Approved for Public Release 13th PARARI, 21~23, Nov Mechanical Failure Prediction of Composite Rocket Cases

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1 Mechanical Failure Prediction of Composite Rocket Cases Roger Li 1 Weapons and Combat Systems Division, DST This paper demonstrates mechanical failure analysis of a pressurised 10 rocket case made of epoxy carbon fibre composite. The mechanical failure modes were simulated in finite element analysis (FEA) using LS/DYNA. The example rocket motor case uses a quasi-isotropic layup similar to 0 /90 /- 45 /+45, and is well-suited to cope with the different failure modes, and particularly in-plane shear failures which cause fibre tow splitting in the dome areas. The material properties of the quasi-isotropic composite were captured by experimental coupon tests and test simulation in LS/DYNA. Then these quasi-isotropic composite material properties were used in the FEA models of the rocket case to predict the failure modes and burst pressure. This paper will discuss the simulation results, based on a rocket case of 3 mm thickness made from T700 grade carbon fibre composite. Keywords: Solid Rocket, Composite Case, Failure Prediction Quasi-isotropic Laminate. 1 Introduction Rocket performance is characterised by thrust generated by high speed, high pressure fluids from its nozzle. The propulsion parameters include the ratio of nozzle exit pressure to the ambient pressure. Higher is the rocket case pressure, higher is the propulsion performance. Advanced rocket cases can employ filament winding or 3D woven composite technologies to integrate cylindrical and dome parts, and even bring nozzle throat and expansion cones together into a single composite structure without the need for bolted or bonded joints. Such design features, married with the reduced weight offered by carbon, Kevlar or poly(p-phenylene benzobisoxazole) (PBO) fibres, can produce high performance rocket cases with a structure weight rather than propellant less than 10% of total rocket weight. 1 roger.li@dst.defence.gov.au

2 Figure 1 A DST 24 composite rocket case demonstrator (igniter side up) However, such an integrated structure also introduces multiple failure modes to the pressurised case, which can appear during hydroburst proof tests and live firings. They could be carbon fibre tensile failure in the cylinder area caused by hoop stress, and particularly in-plane shear failures which cause fibre tow splitting in the dome areas. The key in optimisation case design minimising case structure weight is to avoid excessive design safety margin in each of failure modes. Efficient and optimised rocket cases must possess failure modes which occur at roughly the same case pressures. There is thus a critical requirement to accurately predict these failure modes and loads. This paper demonstrates mechanical failure analysis of a pressurised 10 rocket case made of epoxy carbon fibre composite. The mechanical failure modes were simulated in finite element analysis (FEA) using LS/DYNA. The example rocket motor case uses a quasi-isotropic layup similar to 0 /90 /- 45 /+45, and is well-suited to cope with the different failure modes, and particularly in-plane shear failures which cause fibre tow splitting in the dome areas. The strength of quasi-isotropic carbon fibre composite was determined by coupon tests. The coupon tests were subsequently simulated in LS/DYNA, thereby capturing the whole set of quasi-isotropic material properties of the composite derived from such a layup sequence. By subsequently feeding the quasi-isotropic composite material properties into the LS-DYNA FEA model of the rocket case, the failure modes and burst pressure of the all-up case were predicted. 2 Composite coupon tests and FEA models 2.1 ASTM D2290 ring split disk tensile testing ASTM D2290 ring split disk tensile testing was chosen as the coupon test to capture the material properties of composite rocket cases because the coupons for this test are cut from composite cylinder made of similar quasi-isotropic layup, as shown in Figure 2. Cut from a cylinder, these ring specimens are more representative to composite

3 rocket motor cases than flat coupons normally used in dumbbell tensile or three point bending tests. Figure 2 5 3/4 mandrel and composite tube for ASTM D2290 split disk ring tensile testing A quasi-isotropic layup similar to 0 /90 /-45 /+45 has four or more fibre orientation angles, is well-suited to cope with the different failure modes, particularly in-plane shear failures which cause fibre tow splitting in the dome areas. The strength of composite used for rocket motor cases was determined by ASTM D2290 split disk ring tensile testing by repeating the same quasi-isotropic layup of carbon fibre orientation as much as possible, as shown in Table 1. Table 1 Quasi-isotropic layups in this work Orientation angles Hoop tow Helical tow Polar tow D2290 ring ±89 ±37 ±9 24 case ±88 ±35 ±17 10 case ±88 ±35 (50%±25 and 50%±45 ) ±18 For such quasi-isotropic composites with at least quadriaxial fibrous orientation angles, Hart-Smith [1] has proposed a "Ten-Percent Rule" that each 45 or 90 ply was considered to have one-tenth of the axial stiffness and strength of a reference 0 ply, based on his empirical discoveries that each 45 ply has about 12%, 90 about 8% of the axial stiffness and strength of a 0 ply. This "Ten-Percent Rule" also considers that each 0 or 90 ply has only one-tenth of the in-plane shear stiffness and strength of an equivalent ±45 ply. In other words, the in-plane shear strength of a cross-plied laminate depends on greatly whether there is fibre tows aligning with maximum shear direction (normally ± 45 ). Typical loading curves of ASTM D2290 split disk ring tensile testing of T700 composite rings are shown in Figure 3.

4 Figure 3 Loading curves of ASTM D2290 split disk ring tensile testing of T700 composite rings Having subtracted the system compliance from the loading displacement, the ASTM D2290 testing results are shown in Table 2. Table 2 Results of T700 quasi-isotropic composite disks Fibre type Maximum tensile stress/mpa Tensile extension at maximum load/mm T ASTM D2290 ring split disk tensile testing simulation A number of LS/DYNA models were created to simulate the ASTM D2290 ring split disk tensile testing with various material failure algorithms. One of them is shown in Figure 4. The model was built with 4032 brick elements and 5054 nodes. Figure 4 Simulation of ASTM D2290 split disk tensile test of quasi-isotropic composite ring Two material models were found able to reproduce the test results in LS/DYNA simulation as shown in Figure 5. They are Types 022 Composite_Damage and 040 Nonlinear_Orthotropic material models [2], referred as Damage and Burst

5 respectively in Figure 5. When the material fails, its strength is downgraded to 10% of pristine material in the Damage model, and to zero (the failed elements are deleted from the mesh) in the Burst model respectively. The former can reproduce the postfailure load versus displace detail while the latter looks more realistic in instant post-failure load drop in time scale. Figure 5 Test and FEA comparison of No.2 specimen in ASTM D2290 test With the coupon test results were simulated in LS/DYNA, the whole set of quasiisotropic material properties of the composite can be derived either in Types 022 Composite_Damage or 040 Nonlinear_Orthotropic material model formats [2] composite rocket case hydroburst testing simulation A number of LS/DYNA models were created to simulate the 10 composite rocket case hydroburst testing with various material failure algorithms. One of them is simulating one quarter of 10 composite rocket case using two symmetric conditions, as shown in Figure 6. The model was built with 9342 brick elements and nodes. This case model has a 3 mm uniformly thickness, is different from realistic composite rocket cases whose two domes always have increased thickness from the cylinder to openings because of fibre tow build-up. Figure 6 Simulation of 10 inch rocket case made of quasi-isotropic composite in LS/DYNA

6 Both the types 022 Composite_Damage and 040 Nonlinear_Orthotropic material models [2] have been used in the 10 composite rocket cases. They predict very close burst results in hydroburst test simulation. In the following sections of this paper, only the Damage model results are presented. 3 Results and discussions 3.1 Failure predictions Using the materials of the quasi-isotropic derived from above exercise, the implicit solution of LS/DYNA predicts the sample 10 composite case, excluding the two fibre tow built-up areas around two openings, would fail at a burst pressure of 17.5 MPa, as shown as time = 175 in Figure 7. At this failure point, the maximum hoop stress is MPa for the cylinder area. Figure 7 Tensile stress of the sample 10 composite rocket case excluding the tow build-up areas at the predicted failure point However, if the two fibre tow built-up areas are included, the maximum tensile stress is 2753 MPa there at the same failure point, more than three times higher than MPa for the cylinder area, as shown in Figure 8. Figure 8 Tensile stress of the sample 10 composite rocket case including the tow build-up areas at the predicted failure point

7 Nevertheless a true composite case would not fail around the openings by tension due to the facts that there are the thickness would be more than tripled by fibre tow builtup, and the fibre tows is more aligned with the maximum principal stress direction so that the strength in that direction should be much higher than the quasi-isotropic one derived from the ASTM D2290 ring tension test. 3.2 Case deformations At the same failure point, the maximum longitudinal and radical deformations are 6.8 and 2.0 mm respectively (X and Z here are the global coordinate longitudinal and radical directions of composite rocket case). Figure 9 Deformation of the sample 10 composite rocket case at the failure point Such case deformation cause about 0.5 mm dislocation of case opening against the aft boss, as shown in Figure 10. This dislocation requires a highly elastic shear ply in place to seal the gap between the case and the aft boss, or there will be a shear-out failure before the predicted 17.5 MPa pressure by hoop stress in the cylinder area. A B Figure 10 Relative movement of case opening against aft boss (A: unloaded, B: at the failure point) At the same failure point, the maximum in-plane shear stress of composite case is 29.9 MPa (X and Y here are two in-plane directions of materials coordinate of composite brick elements). This shear stress level is only half of normal 10 ksi shear strength of matrix resin, The quasi-isotropic layup here does smooth the stress down and prevents the tow splitting shear failure of composite in the dome areas.

8 Figure 11 In-plane shear stress of composite case at the failure point 4 Conclusions Using the materials of the quasi-isotropic derived from ASTM D2290 test, LS/DYNA predicts the sample 10 composite case would fail at a burst pressure of 17.5 MPa by high hoop stress in the cylinder area. At the same failure point, the maximum longitudinal and radical deformations are 6.8 and 2.0 mm respectively, causing ~ 0.5 mm dislocation of case opening against the aft boss. This dislocation requires a highly elastic shear ply between the composite case and aft boss, or there will be a shear-out failure before the predicted 17.5 MPa pressure by hoop stress in the cylinder area. At the same failure point, the maximum in-plane shear stress of composite case is 29.9 MPa, is only half of normal 10 ksi (69MPa) shear strength of matrix resin, demonstrating the advantage of a quasi-isotropic layup for prevent the tow splitting shear failure of composite in the dome areas. 5 References 1. Hart-Smith, L. J., The ten-percent rule for preliminary sizing of fibrous composite structures AA(Douglas Aircraft Co., Long Beach, CA) Publication, Weight Engineering (ISSN ), vol. 52, no. 2, p LSTC, LS-DYNA Keyword User s Manual Vol II: Material Models, Livermore Software Technology Corporation (LSTC), 05/26/16 (r:7647). 6 Acknowledgments The author sincerely appreciates DST Weapons Propulsion Group staff, in particular Dr Ian Johnston for various professional advice, and Dr Greg Yandek of US Air Force Research Lab for S&T advice in composite rocket case design and manufacture.