(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.