The measured strains for the combined and transverse specimens are presented in Fig. 28.8. The directions for the strains on the surface of each sample is shown in Fig. 28.8a. Each specimen was subjected to a C-type thermal cycle. The dwell strains for both the combined and transverse bending specimens decrease during the first heat cycle stage. Residual strains for the combined and tranverse specimens range from 1500μ. The measured negative residual strain in all samples is due to the unwrapping of the bend due to stress relaxation. A comparison of the strain offset between the estimated thermal strain due to thermal expansion and the measured strains for each specimen subjected to varying heat cycles is shown in Fig. 28.9. The average strain offset for all of the experiments is 617.90 μ/ C and the 95 % confidence interval lies between 312.71 and 923.10 μ/ C. The plot displays that for unstrained specimens or unstrained specimen directions residual strains are held to a minimum. Once the strain offset occurs after the initial cooling sequence the subsequent reheating of the sample to 160 C has a minimal effect on the residual strains in each specimen. This plot also suggests that the residual strain is not sensitive to level of non-zero strain, prestrain type, nor the heating profile. The radius of curvature was calculated around the bend for each sample throughout the thermal testing process as shown in Fig. 28.10. As the temperature of each specimen increased the radius of the sample increased as well. After the initial increase in radius due to the first dwell of the heating cycle, a residual increase in radius remained in the sample after cooling and was not affected by the second dwell of the heating cycle. Overall, the increase in radius for each specimen was small but the specimens with the largest increase also had the largest residual strains. The increase in strain supports the assumption that the bend is unwrapping during thermal cycling. A summary of the increase in radius for each specimen is displayed in Table 28.4. The vertical displacement at the center of the gage section for a dogbone specimen subjected to uniaxial prestrains of 0 and 20 % then bolted to a steel plate and subjected to an A type thermal cycle is displayed in Fig. 28.11. The displacements after the two separate cooling periods show little deviation. The amount of prestrain also has little effect on the residual displacements as each experiment lands between 0.1 and 0.2 mm. Initial modeling of the metal under these conditions adequately predicts the out of plane deformation as well as the residual strain in the specimen. 4000 3000 2000 1000 Strain (m ) 0 -1000 -2000 0 5000 10000 15000 Time (s) 20000 25000 0 5000 10000 15000 Time (s) 20000 25000 b a 5000 4000 3000 2000 Strain (m ) 1000 0 -1000 A- xx C- xx A- est C- est A- est C- est A- yy C- yy ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ ∋ Fig. 28.7 Experimental data from a 20 % prestrained bending specimen during A and C thermal cycles: (a) Strains measured around the bend axis compared to the estimated thermal strain. (b) Strains measured parallel the bend axis compared to the estimated thermal strain 28 Thermal Deformation Analysis of an Aluminum Alloy Utilizing 3D DIC 231
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