ABSTRACT

We develop an extension of the Maugis-Dugdale solution for viscoelastic spheres. We show that we can define two characteristic Tabor parameters, a larger one ${\mu }_R$ corresponding to relaxed modulus $E_R$ and a smaller one ${\mu }_I$ for instantaneous modulus $E_I$ of the material. Only if both are very large (corresponding to the JKR regime, ${\mu }_R>{\mu }_I>5$) the pull-off load increase due to viscoelastic effect is possibly very large at large pulling speeds, as given by existing solutions and approximately equal to the ratio $E_I/E_R$, and otherwise the amplification at very high speeds is much reduced and we give a very simple upper bound of the pull-off load as a function of the relaxed Tabor parameter, independently on the exact form of the viscoelastic linear modulus. An example detailed calculation is given for standard material and constant velocity of load reduction. A dependence on preload is found.

摘要

我们为粘弹性球开发了 Maugis-Dugdale 解决方案的扩展。我们证明我们可以定义两个特征 Tabor 参数，一个较大的${\mu }_R$对应于松弛模量${乙}_R$和一个较小的${\mu }_{我}$瞬时模量${乙}_{我}$的材料。只有当两者都非常大时（对应于 JKR 制度，${\mu }_R>{\mu }_{我}>5$）由于粘弹性效应导致的拉断载荷增加在大拉速下可能非常大，如现有解决方案所给出的，并且大约等于比率${乙}_{我}/{乙}_R$，否则在非常高的速度下的放大率会大大降低，我们给出了一个非常简单的拉断载荷上限作为松弛 Tabor 参数的函数，独立于粘弹性线性模量的精确形式。给出了标准材料和恒速减载的详细计算示例。发现对预加载的依赖性。