Analytical, numerical and experimental study of the self-heating of a shape memory composite

Shape memory polymers (SMP) and their composites (SMC) are smart materials having morphing capabilities that are applied in several fields such as aerospace, biomedical or textile engineering. Among the possible shape change triggering methods, electroactive SMC have steadily gained interest within the range of shape memory materials in the recent years due to the fast and efficient triggering through Joule resistive heating. During this process, the heat is generated directly within the material. However, in order to produce a well-defined shape change, the temperature increase resulting from self-heating should be accurately predicted. The temperature is time-variant and non-uniform within the material. This directly affects the amount of heat generated since the electrical resistivity is, in general, found to be dependent on the local temperature of the SMC.
In this study we examine in detail the self-heating phenomenon of an electroactive SMC when an electric current is injected at constant power. The study aims at identifying the parameters that are crucial for predicting the temperature increase and at understanding how any variation of them affects the self-heating process. The SMC is chemically crosslinked poly(ε-caprolactone) filled with 3 wt% of multiwall carbon nanotubes. The self-heating phenomenon is studied by means of analytical formulas, a 3D thermo-electric numerical model and surface temperature measurements. We derive analytical expressions of the 2D temperature distribution within a parallelepipedic SMC, either with constant or linearly-dependent electrical resistivity. The analytical expressions are able to reproduce the principal features of the temperature distribution across the sample. The temperature increase depends on many parameters related to the heat transfer process, both within the SMC and at the inter-face between the SMC and its environment. The results show that, for this particular SMC, the temperature dependence of the resistivity has little effect on the final temperature, whereas the thermal conductivity plays a significant role. The transient characteristics of the temperature evolution are shown to be influenced by the highly non-linear temperature dependence of the heat capacity. The self-heating phenomenon appears to also be strongly dependent on the contact with external objects, such as clamps or grips, that are frequently used during the shape memory cycles.