properties of the welded defective joints of high-speed rail bogies, SMA490BW steel cruciform welded joints were employed with artificial defects treatment. Consequently, fatigue tests were conducted on the specimens. Fatigue fracture morphology was studied via scanning electron microscopy. The ABAQUS (version 2022) finite element software was used to calculate the stress distribution and concentration factor of cruciform welded joints with defects. The results show that the fatigue limits of 1 and 2.4 mm defect specimens were approximately 57.2 and 53.75 Mpa, respectively. Furthermore, the stress concentration factor of no, 1 mm, and 2.4 mm defects were 2.246, 4.441, and 6.684, respectively, indicating that the stress concentration factor of 1 and 2.4 mm defects increased by 98 and 198%, respectively, with respect to the no-defect case.

Analytical Study of SH Wave Scattering by a Circular Pipeline in an Inhomogeneous Concrete with Density Variation.

In this paper, the shear horizontal (SH) wave scattering by a circular pipeline in an inhomogeneous concrete with density variation is studied. A model of inhomogeneous concrete with density variation in the form of a polynomial-exponential coupling function is established. By using the complex function method and conformal transformation, the incident and scattering wave field of SH wave in concrete are obtained, and the analytic expression of dynamic stress concentration factor (DSCF) around the circular pipeline is given. The results show that the inhomogeneous density parameters, the wave number of the incident wave and the angle of the incident wave in concrete are important factors affecting the distribution of dynamic stress around the circular pipe in concrete with inhomogeneous density. The research results can provide a theoretical reference and a basis for analyzing the influence of circular pipeline on elastic wave propagation in an inhomogeneous concrete with density variation.

Micromechanics Modeling of Transverse Tensile Strength for Unidirectional CFRP Composite.

Transverse tensile strength of unidirectional (UD) composites plays a key role in overall failure of fiber-reinforced composites. To predict this strength by micromechanics, calculation of actual stress in constituent matrix is essentially required. However, traditional micromechanics models can only give the volume-averaged homogenized stress rather than an actual one for a matrix, which in practice will cause large errors. In this paper, considering the effect of stress concentration on a matrix, a novel micromechanics method was proposed to give an accurate calculation of the actual stress in the matrix for UD composite under transverse tension. A stress concentration factor for a matrix in transverse tensile direction is defined, using line-averaged pointwise stress (obtained from concentric cylinder assemblage model) divided by the homogenized quantity (obtained from a bridging model). The actual stress in matrix is then determined using applied external stress multiplied by the factor. Experimental validation on six UD carbon fiber-reinforced polymer (CFRP) specimens indicates that the predicted transverse tensile strength by the proposed method presents a minor deviation with an averaged relative error of 5.45% and thus is reasonable, contrary to the traditional method with an averaged relative error of 207.27%. Furthermore, the morphology of fracture section of the specimens was studied by scanning electron microscopy (SEM). It was observed that different scaled cracks appeared within the matrix, indicating that failure of a UD composite under transverse tension is mainly governed by matrix failure. Based on the proposed approach, the transverse tensile strength of a UD composite can be accurately predicted.

Stress Concentration Factors of Concrete-Filled T-Joints under In-Plane Bending: Experiments, FE Analysis and Formulae.

Experimental and numerical investigations on seven cold-formed steel square hollow section (SHS) T-joints with concrete-filled chords were conducted for the determination of stress concentration factors (SCFs). The SCFs were experimentally determined using strain gauges and then numerically determined using Abaqus finite element analysis (FEA) software under static in-plane brace bending. Good agreement was observed between the two investigations. After validating the FEA results, a parametric study was conducted on the SCFs of concrete-filled SHS-SHS T-joints using Abaqus FEA to evaluate the effects of the non-dimensional parameters on the SCFs. Subsequently, design formulae for predicting the SCF of concrete-filled SHS-SHS T-joints subjected to in-plane bending were proposed. Comparable results were obtained between the numerical SCFs with SCFs calculated from the proposed design equations. The maximum SCF of concrete-filled SHS T-joints under in-plane brace bending occurred at different locations. The overall mean of the experimental reduction percentage in peak SCF due to concrete infill is 22% and the overall mean of the numerical reduction percentage in peak SCF due to concrete infill is 19%. The determination of SCFs in concrete-filled SHS-SHS T-joints under in-plane bending has been the subject of little research, and more information regarding the behavior of concrete-filled T-joints with SHS under in-plane bending needs to be provided to practicing engineers.

The Effect of the Doping Amount on Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration around Defects in BNT Doped FN Materials.

Sodium bismuth titanate (Bi0.5Na0.5TiO3, BNT) has attracted much attention because of its excellent dielectric, piezoelectric and electromechanical properties. The microstructure of sodium bismuth titanate-doped ferrum niobium material (Bi0.5Na0.5TiO3 doped (Fe0.5Nb0.5)4+, BNT-xFN) shows a triangle as its typical defect shape. Since piezoelectric devices usually operate under dynamic loads, they fail easily owing to dynamic stress concentration or dynamic fracture. Elastic waves can simulate many types of dynamic loads, and the dynamic stress concentration caused by an anti-plane shear wave is the basis for the calculation of the stress field strength factor of type Ⅲ-dynamic fractures. In this study, the electroelastic coupled-wave diffraction and dynamic stress concentration of BNT-xFN materials with triangular defects under the incidence of anti-plane shear waves were studied. Maxwell equations are decoupled by auxiliary functions, and the analytical solutions of the elastic wave field and electric field are obtained. Based on the conformal mapping method, the triangle defect was mapped to the unit circle defect, and the dynamic stress concentration coefficient around the triangle defect was obtained by calculating the undetermined mode coefficients in the expression through boundary conditions. The numerical calculation shows that the size of the triangular hole, the frequency of the applied mechanical load, the incidence angle of mechanical load and the amount of FN doping have a great influence on the stress concentration of BNT-xFN materials.

Investigations for Design Estimation of an Anisotropic Polymer Matrix Composite Plate with a Central Circular Hole under Uniaxial Tension.

Composite plates with holes are common in engineering applications, such as the automotive and aerospace industries. Three-dimensional braided carbon/epoxy polymers are an advanced textile composite and are used in various structures due to their high damage resistance and relatively low manufacturing cost. When a braided polymer plate with a hole is used in engineering applications, it is necessary to know its mechanical behavior under loading conditions using analysis theory to design it better. However, the effects of stress distribution with shear deformation theories on the variable thickness of the braided polymer plate (carbon/epoxy) with a hole under tensile loading have not been reported yet. In this paper, a study is conducted to evaluate shear deformation theories for a braided polymer plate with variable thickness and a hole in the center, analyzing the stresses and their concentration variations. First, multiscale modeling and analysis are performed to determine the mechanical properties of the plate. Then, finite element analyses are performed on a homogenized macro plate with a hole. The analysis process is verified by comparison with the available literature. Results show that the first-order shear deformation theory calculates 37, 56, and 70 percent less maximum transverse shear stress than the high-order shear deformation theory (Reissner-Mindlin) and the elasticity theory for thin, moderately thick, and thick braided polymer plates, respectively. Additionally, changing the theory has no significant effect on circumferential stress, radial stress, Von Mises stress, and stress concentration factor. As a result, this research can provide researchers and designers with structural intuition for a braided polymer plate with a center hole.

Tensile Strength Prediction of Short Fiber Reinforced Composites.

Essentially, every failure of a short fiber reinforced composite (SFRC) under tension is induced from a matrix failure, the prediction of which is of fundamental importance. This can be achieved only when the homogenized stresses of the matrix are converted into true values in terms of stress concentration factors (SCFs) of the matrix in an SFRC. Such an SCF cannot be determined in the classical way. In this paper, a closed-form formula for the longitudinal tensile SCF in the SFRC is derived from the matrix stresses determined through an elastic approach. The other directional SCFs in an SFRC are the same as those in a continuous fiber composite already available. A bridging model was used to calculate the homogenized stresses explicitly, and a failure prediction of the SFRC with arbitrary fiber aspect ratio and fiber content was made using only the original constituent strength data. Results showed that the volume fraction, the aspect ratio, and the orientation of the fiber all have significant effect on the tensile strength of an SFRC. In a certain range, the tensile strength of an SFRC increases with the increase in fiber aspect ratio and fiber volume content, and the strength of the oriented short fiber is higher than that of the random short fiber arrangement. Good correlations between the predicted and the available measured strengths for a number of SFRCs show the capability of the present method.

Generalized SCF Formula of Out-Of-Plane Gusset Welded Joints and Assessment of Fatigue Life Extension by Additional Weld.

The existing S-N curves by effective notch stress to assess the fatigue life of gusset welded joints can result in reduced accuracy due to the oversimplification of bead geometries. The present work proposes the parametric formulae of stress concentration factor (SCF) for as-welded gusset joints based on the spline model, by which the effective notch stress can be accurately calculated for fatigue resistance assessment. The spline model is also modified to make it applicable to the additional weld. The fatigue resistance of as-welded and additional-welded specimens is assessed considering the geometric effects and weld profiles. The results show that the error of SCFs by the proposed formulae is proven to be smaller than 5%. The additional weld can increase the fatigue life by as great as 9.4 times, mainly because the increasing weld toe radius and weld leg length lead to the smaller SCF. The proposed series of S-N curves, considering different SCFs, can be used to assess the welded joints with various geometric parameters and weld profiles.

Stress Concentration Factors for Welded Plate T-Joints Subjected to Tensile, Bending, and Shearing Loads.

The paper deals with the problem of stress concentration at the weld toe of a plate T-joint subjected to axial, bending, and shearing loading modes. Theoretical stress concentration factors were obtained from numerical simulations using the finite element method for several thousand geometrical cases, where five of the most important geometrical parameters of the joint were considered to be independent variables. For each loading mode-axial, bending, and shearing-highly accurate closed form parametric expression has been derived with a maximum percentage error lower than 2% with respect to the numerical values. Validity of each approximating formula covers the range of dimensional proportions of welded plate T-joints used in engineering applications. Two limiting cases are also included in the solutions-when the weld toe radius tends to zero and the main plate thickness becomes infinite.

Parametric Formula for Stress Concentration Factor of Fillet Weld Joints with Spline Bead Profile.

The existing parametric formulae to calculate the notch stress concentration factor of fillet welds often result in reduced accuracy due to an oversimplification of the real weld geometry. The present work proposes a parametric formula for the evaluation of the notch SCF based on the spline weld model that offers a better approximation of the real shape of the fillet weld. The spline model was adopted in FE analyses on T-shape joints and cruciform joints models, under different loading conditions, to propose a parametric formula for the calculation of the SCF by regression analysis. In addition, the precision of parametric formulae based on the line model was examined. The magnitude of the stress concentration was also analyzed by means of its probability distribution. The results show that the line model is not accurate enough to calculate the SCF of fillet weld if the weld profile is considered. The error of the SCF by the proposed parametric formulae is proven to be smaller than 5% according to the testing data system. The stress concentration of cruciform joints under tensile stress represents the worst case scenario if assessed by the confidence interval of 95% survival probability.

Application of DIC Method in the Analysis of Stress Concentration and Plastic Zone Development Problems.

The paper presents the assessment of the possibility and reliability of the digital image correlation (DIC) system for engineering and scientific purposes. The studies were performed with the use of samples made of the three different materials-mild S235JR + N steel, microalloyed fine-grain S355MC steel, and high strength 41Cr4 steel subjected to different heat-treatment. The DIC studies were focused on determinations of dangerous zones with large stress concentrations, plastic deformation growth, and prediction of the failure zone. Experimental tests were carried out for samples with different notches (circular, square, and triangular openings). With the use of the DIC system and microstructure analyses, the influence of different factors (laser cutting, heat treatment, material type, notch shape, and manufacturing quality) on the material behavior were studied. For all studied cases, the stress concentration factors (SCF) were estimated with the use of the analytical formulation and the finite element analysis. It was observed that the theoretical models for calculations of the influence of the typical notches may result in not proper values of SCFs. Finally, the selected results of the total strain distributions were compared with FEM results, and good agreement was observed. All these allow the authors to conclude that the application of DIC with a common digital camera can be effectively applied for the analysis of the evolution of plastic zones and the damage detection for mild high-strength steels, as well as those normalized and quenched and tempered at higher temperatures.

Stress Concentration Factors for Butt-Welded Plates Subjected to Tensile, Bending and Shearing Loads.

This paper deals with the analysis of stress concentration at the weld toe of a Double-V and a Single-V butt-welded joints subjected to tensile, bending and shearing loads. For each geometrical and loading case accurate close form stress concentration factor formula based on more than 3.3 thousand finite element method solutions were obtained. The percentage error of the formulas is lower than 2.5% for a wide range of values of geometrical parameters including weld toe radius, weld width, plate thickness and weld toe angle. The limiting case, in which the weld toe radius tends to zero is also considered. In the cases of shearing loads, a plane model based on thermal analogy was developed. The whole analysis was performed assuming that a circular arc represents the shape of the excess weld metal. Presented solutions may be used in computer aided fatigue assessment of structural elements.

Parametric Formulae for Elastic Stress Concentration Factor at the Weld Toe of Distorted Butt-Welded Joints.

The evaluation of the stress concentration factor (SCF) at the notches of welds is of importance, especially for butt-welded joints that are widespread in the industry. Some empirical formulae can be found in the literature to estimate the SCF at the weld toes of butt-welded joints, while few solutions are available for the distorted joints under tensile fatigue test conditions. In the present study, the existing SCF formulae for butt-welded joints loaded in tension are examined and discussed. The influence of the weld width on SCF, which is commonly ignored or misestimated by existing solutions, is investigated comprehensively based on a large set of two-dimensional (2D) finite element analyses. Consequently, a new precise parametric formula for the elastic SCF at the weld toe of geometrically symmetric butt-welded joints under tension is proposed, together with a wide application range. Moreover, the analysis is also extended to consider joints with angular distortion. A two-step finite element analysis is employed to simulate the clamping and loading procedures in the fatigue test. Similarly, the parametric formulae for the assessment of clamping-induced stress and SCF caused by angular distortion are carried out as well based on the results from finite element analyses. The formulae proposed by this paper are finally tested and proved to be valid and precise.

Influence of Strengthening Material Behavior and Geometry Parameters on Mechanical Behavior of Biaxial Cruciform Specimen for Envelope Material.

The stratospheric airship envelope material is operated in biaxial stress, so it is necessary to study the in-plane biaxial tensile strength. In this paper, a theoretical model is developed to evaluate the mechanical properties of in-plane biaxial specimens. Being applied to the finite element analysis, the theoretical model is employed to evaluate the influence of strengthening material behavior (E*) and geometry parameters on the mechanical behavior in the central. The follows results are drawn: (i) smaller the length of the central region (Lcen), E* and larger the central region corner radius (r) contribute to smaller coefficient of variation (CV); (ii) smaller Lcen and larger E* contribute to smaller stress concentration factor (k), k in the limit state of r is larger than that in other conditions. (iii) The CV and k under stress ratio of 1:1 are smaller than those under other stress ratios. The study can provide a useful reference for the design of biaxial specimens.

Stress Concentration and Damage Factor Due to Central Elliptical Hole in Functionally Graded Panels Subjected to Uniform Tensile Traction.

Functionally graded material (FGM) can optimize the mechanical properties of composites by designing the spatial variation of material properties. In this paper, the stress distribution of functionally graded panel with a central elliptical hole under uniaxial tensile load is analyzed. Based on the inhomogeneity variation and three different gradient directions, the effects of the inhomogeneity on the stress concentration factor and damage factor are discussed. The study results show that when Young's modulus increases with the distance from the hole, the stress concentration factor decreases compared with that of homogeneous material, and the optimal design of r-FGM is better than that of x-FGM and y-FGM when the tensile load. In addition, when the associated variation of ultimate stress is considered, the choice of scheme to reduce the failure index is related to the strength-modulus exponent ratio. When the strength-modulus exponent ratio is small, the failure index changes with the index of power-law, which means there is an optimal FGM design. But when the strength-modulus exponent ratio is large, the optimal design modulus design is to select a uniform material that maximizes the modulus at each point. These research results have a certain reference value for further in-depth understanding of the inhomogeneous design for FGM.