Residual stresses in press-braked stainless steel sections,II: Press-braking operations

The manufacturing process of cold-formed thin-walled steel members induces cold work which can be characterized by the co-existent residual stresses and equivalent plastic strains and has a significant effect on their structural behaviour and strength. The present paper and the companion paper are concerned with the prediction of residual stresses and co-existent equivalent plastic strains in stainless steel sections formed by the press-braking method. This manufacturing process consists of the following two distinct stages: (i) coiling and uncoiling of the sheets, and (ii) press-braking operations. This paper first presents an analytical solution for the residual stresses and the co-existent equivalent plastic strains that arise from the second stage while a corresponding analytical solution for the first stage is presented in the companion paper. In both solutions, plane strain pure bending is assumed and the effect of material anisotropy is taken into account. On the basis of these two analytical solutions, an analytical model is presented to predict residual stresses and equivalent plastic strains in press-braked stainless sections. The predictions of the analytical model are shown to be in close agreement with results from a finite element-based method, demonstrating the validity and accuracy of the analytical model. The analytical model provides a much simpler method for the accurate prediction of residual stresses and equivalent plastic strains in different parts of a press-braked stainless steel section than a finite element-based method.     

Cold-forming effect on stainless steel sections

Stainless steel exhibits greater extent of strain hardening than carbon steel, which leads to significant change in mechanical properties (increase in yield strength and decrease in ductility) of the stainless steel material due to the cold forming process. These changes of the mechanical properties depend mainly on the magnitude of residual stresses and equivalent plastic strain induced by the cold working. This paper presents an analytical model for determining the residual stresses and the corresponding plastic strain by means of Maple software simulating the cold forming process. The analytical model in Maple is validated by the previous numerical and experimental data of cold formed sheets. The increased material properties are determined after cold forming for corners and flat faces of sections considering the residual stresses and plastic strain and validated with the previous test results. For the prediction of the increased yield strength, new material properties with respect to the induced plastic strain based on tests are set for cold bending process in the analytical model. The analysis for the increased yield strength is calculated for four stainless steel grades, i.e., austenitic (1.4404), ferritic (1.4003), lean-duplex (1.4162) and duplex (1.4462) and the results are compared with the previous predictive models of the strength increase.     

Residual stresses in cold-rolled stainless steel hollow sections

Stainless steel exhibits a pronounced response to cold-work and heat input. As a result, the behaviour of structural stainless steel sections, as influenced by strength, ductility and residual stress presence, is sensitive to the precise means by which the sections are produced. This paper explores the presence and influence of residual stresses in cold-rolled stainless steel box sections using experimental and numerical techniques. In previous studies, residual stress magnitudes have been inferred from surface strain measurements and an assumed through-thickness stress distribution. In the present study, through-thickness residual stresses in cold-rolled stainless steel box sections have been measured directly by means of X-ray diffraction and their effect on structural behaviour has been carefully assessed through detailed non-linear numerical modelling. Geometric imperfections, flat and corner material properties and the average compressive response of stainless steel box sections were also examined experimentally and the results have been fully reported. From the X-ray diffraction measurements, it was concluded that the influence of through-thickness (bending) residual stresses in cold-rolled stainless steel box sections could be effectively represented by a rectangular stress block distribution. The developed ABAQUS numerical models included features such as non-linear material stress-strain characteristics, initial geometric imperfections, residual stresses (membrane and bending) and enhanced strength corner properties. The residual stresses, together with the corresponding plastic strains, were included in the FE models by means of the SIGINI and HARDINI Fortran subroutines. Of the two residual stress components, the bending residual stresses were found to be larger in magnitude and of greater (often positive) influence on the structural behaviour of thin-walled cold-formed stainless steel sections.     

Prediction of residual stresses and strains in cold-formed steel members

The objective of this paper is to provide an unambiguous mechanics-based prediction method for determination of initial residual stresses and effective plastic strains in cold-formed steel members. The method is founded on basic physical assumptions regarding plastic deformations and common industry practice in manufacturing. Sheet steel coiling and cross-section roll-forming are the manufacturing processes considered. The structural mechanics employed in the method are defined for each manufacturing stage and the end result is a series of closed-form algebraic equations for the prediction of residual stresses and strains. Prediction validity is evaluated with measured residual strains from existing experiments, and good agreement is shown. The primary motivation for the development of this method is to define the initial state of a cold-formed steel member for use in a subsequent nonlinear finite element analysis. The work also has impact on our present understanding of cold-work of forming effects in cold-formed steel members.     

冷成型钢截面残余应力的有限元分析

冷成型钢截面上的残余应力可能是决定其性能和强度的一个重要因素。通过破坏性的试验方法对残余应力进行测量不仅费时,精度也很有限。本文提出了一个预测压弯成形薄壁截面上残余应力的有限元方法,该方法克服了实验室测量的缺点,提供了一个有力的工具来考察不同的成形参数对残余应力的大小和分布的影响,并因此可以对这些成形参数进行优化。在该方法中,通过解析的方法考虑了成卷和开卷的影响,并将得到的残余应力作为随后的冷弯过程有限元模拟的初始应力。经比较,本文方法的数值结果和实验室实测值吻合很好,证明了该方法的可行性和精度。本文方法给出了整个截面残余应力的分布和沿壁厚的变化,并解释了两个相同截面中残余应力可能会存在很大差别的原因。     

Residual stress distributions in welded stainless steel sections

Residual stress magnitudes and distributions in structural stainless steel built-up sections have been comprehensively investigated in this study. A total of 18 test specimens were fabricated from hot-rolled stainless steel plates by means of shielded metal arc welding (SMAW). Two grades of stainless steel were considered, namely the austenitic grade EN 1.4301 and the duplex grade EN 1.4462. Using the sectioning method, the test specimens were divided into strips. The residual stresses were then computed by multiplying the strains relieved during sectioning by the measured Young׳s moduli determined from tensile and compressive coupon tests. Residual stress distributions were obtained for 10 I-sections, four square hollow sections (SHS) and four rectangular hollow sections (RHS). Peak tensile residual stresses reached around 80% and 60% of the material 0.2% proof stress for grades EN 1.4301 and EN 1.4462, respectively. Based upon the test data, simplified predictive models for residual stress distributions in stainless steel built-up I-sections and box sections were developed. Following comparisons with other available residual stress test data, the applicability of the proposed models was also extended to other stainless steel alloys. The proposed residual stress patterns are suitable for inclusion in future analytical models and numerical simulations of stainless steel built-up sections.     

Residual stress influence on material properties and column behaviour of stainless steel SHS

The paper describes the influence of forming-induced residual stresses in stainless steel SHS (Square Hollow Sections) on both the material itself and the behaviour of compressed members. The residual stress contribution to the stress–strain diagram concerning the initial modulus of elasticity and non-linearity is shown by the comparison of as-delivered and stress-relieved material. An analytical model covering the influence of residual stresses on material behaviour was developed and verified numerically. The FE study using the Abaqus software determines the influence of residual stresses in compressed members both on local and global buckling. Finally, the study on behaviour of member includes the influence of a varying degree of material non-linearity as an independent parameter representing the behaviour of various steels in long and stub columns with residual stresses.     

Residual stress analysis of structural stainless steel sections

The magnitude and distribution of residual stresses in structural carbon steel sections have been thoroughly investigated. However, few residual stress measurements have been made on structural stainless steel sections. Stainless steel has differing material stress-strain characteristics and thermal properties to carbon steel, both of which influence the formation of residual stresses. This suggests that established carbon steel residual stress models may not be appropriate for stainless steel. With increased use of stainless steel in load bearing applications, it is important to establish the residual stresses that exist within structural members. An experimental program to quantify the residual stresses in stainless steel sections from three different production routes has therefore been carried out. Comprehensive residual stress distributions have been obtained for three hot rolled angles, eight press braked angles and seven cold rolled box sections, with a total of over 800 readings taken. This paper presents the experimental techniques implemented and the residual stress distributions obtained as well as discussing the assumptions commonly made regarding through thickness residual stress variations. In the hot rolled and press braked sections, residual stresses were typically found to be below 20% of the material 0.2% proof stress, though for the cold rolled box sections, whilst membrane residual stresses were relatively low, bending residual stresses were found to be between 40% and 70% of the material 0.2% proof stress.     

Testing and modeling of shear and peel behavior for bonded steel/FRP connections

This paper presents a technique used to evaluate the shear and peel stiffness of an adhesive system that bonds fiber reinforced plastic (FRP) and steel sections. The technique combines experimental results and analytical solutions and involves the simulation of the shear and peel behavior of the adhesive through two continuous spring systems. The experiments involve shear lap testing of FRP sheets bonded to hollow steel sections. A closed form analytical solution was derived for both the in-plane and out-of-plane behavior of the tested FRP sheets. The measured in-plane load-displacement relations were incorporated into the closed form solution to evaluate the spring constant simulating the shear behavior of the adhesive. The out-of-plane behavior of the FRP sheets was identified experimentally through outer face strain and out-of-plane displacement measurements. A curve fitting approach in which the closed form analytical solution was fitted to the measured out-of-plane displacement profile was then used to evaluate the spring constant simulating the peel behavior of the adhesive. The study focused on a methacrylate adhesive system since preliminary investigation has shown it is suitable for applications involving bonding plastic and metal surfaces. The spring constants evaluated in this study can be used to perform detailed modeling of a bonded FRP/steel connection under a general state of loading.     

Strength and ductility of corner materials in cold-formed stainless steel sections

The cold work from the manufacturing process of cold-formed steel members can enhance the strength but reduce the ductility of materials. Due to a high cost of stainless steels, it is desirable to utilize this enhanced strength and avoid the early fracture in cold-formed stainless steel members. The paper is concerned with the prediction of the enhanced stress–strain behaviour and reduced ductility of corner materials in cold-formed stainless steel sections. The enhanced strength of corner materials has been traditionally determined using empirical models. However, most of these empirical models are only able to predict the enhanced 0.2% proof strength, but are neither capable of predicting the enhanced ultimate strength nor able to determine the reduced ductility. This paper first presents a modified weighted-average method for predicting the post-ultimate stress–strain behaviour and the fracture strain for stainless steels. An advanced numerical approach is next presented for predicting the full-range stress–strain behaviour of corner materials in cold-formed stainless steel sections, in which the modified weighted-average method is incorporated. The accuracy of this approach is demonstrated by comparing its predictions with test results. The proposed approach is generally applicable to cold-worked materials for predicting their enhanced strength, reduced ductility and full-range stress–strain behaviour. The proposed method and numerical results can explain why and how the ultimate strength of cold-formed steels can be increased and how the post-ultimate stress–strain behaviour can be utilized through cold working.     

不锈钢构件截面的残余应力分析

对碳钢结构截面的残余应力的大小及分布的研究已经比较成熟,但是对不锈钢截面的残余应力研究却还很少见。不锈钢与碳钢有着不同的材料应力-应变特性和热性能,它们都影响着残余应力的形成。这意味着已确定的碳钢残余应力模型可能并不适合不锈钢。随着不锈钢的应用日益增多,对其残余应力的研究显得尤为重要。     

Analysis of residual stress in stainless steel pipe weld subject to mechanical axial tension loading

This paper presents the characteristics of welding residual stresses in circumferentially butt-welded stainless steel pipe by utilizing three-dimensional (3-D) uncoupled thermo-mechanical finite element (FE) analysis method. Moreover, stress variations in welded joints of the pipe under superimposed mechanical axial tension loading are further investigated employing the welding residual stresses and plastic strains obtained from the thermo-mechanical FE analysis as an initial condition. Results show that spatial variations of the welding residual stresses are present along the circumference and a rapid change of the residual stresses exists at the welding start/stop position, hence 3-D FE analysis is essential to accurately simulate circumferential welding of a pipe component. When mechanical axial tension loading is applied to the circumferentially butt-welded stainless steel pipe, bending moment is generated at the welded joints caused by the circumferential shrinkage of the weld region during welding; thus affecting the axial and hoop stress evolutions in the course of the superimposed mechanical loading.     

冷成型双相不锈钢截面材料特性

给出了6个不同截面冷成型双相不锈钢的特性,其中2个为圆形中空截面,4个为矩形中空截面。试样为冷轧双相不锈钢带。确定方形和矩形中空截面高强度冷成型双相不锈钢的材料特性。对每种型材的薄弱和转角处进行拉伸试验,由此测量每种型材的弹性模量、0.2%弹性极限、1.0%弹性极限、抗张强度、断裂延伸率和Ramberg-Osgood参数(n)。通过短柱试验获得冷轧状态全截面的材料特性。测量6种型材的初始局部几何缺陷,绘制每种型材含初始几何缺陷的横截面图。采用断面法测量150×50×2.5截面的残余应力,测量并绘制截面上薄膜屈曲残余应力分布图。此外,给出适用于短柱的有限元模型,并与试验结果进行对比。将不锈钢短柱的试验强度与美国规范、澳大利亚/新西兰规范和欧洲规范的设计强度进行对比。总体看来,三种规范的计算结果都较为保守,其中欧洲规范的计算结果最为保守。     

Proposed residual stress model for roller bent steel wide flange sections

The manufacturing process of structural wide flange steel sections introduces residual stresses in the material. These stresses due to hot-rolling or welding influence the inelastic buckling response of structural steel members and need to be taken into account in the design. Based on experimental data standardized residual stress models have been proposed for inclusion in inelastic buckling analyses. By incorporating these residual stress models their effect on the resistance of beams and columns can be obtained. Residual stress models for roller bent steel sections are currently not available. Roller bent wide flange sections are manufactured by curving straight members at ambient temperature. This manufacturing technique, which is also known as roller bending, stresses the material beyond its yield stress, thereby overriding the initial residual stresses prior to bending and generating an entirely new pattern. This paper proposes a residual stress model for roller bent wide flange sections, based on earlier conducted numerical investigations which were validated by experimental research performed at Eindhoven University of Technology. The proposed residual stress model can serve as an initial state of a roller bent steel section in fully non-linear finite element analyses to accurately predict its influence on the inelastic buckling response.     

Numerical Modelling of Thin-Walled Stainless Steel Structural Elements in Case of Fire

In this paper, the structural response of stainless steel thin-walled elements submitted to fire is analysed numerically by means of the geometrically and materially non-linear Finite Element program SAFIR, including imperfections. In order to make these simulations, two main changes in the program were made: (i) the code was changed in order to deal with the stainless steel 2D material constitutive law to be used with shell elements and (ii) the possibility of the program to take into account residual stresses with shell finite elements was introduced. The stainless steel stress–strain relationship at high temperatures was based on the one presented in part 1.2 of Eurocode 3. To model the strain hardening exhibited by the stainless steels, using the shell element formulation, an approximation to the Eurocode 3 constitutive law was needed. Local and global geometrical imperfections were considered in the simulations. The paper shows the influence of the residual stresses on the ultimate load-carrying capacity of thin-walled stainless steel structural elements in case of fire.     

Structural performance of cold-formed high strength stainless steel columns

This paper describes an accurate finite element model for the structural performance of cold-formed high strength stainless steel columns. The finite element analysis was conducted on duplex stainless steel columns having square and rectangular hollow sections. The columns were compressed between fixed ends at different column lengths. The effects of initial local and overall geometric imperfections have been taken into consideration in the finite element model. The material nonlinearity of the flat and corner portions of the high strength stainless steel sections were carefully incorporated in the model. The column strengths and failure modes as well as the load-shortening curves of the columns were obtained using the finite element model. Furthermore, the effect of residual stresses in the columns was studied. The nonlinear finite element model was verified against experimental results. An extensive parametric study was carried out using the verified finite element model to study the effects of cross-section geometries on the strength and behaviour of cold-formed high strength stainless steel columns. The column strengths predicted from the parametric study were compared with the design strengths calculated using the American Specification, Australian/New Zealand Standard and European Code for cold-formed stainless steel structures. The results of the parametric study showed that the design rules specified in the American, Australian/New Zealand and European specifications are generally conservative for cold-formed high strength stainless steel square and rectangular hollow section columns, but unconservative for some of the short columns.     

不锈钢焊接工字形截面残余应力分布试验研究

通过焊接加工10个不锈钢工字形截面试件（选材包括奥氏体型S30408和双相型S22253两种），采用分割法将试件截面切分成条带，量测释放的残余应变，计算得出截面的残余应力大小与分布形态。结果表明：试件截面的残余拉应力峰值低于材料的名义屈服强度，对于奥氏体型S30408和双相型S22253两种不锈钢试件的截面残余拉应力峰值分别约为其名义屈服强度的80%和60%。基于试验结果对现有简化分布模型的评估表明其应用的局限性，提出可以较准确描述不锈钢焊接工字形截面残余应力分布的建议简化模型，结合现有的其他试验数据，对建议简化分布模型的适用范围进行了验证和推广，可以为不锈钢结构构件的稳定性研究和设计提供参考。     

Experimental and numerical investigation of high strength stainless steel structures

The paper summarises research on high strength stainless steel tubular structures conducted at the University of Hong Kong, and the Hong Kong University of Science and Technology. Square and rectangular hollow sections were investigated. The test specimens were cold-rolled from high strength austenitic and duplex stainless steel sheets. The material properties of the test specimens were determined by tensile coupon tests at normal room and elevated temperatures. The initial geometric imperfection and residual stress of the specimens were measured. The experimental and numerical investigation focused on the design and behaviour of cold-formed high strength stainless steel structural members. The results were compared with design strengths calculated using the American, Australian/New Zealand and European specifications for cold-formed stainless steel structures.     

Recommendations on imperfections in the design of plated structural elements of bridges

High-yield strength steel-plated structures represent competitive solutions when used in steel and steel–concrete composite bridges. Nevertheless, further modifications may still be introduced at the design stage in the case of slender sections, in order to minimize the number of their stiffeners and thereby economize on manufacturing costs. Eurocode 3 “Design of steel structures” specifies design methodologies for slender plates subjected to compression and for stiffeners. Moreover, the use of Finite Element Method (FEM) software is fast becoming an alternative analytical method for the design of complete structures or structural elements, as it offers a more realistic approach. This paper makes recommendations for FEM assessments of plated sections in bridges that take the initial imperfections, geometric imperfections and residual stresses of the sections into account, in order to arrive at realistic results.     

A numerical investigation of local–overall interaction buckling of stainless steel lipped channel columns

A detailed finite element (FE) model is presented, which was developed with the aim of studying the interaction of local and overall buckling in stainless steel columns. The model incorporates non-linear stress–strain behaviour, anisotropy, enhanced corner properties and initial imperfections. The model was verified against a program of 29 laboratory tests on stainless steel lipped channels, described in a companion paper [Becque J, Rasmussen KJR. Experimental investigation of the interaction of local and overall buckling of stainless steel lipped channel columns. Journal of Constructional Steel Research 2009; 65(8–9): 1677–84] and yielded excellent predictions of ultimate strength and specimen behaviour.The FE model was further used in parametric studies, varying both the cross-sectional slenderness and the overall slenderness. Three stainless steel alloys were considered: AISI304, AISI430 and 3Cr12. The results are compared with the governing design rules of the Australian, North American and European standards for stainless steel structures.