13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- determination of the DECs is also given in Table 3 for each grain family. Fig. 4 (a) and (b) show the influence of prior deformation at high temperature on the response of the lattice strains to the applied stress for the {200} and the {220} grain families, respectively. They are illustrated by the deviation from linearity. A negative value indicates the presence of a micro-yielding in a particular grain family and a positive value indicates the effects of sharing load due to yielding of other grain families. The uncertainties shown in the Figs. 4 (a) and (b) are based on the uncertainties in the determination of DECs, summarised in Table 3. This applies to all specimens shown in Figs. 4 (a) and (b). In terms of the {200} grain family, Fig. 4 (a), the magnitude of the deviation from linearity (positive values), decreased to a minimum value from specimen 1 to specimen 3, but increased slightly for specimen 4. The deviation from linearity observed in specimen 3 was typically less than 100×106 and thus was less than the uncertainty. In terms of the {220} grain family, a very small decrease in the magnitude of the deviation from linearity (negative values) was observed from specimen 1 to specimen 3, Fig. 4 (b). However, specimen 4 showed a different lattice strain response, compared with the other three. Table 3. Summary of diffraction elastic constants (DECs) and elastic limits of specimens Specimen ID Prior deformation E{111}, GPa E{200}, GPa E{220}, GPa E{311}, GPa Elastic limit (measured at 0.01% bulk plastic strain), MPa Specimen 1 No creep 225±12 167±5 209±16 170±16 184 Specimen 2 As loaded 255±21 155±4 211±8 172±8 333 Specimen 3 Primary 264±16 146±6 201±7 204±15 344 Specimen 4 Secondary 254±4 171±9 255±16 208±12 377 Averaged DECs 250±16 160±11 219±24 188±20 Elastic lattice strain measured along axial direction, 106 0 400 800 1200 1600 2000 2400 2800 Applied true stress, MPa 0 50 100 150 200 250 300 350 400 {111} DEC prediction {200} DEC prediction {220} DEC prediction {311} DEC prediction Rietveld analysis Elastic limit Deviation from linearity, ε∗106 -600 -400 -200 0 200 400 600 800 Applied true stress, MPa 0 50 100 150 200 250 300 350 400 {111} {200} {220} {311} Elastic limit Bulk Plastic Strain (a) (b) Figure 3. (a) ND measured elastic lattice strain along the axial direction of specimen 1 for {111}, {200}, {220} and {311} grain families; (b) Deviation of the measured lattice strain from the extrapolated elastic lattice strain using DECs. Note: Measurement uncertainties are from the single peak fitting error Neutron diffraction measurements undertaken at 5MPa after each step of unloading over the process of incremental tensile deformation at room temperature, see Fig. 1 (b), revealed the evolution of the residual elastic lattice strain. Figs. 5 (a) and (b) show the changes in the residual lattice strains with the increase in the bulk plastic strain measured by the extensometer attached on the specimen, for the {200} and {220} grain families, respectively. In terms of the {200} grain family, specimen 4 which was subjected to prior secondary creep deformation, had the highest compressive residual lattice strain, but specimen 1 had the highest tensile residual lattice strain. In terms of the {220}
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