Shape memory alloys (SMA) are widely used in aeronautics, astronautics, architectonics and biomedical industry, because of their special properties such as shape memory effects and transformation pseudo-elasticity etc. [1][2] However, the applications of SMA are greatly limited because of its extremely complicated mechanical properties in serving temperature, especially, the nonlinear relationship between load and displacement and the temperature hysteresis .[2] The recovery rate of shape memory alloy is linearly related to temperature in some temperature ranges although this relationship is non-linear in the whole recovery process. To the best of my knowledge, there are hardly any reports on the linear recovery effect of SMA. [1][2][3][4] The present researches focus on the recovery properties of TiNi SMA spring and improvements of the linear recovery effect through heat treatment and rare-earth thermochemical treatment.Linear recovery behavior of shape memory alloy (SMA): For a one-way shape memory effect, if it is deformed in Martensitic state, it will recover when heated, and the recovery quantity depends on temperature. Besides, the recovery proportion of SMA could be defined as the function of temperature. In addition, there is an obviously linear segment on its recovery curve, which indicates that the recovery quantity is linearly related to temperature. This linear recovery phenomena in SMA could be defined as the linear recovery behavior. In what follows, we do not consider the complete recovery curve but focus only on the linear portion of it. The recovery curve of TiNi SMA spring is shown as Figure 1 and Figure 2. If an original length of sample is defined as L 0 in Martensitic state and the length after drawn L 1 , the elongation is described as below:If it is assumed that its length is L after heated, its reversion could be illustrated as the following:After reversion completed, the length is L 2 . So the total reversion is the following:As a result, the recovery extent P and the total recovery proportion R T could be defined as the below formulas, respectively:If the total reversion (L 1 -L 2 or r 2 ) equal to the elongation (L 1 -L 0 or r 0 ) after reversion completed, the total recovery proportion R T equals to 100 %. If the reversion is not enough, R T is less than 100 %. If the nonlinear reversion under point S is described as r S , the nonlinear recovery extent is R S = d S /d 0 . The segment from point S to point E is linear. If the linear reversion is as below:the linear recovery proportion is as following:

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