SQUEEZE FLOW OF A POWER-LAW VISCOPLASTIC SOLID

A cylinder of height it is squeezed between two parallel circular plat es of radius R much greater than h. The cylinder is assumed to behave as a generalised Newtonian material in which the stress and strain rat e are coaxial: the particular cases of a rigid-plastic solid and power -law fluid are considered in detail. It is assumed that the frictional stress at the walls is a fixed fraction m of the yield stress in shea r, k, in the case of the plastic material, and a fixed fraction of the effective Mises stress in the case of the power-law fluid. This bound ary condition, often used in plasticity analysis, leads in both cases to a constant shear stress at the walls, rather than a no-slip boundar y condition. Hoop stresses are included in an approximate analysis in which stresses and velocities are expanded as series in inverse powers of the radial coordinate r: these expansions break down near the axis r = 0 of the cylinder. The force required to compress the rigid-plast ic cylinder is F = 2/3mk pi R(3)h(-1) + 1/2 root 3k pi R(2)[(l - m(2)) (1/2) + m(-1) sin(-1) m] + O(kRh), independent of the speed of compres sion. The analysis can be extended to other solids and fluids characte rised by a coaxial constitutive relation: by way of example, results a re presented for the Bingham fluid.