Search

Explicit expressions for the minimum free energy of a linear viscoelastic material and Noll's definition of state are used here to explore spatial energy decay estimates for viscoelastic bodies, in the full dynamical case and in the quasi-static approximation. In the inertial case, Chirita et al. obtained a certain spatial decay inequality for a space-time integral over a portion of the body and over a finite time interval of the total mechanical energy. This involves the work done on histories, which is not a function of state in general. Here it is shown that for free energies which are functions of state and obey a certain reasonable property, the spatial decay of the corresponding space-time integral is stronger than the one involving the work done on the past history. It turns out that the bound obtained is optimal for the minimal free energy. Two cases are discussed for the quasi-static approximation. The first case deals with general states, so that general histories belonging to the equivalence class of any given state can be considered. The continuity of the stress functional with respect to the norm based on the minimal free energy is proved, and the energy measure based on the minimal free energy turns out to obey the decay inequality derived Chirita et al. for the quasi-static case. The second case explores a crucial point for viscoelastic materials, namely that the response is influenced by the rate of application of loads. Quite surprisingly, the analysis of this phenomenon in the context of Saint-Venant principles has never been carried out explicitly before, even in the linear case. This effect is explored by considering states, the related histories of which are sinusoidal. The spatial decay parameter is shown to be frequency-dependent, i.e. it depends on the rate of load application, and it is proved that of those considered, the most conservative estimate of the frequency-dependent decay is associated with the minimal free energy. A comparison is made of the results for sinusoidal histories at low frequencies and general histories. [ABSTRACT FROM AUTHOR]

Recent work conducted at the Non-Destructive Evaluation Centre of University College London on the residual stress decay detection using the new alternating current stress measurement (ACSM) technology is presented. Flat bar mild steel specimens were used in the experimental study. An equal biaxial compressive residual stress field was introduced into the specimen surfaces by shot peening. The specimens were then subjected to a constant-amplitude cyclic load on a fatigue-testing machine. Under this loading situation, hole-drilling tests indicated that only the residual stress component in the cyclic loading direction had significantly relaxed. Test results showed that this relaxation could be detected by using the existing ACSM system. Further theoretical and experimental efforts are needed to make this technology available for a wide range of practical applications. [ABSTRACT FROM AUTHOR]