Effect of roller leveling on the bending behaviour of aged steel strip

The common grades of steel used in roll forming are: hot rolled carbon steel, high strength low alloy and recovery annealed cold rolled sheet. These steels are prone to ageing and are often skin passed and/or roller leveled to eliminate ageing as it can lead to problems in forming. In roll forming, shape defects such as bow, twist and camber are considered to be related to very small plastic strains in the longitudinal direction and hence knowledge of the material properties in the elastic plastic transition range is necessary if the process is to be modelled accurately. Previous studies with aluminium have indicated that skin pass rolling can lead to residual stresses in the strip. In this work, the study was extended to aged carbon steel and to the effect of roller leveling on both aged material and strip that had been given a light cold rolling to simulate a skin pass treatment. The results suggest that roller leveling reduced the magnitude of residual stresses resulting from skin pass rolling.

The significant differences observed between tensile and bending test results, at and near, the elastic plastic transition reinforces the need to consider bending properties when assessing the effect of prior processing on strip for roll forming.

Effect of tensile pre-strain on bending and unloading of automotive steels

In recent years, advanced high strength steels (AHSS) have been used in a wide range of automotive applications; they may have property variations through the thickness and the properties may also be dependent of prior processing including pre-straining. In order to model forming processes precisely using, for example, finite element analysis, it is important that material input data should adequately reflect these effects. It is known that shape defects in roll forming are related to small strains in material that has undergone prior deformation in a different strain path. Much research has already been performed on the change in the Young’s Modulus once a steel sheet has been plastically deformed,however many of these tests have only been conducted using tensile testing, and therefore may not take into account differences in compressive and tensile unloading. This research investigates the effect of tensile pre-straining on bending behaviour for various types of material;in bending, one half of the sheet will load and unload in compression and hence experience deformation under a reversed stress. Four different materials were pre-strained in tension with 1%, 3%, 7%, 11% and 25% elongation. Using a free bending test, moment curvature diagrams were obtained for bending and unloading. The results showed that the characteristics of the moment curvature diagram depended on the degree of pre-straining; more highly strained samples showed an earlier elastic-plastic transformation and a decreased Young's Modulus during unloading. This was compared to previous literature results using only tensile tests. Our results could influence the modeling of springback in low tension sheet operations, such as roll forming.

Asymmetric rolling of interstitial-free steel using differential roll diameters. Part I : mechanical properties and deformation textures

IF steel sheets were processed by conventional symmetric and asymmetric rolling (ASR) at ambient temperature. The asymmetry was introduced in a geometric way using differential roll diameters with a number of different ratios. The material strength was measured by tensile testing and the microstructure was analyzed by optical and transmission electron microscopy as well as electron backscatter diffraction (EBSD) analysis. Texture was also successfully measured by EBSD using large surface areas. Finite element (FE) simulations were carried out for multiple passes to obtain the strain distribution after rolling. From the FE results, the velocity gradient along selected flow lines was extracted and the evolution of the texture was simulated using polycrystal plasticity modeling. The best mechanical properties were obtained after ASR using a roll diameter ratio of 2. The textures appeared to be tilted up to 12 deg around the transverse direction, which were simulated with the FE-combined polycrystal plasticity modeling in good agreement with measurements. The simulation work revealed that the shear component introduced by ASR was about the same magnitude as the normal component of the rolling strain tensor.

Asymmetric Nash bargaining solutions: a simple Nash program

This article proposes a simple Nash program. Both our axiomatic characterization and our noncooperative procedure consider each distinct asymmetric and symmetric Nash solution. Our noncooperative procedure is a generalization of the simplest known sequential Nash demand game analyzed by Rubinstein etal. (1992). We then provide the simplest known axiomatic characterization of the class of asymmetric Nash solutions, in which we use only Nash's crucial Independence of Irrelevant Alternatives axiom and an asymmetric modification of the well-known Midpoint Domination axiom.

Development of an inverse routine to predict residual stresses in the material based on a bending test

Bending and reverse bending are the dominant material deformations in roll forming, and hence property data derived from bend tests could be more relevant than tensile test data for numerical simulation of a roll forming process. Recent investigations have shown that residual stresses change the material behavior close to the yield in a bending test. So, residual stresses introduced during prior steel processing operations may affect the roll forming process, and therefore they need to be included in roll forming simulations to achieve improved model accuracy. Measuring the residual stress profile experimentally is time consuming and has limited accuracy while analytical models that are available require detailed information about the pre-processing conditions that is generally not available for roll forming materials. The main goal of this study is to develop an inverse routine that determines a residual stress profile through the material thickness based on experimental pure bend test data. A numerical model of the skin passing (temper rolling) process is performed to introduce a residual stress profile in DP780 steel sheet. The skin passed strips are used in a pure bending simulation to record moment-curvature data and this data is then applied in an inverse analysis to predict the residual stress profile in the material. Comparison of the residual stress profile predicted by the inverse routine with that calculated by finite element analysis (FEA) indicates an inverse approach combined with pure bend test may present an alternative to predict residual stresses in sheet metals.

Bending behaviour of step-wise graded carbon nanofiber/polymer nanocomposites

In this study, a finite element-based model was developed to investigate the mechanical behavior of step-wise graded carbon nanofibre/phenolic nanocomposites. Four step-wise graded nanocomposites (FGNs), a non-graded nanocomposite (NGN), and a pure phenolic with the same geometry and total carbon nanofiber content were designed, fabricated and analyzed. Flexural tests were conducted to validate the finite element model. Close agreement was obtained between experimental results and numerical predictions. The results showed that flexural modulus was highly influenced by the compositional gradients.

Asymmetric rolling of interstitial-free steel using differential roll diameters. Part II : microstructure and annealing effects

The effects of annealing on the microstructure, texture, tensile properties, and R value evolution of an IF steel sheet after room-temperature symmetric and asymmetric rolling were examined. Simulations were carried out to obtain R values from the experimental textures using the viscoplastic self-consistent polycrystal plasticity model. The investigation revealed the variations in the textures due to annealing and symmetric/asymmetric rolling and showed that the R values correlate strongly with the evolution of the texture. An optimum heat treatment for the balance of strength, ductility, and deep drawability was found to be at 873 K (600 _C) for 30 minutes.

State dependent asymmetric loss and the consensus forecast of real U.S. GDP growth

It has been well documented that the consensus forecast from surveys of professional forecasters shows a bias that varies over time. In this paper, we examine whether this bias may be due to forecasters having an asymmetric loss function. In contrast to previous research, we account for the time variation in the bias by making the loss function depend on the state of the economy. The asymmetry parameter in the loss function is specified to depend on set state variables which may cause forecaster to intentionally bias their forecasts. We consider both the Lin–Ex and asymmetric power loss functions. For the commonly used Lin–Ex and Lin–Lin loss functions, we show the model can be easily estimated by least squares. We apply our methodology to the consensus forecast of real U.S. GDP growth from the Survey of Professional Forecasters. We find that forecast uncertainty has an asymmetric effect on the asymmetry parameter in the loss function dependent upon whether the economy is in expansion or contraction. When the economy is in expansion, forecaster uncertainty is related to an overprediction in the median forecast of real GDP growth. In contrast, when the economy is in contraction, forecaster uncertainty is related to an underprediction in the median forecast of real GDP growth. Our results are robust to the particular loss function that is employed in the analysis.