Modelling of Adaptive Composite Materials with Embedded Shape Memory Alloy Wires
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2. EXPERIMENTAL DATA ON DISCRETE SMA-WIRES
As explained in the introduction, the functional properties of SMA-composites are directly related to the generation of recovery stresses by prestrained SMA-wires which operate during heating against the elastic stiffness of the matrix material. A remarkable feature of the literature on SMAcomposites is that quantitative experimental data on the generation of recovery stresses are very scarce and of dubious quality. Moreover, quantitative data on the generation of recovery stresses by thin SMA-wires, matching the above mentioned biasing and temperature conditions, are completely absent. Many papers refer for quantitative data on generation of recovery stresses to an old NASA-report, published in 1972 [Ja72]. However, the data in this NASA-report refer to preparatory measurements during the first heating cycle for thick Ni-Ti wires in isostrain conditions. These conditions are completely different from the cyclic heating of thin Ni-Ti wires for the complex biasing conditions in SMA-composites.
Experimental data are an essential part of constitutive modelling. Firstly, some parameters in the modelling have to be determined experimentally. Secondly, the accuracy of the modelling has to be verified and optimised by comparison with experimental results. For these purposes, the authors have performed numerous series of experiments. The experiments have been performed on a fully computerised apparatus which offers the possibilities for complex coupled control of stress, strain and temperature and for real-time data acquisition and processing [St92]. 350
Figure 1: Stress-strain curves of discrete
300
SMA-wires during loading, starting from the complete austenitic condition, for different temperatures. The temperatures (in °C) are respectively 47.2, 49.2, 53.2, 57.2 and 61.2. The stress levels increase with temperature. The elastic modulus Es and pseudoelastic modulus Ps, both used in the thermodynamic modelling, are determined by a linear approximation as indicated in the figure.
250250 200
E 255.2, 0 150 10050 0 0
1
2
3
Strain in % 2-
1.5 •E
"1
U)
0.5
0 30
40
50
60
70
80
Temperature in °C 120
Figure 2: Strain-temperature curve of the SMA-wire during free recovery. The sample was (i) heated to 353 K, which is above Af, (ii) loaded with a stress equal to 235 MPa, (iii) cooled to 303 K, which is below Mf, (iv) unloaded and (v) heated to 363 K. The strain-temperature curve during the latter heating is shown. The dots correspond to data that have been used as input data in the thermodynamic modelling.
350 300
a.M C
250 200
0= 150 100
0
45
t
II
55
I
65
75
85
Temperature in °C
Figure 3: Stress-temperature curves measured on discrete SMA-wires, showing the generation of recovery stresses. In these experiments, steps (i) to (iv) are identical to the experimental procedure in figure 2. In step (v) free recovery was allowed until a programmed contact strain ec was obtained. During further heating the strain e was controlled as a linear function of the te
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