Papers by Keyword: Thermoplastic Instability

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Authors: Zoltán Pálmai
Abstract: The author developed a three-dimensional model for the description of fast plastic deformation of metals in the case of cutting. Shear strain occurring as a result of shear stress has a reverse effect on stress, while the temperature of the material is increasing. These counteracting effects may lead to thermomechanic instability, which may result in aperiodic chaotic conditions besides periodic fluctuation due to the non-linear nature of the process. Apart from bifurcation and multi-cycle periodic deformation, the model also describes aperiodic chaotic deformation, which is proven by experimental results.
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Authors: Zoltán Pálmai
Abstract: 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.
369
Authors: Zoltán Pálmai
Abstract: We have developed a technological and mathematical model for the fast deformation of metals, which, as a result of the non-linear nature of the process, is equally suitable for the description of stable (continuous or periodic) and also chaotic states. In the case of stable solutions, the various numerical methods generally give consistent results, but in chaotic cases significant differences can be observed in the space of state characteristics, especially within the range determined by the strange attractor.
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