Maximum Stress Concentration Factor Research Articles

Stress concentration around of pin-loaded hole in unidirectional multi-layered metallic matrix composite material

The objective of this study is to examine the stress concentration factor around a pin-loaded hole in a metallic matrix composite material, analytically and numerically. It is assumed that all unidirectional fibers lie in the metallic matrix while the shear stress in fibers is discarded. To generally derive the equilibrium equation for all fibers and the metallic matrix, the previous shear-lag theory had been improved and the extension in the metallic matrix was considered. Afterwards, the equilibrium equation was solved by the eigenvalue method while the displacement field and stress distribution around the pin-loaded hole were computed. Having calculated stress concentration factors and the displacement field in a unidirectional multi-layered composite material, we compared the analytical results with those numerical values from other references. Additionally, the effect of the pin’s diameter, as well as the edge-hole distance on maximum stress concentration factor was investigated. To recapitulate, it is seen that the modified shear-lag theory can simulate the mechanism of the load transfer between metallic matrices.

Stress concentration factor parametric formulae for concrete-filled rectangular hollow section K-joints with perfobond ribs

A new type of tubular joint made of rectangular hollow section (RHS) braces welded onto concrete-filled RHS (CFRHS) chords stiffened by longitudinally welding perfobond ribs to the inner faces has been studied earlier and demonstrated a better fatigue behaviour than a conventional empty RHS joint. In this paper, stress concentration factor (SCF) parametric design equations were developed for CFRHS K-joints with perfobond ribs through finite element (FE) analysis to fill a gap in current design guides for this type of K-joints. Three-dimensional FE models were developed using the ABAQUS software to simulate the hot spot stress distribution at the brace-chord intersection. FE results were successfully verified using experimental results of nine Y-joints from literature and one truss K-joint in this research. A comprehensive parametric study including 570 models was then carried out on CFRHS K-joints with perfobond ribs to examine the SCFs with five key dimensionless geometric parameters and three basic loading conditions involving axial loading in the chord and brace and bending in the chord. Consequently, a total of 36 SCF parametric equations were established using regression analysis. Subsequently, the number of formulae was reduced to six equations to predict the maximum SCFs for practical application.

A Stress concentration factor for interacting surface notch and subsurface hole

We propose a conservative method for the calculation of the maximum stress concentration factor (SCF) for an interacting notch-hole pair and for a double semi-circular notch (i.e., a notch that has an additional small semi-circular notch ahead of its tip). The method is based on a linearly elastic Airy stress function solution for a circular hole. The notch-hole and double notch configurations are aligned vertically with respect to uniform uniaxial (horizontal) stress. This means, a uniform horizontal tension is applied to a notch-hole pair that lie on a vertical axis. For the notch-hole pair, the maximum interacting SCFs are calculated for edge to edge gaps equal to hole sizes of 2.5a, 5a, 10a and 15a, where a is the hole radius. The analytical results are validated by 2-D finite element calculations. The presented simple approach provides good results with errors well below 10% in most cases compared to the detailed finite element analyses. Fatigue notch factors that can be thought of as the effective SCFs in fatigue analyses are determined. By using the simple approach, computationally costly finite element analysis can be avoided.

Parametric study and equations of the maximum SCF for concrete filled steel tubular T-joints under in-plane and out-of-plane bending

Due to being increasingly used in infrastructure, studying stress concentration in concrete-filled steel tubular joints is necessary. In this study, the variation of the maximum Stress Concentration Factor (SCFmax) with non-dimensional geometric parameters in steel circular hollow section brace welded to concrete-filled circular hollow section chord (CHS-to-CFCHS) T-joints under in-plane and out-of-plane bending moment has been investigated. A database of the maximum SCFs in CHS-to-CFCHS T-joints under in-plane and out-of-plane bending moment is developed based on three-dimensional (3D) finite element (FE) models. The 3D FE models developed using ABAQUS software, have been verified using experimental results. Graphs showing variation of the maximum SCF, in CHS-to-CFCHS T-joints, with non-dimensional geometric parameters have been produced and compared with those for non-filled empty T-joints. Parametric equations for predicting the maximum SCFs in CHS-to-CFCHS T-joints under in-plane and out-of-plane bending moment have been developed in a multiple nonlinear regression analysis. There is a good agreement between the maximum SCFs predicted by the parametric equations and those determined from the experiments.

EXPERIMENTAL STRESS CONCENTRATION FACTOR IN CONCRETE-FILLED STEEL TUBULAR T-JOINTS

An experimental investigation of stress concentration factor (SCF) in Steel circular hollow section brace welded to concrete-filled circular hollow section chord (CHS-to-CFCHS) T-joints has been performed under axial tension, axial compression, in-plane bending and out-of-plane bending. The distribution of SCF around the welded brace-to-chord intersection on both the brace and chord has been investigated using three CHS-to-CFCHS T-joint specimens. The experimental SCF results have been compared with the predicted SCF in empty T-joints. The relationship between the maximum SCF in relation to parameter β, with fixed other geometrical parameters, has been investigated for the basic load conditions. The experimental maximum SCF under axial tension has been compared with the predicted maximum SCF from parametric equations for CHS-to-CFCHS T-joints previously developed by the authors. The results show that the concrete has a significant effect in reducing the SCF, mostly under axial tension and the parametric equations for predicting SCFs in empty T-joints are not suitable for CHS-to-CFCHS T-joints. The effect of parameter β on the maximum SCF in CHS-to-CFCHS T-joints is significant under axial tension and out-of-plane bending moment.

Parametric study and equation of the maximum SCF for concrete filled steel tubular T-joints under axial tension

Concrete-filled steel tubular joints are increasingly being used for built infrastructure such as bridges and towers. In this study, the variation of the maximum Stress Concentration Factor (SCFmax) with non-dimensional geometric parameters in concrete-filled steel tubular (CFST) T-joints under axial tension has been investigated. A database of the maximum SCFs in CFST T-joints under axial tension is developed based on three-dimensional (3D) finite element (FE) models. The 3D FE models developed using ABAQUS software have been verified using experimental results. Graphs showing variation of the maximum SCF, in CFST T-joints, with non-dimensional geometric parameters have been produced and compared with those for non-filled empty T-joints. A parametric equation for predicting the maximum SCFs in CFST T-joints, a useful parameter for design, has been developed in a multiple nonlinear regression analysis. There is a good agreement between the maximum SCFs predicted by the parametric equation and those determined from the experiments.

Stress concentration factors (SCFs) of bulge formed K-joints under balanced axial loads

A novel stiffened joint called bulge formed joint was put forward. Compared with the unstiffened joint, an additional bulge plate is utilized to connect the chord and braces. Based on the finite element (FE) and experimental method, stress concentration factors (SCFs) were investigated for both a bulge formed K-joints and the corresponding unstiffened joint. By the verification of experimental data, the FE models were used to investigate the SCFs of the bulge formed joints. The maximum SCF of the bulge formed K-joint under balanced axial loads is located at the position φ=105°, which is close to but not exactly the saddle. The SCFs around the intersection weld can decrease remarkably compared with the unstiffened joint by the change of geometrical parameters of the bulge plate. Then 2117 FE analyses were conducted to investigate the geometrical effects on SCFs of the bulge formed joint. These dimensionless geometrical parameters include τs, η1, η2, θ, β, γ, τ, among which, the first three parameters are typical of the bulge formed joints, while the others are same as the definitions in the unstiffened joints. Finally, a set of SCF parametric formulas were obtained by nonlinear regression analyses.

Experimental Investigation on the Fatigue Behaviour of Heat-Treated Tubular T-Joints

The stress distribution along the weld toe (SCF test) and the fatigue life of tubular T-joints (Fatigue test) were experimentally investigated in this study. Three specimens with identical geometric properties were tested to failure under fatigue cyclic loading at the brace end. Prior to the loading tests procedure, SCF and Fatigue tests, two specimens went through one cycle of heating and cooling naturally. The SCF test results showed that the maximum Stress Concentration Factor (SCF) occurred at the chord saddle for all the specimens. The fatigue cracks were initiated at the chord saddles of the three tested specimens. The fatigue test results showed that the fatigue life was longer the higher the target maximum temperature was. The development of the crack aspect ratio with the normalised crack length was discussed among the specimens. Finally, the fatigue life results obtained from the experiment compared with those from CIDECT and API guidelines.

Stress concentration factors of circular chord and square braces K-joints under axial loading

A series of tests were carried out by using the verified finite element model to measure the SCF of circular chord and square braces K-joints with a reasonable range of three important parameters, i.e. β(ratio of brace side length to chord diameter), 2γ(ratio of chord diameter to chord thickness), τ(ratio of brace thickness to chord thickness). Maximum stress concentration factors of circular chord and square braces K-joints under axial loading usually occurred at the heel point on brace and chord sides. Stress concentration factor of toe point in five specimens was all less than 0.4. Maximum stress concentration factors on chord and braces increased as 2γ increased. Maximum stress concentration factors on chord and braces decreased as τ increased. Effect of β on maximum stress concentration factors was very complicated. Compared with 2γ and τ, the influence of β on maximum stress concentration factors was much smaller than that of 2γ and τ. The design rules for the SCFs specified in the CIDECT Design Guide are generally quite conservative for circular chord and square braces K-joints. Finally SCF formula were proposed for circular chord and square braces K-joints under balanced axial loading. It is shown that the SCFs calculated from the proposed unified design equation are generally in agreement with the values calculated from finite element analysis.

Effect of Geometric Discontinuity on Stress Concentration Factor of Al6061T6 Alloy under Bending Load

Geometric discontinuity plays a vital role in failure of mechanical members. Grooved or cracked components cannot be replaced immediately, the reason being their high cost and restrictions offered by practical operational features. Such circumstances lead to the requirement of assessing the reliability of grooved or cracked specimen. The objective of present work is to determine relatively safest geometric discontinuity which provides higher reliability under the action of bending loads. Uniform cylindrical specimens of different geometric discontinuities were machined in such a way that all specimens have approximately same cross sectional area at the groove geometry. The specimens were subjected to bending load with a loading rate of 0.5 mm/min on Universal Testing Machine. The maximum stress and stress concentration factor (SCF) for each specimen are calculated and the failure behavior is analyzed. The results show that, the elliptical grooved specimen deform plastically with SCF of 1.4 absorbing a large magnitude of energy whereas the V-groove specimen with SCF of 1.73 failed in a brittle manner with relatively negligible deflection.

Numerical simulation of the double pits stress concentration in a curved casing inner surface

Sour or sweet oil fields development is common in recent years. Casing and tubing are usually subjected to pitting corrosion because of exposure to the strong corrosion species, such as CO2, H2S, and saline water. When the corrosion pits formed in the casing inner surface, localized stress concentration will occur and the casing strength will be degraded. Thus, it is essential to evaluate the degree of stress concentration factor accurately. This article performed a numerical simulation on double pits stress concentration factor in a curved inner surface using the finite element software ABAQUS. The results show that the stress concentration factor of double pits mainly depends on the ratio of two pits distance to the pit radius ( L/R). It should not be only assessed by the absolute distance between the two pits. When the two pits are close and tangent, the maximum stress concentration factor will appear on the inner tangential edges. Stress concentration increased by double pits in a curved casing inner surface is more serious than that in a flat surface. A correction factor of 1.9 was recommended in the curved inner surface double pits stress concentration factor predict model.

Toughening Mechanism and Mechanical Properties Simulation of Rubber-Toughened Polymers

When blending rubbers into polymers, different rubber distribution status and fraction due to different mechanical property. In this research, effective mechanical properties of rubber-toughened polymers with four blending fraction in six kinds of particle distribution status are simulated numerically by using finite element method. Rubber particle distribution model include four 2D models and two 3D models. Typical effective mechanical properties such as yield stress, Young's modulus, Poisson's ratio and stress-strain curve of each status are obtained. The Results show that all models Young's modulus and Poisson's ratio decrease with rubber particle volume fraction increasing. Young's modulus and Poisson's ratio of three-dimensional body-centered cubic and face-centered cubic models are in a close magnitude range, it means rubber particle volume fraction has less effect on 2D models and two 3D models. As we all known, Matrix yielding, crazing and interface debond. All play an important role in the toughening process of rubber-toughened polymers. So in this paper we also study on toughening mechanism using same models. Our simulation takes use of stress concentration factor, yield ratio and interface elements' strain difference which is related with matrix yielding, crazing and interface debond to study the toughening mechanism. Simulation shows that the maximum stress concentration factor increases with particle volume fraction. The shear yielding occurs first at the equator of rubber particle, and then yield region expands from the equator to the pole of the particle with loads increasing.

Effect of Electrical Discharge Machining on Stress Concentration in Titanium Alloy Holes.

Titanium alloys have several advantages, such as a high strength-to-weight ratio. However, the machinability of titanium alloys is not as good as its mechanical properties. Many machining processes have been used to fabricate titanium alloys. Among these machining processes, electrical discharge machining (EDM) has the advantage of processing efficiency. EDM is based on thermoelectric energy between a workpiece and an electrode. A pulse discharge occurs in a small gap between the workpiece and electrode. Then, the material from the workpiece is removed through melting and vaporization. However, defects such as cracks and notches are often detected at the boundary of holes fabricated using EDM and the irregular profile of EDM holes reduces product quality. In this study, an innovative method was proposed to estimate the effect of EDM parameters on the surface quality of the holes. The method combining the finite element method and image processing can rapidly evaluate the stress concentration factor of a workpiece. The stress concentration factor was assumed as an index of EDM process performance for estimating the surface quality of EDM holes. In EDM manufacturing processes, Ti-6Al-4V was used as an experimental material and, as process parameters, pulse current and pulse on-time were taken into account. The results showed that finite element simulations can effectively analyze stress concentration in EDM holes. Using high energy during EDM leads to poor hole quality, and the stress concentration factor of a workpiece is correlated to hole quality. The maximum stress concentration factor for an EDM hole was more than four times that for the same diameter of the undamaged hole.

Stresses and Strains in Thick Perforated Orthotropic Plates

AbstractStress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka spruce wood are emphasized, although some for carbon-epoxy composites are included. While some results are similar to those for isotropy, there are significant consequences due to material orthotropy. Maximum stress and strain concentration factors occur at midplane for thin plates but closer to the external traction-free surfaces for thick plates. These factors decrease as the plate surface is approached and reach lower values unrepresentative of the maximum values. Differences between the midplane and/or maximum and surface stress or strain concentration factors in Sitka spruce, range from 8% if the wood grain is parallel to the vertically applied load to 15% when the grain is perpe...

Probabilistic analysis of stress concentration factors in unstiffened gap tubular KT-joints of jacket structures under the out-of-plane bending moment loads

The stress concentration factor, which is one of the primary input parameters for the fatigue reliability analysis of tubular joints commonly found in offshore jacket structures, shows substantial scatter that highlights the importance of accurate derivation of its governing probability function. In this article, results of 144 finite element stress analyses, validated using experimental data, were used to derive the probability density functions for the stress concentration factors in unstiffened gap tubular KT-joints under four types of out-of-plane bending moment loadings. Based on a parametric finite element study, a sample database was prepared for the maximum chord-side stress concentration factors of central and outer braces, and density histograms were generated for these samples. Nine different probability density functions were fitted to these histograms. The maximum likelihood method was used to estimate the parameters of fitted distributions. In each case, Kolmogorov–Smirnov test was applied to assess the goodness-of-fit. Finally, the inverse Gaussian model was selected as the best-fitted distribution, and after substituting the values of estimated parameters, six fully defined probability density functions were proposed for the maximum chord-side stress concentration factors of central and outer braces in unstiffened gap KT-joints under four types of out-of-plane bending loading.

Characterization of Damage Induced by Impacting Objects in Udimet-500 Alloy

Foreign object damage (FOD) is one of the common mechanisms in turbine blade failures which reduces high cycle fatigue life and contributes significantly to premature failure. Therefore, this study experimentally simulated FOD on the first stage blade of a gas turbine. Foreign objects with two parameters of object nose shape (spherical, conical, and flat) and impact angle (90° and 45° relative to the blade surface) were impacted on the surface of flat specimens of Udimet-500 at a temperature of 733°C with velocity of 300 m/s (same as working condition of blades). In order to evaluate the impact site morphologies, induced craters were first studied by scanning electron microscopy (SEM). Then samples were sectioned symmetrically, and by using image analysis tool software, the depth of each crater was measured. Finally, based on the results, it was found that maximum and minimum stress concentration factors and induced microcracks, respectively, are regarding to flat projectiles with impact angel of 45° and spherical at impact angle of 90°.

Inversion of stress field evolution consisting of static and dynamic stresses by microseismic velocity tomography

In order to reveal the stress precursors of the “3.15” rockburst disaster that occurred in the No. 1 working face of Junde coal mine, the combined stress field inversion including static and dynamic stresses was conducted by using P-wave velocity tomography, and the static high-stress concentration regions were further designated. Simultaneously, the evolution of dynamic stress generated by seven periodical caving events of primary roof was analyzed, and the fracturing characteristics were described in detail. Ultimately, the stress precursors of the “3.15” rockburst for early warning were clearly revealed. The main conclusions are as follows: (1) the micro-fissures inside coal and rock mass produce the significant reflection and refraction on the propagation of microseismic (MS) waves, and thus P-wave overall characterizes with lower velocity and higher velocity gradient; (2) after the slightly fracturing of primary roof on March 9, 2013, the maximum stress concentration factor suddenly rises to 20. This sign can be viewed as an early warning precursor of rockburst; (3) until March 12, 2013, the large-scale micro-fractures begin to form inside primary roof, and thus the corresponding high velocity gradient regions are generated. This phenomenon can be regarded as an effective precursor of macroscopic fracturing of primary roof; and (4) before the “3.15″ rockburst, the scope of P-wave velocity gradient in the No. 1 working face does not change significantly. The above findings may put forward a certain reference for accurately warning the stress precursors of rockburst by P-wave velocity tomography.

A probability distribution model for SCFs in internally ring-stiffened tubular KT-joints of offshore structures subjected to out-of-plane bending loads

The stress concentration factor (SCF) is one of the principal inputs in the fatigue reliability analysis of tubular joints. The SCF shows substantial scatter that highlights the necessity of deriving its governing probability function accurately. In the present research, results from 432 finite element (FE) stress analyses, verified against experimental data, were used to develop a probability distribution model for the SCFs in tubular KT-joints reinforced with internal ring stiffeners subjected to four types of out-of-plane bending (OPB) loads. Based on a FE parametric investigation, a sample database was prepared for the maximum chord-side SCFs of central and outer braces; and density histograms were generated for these samples. Nine different probability density functions (PDFs) were fitted to these histograms. The maximum likelihood method was used to determine the parameters of fitted distributions. In each case, using a developed computer code, Kolmogorov–Smirnov test was applied to assess the goodness of fit. Finally, the Generalized Extreme Value model was selected as the best-fitted distribution and after substituting the values of estimated parameters, six fully defined PDFs were proposed for the maximum chord-side SCFs of central and outer braces in internally ring-stiffened tubular KT-joints subjected to four types of OPB loading.

Parametric study and formulae of SCFs for positive large eccentricity CHS N-joints

This paper put forward the importance of stress concentration factors (SCF) of positive large eccentricity CHS N-joints under compression in vertical brace although the static behavior of the N-joints has been researched. The four positive large eccentricity CHS N-joints were first tested for the verification and calibration of finite element (FE) models. As eccentricity increased, the experimental results and FE analysis showed that the position of maximum SCF moved from the crown heel point to the saddle point at the chord and vertical brace intersection. At the inclined brace and chord intersection, the position of maximum SCF moved from the saddle point to the crown toe point with the decrease of eccentricity. A set of parametric formulae was proposed to predict the SCFs of positive large eccentricity CHS N-joints based on 256 FE models. For positive large eccentricity CHS N-joints, SCF increased as τ increased. As β and 2γ increased, SCF distribution was complex. SCF linearly increased with the increase of eccentricity to chord diameter ratio (ε) at the chord and vertical brace intersection welding seam. SCF of N-joint around inclined brace and chord intersection increased when the value of θ increased. The assessment of the proposed formulae and CIDECT formulae were based on the database of FE analysis results. Simple method for predicting SCFs of positive large eccentricity CHS N-joints given in CIDECT was unreliable. The new formulae of SCFs were proposed for positive large eccentricity CHS N-joints under axial loading, which were verified to be accurate and reliable.

3D Morphology of Al5FeSi inclusions in high Fe-content Al-Si-Cu Alloys

The 3D morphology of the brittle platelet-like ß-Al5FeSi inclusions was analyzed in order to understand the effect of these particles on the degradation of the fracture-resistance of high Fe-content cast Al-Si-Cu alloys. The 3D data of the ß-Al5FeSi compounds was obtained with micro-computed tomography and revealed complex morphology of ß-Al5FeSi inclusions. Tensile tests were conducted and massive ß-Al5FeSi platelets were observed as the main crack initiation sites in the SEM fracture surface observations. The 3D geometry of the largest segmented ß-Al5FeSi phase was exported to a FE software and the maximum stress concentration factors were calculated. After heat treatment, a dissolved morphology of the ß-Al5FeSi inclusions was observed and ductility increased significantly.