Longitudinal strain development in Chain-die forming AHSS products: Analytical modelling, finite element analysis and experimental verification

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Abstract

Chain-die forming is a new sheet metal forming technology which has been developed as a supplement to roll forming in fabricating Advanced High-Strength Steel (AHSS) products. It has an advantage by reducing redundant plastic deformation during the forming process. The implementation is achieved through increasing the deformation length, via increasing the virtual roll radii. The rolls with large radii are assemblies of shaped die-blocks through chains and therefore it is called “Chain-die Forming”. In this paper, a simplified analytical model, purely based on the geometric relationships of forming parameters is established to estimate the longitudinal strain development in Chain-die forming. The analytical model is verified successfully by finite element analysis (FEA) and experimental work. The factors affecting the peak longitudinal strain are also investigated. The study is expected to be useful to tooling designers to quickly assess the severity of a Chain-die forming process in the tooling design stage in order to shorten the tooling development time.

Introduction

Advanced High-Strength Steel (AHSS), especially the dual phase steel, is more and more readily being employed by automakers for structural parts of a motor vehicle due to its advantages for weight reduction and safety improvement. AHSS has the required high strength but the elongation is not generous enough. These characteristics bring more challenges in fabricating AHSS products. A comprehensive review of AHSS research is provided by Rizzo et al. (2010).

Roll forming is a widely accepted fabrication method for massive production of sheet metal products. As introduced by Paralikas et al. (2009), it can be understood as a continuous bending operation which the metal strips are gradually formed through consecutive sets of rolls into various profiles. A schematic diagram of a typical roll forming process was presented by Hobbs and Duncan (1979), as shown in Fig. 1. Suzuki et al. (1972) proposed a tri-axial surface deformation model to describe the roll forming process. The deformation model includes longitudinal stretching and bending and other undesirable redundant strain components. The advantages of roll forming, such as high efficiency and low cost, make it suitable for the manufacturing of automotive structural and crash components. Nevertheless, as the elongation of AHSS reduces with the increase of the material strength, a fracture often occurs during the process, as summarized by Rizzo et al. (2010). Moreover, as the magnitude of springback correlates with the elastic modulus and the hardening behavior of a material, the severity of springback of AHSS is even more significant than that of mild steel. Davis and Semiatin (1988) concluded that due to unpredictable redundant deformation in the roll forming process, occasionally some typical product defects occur, such as bowing, twisting, corner buckling and so on. These issues greatly limit the applications of roll formed AHSS products.

Chain-die forming, as a novel sheet metal forming method, is therefore proposed by Ding et al. (2008) to break the bottleneck of fabricating AHSS products. It has potential to be a more economical and energy-saving method compared to conventional roll forming, due to its technical characteristics of both bending and stamping. As Ding et al. (2008) and Zhang (2014) introduced, the principle of Chain-die forming is to prolong effective forming distance by extending the virtual roll radii. To be more specific, a Chain-die former is structured as follows: it has a pair of track boards which have very large radii (R>30m) with specially designed chain joints moving on it, and also forming dies are assembled on the chains, as shown in Fig. 2(a). The virtual rolls are implemented by a series of discrete forming dies running on the track boards. In practical operation, the metal strip is fed into the forming space at the entrance. The friction between the forming tools and workpiece will drive the workpiece to move forward. The gap between the opposite die blocks is gradually reduced with the synchronous motions of the forming dies. Consequently, the workpiece in the deformation space is gradually formed to the designed profile through a much longer deformation length than in roll forming, as shown in Fig. 2(b). It should be pointed out that in roll forming, the deformation area includes the contact and non-contact zones, and the length of the contact zone is generally very limited, as shown in Fig. 2(c). Increasing the roll radii can increase the deformation area, via increasing the contact zone and decreasing the non-contact zone. As Chain-die forming employs very large radii virtual rolls, the deformation area is nearly equal to the contact zone. Hence, in contrast with roll forming, the workpiece is always contacted and fully restricted by the forming dies. As a consequence, there is a significant increase of the forming length in a Chain-die forming process. The increase of deformation length shown as in Fig. 2(c) results in the reduction of the peak longitudinal strain and the residual longitudinal strain. That is, the large roll radii can significantly reduce or even eliminate the redundant plastic deformation occuring in roll forming. The typical defects of roll formed products can therefore theoretically be avoided, thus improving the quality of products.

(Note:R are the radii of the top and bottom rolls of Chain-die forming and R is the radius of a roll of conventional roll forming.)

Zhang and Ding, 2012a, Zhang and Ding, 2012b performed a series of experiments of Chain-die forming U-profile AHSS channels with pre-made holes. They proved that the technology has the advantage of conserving the material’s ductility. It means that Chain-die forming can be used to fabricate AHSS products, even though some of them have poor ductility, as there is almost no redundant plastic deformation in the non-deformed areas. Similar conclusions are also made by Ding et al. (2008) and Zhang and Ding (2013).

Farzin et al. (2002) pointed out that the longitudinal strain is caused by the stretched longitudinal fibers in a flange in a metal forming process. When the peak longitudinal strain is larger than the elastic limit of strain of the material to be formed, plastic deformation occurs and if the stresses/strains are unbalanced after unloading, then product defects are induced. The longitudinal strain development in a forming process is one of the most crucial indicators that can be used to estimate the severity of a fabrication process. Thus, it is always emphasized in relevant studies. For example, Bui and Ponthot (2008) evaluated the influences of the yield limit and the work-hardening of material on the longitudinal strain development in roll forming a U-profile channel. Paralikas et al. (2009) employed finite element analysis (FEA) to investigate how the main forming parameters, including rolls diameter, rolls gap, etc., affect the longitudinal strain development in roll forming a V-section AHSS sample.

Liu et al. (2015) mentioned that analytical modelling of a roll forming process is an important approach to judge the severity of a roll forming process. It does not involve capital expenditure, and its applications are much wider compared with experimental work and numerical analysis. By using a minimum energy method, Bhattacharyya et al. (1984) derived an expression for the deformation length in a roll forming process. This proved for the first time the existence of deformation length and its independence to span space. By consideration of minimizing plastic work, Chiang (1984) established an expression for estimating the peak longitudinal strain. Nevertheless, the further application of their works is limited by the undefined parameters in the equations. Taking the material property of the workpiece into account, Zhu (1993) presented an analytical model for estimating the deformation length by assuming a rigid-perfectly plastic material behavior of the workpiece. Panton et al. (1994) analyzed the geometric restrictions imposed only by the bottom roll. They also derived an analytical expression which can be used to predict the strain development for the fundamental deformation types. A shape function was introduced by Kiuchi et al. (1995) to describe the deformed surface which determines the pattern of the spatial locus, or the flow line, in roll forming tube sections. The main drawback of the approach proposed is that the method assumed the deformed surface follows specific functions in each direction. Lindgren (2007) established a modification of Bhattacharyya’s deformation length model using experimental and numerical methodologies. In order to analyze the bend angle distribution and longitudinal strain development in a roll forming process, Liu et al. (2015) developed a new analytical expression on the basis of the geometric contact boundary conditions of the forming dies and the metal strip. Their research indicates that the longitudinal strain development is related to the geometric parameters of the forming tools and the transverse section of the workpiece. Abeyrathna et al. (2016) employed an analytical method to describe the axial extension and curvature in the flange. Their analytical models are solely geometric while being adequate to optimize any flower pattern and to enable the evolution of a flower pattern rapidly and simply. They proved that the longitudinal edge strain is greatly influenced by the forming angle, the flange length and the inter-station distance. They also determined that the flower pattern giving the shortest distance in the plane development will lead to the lowest value of the longitudinal edge strain in the flange. Some classic analytical models for predicting the longitudinal strain in roll forming process have been summarized in Table 1. From the summarized analytical models, it is concluded that most of the expressions of the longitudinal strain development are established purely on the basis of the geometric contact relationships between forming tools and deformable strip.

As a U-profile channel is a special product that enables maximum internal residual stress release after fabrication, it is therefore recognized as an extremely difficult profile to form without extra correction operations. This study firstly proposes a simplified geometric analytical model for determining the longitudinal strain developments in Chain-die forming U-profile AHSS channels. Similar to the previous analytical modelling approaches (see examples Bhattacharyya et al. (1984), Chiang (1984) and Panton et al. (1994)), the model is purely based on the geometric boundary conditions of the workpiece and the forming tools. FEA and experimental work are then employed to examine the validity of the analytical expression. Furthermore, the influential parameters which affect the peak longitudinal strain are analyzed and discussed. Finally, some critical conclusions for future tooling development are summarized.

Section snippets

Simplified analytical model of the geometric contact conditions

The relationships between the geometric parameters and process parameters are analyzed firslty in this section. Subsequently, the analytical models for determining the longitudinal membrane strain and overall longitudinal strain are then presented.

Experimental verification

The experiments facilities are introduced firstly and followed by the demonstration of the details of the experimental samples used. The procedures of the experimental work are then addressed in this section.

Simulation verification

The procedures of FEA modelling are firstly clarified. Subsequently, the material properties of the workpiece adopted are illustrated. The contact and friction properties between the forming tools and workpiece are then introduced. Finally, the simulation sequences are presented in this section.

Results and discussions

The results comparisons of the longitudinal strain development of Chain-die forming U-channels are firstly presented. The details of the longitudinal membrane strain development are then addressed followed by the discussions of the overall longitudinal strain development.

Influential parameters affecting the longitudinal strain development

One of the possible tasks in Chain-die forming is to control or even eliminate the redundant plastic deformation which directly relates to the product quality. It is therefore important to understand how these parameters affect the longitudinal strain development. According to Eq. (12), there are four independent parameters which directly affect the longitudinal strain development: flange height, thickness, bend corner radius of bottom die and virtual roll radii. Trial parameters values are

Conclusions and future work

In order to shorten the tooling development time of Chain-die forming, a new simplified analytical model is established purely on the basis of the geometric boundary conditions of the workpiece and the forming tools. It is employed to predict and analyze the longitudinal strain developments in Chain-die forming U-profile AHSS channels. The analytical model is verified successfully by FEA and experimental work. The effects of flange height, thickness, corner radius of the bottom die and virtual

Acknowledgements

The authors would like to thank for the financial support from the Baosteel-Australia Joint Research and Development Centre (BAJC), Ningbo SaiRolf Metal Forming Co., Ltd. and China Scholarship Council. The advices of Professor Han Huang and Dr Sheng Liu and the assistances of Mr Chenhao Wang, Mr Haibo Lu, Mr Zhen Qian and other colleagues are gratefully acknowledged. Finally, the authors would like to give special thanks to Baosteel Co., Ltd. for providing the material properties of the

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