PSI - Issue 18

Andrzej Katunin et al. / Procedia Structural Integrity 18 (2019) 20–27 Author name / Structural Integrity Procedia 00 (2019) 000–000

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including heat transfer between the composite structure under cyclic loading and ambient medium. Heat transfer results in the energy conservation requirement which can be defined as (Incropera et al., 2007): � � � � � � � � � � � � �, (3) where q d ( t ) is the heat released by the composite structure under cyclic loading, q c ( t ) is the heat transferred by convection, and q r ( t ) is a heat transferred by radiation. The q c ( t ) and q r ( t ) are defined as follows (Incropera et al., 2007): � � � � ��� � � � � �, (4) � � � � ���� � � � � �� �, (5) where A is the overall area of the composite structure and e is its emissivity,  is the heat transfer coefficient,  denotes the Stefan-Boltzmann constant (5.67×10 -8 W/m 2 K 4 ) and  0 is a temperature of the ambient medium in (4), as well as a temperature of surroundings in (5). The temperature variability of a composite structure under cyclic loading is relatively small, thus the amount of heat transferred by radiation (5) is very small as well. In consequence, one can assume that q r << q c and finally q c + q r  q c . The heat transfer q c (t) can be controlled by means of air cooling. In general, application of air cooling allows to change the value of  . Since  0 in (4) is an independent variable, and it is assumed to be constant, q c (t) is controlled only by changing the value of  , which is represented on the schematic plot in Fig. 1.

Fig. 1. The diagram of relation of the self-heating temperature profile with three possible cases of heat removal by means of air cooling.

Following Ratner and Korobov (1965) and assuming the stationarity of  0 and  , three cases of heat transfer between cyclically loaded composite structure and ambient medium can occur (see Fig. 1). The first one occurs when q d < q c (Fig. 1). In this case, significant amount of heat released by composite structure is transferred to the ambient medium, and the temperature  ( t ) is stable (see Fig. 2, curve no. 1) during the whole process of fatigue degradation. The second case is when q d > q c (see Fig. 1). In this case, the composite structure accumulates significant amount of heat released during cyclic loading. The temperature  ( t ) increases monotonically (see Fig. 2, curve no. 2) and fatigue degradation of composite structure is accelerated.