(c)
Figs.8: (a) The fitted curves of the calculated hysteresis area,Ah , for the MTP specimens using different scaling
factor values as shown in Fig.7, illustrating obvious geometry
constraint effect on hysteresis response; (b) The ultimately determined
scaling factor deceases with increasing ofl0 /d0 for the MTP
specimens; and (c) The predicted peak stress evolution using the
finalized identified scaling factors for the MTP specimens of FV566 at
600 °C, indicating the geometry constraint effect on cyclic response.
To further examine the mechanical deformation behavior of the three MTP
specimens, Figs.9 illustrate the stress and strain distribution under
the determined scaling factors (e.g., see Table 2) from loading
direction at 600 °C for FV566. Noted that the spatial distribution is
extracted from the maximum applied displacement point of the initial
cycle at a strain-range of 0.7%. The parallel gauge length regions are
marked between the two highlighted lines. In order to make the
comparison easier, stress contour plots have been presented using the
identical scale. It can be clearly seen from Fig.9a that the highest
predicted stress field shows a common uniform pattern at all the
parallel gauge length regions, with an approximate average value of
~ 420 MPa, which is nearly close to the peak stress
value that SSFS experimental LCF test exhibits at the same loading point
in Fig.7. Additionally, stress heterogeneities can be found at the
fillet radius regions due to the non-uniform geometry and unevenly
distributed loading. Similarly, strain contours have also been presented
in Fig.9b using the same scale for comparison. As can be seen, the
highest strain field from loading direction exhibits an average value of
~ 0.7% between the parallel gauge length, which is the
expected mechanical deformation of MTP specimen in this study. Once
again, strain heterogeneities can be observed at the fillet radius
regions. Thus, according to the numerical perspective in this
subsection, it can be confirmed that the proposed reference strain
approach coupled with UVP model is capable to identify the correct
scaling factor. Furthermore, by using MTP testing, it is possible to
obtain consistent high temperature LCF hysteresis deformation as SSFS
testing under the equivalent condition, despite the experimental errors
and the simplicity of the identification procedure.
Due to the occurrence of geometry constraint effect in non-standard MTP
specimen, the multi-axial stress state at the total effective gauge
length regions can aggravate the accumulated damage and promote failure
such as premature crack initiation under LCF test even a relatively
uniform stress-strain pattern is achieved at the initial fatigue cycle.
Therefore, it is more useful and necessary to examine the visco-plastic
multiplier predicted by the UVP model to see the geometry constraint
effect on the subsequent cyclic behavior. Fig.9c presents the predicted
visco-plastic multiplier distribution for the three MTP specimens using
the determined scaling factors in Table 2 until 58thcycle. Noted that the visco-plastic multiplier contours are set to be
with the fixed minimum and maximum scale for a better comparison. As can
be seen from Fig.9c, the highest accumulation of plastic strain occurs
at the center of MTP-1 specimen with the maximum value of
~ 0.022%, while MTP-2 is capable to carry less amount
of plastic strain with the maximum value of ~ 0.019%
comparing to MTP-1. The accumulation of plastic strain distribution
becomes more mitigated with the maximum value of ~
0.017% in the case of MTP-3 due to the weakest geometry constraint
effect. It can be deduced here that, due to the strongest geometry
constraint effect, the plastic strain accumulates at the fastest rate in
MTP-1, and consequently leading to the shortest fatigue life in the
proposed three non-standard MTP specimens.