The effect of die radius on thickness distribution of SS304 stainless steel sheet in deep drawing of cylindrical cup

Thickness distribution of deep drawing products has been studied in recent decades since it has a significant influence on the product quality. In this paper a numerical simulation with experimental verification was conducted to examine the influence of die radius on the thickness distribution of cilindrical cup in deep drawing for SS304 stainless steel. Thickness distribution of the cup was analyzed through the stress-strain state during deep drawing by Deform 3D software. The obtained results allow choosing a reasonable die radius to achieve more uniform wall thickness of the cup, that optimizes tool design and reduces manufacturing costs.

Experimental Modeling of Pressure in the Hydrostatic Formation of a Cylindrical Cup with Different Materials

Forming complex sheet products using hydrostatic forming technology is currently a focus of the majority of forming processes. However, in order to increase stability during the forming process, it is necessary to identify and analyze the dependency of the forming pressure and the quality of a product on input parameters. For the purpose of modeling the forming pressure, this paper presents empirical research on the product of a cylindrical cup made of various materials, including carbon steel (DC04), copper (CDA260), and stainless steel (SUS 304) with different thicknesses (0.8 mm, 1.0 mm, and 1.2 mm), under a defined range of binder pressures. The regression method is selected to formulate an equation that shows the relationship between the input parameters, including the materials (ultimate strength and yield stress), workpiece thickness, binder pressure and the output parameter, and the formation of fluid pressure. The mathematical equation allows us to determine the extent of the effect of each input on the forming pressure. The experimental results can be used for the easier planning and forecasting of the process and product quality in hydrostatic forming.

Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations

In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.

Construction of Aluminum Alloy Constitutive Model Based on BP Neural Network and the Study of Non-isothermal Hydroforming

With the continuous development of high-end technology in aerospace and automotive, in order to meet the needs of high performance, high precision and lightweight of parts, the materials used are lightweight and strong, but very difficult to deform, so it is difficult to obtain high-quality, high-precision parts. In order to improve the forming quality and precision of parts, taking 6061-T6 aluminum alloy cylindrical cup with spherical bottom as the research object, the non-isothermal hydroforming process is studied by combining numerical simulation with experiment. The key of numerical simulation technology lies in the accuracy of simulation, which depends on the establishment of a suitable rheological stress relationship. So, a constitutive model that can truly reflect the thermoforming characteristics of 6061-T6 aluminum alloy materials is established through a uniaxial tensile test and BP neural network. Applying the constitutive model to the study of numerical simulation of non-isothermal hydroforming, the cylindrical cup with spherical bottom with high quality is obtained through the optimization of non-isothermal process parameters. After experimental verification, the results of numerical simulation are highly compatible with the actual forming results of parts, and have high reliability.

Effect of Single Crystal Orientation on Forming

Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is the intrinsic anisotropy of the constituent crystals. In this paper, we present the single-crystal yield criterion recently developed by Cazacu et al. [1] and its application to the prediction of anisotropy in uniaxial tension of strongly textured polycrystalline sheets. Namely, it is shown that using this single crystal yield criterion the Lankford coefficients exist and have finite values for all loading orientations. Moreover, the variation of both the yield stress and Lankford coefficients with the crystallographic direction can be expressed analytically. An application of this criterion to forming a cylindrical cup from a single crystal of (100) orientation is presented. Finally, we show that using this single-crystal model, one can describe well the effect of the spread around an ideal texture component on the anisotropy in uniaxial tensile properties of a polycrystal.

On the thinning variations in hydrostatic forming of sheet metal

In sheet metal forming, thinning phenomenon is one of the most concerned topics to ameliorate the final quality of the manufactured parts. The thinning variations depend on many input parameters, such as technological parameters, geometric shape of die, workpiece’s materials, and forming methods. Hydrostatic forming technology is particularly suitable for forming thin-shell products with complex shapes. However, due to the forming characteristics, the thinning variations in this technology are much more intense than in other forming methods. Therefore, in this paper, an empirical study is developed to determine the thinning variations in hydrostatic forming for cylindrical cup. Measurement of thickness at various locations of deformed products are conducted to investigate the thickness distribution and determine the dependence of the largest thinning ratio on the input parameters (including the blank holder pressure, the relative depth of the die and the relative thickness of the workpiece). The results are expressed in charts and equation which allow determining the effect of each input parameter on the largest thinning ratio.

A simple and computationally efficient stress integration scheme based on numerical approximation of the yield function gradients: Application to advanced yield criteri

In this paper, we have modi?ed the stress integration scheme proposed by Choi and Yoon (2019), which is based on the numerical approximation of the yield function gradients, to implement in the ?nite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p (Barlat et al., 2005), CPB06ex2 (Plunkett et al., 2008) and Yld2011-27p (Aretz and Barlat, 2013) criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon (2019), and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the ?finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations.