Resulting Stress Concentration Research Articles

Location Results for Brace Spacing in Gap Tubular “K” Joints Using FEM

The 8-node iso-parametric thin shell element was employed in the study of stress concentrations in the welded tubular “K” joint. Element equilibrium equations were derived using isoparametric formulation based on thin shell theory. After assembly, the resulting system equations were solved using existing fortran programs. Numerical experiments were conducted to isolate and locate ideal gap (positions) for the two braces of the “K” joint. The nominal stresses were calculated from which stress concentration factors were obtained. The resulting stress concentration factors were presented both as tables and as figures. A good agreement between our solutions and those for model joints in the literature is good and acceptable. It was found that the wider apart the brace spacing is, the weaker the strength of the joint. It was also found that the best location for the braces occurs when the stress level changes sign either from positive to negative or vice versa at a critical sampling point.

Self-expanding stent modelling and radial force accuracy

Computational simulations using finite element analysis are a tool commonly used to analyse stent designs, deployment geometries and interactions between stent struts and arterial tissue. Such studies require large computational models and efforts are often made to simplify models in order to reduce computational time while maintaining reasonable accuracy. The objective of the study is focused on computational modelling and specifically aims to investigate how different methods of modelling stent–artery interactions can affect the results, computational time taken and computational size of the model. Various different models, each with increasing levels of complexity, are used to simulate this analysis, representing the many assumptions and simplifications used in other similar studies in order to determine what level of simplification will still allow for an accurate representation of stent radial force and resulting stress concentrations on the inner lining of the vessel during self-expanding stent deployment. The main conclusions of the study are that methods used in stent crimping impact on the resulting predicted radial force of the stent; that accurate representation of stent–artery interactions can only be made when modelling the full length of the stent due to the incorporation of end effects; and that modelling self-contact of the stent struts greatly impacts on the resulting stress concentrations within the stent, but that the effect of this on the unloading behaviour and resulting radial force of the stent is negligible.

Ductile Fracture Mechanism of Low-Temperature In-48Sn Alloy Joint Under High Strain Rate Loading

The failure behaviors of In-48Sn solder ball joints under various strain rate loadings were investigated with both experimental and finite element modeling study. The bonding force of In-48Sn solder on an Ni plated Cu pad increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloy. In contrast to the cases of Sn-based Pb-free solder joints, the transition of the fracture mode from a ductile mode to a brittle mode was not observed in this solder joint system due to the soft nature of the In-48Sn alloy. This result is discussed in terms of the relationship between the strain-rate of the solder alloy, the work-hardening effect and the resulting stress concentration at the interfacial regions.

Finite Element Analysis of Elastic Stresses around Holes in Plate Subjected to Uniform Tensile Loading

The author reported stress analysis of infinite isotropic plate with a cylindrical circular hole and oblique hole. The present work deals with infinite isotropic plate under uniform tensile load. Three components of different material with different obliquity angle were used for analysis. These components having holes circular & oblique at angles 0, 30 and 60 degree are considered for study. The long twisted blades of gas turbine blade will be treated as infinite plate with oblique holes/cooling holes constituting a geometrically complex, three- dimensional body that is subjected to the action of systems centrifugal force. Stress concentration and stress field around oblique holes is a major challenge area in design of aerofoil in aerospace applications for safety because of their highly specialized applications in aerospace field under severe operating conditions. In design, Stress Concentration Factor (SCF) can be used as multiplication factor, and using that maximum stress can be predicted, thus it shows the stress field around local region. The experimental methods used are photo elastic and strain gauge techniques. When a infinite plate containing a cylindrical oblique hole is subjected to remotely applied uniform tensile load, the circumferential stresses along the boundary of the hole are produced which have been successfully used to predict stresses around holes. The resulting Stress Concentration Factor (SCF) obtained by Finite Element (FE) analysis are compared with experimentally obtained values. The results of FEA technique are in good agreement with experimental values, thus providing a means of analysing more effectively realistic Gas turbine blades. For analysis FEA software MSC/PATRAN, MSC/ NASTRAN-NX v7.0 has been used.

Mechanical strength and fracture mode transition of Sn-58Bi epoxy solder joints under high-speed shear test

The shear force and failure behaviors of the Sn-58Bi epoxy solder joints with various surface finishes under the high-speed shear test were investigated. The relationships between the shear speed, shear force, and fracture mode are elucidated in this study. The shear force of the Sn-58Bi solder joints increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloys. Brittle interfacial fractures were more easily achieved at higher shear speed in the high-speed shear test. This result was discussed in terms of the relationship between the strain-rate of the solder alloy, the work-hardening effect, and the resulting stress concentration in the interfacial regions. The fracture mode changed from ductile solder fracture to brittle interfacial fracture with increasing shear speed. On the other hand, the different surface finish materials did not affect the shear force and fracture mode of the Sn-58Bi solder joints under high-speed shear loading.

The segmented expanding cone-mandrel test revisited as material characterization and component test for fuel claddings

This paper presents an assessment of the segmented expanding mandrel (SEM) test for material characterization and structural integrity assessment of nuclear fuel claddings. The loading is induced by expanding segments, which are placed inside a cladding tube, radially to simulate cracked fuel that expands thermally. Experimental results are presented for zircaloy-2 cladding tubes for different number of segments. The tests are analysed with semi-analytical models and two-dimensional finite element models. A complex stress field with stress concentrations occurs at the edge of the segments, which simulates pellet cladding interaction. The variation of the stresses and the strength of the stress and strain concentrations increases with fewer segments and increases strongly with higher friction coefficient between segments and the cladding tube. By increasing the number of segments and ensuring a low friction coefficient, the deformation is close to axi-symmetric and the SEM can be used to determine qualitatively the material properties such as fracture criteria and stress–strain curves, but the test is more appropriate for assessment of how defects and microstructure affect ductility. For simulation of mechanical pellet-cladding interaction it is important that the friction coefficient is representative. The resulting stress concentrations promote failure at lower loads and need to be taken into account for the integrity assessment. The SEM test can then be used as a relatively simple test for assessment of pellet fuel cladding interaction.

Role of Slip Mode on Stress Corrosion Cracking Behavior

In this article, we examine the effect of aging treatment and the role of planarity of slip on stress corrosion cracking (SCC) behavior in precipitation-hardened alloys. With aging, the slip mode can change from a planar slip in the underage (UA) to a wavy slip in the overage (OA) region. This, in turn, results in sharpening the crack tip in the UA compared to blunting in the OA condition. We propose that the planar slip enhances the stress concentration effects by making the alloys more susceptible to SCC. In addition, the planarity of slip enhances plateau velocities, reduces thresholds for SCC, and reduces component life. We show that the effect of slip planarity is somewhat similar to the effects of mechanically induced stress concentrations such as due to the presence of sharp notches. Aging treatment also causes variations in the matrix and grain boundary (GB) microstructures, along with typical mechanical and SCC properties. These properties include yield stress, work hardening rate, fracture toughness K IC , thresholds K Iscc, and steady-state plateau velocity (da/dt). The SCC data for a wide range of ductile alloys including 7050, 7075, 5083, 5456 Al, MAR M steels, and solid solution copper-base alloys are collected from the literature. Our assertion is that slip mode and the resulting stress concentration are important factors in SCC behavior. This is further supported by similar observations in many other systems including some steels, Al alloys, and Cu alloys.

Failure mechanism of Pb-bearing and Pb-free solder joints under high-speed shear loading

The failure behaviors of ball grid array (BGA) solder ball joints under the various loading speeds of the high-speed shear test were investigated both experimentally and with non-linear, 3-dimensional finite element modeling. Conventional Sn-37Pb and Pb-free, Sn-3.5Ag solder alloys were used to compare the failure behaviors. Far greater shear forces were measured by the high-speed shear test than by the low-speed shear test. The shear force further increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloys. Brittle interfacial fractures were more easily achieved by the high-speed shear test in the Sn-3.5Ag solder joints, especially at higher shear speed. This result was discussed in terms of the relationship between the strain-rate of the solder alloy, the work-hardening effect, and the resulting stress concentration in the interfacial regions. However, no transition of the failure mode was observed in the high-speed shear test of the Sn-37Pb solder joints.

FAILURE BEHAVIORS OF FLIP CHIP SOLDER JOINTS UNDER VARIOUS LOADING CONDITIONS OF HIGH-SPEED SHEAR TEST

The failure behaviors of flip chip solder joints under various loading conditions of the high-speed shear test (H-SST) were investigated with an experimental and non-linear 3-dimensional finite element modeling study. The solder composition used in this study was Sn -3.0 Ag -0.5 Cu ( in wt .%). The shear forces were far greater by H-SST than by low-speed shear test (L-SST). The shear force further increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloy. Brittle interfacial fractures were more easily achieved by H-SST, especially at the higher shear speed. This was discussed in terms of the relationship between the strain-rate and work-hardening effect and the resulting stress concentration at the interfacial regions

Failure behaviors of BGA solder joints under various loading conditions of high-speed shear test

Failure behaviors of ball grid array (BGA) solder ball joints under various loading conditions of high-speed shear test were investigated with an experimental and non-linear 3-dimensional finite element modeling work. A representative Pb-free solder alloy, Sn-3.0Ag-0.5Cu, was employed in this study. Far greater shear forces were measured by high-speed shear test than by low-speed shear test. The shear force further increased with shear speed mainly due to the high strain-rate sensitivity of the solder alloy. Brittle interfacial fractures can be more easily achieved by high-speed shear test, especially in higher shear speed. This was discussed with the relationship between the strain-rate and work-hardening effect and resulting stress concentration at interfacial regions. Shear force decreased with shear height, and it could be found that excessively high shear heights unfavorably affected the test results leading to unexpectedly high standard deviation values or shear tip sliding from the solder ball surface.

Finite Element Simulation of Elastic Contact Between Two Cylinders

Contact problems are central to solid mechanics as contact is the principal method of applying loads to a deformable body and the point with resulting stress concentration is often the most critical point within the body. This paper presents a finite element model for the elastic contact between two cylinders at several positions. The effects of friction and surface roughness have been considered. The contact between two skew cylinders is also investigated. Results from finite element model show a good agreement with those of analytical solutions available in the literature. It was seen that the geometry of contacting bodies and orientation of applied load effect highly on contact stresses. Although the effect of surface roughness was seen to be more than that of friction, both of them can be assumed negligible in elastic contact problems.

Effects of porosity on the fatigue performance of polymethyl methacrylate bone cement: An analytical investigation

Porosity has been shown to affect the fatigue life of bone cements, but, although vacuum mixing is widely used to reduce porosity in the clinical setting, results have been mixed and the effects of porosity are not well understood. The aim of this study was to investigate the effects of porosity using stress analysis and fracture mechanics techniques. The stress concentrations arising at voids in test specimens were found using analytical solutions and boundary element methods. The fatigue life of specimens containing voids of various sizes was predicted using fracture mechanics techniques. For spherical voids that do not occupy a significant proportion of the cross-section, the resulting stress concentration is independent of void size and too small to account for the observed crack initiation. Cracks must therefore initiate at additional stress raisers such as radiopacifier particles or additional voids. For large voids, the stress increases as the remaining cross-section of the specimen decreases, and this may account for much of the observed reduction in fatigue strength in hand-mixed cement. Although crack initiation may be largely independent of void size, there is an effect on crack growth rate. Cracks are predicted to grow faster around larger voids, since they remain in the stress concentration around the void for longer. This effect may account for the relationship between porosity and fatigue life that has been observed in samples without large voids. Since porosity appears to affect crack growth more than initiation, it may be less damaging in high-cycle clinical fatigue, which may be predominantly initiation controlled, than in short laboratory tests.

Prediction of stress concentrations associated with interacting stress-raisers within aircraft design: Methodology development and application

In the design and manufacture of aerostructures and associated mechanical systems, situations arise where two or more stress-raisers are placed in proximity such that their associated stress fields interact. Under such circumstances, it is essential to determine accurately the resulting stress concentration effect, in order to evaluate the susceptibility of the structure to fatigue. The paper reports on new methodologies for predicting the location and magnitude of the maximum stress concentration around a range of commonly occurring two- and three-dimensional problems of feature interaction. The background research into the impact of multiple stress-raisers in proximity is reported and new techniques for the accurate prediction of stress concentrations associated with interacting features are described. The application and implementation of the methodologies within BAE SYSTEMS are discussed and the approach developed is illustrated by means of a case study.

Simultaneous considerations of length and boundary conditions on theoretical stress concentration factors

This work is concerned with the consequences of switching the uniformly loaded end, and accordingly the supported end, that is, exchanging boundary conditions in shouldered shafts with fillet radius, subjected to uniform tension, on the resulting stress concentration factor magnitudes when the length of the member is taken into account. Notably different values of the stated factors result under the conditions of the study reported herein. An issue of importance is the reliability of design and analyses involving fatigue of mechanical and structural members. Transition length values from long to short length regimes are reported as well.

６．地震の力学問題 鋼製ラーメン隅角部の補強に関する基礎的研究

Since large resultant forces and stress concentration can take place, the design of beam-to-column connections is important for a steel moment frame. To date, the elastic design based on the analytical study of stress concentration has been the standard method for these connections exclusively. However, such a design approach is not practical against large earthquake. Also, many existing connections that were conventionally designed have been found to suffer from fatigue cracks. In the present study, the effectiveness of the fillets and haunches of various sizes is studied for the reinforcement of a beam-to-column connection under ordinary and large seismic loadings.

A comparison of as-fatigue and re-consolidation residual properties for notched quasi-isotropic [0/45/90/−45]2S and cross-ply [0/90]4S AS4/PEEK composite laminates

A comparison of the as-fatigued and re-consolidated properties have been made between notched quasi-isotropic [0/45/90/ 2 45]2S and cross-ply [0/90]4S AS4/PEEK laminates. For the former, the ^458 plies tend to constrain longitudinal damage development so that damage growth primarily occurred in the transverse direction, causing more widespread damage. This led to prominent mechanical properties degradation, shorter fatigue lives and lower residual strengths. For cross-ply laminates, quick and extensive longitudinal crack tangential to the hole and the corresponding 908 fiber shear off brought about effective stress concentration alleviation. This discouraged further damage development. Hence, their fatigue lives exceeded one million cycles even at high cyclic stress levels and their residual strengths were significantly higher than their virgin strength. On the other hand, the re-consolidation process removed most of the defects that alleviated the stress concentration and thus decreased the strengths. Detailed study of the residual strength changes and damage development history revealed that the residual as-fatigued and re-consolidated strengths were governed by the competition between local structural decay and its resulting stress concentration alleviation. q 2002 Elsevier Science Ltd. All rights reserved.

Application of high strength plate bolts in friction grip joints

High Tension Bolts (HTB) are known to exert a significant influence on the strength characteristics of connections and have a significant influence on the ductility and behaviour of the joint. Normally HTB failure occurs in the shape resultant high stress concentration neck and thread areas resulting in relatively low ductility characteristics. Creep and relaxation occur after HTB tightening causing shaft tension loss and further stress redistribution in the connected components. Past research has shown that waisting the HTB shaft diameter reduces stress concentrations, shaft tension loss and increases ductility. With the further modification of making the HTB head plate shape counter sunk, a plate HTB with an aesthetically pleasing flat surface less susceptible to rain corrosion results. In this research, tensile, relaxation and friction grip joint slip experiments were done on waisted shank, counter sunk plate head HTB to ascertain the ductility improvement, the resulting decrease in shaft tension loss and its magnitude, as well as their applicability in friction grip steel connections. Apart from significant shaft tension loss reduction, no detrimental effects are induced in the slip coefficient results when these HTBs are applied in friction grip joints. Within these experimental parameters, the closest to ideal HTB shape is proposed. (Journal of Civil Engineering, JKUAT: 2002 7: 67-80)

Contact mechanics

Contact problems are central to Solid Mechanics, because contact is the principal method of applying loads to a deformable body and the resulting stress concentration is often the most critical point in the body. Contact is characterized by unilateral inequalities, describing the physical impossibility of tensile contact tractions (except under special circumstances) and of material interpenetration. Additional inequalities and/or non-linearities are introduced when friction laws are taken into account. These complex boundary conditions can lead to problems with existence and uniqueness of quasi-static solution and to lack of convergence of numerical algorithms. In frictional problems, there can also be lack of stability, leading to stick–slip motion and frictional vibrations. If the material is non-linear, the solution of contact problems is greatly complicated, but recent work has shown that indentation of a power-law material by a power law punch is self-similar, even in the presence of friction, so that the complete history of loading in such cases can be described by the (usually numerical) solution of a single problem. Real contacting surfaces are rough, leading to the concentration of contact in a cluster of microscopic actual contact areas. This affects the conduction of heat and electricity across the interface as well as the mechanical contact process. Adequate description of such systems requires a random process or statistical treatment and recent results suggest that surfaces possess fractal properties that can be used to obtain a more efficient mathematical characterization. Contact problems are very sensitive to minor profile changes in the contacting bodies and hence are also affected by thermoelastic distortion. Important applications include cases where non-uniform temperatures are associated with frictional heating or the conduction of heat across a non-uniform interface. The resulting coupled thermomechanical problem can be unstable, leading to a rich range of physical phenomena. Other recent developments are also briefly surveyed, including examples of anisotropic materials, elastodynamic problems and fretting fatigue.

A method based on singularity theory to predict edge delamination of laminates

Delamination starting from a stress free edge is the main mode of failure of cross-ply laminates. The analysis of singularities and resulting stress concentrations at interfaces along these edges are not sufficient to provide a satisfying model of onset mechanisms. In particular, the model is by far less sensitive to the layers thickness than observed in traction experiments. A refined asymptotic process is proposed which takes into account the existence of surface flaws (micro-cracks or notches). Numerical results prove that this model is much more in agreement with the experiments. Moreover, the knowledge of the interface toughness, in addition with the experiments, allows to estimate a characteristic fracture length, a kind of process zone. It is a material property and in a first approximation it arises to be of the same order of magnitude than the characteristic inhomogeneity length of the components, i.e. the fibers diameter.

Minimization of stress concentration factors in fatigue crack repairs

A numerical study is reported of a repair by flaw removal on a conventional welded joint. The repair profile is optimized with respect to the flaw and joint dimensions in order to minimize the resulting stress concentration factor ( SCF). Two dimensional (edge repair) and three dimensional (surface repair) finite element analyses were made for the determination of SCF values and a graphical representation of results is presented. A relation between edge repair and surface repair is obtained and short and long repairs are defined. The weld geometry and repair orientation effects on SCF values are discussed. Finally, implications on using short and long repairs on fatigue initiation and inspection are presented.