Frictional aging is observed at a wide range of length- and time-scales, and plays a crucial role in functioning of micro- and nanomachines, as well as in the nucleation and recurrence of earthquakes. Here, we developed an analytical model for description of frictional aging mediated by dynamical formation and rupture of microscopic interfacial contacts. The model accounts for the presence of various types of contacts at the frictional interface and exhibits three different aging regimes: (i) linear aging at short hold times, (ii) logarithmic (or logarithmic-like) aging for intermediate time scales and (iii) levelling off in the static friction for long hold times. It is demonstrated that the linear aging regime is a universal feature of frictional aging for the interfaces including various types of contacts, and the slope of variation of the static friction with the hold time depends on a distribution of energy barriers for contact formation. The conditions for the existence of a pronounced logarithmic aging regime, covering a long-time interval, have been established. Frictional aging has been found to manifest itself not only in slide-hold-slide measurements, but also in sliding experiments exhibiting stick-slip mode of motion, and a relationship has been established between these two regimes of aging. The predicted dependencies of frictional aging on the normal load and temperature are in good agreement with the experimental observations. Our work shows that experimental studies of load and temperature dependencies of aging, carried out over a wide range of time scales, offer promising opportunities for understanding the microscopic mechanisms of frictional aging and revealing the physical meaning of state variables that determine temporal evolution of friction described by phenomenological rate and state laws.

在广泛的长度和时间尺度上观察到摩擦老化，并且在微型和纳米机器的功能以及地震的成核和复发中起着至关重要的作用。在这里，我们开发了一个分析模型，用于描述由微观界面接触的动态形成和破裂介导的摩擦老化。该模型说明了摩擦界面处存在各种类型的接触，并展示了三种不同的老化状态：（i）短保持时间的线性老化，（ii）中间时间尺度的对数（或类似对数）老化和（iii） ) 在静摩擦中保持平稳，以便长时间保持。证明了线性老化状态是界面摩擦老化的普遍特征，包括各种类型的接触，静摩擦随保持时间变化的斜率取决于接触形成的能垒分布。已经建立了存在明显的对数老化状态的条件，覆盖了很长的时间间隔。已经发现摩擦老化不仅在滑动-保持-滑动测量中表现出来，而且在表现出粘滑运动模式的滑动实验中表现出来，并且已经在这两种老化状态之间建立了关系。摩擦老化对正常载荷和温度的预测依赖性与实验观察结果非常吻合。我们的工作表明，老化的负载和温度依赖性的实验研究在广泛的时间范围内进行，