CHAPTER 7 EFFICACY OF THE INHERENT STRAIN METHOD
7.2 Comparison of Results
7.2.1 Central Grid Comparison
Since the experimentally measured RS in the central grid measurements were almost exclusively compressive, positive stress differences of the simulations indicate an under prediction of compressive RS with negative differences indicating over prediction of compressive RS. The resulting stress differences on the central measurement of the 0° HR specimen are shown in Figure 7-3 as contour plots for the different ISMs.
A). B).
X = 7.5[mm]
Z = 7.5[mm]
Figure 7-3: Difference between simulated and measured RS for 0° HR specimen.
The simulations of the cube with no HR showed a tendency of predicting too high a stress at the top center of the cubes and too low toward the bottom surfaces for the σxx RS. Further the simulation types maximum and minimum RS differences were very nearly the same, however, an average absolute RS difference of only 42 MPa indicated that the isotropic simulation most accurately determined the overall distribution of the σxx RS on the central measurement grid, this was however only slightly better than the other simulations, with the orthotropic and thermomechanical ISMs indicating averaged difference values of 77 MPa and 54 MPa respectively.
The σyy RS was largely over predicted by the isotropic and thermomechanical ISMs at average stress differences of 231 MPa and 224 MPa respectively, however, this was expected as this components’ RS is highly influenced by scan track length and as such would require unique inherent strains or volumetric expansion factors to adequately determine the RS directions parallel and perpendicular to the scan tracks. For this stress direction only the orthotropic simulation type was able to determine the values to an average absolute stress difference of less than 50 MPa throughout the central grid region. From the contour mapping of the orthotropic ISM differences,
it can also be seen that for the σyy stress direction, maximum compressive stress differences occur in the center of the cubes with under prediction of the compressive RS towards the outer surfaces. From this it can be assumed that the orthotropic inherent strain allocated parallel to the Y-axis (ԑyy) and derived from the laterally scanned 0° HR cantilever was too large.
The σzz RS differences showed a very similar distribution in the contour mapping of the various simulation types, with simulations all indicating a trend of over prediction of compressive RS towards the bottom of the specimen, and under prediction towards the center of the cubes around X = 7.5 mm and Z ≈ 10 mm. These large differences in measured and simulated values may in this case be as a direct consequence of the nature of the ISM where the ԑxx and ԑyy alone affect the RS state, with ԑzz inherent strains showing no direct impact on the RS state in the layer-by- layer approach as indicated by Bugatti et al. [71].
With the incorporation of HR, the cube specimens RS indicated minimal directional preference.
This can be observed by the good agreement of both the isotropic and thermomechanical simulations with regards to the σxx and σyy RS shown in Figure 7-4 for the 67° HR cube, with the 90° HR cube stress difference contours given in Appendix D.
Figure 7-4: Difference between simulated and measured RS for 67° HR specimen.
The averaged absolute stress differences decreased by more than 150 MPa for both the thermomechanical and isotropic σyy values of the 67° and 90° HR cubes when compared to the specimens with no HR. It was also seen that the different ISM simulations for samples with HR had very similar distribution of RS differences; for σxx and σyy the simulations were prone to over prediction of the compressive RS towards the bottoms of the cubes with under predicted compressive values as the height increased beyond Z ≈ 7.5 mm. This following a trend similar to
the results from Pant et al., where a layer-by-layer simulation approach was also validated through ND [85]. Despite these differences in simulated results, the average absolute stress differences were all well below 100 MPa for all ISMs σxx and σyy stress results in the central region, indicating a good agreement of measured and simulated values.
Regarding stresses in the build direction, the σzz values indicated the largest differences for the central grid measurements with similar distribution of stress differences as 0° HR specimen, and with the exception of the thermomechanical simulation of the 90° HR cube, had arbitrary variation of averaged stress differences for the HRs as given in Table 7-1.
Table 7-1: Minimum, maximum and average absolute stress differences of central grid region.
0° HR [MPa] 67° HR [MPa] 90° HR [MPa]
.σxx .σyy .σzz .σxx .σyy .σzz .σxx .σyy .σzz
Isotropic ISM Min -165 -337 -356 -118 -119 -335 -120 -128 -294
Max 75 18 134 130 123 116 74 67 40
Average* 42 231 126 40 56 131 31 39 105 Orthotropic ISM Min -185 -143 -284 -95 -101 -316 -155 -162 -319
Max 108 70 211 126 124 105 38 49 36
Average* 77 46 89 34 45 124 51 62 132 Thermomechanical
ISM
Min -228 -331 -323 -98 -111 -282 -125 -131 -235 Max 108 17 159 152 142 125 121 110 109 Average* 54 224 116 48 62 98 47 54 72 Note: * The average values denote the average absolute stress differences measured, this being done so that under prediction and over prediction of the stresses would not bring the average stress difference towards zero (e.g., The average of +150 and -150 being zero if not using absolute values).
Through determining the peak and average stress differences, the simulations’ ability to determine the RS in the interior regions of the specimens can be seen. The isotropic and thermomechanical approaches were largely ineffective in RS prediction of the specimen with no HR, with the orthotropic ISM being the only viable option of RS prediction for this scanning strategy. Applying a 67° HR allowed the thermomechanical and isotropic ISMs to increase in effectiveness with reductions in σxx and σyy minimum differences, albeit at the cost of an increases in maximum stress differences. Again, the orthotropic ISM showed the best suitability in σxx and σyy determination, with peak and averaged stress differences equal to or less than those of the isotropic and thermomechanical ISMs; indicating that the 67° HR stresses are almost but not fully transversely isotropic in nature.
In order to further define the differences between measured and simulated RS values, the differences were correlated to percentage of the yield strength as shown in Figure 7-5.
Figure 7-5: Isotropic percentage differences from measured values.
As shown in figure for the percentage difference between the isotropic simulations and the measured values very slight differences were seen between the simulated and measured values for the specimen with 90 HR at approximately +10% of the material yield strength for the σxx and σyy directions, whereas this range increased into to the negative values for the specimen with 67 HR at ±10%, causing a range of difference of approximately 20% throughout the measurement area (160 Mpa). Again for the specimen with no HR applied, the difference in measured and simulated values increased to approximately -20% and -40% for the σxx and σyy directions respectively. The σzz again showed much larger differences at approximately 40% of the yield strength of the material for all specimens as previously stated.
Figure 7-6: Orthotropic percentage differences from measured values.
The percentage deviation for the orthotropic simulation types indicated similar results to those of the isotopic simulations, however with the exception of the decreased error range for the 0 HR specimen (Figure 7-6). When no HR was applied the error range decreased from 40% to a maximum of 20% of the material yield strength, the distribution of the differences however remained in a similar form as for the isotropic. In this case however the orthotropic simulations were in an approximate range of 15% (-15%) for the X and Y directions of the 90 HR specimen and 20% (±10%) range for the 67 HR specimen. This was also observed for the simulations utilizing the thermomechanical approach as shown by Figure 7-7. Here the distribution form of the differences as well as the ranges indicated are very similar to those of orthotropic simulation types.
Figure 7-7: Thermomechanical percentage differences from measured values.
Using scan tracks that were fully perpendicular between layers, as for the 90° HR, the isotropic and thermomechanical ISMs were suitable for RS prediction, peak stress differences were all below a magnitude of 150 MPa, with the exception of the σzz stress. The isotropic simulation was the best suited in determining the RS in the σxx and σyy directions, however only slight increases in average stress differences were observed for the thermomechanical ISM. The thermomechanical simulation in this case had the lowest averaged stress difference for the σzz
stress at 70 MPa, whereas both mechanical ISMs were above 100 MPa. As a result, this simulation type appears to have the best suitability in RS prediction for 90° HR, followed by the isotropic and orthotropic methods respectively.
The different ISM simulations were not well suited for determining the RS as found in the σzz
direction in the central grid regions of the specimens, however by making use of a 90° HR during manufacturing, this averaged stress difference could be reduced to less than 100 [MPa], indicating that although some localized RS was being poorly estimated, the overall RS distribution in this region was relatively accurate. The compressive RS differences of the simulations perpendicular to the build direction were also seen to be greatly reduced with incorporated HR, this coming at the expense of increased maximum RS difference, however, the increases to the maximum differences were minimal compared to the improved results.