Stress-strain state of thin-walled pipe blanks during crimping in a curved axisymmetric matrix

The study proposes a computational and analytical model of finding the stress-strain state and force characteristics when crimping thin-walled pipe blanks in a curved axisymmetric matrix. The mathematical model is based on the equilibrium equation of the momentless theory of thin axisymmetric shells taking into account the nonlinear law of plasticity, changes in the wall thickness of the workpiece and contact friction. As a mathematical model of the material, a linear-power approximation of the deformation diagram of an elastic-plastic body is considered taking into account the compressibility of the material. The methodology for estimating the stress-strain state of the workpiece during crimping is constructed using a generalized formulation for an arbitrary curve forming the working contour of the matrix. The basis of the numerical calculation method was the method of variable elasticity parameters, which makes it possible to determine stresses and strains, the thickness distribution in the meridional section, the amount of contact pressure, and also to plot the change in the crimping force depending on the displacement of the point of application of the force relative to the matrix. The distribution of stresses and strains of a thin-walled billet made of aviation aluminum alloy during crimping is calculated using the example of a matrix, the working contour of which is described by a sinusoidal trigonometric function. During crimping, according to the results of the proposed numerical technique, a thickening of the blank wall is noted, as well as an increase in the deforming force when moving the point of application of the force. The proposed mathematical model can be used to calculate the process of crimping workpieces in axisymmetric matrices of complex shapes, with variable curvature, which is especially important in the field of aircraft engineering. The research results make it possible to consider changes in the workpiece’s thickness and physical nonlinearity in the field of plastic strain, when assessing the picture of the stress-strain state.