Internal friction due to thermoelastic martensitic transformation
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I.
INTRODUCTION
S H A P E memory alloys are rapidly becoming a promising class o f functional materials due to their vast potential in the applications o f various heat-sensitive devices and even heat engines. However, the thermoelastic martensitic transformation that determines the shape memory performance in these alloys, particularly the internal friction spectrum associated with the transformation, is not yet fully understood at the present time. Among the several variables that can affect the internal friction o f martensitic transformation, the effects o f the oscillation amplitude seem to be the most controversial. While some have found that internal friction increases as the oscillation amplitude increases, t~-Sl others have found it to increase with decreasing amplitude, t6,7,8] and still others have found it to be independent o f amplitude, tg,~°,~J In this study, the stress-amplitude dependence o f the internal friction was determined after a stable and reproducible internal friction spectrum was established following nine thermal cycles between - 1 2 0 °C and 100 °C. A general physical m o d e l and mathematical treatment are developed to account for the stress-amplitude dependence o f the internal friction and the shift o f transformation temperature. Finally, the correlations between stress-oriented martensitic transformation, internal friction, and two-way shape memory training strain are discussed with respect to the experimental results.
II.
EXPERIMENTAL
The nominal composition o f the alloy used in this study is Cu-13 wt pet Zn-9 wt pct AI. The wire specimen o f 1.2 mm (diameter) x 20 mm (length) was homogenized in t h e / 3 phase by keeping it at 850 °C f o r 10 minutes before quenching into w a t e r held at 17 °C. The dynamic mechanical properties o f the specimen were then studied in a three-point bending configuration using a PERKIN-
ELMER* dynamic
mechanical analyzer.
*PERKIN-ELMER is a trademark Electronics, Eden Prairie, MN.
III.
of Perkin-Elmer Physical
R E S U L T S A N D DISCUSSION
The results o f cooling curves are shown in Figures 1 and 2. The internal friction peak heights (tan ~) and peak temperatures (Mp) are then plotted against the stress amplitude in Figure 3. It can be seen that with the decrease o f stress amplitude, the internal friction peak height increases monotonically until it exceeds the detection limit o f the instrument. However, the peak temperature (Alp) first decreases with decreasing stress until it reaches a minimum and then increases again with further decrease o f stress. T o interpret the results, we present in this article a general physical m o d e l and mathematical treatment o f the internal friction, due to martensitic transformation, with special attention to the effects o f stress-induced martensite. Let us first consider a bar specimen undergoing a sinusoidal tensile stress or = o'0 (1 + sin o00/2 at a temperature above M~ (i.e., in the/3 phase). The pseudoelastic behavior during loading and unloading, with a hysteresis h, is shown in Figure
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