Journal of Mechanics of Materials and Structures vol. 5 (2010 ... - MSP

850 ANDREY V. PYATIGORETS, MIHAI O. MARASTEANU, LEV KHAZANOVICH AND HENRYK K. STOLARSKI
Figure 7. Finite element models used for simulations.
full viscoelastic finite element analysis would be beyond the scope of this paper, though it is possible to
conduct such an analysis.
For simplicity, the Young’s modulus of the binder in FE model was taken to be constant: E = 3 GPa,
the initial value of the binder’s relaxation modulus. The properties of the inner ring and geometric
parameters corresponded to those of an actual ABCD specimen, and are listed on page 847. A full bond
between the binder and the invar ring was assumed. Due to the symmetry of the problem, only a quarter
of the ABCD rings had to be modeled. Two models, one without a hole (Figure 7a) and another with a
hole in the external ring (Figure 7b), were considered. Both were subjected to a temperature change of
�T = −50 ◦ C, and the circumferential strain along the arc AB in Figure 7 was determined.
The results of the FE simulations, shown in Figure 8, reveal that the magnitude of circumferential strain
in the model with a hole (Figure 7b) increases significantly at point A. At this location the difference
reaches ∼55% in comparison with the case when no hole is present in the outer ring. Indeed, the presence
of the hole causes stress concentration around it, and the additional stress causes local bending of the
invar ring. This suggests that experimental strain measurements conducted across the hole cannot be
directly used for the calculation of thermal stresses in the binder based on the results given in Figure 6.
As follows from Figure 8, thermal stress may be estimated more accurately if strain measurements are
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Figure 8. Circumferential strain εθθ(r0) along the arc AB of the finite element models
(Figure 7), with A corresponding to 0 ◦ and B to 180 ◦ .