Surface roughening and formability in sheet metal forming of polycrystalline metal based on r-value of grains

• Based on r-value of grains, a model of plastic deformation of polycrystalline metal and surface roughening after plastic deformation is proposed.
• The formability of sheet metal under biaxial stretching is analyzed based on a model of surface roughening caused by the difference of r-values in the sheet metal.
• The present model does not need the artificial initial groove which is essential in Marciniak and Kuczynski’s model.

The r-value is defined as the ratio of the width strain to the thickness strain. It was pointed out that the r-value can be defined for each grain in polycrystalline metal during plastic deformation. Based on r-value of grains, a model of plastic deformation of polycrystalline metal and surface roughening after plastic deformation is proposed in the present paper. Various experimental features of the surface roughening under uniaxial stress are well explained with the present first model.Meanwhile, the r-value is also known as a measure of formability in the sheet metal forming process. Marciniak and Kuczynski proposed the so-called M–K model which gives the analytical estimation of the formability of sheet metal under biaxial stretching considering a certain irregularity of the thickness of the sheet metal. Yamaguchi et al. showed that the experimentally measured surface roughness may correspond to the surface irregularity suggested in the M–K model. In the present paper, the formability of sheet metal under biaxial stretching is analyzed based on the surface roughening model caused by the difference of the r-value in sheet metals.

(1) Plastic deformation and surface roughening of polycrystalline metal based on r-values of grains. Model I of plastic deformation of polycrystalline metal having different r-values for respective grains and surface roughening after deformation (uniaxial stress is applied in 1-direction ). (2) Formability of polycrystalline sheet metal based on r-value of grains model II of biaxially stretched thin sheet metal with regions having different r-value.Figure optionsDownload as PowerPoint slide