TECHNICAL REPORT 92-14 - Nagra

NAGRA NTB 92-14 - 45 -
Case 1: Finite elements which have temperatures above the melting temperature
are set inactive at liquefaction and are reset active at solidification.
Since a whole element is set inactive/active because of a temperature
at a single point, the transition temperatures are not sharply defined.
The liquefaction gives no problems. While the material is molten,
the displacements are kept constant at a low effective stress. The
solidification results in an abrupt and sometimes very large jump of
the displacements and an increase of the effective stress with a later
overshoot due to the inaccurately determined stresses at material
transition. The final effective stresses match with those obtained by
Melander.
Case 2: Temperatures above a certain cut-off temperature (1100 °C) are reset
to this temperature, i.e. the material is kept solid at a temperature just
below the melting temperature. Therefore, the final drop of the yield
limit may be avoided in the heat-up phase, thus preventing possible
numerical problems.
Small instabilities in the displacements are observed during the molten
phase, whereas the displacements continue smoothly at liquefaction
and solidification. The final effective stresses match with those
obtained by Melander.
Case 3: The solidifying molten material is reset in a virgin state.
The liquefaction results in large changes of the displacements since no
measures were taken to prevent instabilities. The solidification keeps
the displacements and stresses smooth. The final effective stresses
match with those obtained by Melander.
Case 4: The molten material is simulated by a solid with constant volume
and no thennal expansion; it is further reset in a virgin state
at solidification. Volume conservation was assumed to simulate the
liquefied material more realistically. Melander proposed resetting the
coefficient of thennal expansion to zero to eliminate further expansion;
this procedure gives rise to large thermal strains at liquefaction
and solidification and therefore to numerical problems. However, a
smooth continuation without expansion is reached for temperatures
above melting temperature if the coefficient of thermal expansion is
chosen such that its product with temperature is constant, i.e. equal
to the product at melting temperature.
Along the whole temperature cycle, the displacements develop rather
smoothly and the effective stresses match with those obtained by Melander.
The reset in a virgin state keeps the final plastic strains small
(about 3 %), whereas the large strains obtained by Melander (about
28 %) are mainly produced during the molten material state.