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Formability is an important property requirement in sheet metal forming and mostly useful to automobile and aerospace industries. Every product design starts with finite element simulation before the die design and material selection stage. The forming limit curve along with finite element results acts as tool to investigate whether the design is feasible. Hence, it is of utmost importance that the forming limit curve is accurate over a wide range of strain path. Generally, a forming limit curve is derived from discrete failure strain points corresponding to different strain ratios by fitting a smooth curve. It has been observed from many studies that the generated forming limit curves are devoid of any failure points corresponding to equibiaxial strain path. This is found to be true even when the test conditions are supposed to produce biaxial state of strain. To understand the reason behind this observation, a set of forming limit diagram experiments and finite element analyses were carried out for high-strength interstitial free steel and interstitial free galvannealed steel with three different friction conditions. It was observed that friction plays an important role in right-hand side of the forming limit curve. Finite element results and experimental validation suggest that failure strain points for biaxial strain paths can be obtained only if the tests are conducted with proper lubrication system.

In this paper, a multiple surface sliding controller is designed for an anti-lock braking system to maintain the slip ratio at a desired level. Various types of uncertainties coming from unknown road surface conditions, the variations in normal force and the mass of the vehicle are estimated using an uncertainty estimation technique called the inertial delay control and then the estimate is used in the design of the multiple surface sliding controller. The proposed scheme does not require the bounds of uncertainties. The ultimate boundedness of the overall system is proved. The proposed scheme is validated by simulation under various scenarios of road friction, road gradient and vehicle loading followed by experimentation on a laboratory anti-lock braking set-up for different friction conditions.

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With decreasing grain size, the strength of steel increases due to the well-known Hall–Petch type effects, which is generally neglected in the classical crystal plasticity-based models. In the present work, the classical crystal plasticity-based model has been modified to incorporate the grain size effect. Validation of the present model was carried out with the published experimental results of a dual phase steel and, it was found to be possible to predict the grain size effects quite accurately using the model. The proposed model was used to carry out a parametric study for effects of grain size and was further used to predict the influence of grain size on cross effects during orthogonal loading.

The purpose of this study is to develop a phenomenological model for prediction of the entire forming limit diagram from simple tensile material properties. The phenomenological model is based on the necking and ductile damage theories. In the proposed model, void nucleation is described as a function of the equivalent plastic strain, and void growth is a function of the stress triaxiality. The forming limit curves calculated from the proposed phenomenological model matched reasonably well in the region of uniaxial tension to balance biaxial tension with the experimental forming limit curves generated on C-Mn 440 steel, interstitial-free 340 steel, and interstitial-free steel sheets.

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