FORMULATION OF CONSTITUTIVE EQUATION OF FRICTION BASED ON CONCEPT OF SUBLADING SURFACE

摩擦现象作为本构方程的描述首先是作为刚塑性得到的。此外，它已被扩展到弹塑性，然而，滑动屈服面内部被假设为弹性域，因此，由于滑动屈服面内部的牵引速率而导致的塑性滑动速度没有被描述。因此，接触牵引循环加载引起的塑性滑动累积不能用这些模型来描述。另一方面，本文的第一作者提出了用屈服面内的应力率来描述塑性应变率的次加载面模型。在此基础上，引入下加载面概念，提出了从弹性状态到塑性滑动状态平滑过渡的下加载-摩擦模型。众所周知，当静止的物体开始相互滑动时，首先出现一个高摩擦系数，称为静摩擦，然后它减小到接近一个定值，称为动摩擦。进一步发现，如果滑动停止一段时间，然后再次开始，摩擦系数恢复，并再现与初始滑动时相同的行为。在本研究中，对次加载-摩擦模型进行了扩展，以描述摩擦系数由静摩擦向动摩擦的减小是由于塑性滑动引起的各向同性软化，以及摩擦系数在接触压力作用下由于表面粗糙度的蠕变引起的各向同性硬化而恢复的过程。通过数值实验验证了该模型的定性性质，并与线性滑动现象的试验数据进行了对比，验证了该模型预测实际材料摩擦行为的有效性。

Description of the friction phenomenon as a constitutive equation has been attained first as a rigid-plasticity. Further, it has been extended to an elastoplasticity However, the interior of the sliding-yield surface has been assumed to be an elastic domain and thus the plastic-sliding velocity due to the rate of traction inside the sliding-yield surface is not described. Therefore, the accumulation of plastic-sliding due to the cyclic loading of contact traction cannot be described by these models. On the other hand, the first author of the present article has proposed the subloading surface model which is capable of describing the plastic strain rate by the rate of stress inside the yield surface. Further, the authors proposed the subloading-friction model which describes the smooth transition from the elastic-to plastic-sliding state by incorporating the concept of subloading surface.It is widely known that when bodies at rest begin to slide to each other, a high friction coefficient appears first, which is called the static-friction, and then it decreases approaching a stationary value, called the kinetic-friction. Further, it has been found that if the sliding ceases for a while and then it starts again, the friction coefficient recovers and the identical behavior as that in the initial sliding is reproduced.In this research, the subloading-friction model was extended so as to describe the decrease of friction coefficient from the static-to kinetic-friction by the isotropic softening due to the plastic-sliding and the recovery of friction coefficient by the isotropic hardening due to the creep deformations of surface asperities under the contact pressure. The qualitative property of the present model is examined by numerical experiments and the validity for prediction of friction behavior of real materials is verified comparing with test data for the linear sliding phenomenon.