13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- stress. The lattice spacings measured in the other three specimens, Table 2, were then compared with specimen 1: 1 1 i i hkl hkl hkl hkl d d d ε − = (4) where i hkl ε is the internal strain in specimen i (i=1, 2, 3 or 4 based on Table 2), 1 hkl d is the lattice spacing in {hkl} plane measured from specimen 1 and i hkl d is the lattice spacing measured from specimen i (i=1, 2, 3 or 4 based on Table 2). Internal resistance measurements were undertaken using a combination of loading and unloading steps to enhance the accuracy for the determination of the initial yield point in each specimen, Fig. 1 (b). In practice, the internal resistance is equal to the magnitude of applied stress that produced a deviation from linearity on a peak strain versus applied stress graph ( hkl ε -σa graph). The deviation from linearity was calculated from the difference between the measured elastic lattice strain and the predicted elastic lattice strain from diffraction elastic constants. It should be mentioned that the internal resistance measured using this method does not take into account the presence of internal stress. Thus the corrected internal resistance in each specimen was evaluated by deducting the magnitude of the pre-existing internal stress from the initially determined internal resistance. A series of unloading steps to a nominally zero applied stress (5MPa) was adopted during the incremental tensile deformation, Fig. 1 (b). Using this approach it was possible to track the change in the internal stress introduced by room temperature tensile deformation. This can be then added to the pre-existing internal stress due to high temperature deformation to provide a measure of the evolution of internal stress introduced by the general plastic deformation, i.e. the sum of room temperature plastic deformation and high temperature plastic and creep deformations. 3. Results 3.1. Response of lattice strain responses and deviations from linearity Fig. 3 (a) shows the ND measured lattice strains along the axial direction as a function of increasing applied stress for specimen 1, not subjected to a prior high temperature deformation. The diffraction elastic constants (DECs) for all four grain families were determined from the ND measurement data within the elastic region, the linear portion of the hkl ε -σa graph, below the elastic limit illustrated by the dotted line in Fig. 3 (a). A linear least squares regression method was used to fit the data and obtain the DECs. From the region where the applied stress was above the elastic limit, the measured lattice strains for the {220}, {111} and {311} grain families diverged from linearity towards a lower strain value (to the left hand side of the prediction), whereas the {200} lattice strain diverged to a larger strain value (to the right hand side of the prediction). Fig. 3 (b) shows the calculated difference between the ND measured lattice strain and the predicted lattice strain using the DEC for each grain family. After reaching the applied stress of 375MPa, Fig. 3 (b), the difference was about -500×10-6 strain (compression) for the {220} grain family, however for the {200} grain family the difference was about +500×10-6 strain (tension). In addition the bulk plastic strain measured by the extensometer provided a consistent prediction of the deviation from linearity, Fig. 3 (b). This data analysis procedure was adopted for each specimen. The DECs and elastic limits of all four specimens are summarised in Table 3. Among the four grain families, {200} grain family was the most compliant and the {111} grain family was the stiffest. The progressive increase in the elastic limit from specimens 1 to 4 was consistent with the increase in the total strain introduced by the prior deformation at high temperature. The uncertainty for the
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