To better understand the geometry constraint effect, the predicted
dissipated energy that can be determined by calculating the area in the
hysteresis loop, Ah , are plotted in Fig.8a. The
same principal was also utilized before in the miniature work of Chenet al. 58, and Peng et
al .34. As can be seen from Fig.8a, an exponential
increase is observed in dissipated energy against scaling factor values.
Three exponential equations to determine the scaling factors are fitted
and shown in Fig.8a. By using the fitted equations, the scaling factor
can be possibly determined for a strain-range deformation required by
the MTP high temperature LCF testing under small deformation framework,
once the predicted SSFS responses are provided by the UVP model for
FV566 at 600 °C. Furthermore, as the increase of scaling factor,β , apparent influence can be observed on the resultant dissipated
energy, and this influence is found more pronounced for the finalized
scaling factor value in MTP-3. Fig.8b provides the curve in terms of
finalized scaling factors versus the ratios ofl0 /d0 . Due to the increase
of l0 /d0 , the geometry
constraint effect on the finalized identified scaling factors (see Table
2) is obvious, e.g., the geometry constraint effect becomes weaker asl0 /d0 increases.
Fig.8c shows the computed maximum stress evolution in every cycle until
58th. It is possible to observe that, when the same
material properties are accommodated into the MTP FE models for tension
and compression testing, the UMAT can gives the inconsistent softening
responses due to the geometry constraint effect caused by the changes ofl0 /d0. A continuous
predicted cyclic softening (a decrease in the stress amplitude) can be
observed for all MTP specimens, which can be potentially regarded as an
implication of accumulated damage and fatigue
life2,17,59,60. The largest amount of softening with
the highest decay-rate can be observed in MTP-1 with the determined,β = 4.0, due to the strongest geometry constraint effect. The
intermediate case can be found in MTP-2, while the amount of softening
and decay-rate decelerate in MTP-3. By increasingl0 /d0 to 2.0, the geometry
constraint effect on the decay-rate of softening in MTP-3 has a
relatively small impact comparing with MTP-1 and MTP-2.