The Deep Drawing of a Flanged Square Hole in Thin Stainless Steel Sheet

To manufacture metal products of accurate size and shape by deep drawing requires the precise control of a number of variables. The problem of spring-back after the load has to be avoided, and the prevention of cracks in the product requires careful control of the punch load. In this study, where drawing experiments and simulations were carried out on thin sheets of SUS304 stainless steel, the influence of the scale effect on the thin sheets also needed consideration. This was accomplished by the use of an updated Lagrangian formulation and finite element analysis. Material behavior was simulated using a micro-elastoplastic material model, the performance of which was compared with that of models involving conventional materials. The Dynaform LS-DYNA solver was used for simulation analysis, and pre and postprocessing were carried out to obtain material deformation history as well as to determine thickness change, distribution and material stress, and prepare strain distribution maps. Scaling was necessary to account for the effect of the thickness of the sheet and the relationship between punch load and stroke, the distribution of thickness, stress and strain, and the maximum size (d) of the flanged hole and the maximum height of the flange. The simulation results were compared with experimental results to confirm the accuracy of the three-dimensional finite element analysis of the elastoplastic deformation. The results showed that the size of the fillet radius of the hole (Br) had an effect on the punch load, which increased with an increase in Br. However, the minimum thickness of the formed flange decreased with an increase in Br. The maximum principal stress/strain and height of the flange also increased with an increase in Br. The punch fillet radius (Rp) also had an impact on the process. The punch load decreased with the increase in Rp, while the minimum thickness increased slightly. The average values of the minimum thickness for three models were 0.148, 0.0775, and 0.0374 mm. The forming ratio also had an influence on the process. When the forming limit of the square hole flange was FLR = 0.84, cracking occurred in the corners of the flange, and wrinkles formed over the undrawn area of the sheet. These findings can serve as a valuable reference for the design of deep drawing processes.

A method for calculating the radiation power coefficients of black and gray bodies with dimensions commensurable with the radiated wavelengths

A technique is proposed and the calculations of the dependences of the emissivity of an abso-lute black body (BBB) on the size of the diaphragms of the emitting aperture are performed for hypothetical cases when the sizes of the diaphragms are commensurate with the emitted wavelengths, and the diaphragms are made of a dielectric opaque for radiation. The value of the cutoff wavelength  = 1.772A for the square aperture of the diaphragm was determined, where A is the side of the square and  = 1. 571D for the round hole. where D is the hole di-ameter, i.e. it is shown that the body cannot emit wavelengths λ greater than 1.772A in the case of a square hole and 1.571D in the case of a round hole. It is shown that if the “cut off” wavelengths made any significant contribution to the integral radiation of a blackbody with temperature T at standard diaphragm diameters (i.e., at diameters of much larger radiated wavelengths), then the emissivity of this body becomes less than unity and rapidly decreases when the size of the diaphragms is commensurate with . In these cases, such a body ceases to be an absolutely black body and the laws of Planck and Stefan–Boltzmann cannot be used to calculate the power of its radiation, but the technique proposed in this work can be used.