使用多尺度渐近分析的金属轧制厚度方向建模
Through-Thickness Modelling of Metal Rolling using Multiple-Scale Asymptotics
AI总结：
提出基于多尺度渐近分析的金属轧制半解析模型，首次预测长薄轧辊间隙的厚度方向应力应变振荡，计算快速且与有限元模拟吻合，为复杂厚度行为提供基础。
摘要：
引入了一种新的金属轧制过程半解析模型，该模型首次能够预测存在于长且薄的轧辊间隙中的厚度方向应力和应变振荡。该模型基于多尺度渐近分析，假设长且薄的轧辊间隙和相对较小的Coulomb摩擦系数。主阶解仅在与轧辊间隙长度相对应的长长度尺度上变化，并与slab模型相匹配。下一阶校正在此长长度尺度和与工件厚度相关的短长度尺度上均有变化，并揭示了在轧制方向和厚度方向上的快速应力和应变振荡。在此次初步推导中，该模型假设刚性完全塑性材料行为。尽管有这些强假设，该模型与采用更真实材料行为（包括弹性和应变硬化）的有限元模拟相比表现良好。这些假设使得最简单的模型能够为有限元模拟中观察到的复杂厚度方向行为提供基础理解，同时计算仅需几秒钟。该模型可作为未来具有更复杂力学特性的改进模型的基础。补充材料中提供了用于评估该模型的Matlab代码。
英文摘要：
A new semi-analytic model of the metal rolling process is introduced, which, for the first time, is able to predict the through-thickness stress and strain oscillations present in long thin roll-gaps. The model is based on multiple-scales asymptotics, assuming a long thin roll-gap and a comparably small Coulomb friction coefficient. The leading-order solution varies only on a long lengthscale corresponding to the roll-gap length and matches with slab models. The next-order correction varies on both this long lengthscale and a short lengthscale associated with the workpiece thickness, and reveals rapid stress and strain oscillation both in the rolling direction and through the thickness. For this initial derivation, the model assumes a rigid perfectly-plastic material behaviour. Despite these strong assumptions, this model compares well with finite element simulations that employ more realistic material behaviour (including elasticity and strain hardening). These assumptions facilitate the simplest possible model to provide a foundational understanding of the complex through-thickness behaviour observed in the finite element simulations, while requiring an order of only seconds to compute. This model can form the foundation of further improved models with more complicated mechanics in the future. Matlab code for evaluating the model is provided in the supplementary material.
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