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

将摩擦现象描述为本构方程，首先得到了刚塑性描述。此外，它已扩展到弹塑性，然而，滑动屈服面的内部被假定为弹性域，因此没有描述由于滑动屈服面内部的牵引力而产生的塑性滑动速度。因此，这些模型不能描述由于接触牵引力的循环加载而导致的塑性滑移累积。另一方面，本文的第一作者提出了能够用屈服面内部的应力速率来描述塑性应变率的次加载面模型。在此基础上，通过引入次加载面的概念，提出了次加载-摩擦模型，该模型描述了从弹性滑动到塑性滑动状态的平滑过渡。众所周知，当静止的物体开始相互滑动时，首先出现一个高的摩擦系数，称为静摩擦，然后它逐渐减小，接近一个固定值，称为运动摩擦。进一步研究发现，如果滑动停止一段时间，然后再次开始滑动，摩擦系数就会恢复，并重现与初始滑动相同的行为。在本研究中，扩展了次加载-摩擦模型，以描述由于塑性滑动引起的各向同性软化导致的摩擦系数下降到运动摩擦，以及由于接触压力下表面粗糙面的蠕变变形导致的各向同性硬化导致的摩擦系数的恢复。通过数值实验验证了该模型的定性，并与线性滑动现象的试验数据进行了比较，验证了该模型对实际材料摩擦行为预测的有效性。

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.