Study of the development of plastic instabilities during tests on metallic plates biaxially loaded in their plane, in tension or in compression

Plastic instabilities develop during tension and compression tests on metallic plates biaxially loaded in their plane. They limit the acceptable deformation levels during sheet forming. Carrying out a Linear Stability Analysis, we study the onset of their development. We calculate the growth rate of small symmetrical and antisymmetrical defects with respect to the median plane of the plate, periodic along the loading directions, and we determine the dominant mode. This 3D model applies to dynamic tests whatever the thickness. It retrieves classical results for thin plates statically loaded in tension. Plane tension and compression tests are two particular 2D cases of this model. In plane strain tension on ductile non viscous materials, we retrieve that the first instabilities, which are also long wavelength necking ones, arise very little time before the applied force is maximum; this is consistent with the experimental observations of Considère. As time goes by, antisymmetric modes with shorter wavelengths compete with the symmetric ones