Elastic Stress Concentration Factor Research Articles

The role of corrosion pit topography on stress concentration

Smooth semi-ellipsoids are typically used to simulate the effect of corrosion pits on stress, however, this does not account for pit geometry. Three corrosion pits were identified on Nickel Aluminium Bronze samples. These were scanned and converted to finite element models. The linear elastic stress concentration factor (Kt) of the corrosion pit FE models was 1.32–1.65 times larger than for an equivalent smooth semi-ellipsoid. This suggests that detailed consideration of pit geometry is needed to calculate accurate values of Kt and the assumption of a semi-ellipsoidal pit may not be conservative for fatigue lifetime predictions of pitted components.

Stress concentration in shape memory alloy sheets with circular cavities: Effects of transformation, saturation, and plasticity

The analysis of stress concentration in geometrically heterogeneous smart structures is of great importance. In this study, by utilizing a recent constitutive model which considered both transformation and plasticity of shape memory alloys (SMAs), the stress concentration factor (SCF) in plates with circular cavities is investigated and the effect of phase transformation, saturation, and plasticity which may occur locally is studied. The results show that the conversion of the austenitic phase to the martensite leads to a reduction in SCF. After saturation of phase transformation at the stress concentration point, the SCF increases until the entire sheet enters the martensite phase. In the example under study, the SCF reaches 5.8 which is greatly higher than the elastic SCF. By entering the plastic region locally, the SCF reduces. Also, the modeling of sheets with more than one cavity has been done. It is concluded that extra hole, as a stress relief method, has a stronger effect on decreasing maximum stress concentration of shape memory alloys (considering transformation and plasticity) compared to purely elastic stress concentration studies.

Experimental Investigation of Fracture Performances of SBHS500, SM570 and SM490 Steel Specimens with Notches

High-strength steels (HSSs) with nominal yield stress not less than 460 MPa have been increasingly employed in bridge structures. Compared with SM490 normal-strength steel (NSS), HSSs, including SBHS500 and SM570, have higher strength but lower ductility, and brittle fracture can easily occur in the HSSs members with notches. Therefore, 48 tension specimens with U-notch or V-notch made of SBHS500, SM570 and SM490 structural steels are carried out. The influences of notch depth, U-notch radius, V-notch degree and chemical composition on the mechanical and fracture performances of the steel specimens are investigated. It is concluded from experimental results that SBHS500 and SM570 HSSs with higher yield stress have a relatively higher elastic stress concentration factor, crack initiation appears earlier, and brittle fracture is more likely to occur. Compared to SM570 HSS, SBHS500 HSS has better weldability.

Effect of machine processing scratch on fatigue strength of notched specimen of aluminum alloy

The purpose of this study is to investigate effect of machine processing scratches on fatigue strength of a notched specimen of aluminum alloy. In this study, strain-controlled fatigue tests were carried out for two types of notched specimens with machine processing scratches. The fatigue strengths of notched specimens decreased by more than the elastic stress concentration factor due to the notch. To discuss the fatigue strength reduction, the specimen and fracture surfaces were observed carefully. The observations showed that the fatigue cracks initiated from the machine processing scratches and they are aligned around the notch root due to the stress concentration. As a result, the fatigue strength reduction factor became greater than elastic stress concentration factor.

A Study on Low Cycle Fatigue Life Assessment of Notched Specimens Made of 316 LN Austenitic Stainless Steel

Abstract The local strains obtained from the best-known analytical approximations, namely, Neuber's rule, equivalent strain energy density method, and linear rule, were compared with those resulting from finite element analysis. It was found that apart from Neuber's rule with the elastic stress concentration factor Kt, all the aforementioned analytical methods underestimate the local strains for all notch root radius, strain amplitude levels, at room temperature and 550 °C. Neuber's rule with Kt slightly overestimates the maximum strains for lower notch root radius, namely, 1.25 mm, at high temperature. Based on the analytically and numerically obtained notch root strains, the fatigue lives were estimated using the Coffin–Manson–Basquin equation. Besides, a numerical assessment of fatigue lives was made based on Brown–Miller and maximum shear strain multi-axial fatigue life criteria. It was found that all these methods provide inaccurate fatigue life results for all notch root radius, strain amplitude level, and under both temperatures conditions. Therefore, a new method was suggested, for which only the applied strain amplitude is needed to calculate the fatigue life of notched components. It was revealed that the suggested method provides a good fatigue life prediction at a higher temperature loading state.

Experimental and Numerical Study of the Elastic SCF of Tubular Joints.

This paper provides data on stress concentration factors (SCFs) from experimental measurements on cruciform tubular joints of a chord and brace intersection under axial loading. High-fidelity finite element models were generated and validated against these measurements. Further, the statistical variation and the uncertainty in both experiments and finite element analysis (FEA) are studied, including the effect of finite element modelling of the weld profile, mesh size, element type and the method for deriving the SCF. A method is proposed for modelling such uncertainties in order to determine a reasonable SCF. Traditionally, SCF are determined by parametric formulae found in codes and standards and the paper also provides these for comparison. Results from the FEA generally show that the SCF increases with a finer mesh, 2nd order brick elements, linear extrapolation and a larger weld profile. Comparison between experimental SCFs indicates that a very fine mesh and the use of 2nd order elements is required to provide SCF on the safe side. It is further found that the parametric SCF equations in codes are reasonably on the safe side and a detailed finite element analysis could be beneficial if small gains in fatigue life need to be justified.

Three dimensional analysis of periodic fiber-reinforced composites with randomly broken and debonded fibers

A three-dimensional analysis is presented for the prediction of the behavior of periodic fiber-reinforced composites with numerous broken fibers and debonded fiber-matrix interfaces. The locations of these defects in the composite are randomly determined. The analysis is based on the representative cell method and the higher-order theory. In the framework of the representative cell method, the problem for the representative volume element of the damaged composite that includes multiple fibers is reduced, in conjunction with the triple discrete Fourier transform, to the problem for repetitive cell of undamaged composite including just a single cell. The solution of this boundary-value problem is obtained by the higher-order theory. The inversion of the transform, in conjunction with an iterative procedure, establishes the elastic field at any point of the damaged composite. The optimal size of the representative volume element of the damaged composite within which the computations are performed is determined. The present method is capable of predicting the resulting field distributions in the composite as well as the average values of the effective moduli of the randomly damage composite and the resulting stress concentration factors. These average values and the corresponding standard deviations are determined by repeating the analysis several times (scores). A parametric study of the dependence of the effective elastic moduli and stress concentration factors upon the level of damage is performed. In addition, comparisons with a micromechanical theory predictions which are based on the analysis of a repeating unit cell, established by the assumption of spatial damage periodicity, are given.

Comparison between EDM and grinding machining on fatigue behaviour of AISI D2 tool steel

Non-conventional machining processes, such as the Electrical Discharging Machining (EDM) offers the possibility to machine very hard materials with great potential to generate complex geometries. However, the EDM process involves significant microstructural changes in the as machined surfaces, which are known to have a significant impact on fatigue behaviour of mechanical parts. This study aims at investigating the fatigue behaviour of the AISI D2 tool steel subjected to EDM machining. Both smooth and notched specimens are tested aiming at assessing the fatigue notch sensitivity of this material and results compared with conventional grinding techniques in terms of fatigue resistance and residuals stresses. The AISI D2 steel shows a microstructure composed of large dendritic primary carbides detrimental to the fatigue resistance. Also, the EDM process is responsible for the generation of detrimental tensile residual stresses that justifies the lower fatigue resistance when compared with the ground material that exhibits beneficial compressive residual stresses. The fatigue test data of the notched specimens machined by EDM process show a high fatigue notch sensitivity of the AISI D2 tool steel. The heterogeneous structure of the material, showing large undissolved carbides, leads to a notch fatigue reduction factor that is higher to the apparent theoretical elastic stress concentration factor.

Duality of the fatigue behavior and failure mechanism in notched specimens of Ti-7Mo-3Nb-3Cr-3Al alloy

An interesting phenomenon of dual S-N fatigue behavior is investigated in a metastable β titanium alloy, Ti-7Mo-3Nb-3Cr-3Al notched cylindrical specimens with an elastic stress concentration factor of Kt = 3. Fractographic studies revealed all specimens, and irrespective of lifetime, failed from the specimen surface because of stress concentration occurs at the notch root. Typically, the short-life-distribution is usually associated with surface-failure-without-facets and the long-life-distribution generally occurs due to surface-failure-with-facets. This competing failure leads to increasing the variability in fatigue lifetime and further facilitates the difficulty in prediction of fatigue lifetime. Crack-initiation area characterization was conducted by using mechanical grinding, focused ion beam milling and subsequent electron back-scattered diffraction (EBSD) analysis of the 2D section across faceted grains. Results show that the αp particles (especially the elongated αp particles) well-oriented for basal slip activation is a preferential fatigue-critical microstructural configuration. Additionally, the β+αs matrix has a higher KAM value than the αp particles in fatigued microstructures and significant dislocation activity in the form of dislocation tangles is observed in αp boundaries.

Fatigue Strength Evaluation of Notched Ductile Steel Specimens Using Critical Distances

In the case of AISI 304L austenitic stainless steel it was found that the fatigue strength of specimens characterized by the presence of blunt notches cannot be rationalized either in terms of linear elastic local stress or nominal stress amplitude. This fact was related to the high level of ductility shown by this material also in the case of high cycle fatigue regime. Therefore, in this paper some classical fatigue design methodologies are extended to account for this aspect also in the case of severe notches. On this basis a FEM oriented extension of the concept of geometric elastic stress concentration factor is proposed.

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.

Orientation and size effect of a rectangle cutout on the buckling of composite cylinders

In this article the effect of a rectangular cutout on the buckling behavior of a thin composite cylinder was investigated using numerical and experimental methods. To verify the finite element results, a limited number of tests was carried out on perforated and non-perforated glass/epoxy cylinders with [90/−23/23/90] layups. In the numerical analysis, linear and nonlinear approaches were employed to study the effect of initial imperfections on the buckling of the cylinders. Several key findings including the effects of cutout size and orientation, and the mutual effects of the cutout and initial imperfections on the buckling behavior were investigated in detail.In the presence of cutouts, the effect of initial imperfections on the buckling load is a function of the cutout size. In cylinders with rectangular cutouts, buckling analysis revealed that a rectangular cutout in the circumferential direction causes around 8% more reduction in the buckling load than the same cutout in the axial direction. Also, numerical findings illustrated that elastic stress concentration factors for the circumferential cutouts are much greater than those for the axial cutouts; thus premature failure around the cutout will trigger earlier buckling in the cylinder with circumferential cutouts.

Surface Treatment of Powder-Bed Fusion Additive Manufactured Metals for Improved Fatigue Life

High-cycle fatigue (HCF) tests were conducted on samples fabricated by two powder-bed additive manufacturing techniques. Samples were tested with as-produced surfaces and after various non-contact surface improvement treatments. Ti-6Al-4V samples were made using both electron beam melting (EBM) and selective laser melting (SLM), while Inconel 625 was fabricated using SLM. Ti-6Al-4V was treated with a commercial chemically accelerated vibratory polishing process, with target material removal of approximately 200 µm from each surface for EBM samples and 100 µm for SLM samples. This technique led to increases in both the number of cycles before failure at a given loading condition and endurance limit (at 107 cycles) compared to samples with as-produced surfaces. The results are interpreted as the reduction in elastic stress concentration factor associated with surface defects where fatigue cracks initiate. SLM 625 was treated with both an abrasive polishing method and laser surface remelting. Both methods led to improvements in surface roughness, but these did not lead to improvements in fatigue properties of SLM 625. For abrasive polished samples, the combination of improved measured surface roughness without fatigue property enhancement suggests that surface material is removed, but the roots of surface defects, where fatigue cracks initiate, were left intact. For laser treatment, the remelted surface layer retained a rapidly solidified microstructure that did not increase the number of cycles before crack initiation even though the surface was smoother compared to the surface prior to polishing.

Influence of Design Factors of Butt-welded Sheet Joints on Elastic Stress Concentration Level in Joints

The aim of this study is to determine the influence of design factors of butt-welded sheet joints on the level of elastic stress concentration in joints. The finite element method was used to model the stress-strain state in the zones of constructive concentration of butt sheet joints with double-sided seams. The design model simulated the form of the joint in all the elements since the distribution of stresses and strains in the cross section depends on the joint configuration. The following parameters for butt sheet joints such as sheet thickness, the width of the joint, the bead width and bead height in butt welding joints were varied in the study. A nonlinear model was used to approximate the values of the elastic stress concentration factors obtained for different values of the geometric parameters for butt-welded sheet joints. This model is in good agreement with the values of the elastic stress concentration factors in the transition zone between the weld seam and base metal obtained by the stress-strain state modelling in joints with the help of FEM (the coefficient of determination R2≥0.856).

Does a nucleated crack propagate?

Conditions for propagation or non-propagation of an incipient crack from stress concentrations such as notches, holes, etc., are evaluated using elastic-plastic fracture mechanics methods and the Kitagawa-Takahashi diagram, hence linking smooth specimen behavior to fracture mechanics. The analysis differs from all other previous models which are either empirically based or assume that short crack growth behavior differs from that of long cracks due to crack closure or lack of it. It is shown that the stress intensity factor of an incipient crack decreases and then increases as it moves away from the internal stress field of a notch. Crack propagation is ensured only when the minimum is equal to or greater than the unique fatigue threshold for crack growth. Otherwise non-propagation conditions prevail. Equations are developed to establish the conditions for the minimum stress required for continuous propagation of the originated crack. It is shown that by analyzing published results on notch-fatigue that specimen failure occurs only if the applied stresses exceed the minimum stress required for crack propagation. Otherwise crack arrest occurs resulting in non-propagating cracks. The analysis can be readily used to determine the conditions for failure of a notched specimen if the elastic stress concentration factor, kt, the notch-tip radius, ρ, and fatigue crack threshold, Kth, for the material are known. The analysis, in principle, is applicable to all subcritical crack growth processes.

Comparison between nonlinear FEA and notch strain analysis for modeling elastoplastic stress-strain response in crossbores

The elastoplastic stress-strain response of a crossbore geometry were evaluated using FEA and notch strain analysis based on Neuber and Glinka approaches. The stress and strain in the crossbore were predicted by FEA and analytical models for an autofrettage overload pressure, an unload, and an operating pressure cycle. An elastic FEA simulation was used to define the elastic stress concentration factors (Kt) based on von Mises and maximum normal stress using with two definitions of nominal stress. Four resulting stress concentration expressions were combined with the three forms of the Glinka notch formula and the three forms of the Neuber notch formula. This gives 24 possible expressions that were evaluated for prediction accuracy. From this comparison, the Glinka approach was found to match the FEA results most closely when the stress concentration was based on the ratio of the von Mises stress and nominal stress. However, no single notch equation was found to accurately capture the stress and strain state in the crossbore. By adopting an averaging approach using both the Neuber and Glinka predictions, the analytical model results were found to improve significantly for the entire pressure history.

Local web buckling mechanism and practical design of double-coped beam connections

This paper presents a comprehensive investigation on local web buckling mechanism and design of double-coped beam connections. Following a careful validation study, a series of finite element (FE) models are established, covering a spectrum of geometric and material variables including cope length, cope depth, web slenderness, and steel grade. The study reveals that the main failure mode of the models is either inelastic or elastic local web buckling, and the considered parameters can evidently influence the buckling capacity. The models with short copes tend to fail by inelastic buckling accompanied by excessive shear yielding. For the models with long copes, especially for those with thin webs and high steel grades, stable post-buckling equilibrium path could be sustained after the occurrence of initial buckling, and as a result the ultimate reaction can be evidently higher than that governed by elastic buckling. In addition, stress concentration is significant near the cope corners, and the peak elastic stress concentration factor (SCF) could achieve around 2.0. A further discussion is made on various support and boundary conditions, and these variables are also shown to have clear influences on the local web buckling capacity of double-coped beams. Based on the numerical results, and recognising the potential limitations of the existing design rule, a modified design method, taking account of the various influential factors revealed in this study, is finally proposed. The available experimental and numerical results show that the modified method can effectively improve the accuracy of local web buckling design for double-coped beam connections.

Assessment of tensile fatigue limit of notches using sharp and coarse linear elastic finite element models

The aim of the present paper is to provide an efficient numerical technique to evaluate the linear elastic stress parameters to use in an existing fatigue model. The model allows to assess the tensile fatigue limit of components weakened by defects, cracks, sharp as well as blunt notches with an arbitrary notch opening angle. To apply the fatigue model, both the elastic stress concentration factor of the notch and the notch stress intensity factor of the corresponding sharp notch must be evaluated. Therefore, in principle two different linear elastic stress analyses should be performed. The novel technique proposed in the present paper involves only a single linear elastic stress analysis, consisting of a sharp and coarse finite element model: sharp because the notch tip radius is set to zero, and therefore a sharp V-shaped notch is modelled; coarse because coarse patterns of finite elements can be employed. Approximate values of the elastic stress concentration factor and of the notch stress intensity factor calculated from the sharp and coarse finite element model are compared with very accurate estimations obtained from dedicated analyses. To illustrate the fatigue assessment procedure, experimental notch fatigue limits taken from the literature and characterised by a variety of geometrical configurations are compared with theoretical estimations.

Evaluation of multiaxial low cycle fatigue life for type 316L stainless steel notched specimen under non-proportional loading

This study discusses a multiaxial low cycle fatigue (LCF) life of notched specimen under proportional and non-proportional loading conditions at room temperature. Multiaxial LCF tests controlled by strain were carried out using a smooth and a circumferentially notched round-bar specimens of type 316L stainless steel (316LSS). Four kinds of notched specimens of which elastic stress concentration factors Kt are 1.5, 2.5, 4.2 and 6.0 were employed. The strain paths employed were proportional loading and non-proportional loading. The former is push–pull loading and reversed torsion loading and the latter is circular loading achieved by the strain path of which axial and shear strains are loaded by 90° sinusoidal out-of-phase. Total axial strain and total shear strain ranges were the same ranges based on von Mises. An evaluation of the fatigue life for the notched specimen is discussed based on the experimental results and also by employing an inelastic finite element analysis (FEA). The fatigue life is decreased with increase in Kt at each strain path and is underestimated by a maximum local strain range evaluated by FEA result. A proposed strain range defined by a local mean strain value near the notch calculated from FEA by taking into account the non-proportional effect is an appropriate parameter for life evaluation of 316LSS notched specimen under non-proportional loading.

Validation of the Two-Parameter Fracture Criterion using 3D finite-element analyses with the critical CTOA fracture criterion

A Two-Parameter Fracture Criterion (TPFC) was derived from Inglis’ elastic-stress-concentration equation for an elliptical hole under remote uniform stress and Neuber’s equation relating the plastic stress and strain concentration factors to the elastic stress-concentration factor at the maximum stress location. Elastic–plastic 3D finite-element analyses (FEA) employing the critical crack-tip-opening-angle (CTOA) fracture criterion was used to simulate fracture on thin-sheet middle-crack-tension, M(T), and compact, C(T), specimens made of 7249-T76511 aluminum alloy over a wide range in crack-length-to-width ratios to validate the TPFC. A critical CTOA (7.6°) and the fracture parameters (KF and m) were determined from M(T) test specimens, and these values were then used to predict the failure on C(T) specimens. The FEA predicted failure loads on C(T) specimens were within a few percent; whereas, the TPFC generally over predicted the failure loads (5–15%). The TPFC over prediction on the C(T) specimens is likely related to net-section stress (Sn) being greater than the yield stress of the material for all test data, while the M(T) specimens all had Sn less than the yield stress.