Distribution Of Transverse Stresses Research Articles

Predicting quarter-buckling and herringbone buckling in rolled strip

Although edge-wave and centre-buckles in rolled strip are believed to be largely self-equilibrated, the result of residual stress, formation of herringbone and quarter-buckles in hot- or cold-rolled strip is believed to require application of external stress. It is verified here that stress distributions such as those indicated by Roberts are possible causes of quarter-buckling and herringbone buckling. Quarter-buckling is believed to result from stress in the sheet or strip produced by non-parabolic bending of the work rolls. Herringbone buckling is attributed to local regions of axial tension and compression in the transverse stress distribution, caused by misalignment, which effectively produces a shear in the sheet that may manifest itself in diagonal buckling.

Thermo-mechanics of undamaged and damaged multilayered composite plates: a sub-laminates finite element approach

In this work a plate mixed finite element based on a refined zig-zag plate model is formulated for the analysis of multilayered composite plates subjected to thermal and mechanical loads. The zig-zag plate model is characterised by: (i) through-the-thickness cubic in-plane displacements and linear transverse displacement, (ii) transverse shear stresses continuity, (iii) satisfaction of traction equilibrium conditions on top and bottom faces of the laminate thus allowing for the presence of tangential distributed loads, (iv) the transverse normal deformability is taken into account by means of a σ33 supposed constant along the thickness and by the use of the complete constitutive equations of orthotropic materials, (v) use, as degrees of freedom of the model, of displacements and transverse shear stresses of external faces of the laminate. In particular, this last property may be extended to the associated plate finite element that, having its nodal degrees of freedom on the external faces, allows a through-the-thickness discretisation in some sub-domains called sub-laminates. Some numerical results are presented in order to show that the use of more sub-laminates improves the capability of the approach to capture with high accuracy the though-the-thickness distributions of transverse displacements, strains and stresses also for very thick plates.

Deformation and fracture resistance of butt-welded joints with mild interlayer under elastoplastic tension

Relations are proposed for evaluating the stress-strain state and strength of a butt weld with a mild interlayer under elastoplastic tension in plane-and axisymmetric-strain conditions. The relations allow for the distribution of transverse normal stresses across the interlayer thickness and the interaction and hardening of the metals in the elastoplastic domain. The predicted strain distribution in certain areas of the weld and its strength are verified experimentally

Comprehensive residual stress distributions in a range of plate and pipe components

A comprehensive review of through thickness transverse residual stress distributions in a range of as-welded and mechanically bent components made up of a range of steels has been carried out, and simplified generic transverse residual stress profiles for a plate and pipe components have been proposed. The geometries consisted of welded pipe butt joints, T-plate joints, tubular T-joints, tubular Y-joints and a pipe on plate joints as well as cold bent tubes and pipes. The collected data covered a range of engineering steels including ferritic, austenitic, C-Mn and Cr-Mo steels. Measured residual stress data, normalised with respect to the parent material yield stress, has shown a good linear correlation versus the normalised depth of the region containing the residual stress resulting from the welding or cold-bending process. The proposed simplified generic residual stress profiles based on the mean statistical linear fit of all the data provides a reasonably conservative prediction of the stress intensity factors. Whereas the profiles for the assessment procedures are fixed and case specific, the simple bilinear profiles for the residual stresses obtained by shifting the mean and bending stress from the mean regression line have been proposed and validated.

A generic approach for a linear elastic fracture mechanics analysis of components containing residual stress

A review of through thickness transverse residual stress distribution measurements in a number of components, manufactured from a range of steels, has been carried out. Residual stresses introduced by welding and mechanical deformation have been considered. The geometries consisted of welded T-plate joints, pipe butt joints, tube-on-plate joints, tubular Y-joints and tubular T-joints as well as cold bent tubes and repair welds. In addition, the collected data cover a range of engineering steels including ferritic, austenitic, C–Mn and Cr–Mo steels. The methods used to measure the residual stresses also varied. These included neutron diffraction, X-ray diffraction and deep hole drilling techniques. Measured residual stress data, normalised by their respective yield stress have shown an inverse linear correlation versus the normalised depth of the region containing the residual stress (up to 0.5 of the component thickness). A simplified generic residual stress profile based on a linear fit to the data is proposed for the case of a transverse residual tensile stress field. Whereas the profiles in assessment procedures are case specific the proposed linear profile can be varied to produce a combination of membrane and bending stress distributions to give lower or higher levels of conservatism on stress intensity factors, depending on the amount of case specific data available or the degree of safety required.

A Study on Residual Stress Relaxation under Quasi-Static Load

Investigation on the quasi-static residual stress relaxation is an important aspect of component design and life management. After taking into account the influence of transverse stress and strength distribution, this paper proposes a new criterion of residual stress relaxation under quasi-static load as follow: the surface residual stress tends to relax as long as the Mises effective stress anywhere exceeds the local yield point. In addition, by X-ray tensile test, a method of determining superficial yield strength based on the Von Mises hypothesis was applied at the shot-peened surface of a martensitic stainless steel 0Cr13Ni4Mo. The experimental results show that the yield strength of superficial layer is larger than that of core material. According to the experimental results, a simplified ladder-shaped model of the depth distribution of yield strength is proposed. On the basis of the above-mentioned relaxation criterion and the strength distribution model, a new method is presented to calculate the relaxation amount. The calculated results coincide with the experimental results.

Stress Intensity Factors Due to Residual Stresses in T-Plate Welds

Residual stress distributions in ferritic steel T-plate weldments have been obtained using the neutron diffraction method. It is shown that the transverse residual stress distribution for two plates of different yield strength are of similar shape and magnitude when normalized appropriately and peak stresses are on the order of the material yield strength. The resultant linear elastic stress intensity factors for these stress distributions have been obtained using the finite element method. It has been shown that the use of the recommended residual stress distributions in UK structural integrity procedures leads to a conservative assessment. The stress intensity factors for the welded T-plate have been shown to be very similar to those obtained using a smooth edge cracked plate subjected to the same local stress field.

A state space finite element for laminated composites with free edges and subjected to transverse and in-plane loads

On the basis of the theory of three-dimensional elasticity, this paper presents a state space finite element solution for the stresses in cross-ply laminates subjected to combined transverse and in-plane loads. The state space formulation is introduced to solve for through-thickness stress distributions, while the traditional finite elements are used to approximate in-plane variations of the state variables. One of the direct applications of this solution is for the analysis of free-edge effect in cross-ply laminates. By appropriately describing the applied in-plane boundary tractions or boundary displacements, plates having complete free edges or boundary cross-sections with localized stress-free surfaces can be analyzed. Compared with the traditional finite element method, the new solution provides not only continuous through-thickness distributions of both displacements and transverse stresses, but also excellent approximations to the stress singularities in the vicinity of free edges or the above-mentioned localized stress-free surfaces.

厚板解析における横荷重の影響に関する一考察

Since Reissner and Mindlin proposed their classical thick plate theories, many authors have presented refined theories including transverse shear deformation Most of those plate theories are derived through expanding displacements and stresses into power series along the thickness. In general, the higher the order of the theories is, the higher the accuracy of those is. However, the conciseness of the classical theories has been lost. On the other hand, the importance of transverse load effect is not noticed in those plate theories. In this paper, we pay attention to formations of the load of plates. The formations of load are represented by rate parameters, which indicate portions of a body force and surface tractions. When we introduce the rate parameter for loads and consider the transverse normal stress distribution, we can establish a quite simple plate theory including transverse shear deformation. In addition, the new theory presented here gives us excellent results of a deflection and bending moments.

Residual Stress Distributions in Welded Ferritic Steel T-plate Joints

Transverse and longitudinal residual stress distributions in welded ferritic steel T-plate joints of two different plate sizes are presented. The stresses have been measured by the deep hole drilli...

A three-dimensional state space finite element solution for laminated composite cylindrical shells

On the basis of the theory of three-dimensional elasticity, this paper presents a state space finite element solution for stress analysis of cross-ply laminated composite shells. This is a continuation of the authors’ previously published work on laminated plates [Compos. Struct. 57 (1–4) (2002) 117; Comput. Methods Appl. Mech. Engrg. 191 (37–38) (2002) 4259]. Once again a state space formulation is introduced to solve for through-thickness stress distributions, while the traditional finite elements are used to approximate the in-surface variations of state variables. A three-dimensional laminated shell element is established in an arbitrary orthogonal curvilinear coordinate system, while the application of the element is shown by calculating stresses in laminated cylindrical shells. Compared with the traditional finite element method, the new solution provides accurate continuous through-thickness distributions of both displacements and transverse stresses.

Residual Stress Distribution in Butt Welded Joints – Effect of the Weld Groove Shape

The influence of the V-groove, X-groove and square butt edges, as well of the weld sequence on the residual stress distribution in butt welds is reported in this paper. Coupon plates with 400 x 180 x 11 mm size were prepared with square butt edges, V-groove and X-groove edges, stress relief heat treated and welded with two beads in each, using the gas metal arc welding process. Longitudinal and transverse residual stresses were measured in each coupon plate after the stress relief treatment and after each weld bead, following lines perpendicular to the weld direction and also along the central line of the weld. Residual stresses evaluation was conducted using an X-ray diffraction method. Residual stress distribution after the first weld bead is similar in the three types of weld grooves, nevertheless using weld X-groove longitudinal tensile residual stress tends to present the highest level in the weld metal and heat-affected zone. The execution of the second weld layer originates a small increase of the longitudinal residual stresses, but X-groove welds continue to present the highest level. The weld groove type seems to have a reduced effect on transverse residual stress distribution, though the second weld layer produces an increase in magnitude of the transverse residual stress in welds with X-groove and square butt edges.

A state space finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for the stress analysis of cross-ply laminated composite plates. The method is based on a mixed variational principle that includes the variations of both displacements and stresses. Finite element approximation is introduced only for the in-plane variations of displacements and stresses, while the through-thickness distributions of them are obtained by using the method of state equation. Numerical tests show that the results obtained approach the analytical three-dimensional solutions. Moreover, the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate. Compared with the traditional finite element method, the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces.

On the prediction improvement of transverse stress distributions in cross-ply laminated beams: advanced versus conventional beam modelling

This paper assesses the stress analysis performance of the most commonly used conventional, shear deformable beam theories as well as the advanced beam theories presented in references [Acta Mech. 1997;123:163; Math. Mech. Solids 1997;2:459; Int. J. Solids Struct. 1997;22:2857], by employing a predictor–corrector method. The assessment deals with the accuracy of the distribution of the interlaminar (transverse shear and transverse normal) stresses through the entire beam thickness. As far as simply supported, cross-ply laminated beams are concerned, it compares the corresponding stress analysis results obtained with their exact elasticity counterparts. The conclusions of this type of initial assessment are very much in favour of the advanced beam theories, which involve exponential shape functions of the transverse co-ordinate parameter. Hence, those advanced beam theories are employed for further applications that involve different sets of end boundary conditions for which explicit exact elasticity results are unavailable or very difficult to obtain.

A simplified approach for incorporating thickness stress in the analysis of sheet metal forming using shell elements

AbstractA simplified scheme for considering the thickness stress of shell elements induced by contact is presented which improves the accuracy of sheet metal forming analysis. The yield function formulated on the basis of plane stress conditions is modified to incorporate the effect of transverse normal stress induced by contact forces acting on shell elements and return mapping routine is used to update in‐plane stresses at each time step. The transverse normal stress distributions in the thickness direction are determined using the analytic solution of the cylindrical tube under the internal pressure. As numerical examples, uni‐axial compression, bi‐axial tension and bending tests are treated. The problem of cylindrical cup drawing is also calculated. Each result is compared with the results obtained by the analysis using ABAQUS continuum elements. Copyright © 2002 John Wiley & Sons, Ltd.

Analysis of Compression Stress of a Filler and Bending of a Sandwich Panel under Multipoint Loading

The distribution of transverse stresses in the midlayer of a composite sandwich panel under multipoint loading is investigated. The stresses averaged across the thickness of a soft filler are estimated using a discrete model. Finite expressions for the compression of the filler along the length of the panel are derived by means of superposition of the local effects from the bending of face layers under an infinite system of transverse point forces constant across the panel thickness. The effects of compression and transverse extension of the filler, in the case of a high distribution frequency of these forces, i.e., when the distance between the forces is comparable to the panel thickness, are revealed. Compression of the panel by two systems of forces applied symmetrically or nonsymmetrically to the upper and lower faces is considered. The bending characteristics in the cases of loading with point forces and piecewise distributed loads are compared. The formulas obtained are used to determine the length of a small region on the panel surface for which the local effects from the distributed pressure and the point force are equivalent. The corresponding estimates are obtained in a closed form. The analysis, carried out with varied parameters of the structure, allows us to elucidate the peculiarities of the effect of discontinuous loads on the design characteristics in the local zones, using finite expressions derived by the operational method.

Structural Behavior of Tendon Coupling Joints in Prestressed Concrete Bridge Girders

Segmental construction of prestressed concrete (PSC) girder bridges has, in recent years, been widely used in many countries. In these segmentally built PSC bridges, many construction joints exist, requiring the coupling of tendons to introduce continuous prestress through the superstructure of bridges. The aim of this paper was to closely examine the complex stress distributions around tendon coupling joints in PSC girders. A comprehensive experimental program was set up, and a series of test members were studied to identify the effects of tendon coupling. Results show that longitudinal and transverse stress distributions of PSC girders with tendon couplers are much different from those not having tendon couplers. Approximate amounts of reinforcement are required around coupled joints to avoid serious cracking. This fact is not reflected in current design codes and must be considered for safer and more reliable PSC bridge girder design.

ダンパー付き鋼構造骨組における梁端フランジ溶接部の力学的特性

Of the beam-column frames which are used in vibration-controlled structures, we conducted repeated static and dynamic tests on the model of flange plates at welded beam-end, using steel type and ambient temperature as parameters. As a result, the following conclusions were obtained. 1) While the transverse stress distribution is convex in the elastic zone, it is reversed into concave in the plastic zone. 2) The higher the strength of steel, the smaller the cumulative plastic deformation magnification. However, all test specimens are fully capable of accommodating the damage which they sustain during the period of using a building. 3) The rise of yield strength due to ambient temperature and test speed is more pronounced in low-strength steels. 4) From the viewpoint of the right steel for the right place, SM490A and SN400A are the most suitable for vibration-controlled structural frames with damners as they fully meet requisite performances.

Vibration and Stability of Thick Plates on Elastic Foundations

Natural frequencies and buckling stresses of a thick isotropic plate on two-parameter elastic foundations are analyzed by taking into account the effect of shear deformation, thickness change, and rotatory inertia. Using the method of power series expansion of the displacement components, a set of fundamental dynamic equations of a two-dimensional, higher-order theory for thick rectangular plates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are used to solve the eigenvalue problems of a simply supported thick elastic plate. To assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress are examined in detail. The distribution of modal transverse stresses are obtained by integrating the three-dimensional equations of motion in the thickness direction. The present approximate theories can accurately predict the natural frequencies and buckling stresses of thick plates on elastic foundations as compared with Mindlin plate theory and classical plate theory.

Evaluation Technique of Head/Tape Contact Using Acoustic Emission

A new on-line methodology has been developed for both evaluation and analysis of head/tape interface phenomena. It uses the direct relationships between the power in the acoustic emission (AE) signal and wear, and between the power in the AE signal and the normal force acting on the magnetic head. The AE transducer is directly mounted onto the head assembly of a VCR mechanism in order to measure the head/tape contact behavior. This technique has been used to: (a) monitor the effect of relative humidity on head wear; (b) investigate the wear characteristics of Mn-Zn ferrite as a function of crystallographic orientation without direct measurement of the wear volume; and (c) evaluate tape abrasiveness. Explicit correlations were also obtained for the normal force acting on the magnetic head, the tape wrap angle around the head, and the reproduced signal flatness in terms of the tape transverse stress distribution. Moreover, the normal force as a function of the tape stress distribution is closely related to the longitudinal tape vibration at the head exit region.