Chaotic Phenomena in Fast Plastic Deformation (in the Case of Cutting)
Technologies applied in machining metals are often characterised by highly localised shear strain, which can be regarded nearly as adiabatic, and which might lead to thermoplastic instability in certain cases. In cutting, similar incidents can be observed in the shear zone, in which γ=2–50, dγ/dt≈104 s-1, dT/dt=106 K/s, and under such extreme conditions chaotic phenomena may occur occasionally. Chip formation can be described by a two-dimensional model, where the variation of shear stress τ and temperature T in time are given by autonomous differential equations, while the material characteristics are determined by exponential constitutive functions. The solutions of equations can be classified by the coefficients of the characteristic equation of the Jacobian matrix. Two types of stable focuses and Hopf bifurcation can possibly occur, which corresponds to the two types of chips; continuous chip and segmental chip. The model should be broadened to describe the typical chaotic phenomena.
Z. Pálmai, "Chaotic Phenomena in Fast Plastic Deformation (in the Case of Cutting) ", Materials Science Forum, Vols. 473-474, pp. 369-374, 2005