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Plastic Deformation Instabilities: Lambert Solutions of Mecking-Luecke Equation with Delay

机译:塑性变形不稳定性:具有延迟的Mecking-Luecke方程的Lambert解

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The aim of this paper is the study of instabilities during plastic deformation at constant cross-head velocity. The deformation is supposed to be controlled by the emission of dislocation loops. Under some hypothesis analogous to the Mecking-Liicke relation, we derive a linear delay differential-difference equation. The "retarded" time term appears as the phase shift between the time of loop nucleation and the time at which the mean strain is recorded. We show the existence of the solution of strain equation. We give an analytic approach of solution using Lambert functions. The stability is also investigated close to the stable solution using a linearization of the number of nucleated loops functions.
机译:本文的目的是研究在恒定十字头速度下塑性变形过程中的不稳定性。假定变形由位错环的发射控制。在类似于Mecking-Liicke关系的某些假设下,我们导出了线性延迟微分差分方程。 “延迟”时间项显示为成环时间与记录平均应变的时间之间的相移。我们证明了应变方程解的存在。我们给出了使用Lambert函数的解析方法。还使用有核环函数数的线性化,对接近稳定解的稳定性进行了研究。

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