The approximate locations of the external recorded strain gauges are shown in Figure 5.5. The simulated elastic strains for each strain location are presented
in Tables 5.1 and 5.2 for two dierent internal pressure loads. Physically mea- sured reloading elastic strains (see Figure 4.11 on page 77) are also shown for the corresponding strain gauges. Physical measurements and simulated results that compare well (within 20%) are shown in bold. The relative dierences are calculated using the measured strains as reference.
The simulated elemental strain corresponding to strain gauge "W" does not compare well (within 20%) with the measured strain for this strain gauge at an internal pressure load of 2 MPa. This is largely attributed to the fact that strain gauge "W" is located at the transition from positive to negative hoop strains, as shown in Figure 5.6. The negative strain measured by gauge "E" at both load conditions is supported by the negative hoop strain of the corresponding element as shown in Figure 5.7a on page 88. Under an internal pressure load the shape of the cross section shown in Figure 2.5 (page 9) is forced into a circular shape. This results in high stresses and negative barrel hoop strains in the acute corner. In Table 5.2 it can be seen that at an internal pressure load of 2 MPa the simulated and measured strains for strain gauges "L" and "O" compare better than at an internal pressure load of 1 MPa. However, the measured and recorded strains for strain gauges "N" and "W" compare less favourable. The dierence between the simulated and measured strains for strain gauge "A" could be attributed to the contact surface modelled between the wrapper and barrel. Similar to strain gauge "W", at an internal pressure load of 2 MPa, the discontinuous strain contours in the vicinity of strain gauges "A", "D", "F", "K", "M", "N", "S" and "W" together with the sensitivity in selecting the applicable element seems to be the main reasons for the dierence between measured and simulated strains in Table 5.2. The same conclusions applies for the results in Table 5.1. Also, the smaller the strains are the more sensitive it is to dierences.
Table 5.1: Comparison between simulated and recorded strains at an internal pressure load of 1 MPa with strains measured in µm/m.
Strain gauge Measured Simulated Abs Dierence Rel Dierence (%)
A 222 360 138 62.0 C 159 143 -16 -10 D 233 225 -8 -3.4 E -83 -57 26 31.3 F -110 80 190 172 K 152 210 -58 38.1 L 258 325 67 25.9 M 18 9 -9 -50.0 N 85 102 17 20.0 O 158 196 38 24.0 P 153 186 33 21.5 S 65 -16 -81 124.6 T 154 126 28 18.2 W 69 57 12 17.4 X 237 242 5 2.1
Table 5.2: Comparison between simulated and recorded strains at an internal pressure load of 2 MPa with strains measured in µm/m.
Strain gauge Measured Simulated Abs Dierence Rel Dierence (%)
A 853 682 171 20.0 C 325 308 -17 -5.2 D 551 432 -119 -21.6 E -113 -118 -5 -4.4 F -973 129 1102 113.3 K 242 420 121 57.6 L 620 624 4 0.6 M 8 42 34 425 N 161 182 85 102 O 320 396 21 6.6 P 294 348 54 18.4 S 73 -21 94 128.8 T 196 206 10 5.1 W -322 71 393 122 X 554 529 25 4.5
To support this observation of sensitivity in the selection of the correct ele- ment corresponding to the actual measured strain gauge the simulated strains for elements in close proximity to the strain gauge locations, shown in Fig- ure 4.6, were recorded. The elements with strains closest to the measured
strains and within a radius of 20 mm of the approximate strain gauge loca- tions were used for the recorded strains shown in Tables 5.3 and 5.4. It can be seen that the simulated and measured strains compare well for most strain gauges. This shows that the accuracy of simulated strains for comparison with measured strains are highly sensitive to the selection of the correct elements. The sensitivity exists even though mesh re nement was done and the model converged. It must be noted that the size and shape of the test piece com- plicates the exact measurement of strain gauge locations and the subsequent selection of corresponding elements. Special care was taken in this study to measure exact strain gauge locations from reference points and centerlines used by the manufacturer of the special. The use of specially designed jigs could have been used to con rm the accuracy of these measurements, but there was not su cient time and money available for this. In future studies special atten- tion should be paid to the selection of strain gauge locations with consideration to the possibility of discontinuous strain contours. An attempt should also be made to con rm the accuracy of strain gauge location measurements on the physical test piece. Strains gauges should also be placed in areas where higher strains are expected.
Table 5.3: Comparison between simulated strains for nearby elements and recorded strains at an internal pressure load of 1 MPa with strains measured in µm/m. The simulated strains were recorded with elements in close proximity to the approximate strain gauge locations shown in Figure 4.6.
Strain gauge Measured Simulated Abs Dierence Rel Dierence (%)
A 222 187 -35 -15.7 C 159 135 -24 -15.1 D 233 199 -34 -14.59 E -83 -67 16 19.2 F -110 -89 21 19.9 K 152 177 25 16.4 L 258 232 -26 -10.0 M 18 12 -6 -33.3 N 85 77 -8 -9.4 O 158 132 -26 -16.5 P 153 141 -12 -7.8 S 65 72 7 10.8 T 154 169 15 9.7 W 69 87 18 26.1 X 237 215 -22 -9.3
Table 5.4: Comparison between simulated strains for nearby elements and recorded strains at an internal pressure load of 2 MPa with strains measured in µm/m. The simulated strains were recorded with elements in close proximity to the approximate strain gauge locations shown in Figure 4.6.
Strain gauge Measured Simulated Abs Dierence Rel Dierence (%)
A 853 915 62 7.3 C 325 345 20 6.2 D 551 588 37 6.7 E -113 -80 33 29.2 F -973 -888 85 8.7 K 242 274 32 13.2 L 620 587 -33 -5.3 M 8 2 -6 -75 N 161 145 -16 -9.9 O 320 305 -15 -4.7 P 294 276 -18 -6.1 S 73 45 28 38.3 T 196 175 -21 -10.7 W -322 -259 63 19.6 X 554 498 -56 -10.1
(a) Hoop strains. (b) Longitudinal strains. Figure 5.6: Branch with negative longitudinal and hoop elemental strains on the external surface shown in grey.
(a) Hoop strains. (b) Longitudinal strains.
Figure 5.7: Barrel and wrapper elements with negative longitudinal and hoop elemental strains on external surfaces shown in grey.
In Section 4.6 it was pointed out that there is a dierence in strain magni- tudes between internal and external surfaces. Table 5.5 provides a summary of strains for these internal and external strain gauges. The simulated results show that there is signi cant dierence between strain gauge "A" and "E" as well as "D" and "L" except for the simulated strain between strain gauges "D" and "L". Incidentally, the selection of elements corresponding to the measured strain gauges also aects these results.
Table 5.5: Strain comparison for internal and external surfaces at an internal pressure load of 2 MPa, measured in µm/m.
Strain gauge Simulated Measured Abs Dierence Rel Dierence
A 853 682 -171 -20.0 E -113 -118 -5 -4.4 Absolute Dierence -966 -800 Relative Dierence -113.2 -117.3 D 551 432 -119 -21.6 L 620 624 4 0.6 Absolute Dierence 69 192 Relative Dierence 12.5 44.4