Analysis and Correction of a Design Failure

Transcription

1 Analysis and Correction of a Design Failure Brett Sorensen U.S. Army Research Laboratory AMSRD-ARL-WM-TC, APG, MD Abstract This paper presents a case study of an incremental design process of a kinetic energy (KE) projectile in which simplifying assumptions that were valid for the initial projectile design were found to be inappropriate for a subsequent projectile design, resulting in a flawed design and led to a material failure. After failure of the projectile was observed, a root-cause analysis was conducted and indicated that column buckling was responsible. This was later confirmed by ensuing analyses. After the flawed assumption was eliminated, a modification to the existing projectiles was analyzed and successfully implemented. The projectile was then redesigned to incorporate the features and lessons identified through this process. Background Terminal ballistic evaluation of anti-armor, KE penetrators in an applied research environment usually utilizes a push-launch technology (Figure 1). The high-density penetrator is supported in the radial direction by a low-density sabot, usually nylon, and in the axial direction by a pusher-plate, usually steel. Finally, the bore is sealed by a nylon obturator. The sabot is typically split along the axial direction into four pieces, so at muzzle exit, aerodynamic loads cause the four sabot petals to open and discard from the penetrator, leaving the penetrator to impact the target without any parasitic mass. This arrangement is economic and functions very well until the combination of penetrator aspect ratio (length-to-diameter ratio, L/D) and acceleration initiates plasticity at the base of the penetrator. Obturator Pusher Plate Sabot Penetrator Figure 1. Push-launch nylon sabot configuration As penetrator L/D and velocity requirements increase, forces at the base of the penetrator rise to the point where excessive plastic strain leads to either shear failure, or column buckling of the penetrator. Since the low modulus of the nylon sabot provides minimal radial support, substituting aluminum for the nylon (Fig. 2) has been demonstrated to both control the amount of plastic strain and provide the required radial support to prevent buckling (Sorensen, 1998).

2 Obturator Pusher Plate Sabot Penetrator Figure 2. Push-launch aluminum sabot configuration The initial designs for the aluminum push-launch sabot were used with medium L/D penetrators to achieve impact velocities higher than available with a nylon sabot. Since aluminum has a higher density than nylon, sabot material was removed to keep launch mass low enough to achieve the desired velocities, creating a saddle between the two bore-riding surfaces. Even though the sabot consisted of four petals, the stubby geometry and loading conditions permitted the projectile to be modeled in a two-dimensional (2 D), axisymmetric fashion. As the maximum loads in the sabot were located in the aft full-bore region, the sabot was designed to avoid plasticity within the saddle, thus preventing a plastic hinge leading to a buckling condition in each petal. This simple precaution was deemed sufficient to prevent failure and was supported by successful launches. After the initial successes, the concept was applied to penetrator designs with higher L/Ds and higher velocity requirements. These requirements led to more aggressive sabot designs in which the saddle became longer and thinner. Since the initial model was parametric, new designs were generated new designs were generated without thought toward buckling until recently when poor launch results and penetrator failures were observed. Analysis of radiographic images from these experiments showed that the sabot petals were buckling in the cannon. This paper presents the initial design analyses, the buckling analysis, and the modification and redesign efforts. As the modeling effort includes both contact and plasticity in a three-dimensional (3 D) space, lessons learned about convergence and geometry creation using unbonded vs. bonded contact will also be discussed. Initial Design Figure 3 presents the final geometry of a projectile designed in ANSYS to launch a L/D 30 tungsten alloy (WA) penetrator from a 50-mm high pressure cannon. As previously described, an aluminum push-launch sabot was configured to support the penetrator while in-bore and to cleanly discard from the penetrator at muzzle exit. To meet the velocity objectives of the experiment, sabot mass was minimized, resulting in the slender taper in the saddle region between the two bore-riding surfaces.

3 Obturator Push plate Sabot Figure 3. Final geometry of a L/D 30 WA penetrator with an aluminum push-launch sabot As with previous designs, the axisymmetric PLANE42 element was used with full contact (TARGE169 and CONTA171 elements) at all material interfaces. To provide stiffness between the parts, weak axial springs were placed to assist with convergence until sufficient stress developed across the contact elements to provide the necessary stiffness. Boundary conditions are displayed in Figure 4. An axial constraint was placed at the front of the penetrator and radial constraints are placed at the obturator to simulate the cannon bore. Pressure was applied to the back of the obturator and, to balance the model, the proper acceleration was applied. The loads were applied gradually to permit contact and frictional forces to develop correctly in both the elastic and plastic regimes. Finally, bilinear plasticity models were used for the penetrator and the sabot with yield strengths of 1200 MPa and 565 MPa, respectively. Figure 4. Finite element mesh with boundary conditions Figure 5 presents the stress and strain results for the projectile and the sabot. Examination of the plastic strain results show that the main design goals were achieved; plastic strain in the penetrator was controlled and avoided in the sabot. In the penetrator, maximum through-section plastic strain is between 2.5 and 3.0%, with 60% of the penetrator length in the plastic zone. Without the hydrostatic restraint of the sabot, the penetrator would have failed between 1 and 2% plastic compressive strain; clearly, the sabot is supporting the penetrator. In the sabot, evidence of the plastic penetrator strain is seen by the high stress profile along the interface. The compressive plastic strain results in radial growth due to Poisson s ratio, thus increasing the effective stress in the sabot near the interface.

4 Figure 5. Effective stress and plastic strain results To confirm that the stress and strain results are accurate, the condition of the contact surfaces must be examined for excessive penetration. Figure 6 presents a displacement plot of the penetrator (white), sabot (yellow), and pusher plate (red), showing no nodal penetration along the contact surfaces. To obtain this result, the real constants fkn and ftoln for CONTAC171 were set at 1.0 and 0.05, respectively. These values are very similar to the suggested values of 1.0 and 0.2 provided by the ANSYS documentation. In the initial solutions, convergence was acceptable, but penetration was not; therefore, fkn was increased while ftoln was decreased. However, increases in fkn led to convergence difficulties, so only ftoln was modified until penetration was acceptable. Figure 6. Displacement plot showing that the contact elements have prevented penetration of the different materials

5 After completion of the projectile design and manufacturing, initial experiments were conducted. From the beginning of the experiments, impact conditions of the penetrator on the target were inconsistent, with both excessive yaw and flexure observed in radiographs (Figure 7). Here, two separate exposures with a time delay were taken to so that velocity measurements could be made. The images seen in Figure 7 correspond to the first image of the penetrator (moving right to left) and the second image of the four sabot petals; the back of the penetrator for the second image is also visible. This radiograph clearly shows the penetrator and sabot petals are bent; however, this is not unusual for the sabot petals. The aerodynamic loads which cause the sabot to discard from the penetrator, quite often cause the sabots to bend. Also, instrumentation just off of the shotline is frequently hit by the sabots, causing additional bending and damage. So, upon seeing the initial results, it was not readily apparent why penetrators were bent. Only after several experiments were conducted and the shape of the sabot petals was seen to be repeatable, did the closer examination of the sabots occur. At this point, the consistent shape of the sabot petals led to the conclusions that they were buckling inbore as indicated by the red line in Figure 7 which traces the penetrator/sabot interface of one petal. Once buckling occurred, support to the penetrator was significantly compromised, leading to its excessive deformation. Additionally, with the deformed shape at muzzle exit, sabot discard could also contribute to the disruptive effects to the penetrator. Figure 7. Radiograph of the penetrator and sabot petals just prior to target impact Buckling Analysis To determine if the sabot petals did fail from buckling, a buckling analysis was performed. Using the sabot geometry defined in the 2 D analysis described earlier, the areas were rotated 45 o about the y-axis and meshed with SOLID45 elements (see Figure 8). Ideally, rigid boundaries representing the penetrator, pusher plate, and cannon bore would be used to create 1/8 of the complete model with the proper contact and boundary conditions. However, this would have required a non-linear analysis which was deemed too

6 time consuming; thus, the eigen-value extraction method was chosen. To simulate the boundary conditions, the xy-plane was defined as a symmetry plane and radial constraints were applied to the boreriding surfaces after they were rotated into a cylindrical coordinate system. To fully constrain the model, axial constraints were placed on the front of the forward bore-riding surface. At this point, pressure was applied to the back of the sabot and an acceleration in the y-direction applied to balance the model. Since elastic material properties were being used, the model was solved in a single load step. Figure 8. 3 D half-model of a sabot petal meshed with SOLID45 elements At this point, the analysis type was switched to a buckling analysis and the first mode was extracted. Figure 9 shows the deformed geometry of the first mode, matching the deformed shape observed in Figure 7. Furthermore, it occurred at 88% of the total load, indicating that buckling was responsible for the observed failure. Figure 9. Displacement plot of the first extracted mode of an eigen-value buckling analysis Projectile Modification To use the remaining sabots, it was obvious from the buckling analysis that additional stiffness in the radial direction was required to prevent failure. To determine if this was feasible, the buckling analysis was repeated with the addition of radial supports (via nodal constraints) along the midline at the center of the saddle. This analysis resulted in an increase of the buckling load to 400% of the maximum load. To physically realize the increased radial stiffness, an additional bore-rider was placed in the middle of the saddle in the form of a rib. This rib was created by milling a slot on the midline of each sabot petal and then pressing a plate into the slot. The plate was shaped to contact the penetrator, the outside of the saddle, and the bore of the cannon as displayed in Figure 10. This configuration would keep the penetrator on the centerline of the cannon and the sabot petals from buckling. Figure 10. Proposed rib geometry pressed into the sabot saddle to provide radial stiffness

7 To determine if the presence of the rib would affect performance of the sabot at maximum in-bore loads, a 3 D analysis was performed. To reduce problem size, symmetry was used to model a 45 o section between the midplane of a sabot petal to the split between the next petal. SOLID45 elements were used for the penetrator and pusher plate and SOLID92 elements for the sabot and rib. Contact elements were placed at all material interfaces. Rigid contact surfaces were placed at the interface between the sabot petals (45 o plane) and the cannon bore. For the penetrator and pusher plate, symmetry boundary conditions were placed at both 0 o and 45 o. For the sabot and rib, symmetry boundary conditions were placed at 0 o. Adding an axial constraint at the front of the penetrator fully constrained the model. Results from the 3 D rib analysis are presented in Figure 11. Comparing these results to the axisymmetric results in Figure 5 clearly shows that the axisymmetry assumption was flawed by more than the inability to capture buckling. In Figure 5, plastic strain in the penetrator is localized at the back of the penetrator. In the 3 D analysis, plastic strain is maximized under the rib. The axisymmetry assumption provided radial support through hoop stress, driving the plastic strain to the back of the penetrator where the maximum inertial loads exist. While the rib provides radial support to prevent buckling, it does not provide level of hoop stiffness. This decreased stiffness is reflected by the transfer of plastic strain forward in the penetrator. Stress distribution in the sabot is also different. Here, high contact stresses exist around the rib and the dominant axial inertial loads are also apparent. Away from the rib interface, effective stress magnitude is comparable to those seen if Figure 5, but the radial component along the penetrator interface is missing; again demonstrating the lack of hoop stress provided by the sabot. Regardless, stress distribution in the sabot and rib are well within acceptable levels, and the penetrator strain levels have been adequately managed. Figure 11. Effective stress and plastic strain results of the 3 D model using a rib to prevent buckling Figure 12 presents a striking radiograph of the modified projectile. As the striking velocity and breech pressure were consistent with the previous experiments, the loading conditions are comparable with those in Figure 7 and the ribs have clearly prevented the buckling failure; however, the aerodynamic loads have caused the front bore rider to fail and break off. While this is not unusual, it is generally considered undesirable. To prevent this, an integral rib along the entire length of the sabot would be required. Regardless, the penetrator is straight, if somewhat yawed and, in general, impact conditions were improved.

8 Figure 12. Striking radiograph of the modified sabot after the addition of a rib Future Design Considerations While the design modification appeared to function for the existing sabots, it was impractical to continue once the existing lot of sabots was consumed. For the next lot, a design with an integral rib was required. This rib would prevent buckling and at the same time, keep the sabot petals from breaking at discard. To minimize sabot mass, the rib had to be thin and also provide axial support to minimize the mass of the saddle itself. Results of this design are presented in Figure 13a with the elastic limit only being approached at the back of the rib. To create the model, a thin plate was integrated into the revolved body and meshed with solid elements to create the sabot petal. Generating the model and controlling element size was not an insignificant issue due to the thickness of the rib; too thick for shell elements and too thin for free meshing with tetrahedrons. However, using bonded contact to join dissimilar parts would simplify model creation in the future; thus, two variations of the model were created to examine the effects of bonded contact. In the first, the saddle was created without considering the rib. Then the rib was created using the keypoints, and nodes, on the symmetry plane of the saddle for part of the rib. Depth was added by dragging the areas. Finally, bonded contact was created between the two meshes. The results of this variation are provided in Figure 13b. The second variation was to build the rib separately with no shared keypoints or nodes and provide contact solely through bonded contact. These results are shown in Figure 13c. Review of the results in Figure 13 shows that in the macroscopic view, each interface method returns the same stress distribution. However, in the microscopic view, there are slight differences, particularly along the interface. Comparing Figure 13a and 13b, the increased stress riser along the aft taper on the symmetry plane for 13b and its absence on the opposite view indicates that the bonded contact may attenuate the stress across a discontinuity. In 13b, the higher stresses on the symmetry plane are due to the shared nodes along one edge of the elements creating a notch. Since the stresses are lower for 13b on the free surface of the rib than those for 13a, the bonded contact appears to be more compliant, increasing the effect of the

9 notch. This is supported by 13c where the stress riser along the interface is not apparent in either view. Since the three results are very similar, bonded contact appears to be a very useful means to attach volumes of dissimilar shapes as long as the interface itself is not the controlling, or limiting feature in the design. Figure 13. Effective stress in the sabot for three different methods for modeling the interface between the rib and the saddle. Contours are the same for all cases. The upper image in each shows the symmetry plane. Conclusions This paper presented a case study demonstrating the importance of careful review of all assumptions when starting a new design, or analysis. In this case, an existing projectile design was extrapolated to fit a new, longer penetrator design. Since parametric input decks existed and the previous design had already been demonstrated, the new dimensions were simply entered and modified to achieve all design goals. The assumption of axial symmetry was never questioned as the design became more slender, leading the observed buckling failure. After the new projectile failed, review of the assumptions required a move to a 3 D model to verify the failure mode and determine a feasible modification. The 3 D buckling analysis compared very well with the experimental results and identified the means to correct the design. After adding a stiffening rib, the projectile was successfully tested. Finally, in the process of designing an integral rib for the next projectile, the flexibility of model creation using bonded contact was examined. The new geometry required mapped mesh generation to keep problem size reasonable and still accurately resolve the loads. A full-length, integral rib was added through a variety of methods and showed that bonded contact was effective in resolving the global stresses; however, some accuracy in the local region may have been lost. Regardless, bonded contact is a powerful tool in complex model generation when used appropriately.

10 References Sorensen, B.R., The Design, Experimental Verification, and Failure Analysis of a 50-mm Cannon Launched Projectile: A Case Study, 1998 ANSYS Conference, Pittsburgh, PA, August ANSYS User s Documentation.