Submillimeter Array Technical Memorandum

Number: 107

Date: January 13, 1997

From: Bill Bruckman

Subject: Design of CFRP Bonded Joints for TPI Tubes

Background


A contract was awarded to Thermoplastic Pultrusions, Inc. (TPI) in Bartlesville, OK to build tube assemblies in accordance with the SMA specification, Carbon Fiber Tube Assembly Specification, Dwg. No. 11700490000. This specification defined 27 different tube assemblies (dash 1 thru dash 27 in Figure 1) that consist of a carbon fiber reinforced plastic tube bonded to a 17-7PH, RH950, stainless steel, threaded endfitting. These tubes are used to construct the SMA antenna backup structure (BUS). The specification defined the outer diameter (OD), a geometric envelope, an axial load, a number of load cycles, the type of glue (Hysol EA9460 or equivalent), the bondline thickness, and environmental conditions. Part of TPIÆs responsibility was to design the bonded joint to meet all specified requirements. The purpose of this memo is document the process used to develop the specifications and the process TPI used to design the bonded joint.

Material Selection


17-7PH stainless steel, an age-hardenable stainless steel, was selected as the endfitting material for its combination of corrosion resistance, high strength, and relatively low CTE. Corrosion resistance was needed to meet the expected 30 year life of the array, high strength helped to minimize the size of the fasteners that connect to the nodes (and thereby reduce the size of the nodes and the weight of the reflector), and a low CTE reduced the overall CTE of the antenna structure and was thought to reduce local stress in the bonded joint. Table 1 shows a comparison of the range of properties for plain carbon steel, age hardenable stainless steels, austenitic stainless steels, martensitic stainless steels, ferritic stainless steels, and Invar. Other materials were not considered.

Table 1: Comparison of Properties
Plain Age- Austenitic Martensitic FerriticStainless
Carbon HardenableStainlessStainlessStainlessInvar
SteelStainless
17-7PH
Strength (ksi) 36-120 175 80-100 70-280 65-85 65
CTE (ppm/degF) 7.9-8.4 5.6 8.3-9.6 5.5-6.2 5.2-6.6 0-2.0
Corrosion ResistancePoor Good Good Good Good Good
17-7 PH was chosen over Invar because of its superior strength and lower cost. 17-7PH was chosen over martensitic stainless because it is somewhat easier to machine. 17-7PH was chosen over plain steel for its corrosion resistance and lower CTE. 17-7PH was chosen over ferritic stainless because of strength. 17-7PH was chosen over austenitic stainless because of it higher strength and lower CTE.
The Hysol EA9460 glue made by Dexter was selected based on experience and the recommendation of Dexter. No testing prior to selection was performed nor was a detailed tradeoff between various glues done. The selection was based on Dexter being a leading manufacturer of structural adhesives, DexterÆs verbal recommendations, and data sheets/literature from Dexter. The thickness of the bondline was also based on recommendations from Dexter. Geometry Definition
The geometry of the tube assemblies depended on the geometry of the reflector backup structure (BUS) and the stiffness requirements derived from homology requirements. The homology stiffness requirements were derived from Philippe RaffinÆs finite element model (FEM) (Tech memo #51) and determine the required product of the cross-sectional area and longitudinal modulus (EA) and thus the inner diameter given that the outer diameter is fixed by the overall geometry of the BUS. These requirements established that only seven different EAÆs were required (OD/ID groups). This model was also used to match thermal expansion coefficients within the structure and resulted in the dash 25 tube having an extra long metal endfitting. The complex nature of the structure and the number of tubes intersecting at a node set the OD of the tube assemblies and limited the size of the bolt used to connect the tube.
Loads and Load Cycling


The operational loads were derived from Philippe RaffinÆs FEM. These were added to predictions of loads developed during assembly to get total loads contained in the tube assembly specification. Loads from the FEM combined the effects of a 56 m/s wind (using air density of 0.65 of sea level for Mauna Kea elevation), a 25 degree C global temperature change, and either a horizon gravity load or zenith elevation load. The load for each tube was computed for each load case (See Table 2 attached for reference). The absolute values of the loads for a 56 m/s wind, a 25 degree C global temperature change, and horizon gravity case were added together and the absolute values of the loads for a 56 m/s wind, a 25 degree C global temperature change, and zenith gravity case were added together for each tube type. Then the maximum result for a particular dash no. of tube was carried forward as the operational load. The results for each dash no. are shown in Table 3.
Table 3: Operational loads
Mater- Material name ial # as/tube designation in f.e.m. model) Max load (in LBS.) at elevation 0 deg. = Grav.Load + 56m/s wind + 25deg. C in reflector Max load (in LBS.) at elevation 90 deg = Grav.load + 56m/s wind + 25deg.C in reflector Max. oper load (lbs) Dash no. from spec
27 CFRP/ROD-BW1 650 463 650 1
15 CFRP/ROD-BW2 609 429 609 2
1 CFRP/ROD-WX-BRCGS 581 396 581 3
8 CFRP/ROD-YZ 179 158 179 4
25 CFRP/ROD-CD 250 188 250 5
7 CFRP/ROD-XY 519 460 519 6
18 CFRP/PYR-EZ 76 70 76 7
14 CFRP/ROD-EE 389 268 389 8
26 CFRP/ROD-DE 84 55 84 9
21 CFRP/ROD-AB45 912 723 912 10
13 CFRP/ROD-YY 331 220 331 11
23 CFRP/ROD-BC-BRCGS 651 480 651 12
10 CFRP/PYR-BX 546 401 546 13
16 CFRP/PYR-CX 504 348 504 14
11 CFRP/PYR-CY 392 257 392 15
17 CFRP/PYR-DY 220 159 220 16
12 CFRP/PYR-DZ 151 110 151 17
22 CFRP/ROD-BC 560 422 560 18
9 CFRP/ROD-WX 1138 977 1138 19
5 CFRP/ROD-CC 540 369 540 20
6 CFRP/ROD-DD 618 417 618 21
19 CFRP/ROD-ZZ 564 404 564 22
24 CFRP/ROD-BX-BRCGS 524 471 524 23
2 CFRP/ROD-XX 672 476 672 24
4 CFRP/ROD-BB 2581 2003 2581 25
3 CFRP/ROD-AB00 2138 1786 2138 26
20 CFRP/ROD-AW 2561 2119 2561 27
Assembly loads were calculated based on an assembly error of 0.0005 inches. Each tube is individually shimmed and the resolution of the shims is 0.0005 inches. The load was determined using the formula of P = (d * A * E) / L where: P = load in pounds d = 0.0005 inch A = cross-sectional area of the tube (in2) E = tube modulus (18,000,000 psi) The assembly loads were then added to the operational loads and the maximum for each OD/ID group (dash 1 thru 5, dash 5 thru 10, dash 11 thru 13, dash 14 thru 20, dash 21 thru 23, dash 24 thru 26, and dash 27) was used in the specification. The operational loads, the assembly loads, and the resulting specification load are summarized in Table 4. There is an error in that for the dash 19 and dash 25 tubes the sums for the expected operational and assembly loads exceed the specified load. The source of this error is unknown. The number of load cycles was estimated using a 30 year life and an assumption of approximately 9 slews from zenith to horizon and back per day. It should be noted that the peak wind loads are included as part of the fatigue requirement even though the number of cycles for this loading is much lower.

Environmental Conditions


Environmental conditions were derived from the antenna system specification. The temperature range is the worst case ambient temperature range of -20 degrees C to +30 degrees C. No effects of sun were included because the design includes a shroud that protects the tubes from exposure. Possible higher temperatures during painting/storage/shipment were assumed to be held within these limits. Humidity varies from 5% to 100% with condensation.

Joint Design Process


The joint was treated as a single lap shear joint using the bond area along the longitudinal axis of the tube. The bond area between the end of the tube and the endfitting (the area normal to the longitudinal axis of the tube) was ignored. The allowable shear stress was calculated by starting with a shear strength of 3000 psi (the shear strength is quoted by Dexter as 3500 psi for stainless steel). The 3000 psi was reduced by 43% to account for fatigue loading based on information contained in MIL-HDBK-691B for a similar epoxy bonded to aluminum. The basis for using data on aluminum was that the initial bond strength quoted by Dexter is the same for aluminum and stainless steel. The 43% reduction for fatigue reduced the allowable stress to 1710 psi. The allowable was then reduced by a factor of 2 for safety giving a final allowable bond strength of 855 psi. Bond

Table 4: Summary of operational and assembly loads
Dash no. Designation Max oper. ID OD A Tube Assy Sum of max
Load (mm) (mm) (in2) length load oper and assy
(lbs) (mm) (lbs) (lbs)
1 BWa 650 23.30 26.80 0.21 945 52 702
2 BWb 609 23.30 26.80 0.21 893 55 664
3 WXb 581 23.30 26.80 0.21 958 51 632
4 YZ 179 23.30 26.80 0.21 639 76 255
5 CD 250 23.30 26.80 0.21 627 78 328
6 XY 519 19.20 26.00 0.37 680 126 645
7 EZ 76 19.20 26.00 0.37 530 161 237
8 EE 389 19.20 26.00 0.37 683 125 514
9 DE 84 19.20 26.00 0.37 626 137 221
10 AB45 912 19.20 26.00 0.37 651 131 1043
11 YY 331 23.50 32.00 0.57 513 256 587
12 BCb 651 23.50 32.00 0.57 703 187 838
13 BXa 546 23.50 32.00 0.57 758 173 719
14 CX 504 31.50 40.00 0.74 577 293 797
15 CY 392 31.50 40.00 0.74 668 253 645
16 DY 220 31.50 40.00 0.74 505 335 555
17 DZ 151 31.50 40.00 0.74 646 262 413
18 BCa 560 31.50 40.80 0.82 629 298 858
19 WXa 1138 31.50 40.80 0.82 929 201 1339
20 CC 540 31.50 40.80 0.82 333 562 1102
21 DD 618 19.20 34.70 1.02 512 454 1072
22 ZZ 564 19.20 34.70 1.02 683 340 904
23 BXb 524 19.20 34.70 1.02 882 264 788
24 XX 672 25.80 52.00 2.48 333 1705 2377
25 BB 2581 25.80 52.00 2.48 400 1417 3998
26 AB00 2138 25.80 52.00 2.48 651 871 3009
27 AW 2561 54.50 80.00 4.18 924 1033 3594
lengths were then calculated for each ID/OD group and if the resulting length was less than 0.5 inches the length was then increased to 0.5 inches. The bond lengths were given by L = P / ((ID/25.4) x PI x allowable shear stress) where : L = bond length in inches P = specified load (lbs) ID = tube inner diameter (mm) PI = 3.14.16 Allowable shear stress = 855 psi Table 5 summarizes the tube loads, bond lengths, bond stresses, and margins of safety. The bond shear stress is given by S = Pa / ((ID/25.4) x PI x L) where: S = shear stress (psi) Pa = sum of maximum oper. load and assy load (lbs) ID = tube inner diameter (mm) PI = 3.14.16 L = bond length (in) The margin of safety for shear stress is given by M = ( Allowable shear stress / S ) - 1 where: M = margin of safety (unitless) Allowable shear stress = 855 psi S = shear stress as defined above.
Conclusions and Recommendations


Note that the local effects of temperature changes are not included in this calculation of the margin of safety. Some analysis of temperature effects was performed on the joint and the stresses due to these effects were thought to be small enough to be ignored. I am unable to locate documentation for this analysis and based on the failures that are occurring we should definitely revisit the issue of thermal stresses in the joint. The large variation in Margin of Safety for the 27 different tube types may allow us to continue use some of the TPI tubes without rework, if we can demonstrate that they have a sufficient, reliable allowable strength.

Table 5: Bond lengths and stresses with margins of safety.
Dash no. Desig- Max Assy Sum of Spec ID Req'd Actual Bond Margin of No. of
nation oper. load max oper load (mm) Bond Bond Stress Safety tubes
Load (lbs) and assy (lbs) Length Length (psi) above per
(lbs) (lbs) (in) (in) allowable antenna
1.00 BWa 650 52 702 1240 23.3 0.50 0.50 484 0.77 12
2.00 BWb 609 55 664 1240 23.3 0.50 0.50 458 0.87 12
3.00 WXb 581 51 632 1240 23.3 0.50 0.50 436 0.96 24
4.00 YZ 179 76 255 1240 23.3 0.50 0.50 176 3.86 24
5.00 CD 250 78 328 1240 23.3 0.50 0.50 226 2.78 24
6.00 XY 519 126 645 1450 19.2 0.71 0.71 380 1.25 24
7.00 EZ 76 161 237 1450 19.2 0.71 0.71 140 5.11 48
8.00 EE 389 125 514 1450 19.2 0.71 0.71 303 1.82 24
9.00 DE 84 137 221 1450 19.2 0.71 0.71 130 5.57 24
10.00 AB45 912 131 1043 1450 19.2 0.71 0.71 615 0.39 4
11.00 YY 331 256 587 1100 23.5 0.44 0.50 404 1.12 24
12.00 BCb 651 187 838 1100 23.5 0.44 0.50 576 0.48 24
13.00 BXa 546 173 719 1100 23.5 0.44 0.50 495 0.73 24
14.00 CX 504 293 797 900 31.5 0.27 0.50 409 1.09 48
15.00 CY 392 253 645 900 31.5 0.27 0.50 331 1.58 48
16.00 DY 220 335 555 900 31.5 0.27 0.50 285 2.00 48
17.00 DZ 151 262 413 900 31.5 0.27 0.50 212 3.03 48
18.00 BCa 560 298 858 1200 31.5 0.36 0.50 440 0.94 12
19.00 WXa 1138 201 1339 1200 31.5 0.36 0.50 688 0.24 12
20.00 CC 540 562 1102 1200 31.5 0.36 0.50 566 0.51 24
21.00 DD 618 454 1072 1450 19.2 0.71 0.71 632 0.35 24
22.00 ZZ 564 340 904 1450 19.2 0.71 0.71 533 0.60 24
23.00 BXb 524 264 788 1450 19.2 0.71 0.71 464 0.84 12
24.00 XX 672 1705 2377 3600 25.8 1.32 1.32 564 0.51 24
25.00 BB 2581 1417 3998 3600 25.8 1.32 1.32 950 -0.10 12
26.00 AB00 2138 871 3009 3600 25.8 1.32 1.32 715 0.20 8
27.00 AW 2561 1033 3594 4400 54.5 0.76 0.76 698 0.22 12
Total # of tubes 648
Min. margin of safety -0.1