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					          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


    VERIFICATION AND VALIDATION OF A PENETRATION MODEL FOR THE
               DESIGN OF A BLAST CONTAINMENT VESSEL
                        Part II: Model Validation


                                    Edward A. Rodriguez # , Jason E. Pepin %
                                       Los Alamos National Laboratory
                                       Los Alamos, New Mexico 87545
                                     (505) 665-6195; erodriguez@lanl.gov


                   David S. Riha ∗ , Ben H. Thacker ‡ , Jason B. Pleming ∗ ∗ , James D. Walker †
                                          Southwest Research Institute
                                           San Antonio, Texas 78238
                                        (210) 522-2340; driha@swri.org



                                                  ABSTRACT
The use of computational simulation is increasingly relied upon as performance requirements for engineered
systems increase and as a means of reducing testing. Model verification and validation (V&V) provides a
mechanism to develop computational models that are utilized for engineering predictions and ensure decisions
with quantified confidence. The Los Alamos National Laboratory Dynamic Experimentation (DynEx) program
is designing and validating steel blast containment vessels using limited experiments coupled with computational
models. This paper describes the verification and validation of an analytical and computational model used to
predict the penetration depth of explosively released fragments into the containment vessel structure. A
systematic approach of model V&V is used to compare model predictions and experiments and establish metrics
to quantify confidence. The use of uncertainty quantification is an essential part of V&V as there are inherent
and subjective uncertainties in the model that must be correlated with the uncertainties from the experiments.


                                              INTRODUCTION
At Los Alamos National Laboratory (LANL) the Dynamic Experimentation (DynEx) program is designing,
manufacturing, and validating steel blast containment vessels to support investigations of high-pressure shock
compression behavior of materials. Using a limited set of experiments, coupled with computational detonation
hydrodynamics and structural dynamics models, the DynEx Program is attempting to V&V vessel design for
typical detonation blast loading. Figure 1 depicts the LANL containment vessel, showing four equidistant ports
on the equatorial axis used for radiographic access to image the phenomena through “windows” consisting of
boron carbide ceramic (B4C), beryllium (Be), and aluminum (Al). The top port is utilized for equipment entry
and diagnostic cabling feed-through for monitoring the experiment. The experimental package is situated inside
a hexapod basket attached to the upper port nozzle flange. Figure 2 shows the Dual-Axis Containment System
(DACS) comprised of an outer safety vessel, as a secondary barrier, and the inner containment vessel primary
barrier. Each vessel is manufactured with forged nozzle assemblies to reinforce the radiographic entry and exit
ports.



#
  DynEx Deputy Project Director, ESA-DO, SM-30 Bikini Atoll Road
%
   Technical Staff Member ESA-WR, SM-30 Bikini Atoll Road
∗
  Senior Staff Engineer, Reliability and Materials Engineering, 6220 Culebra Road, 78238
‡
  Director, Materials Engineering Department, 6220 Culebra, 78238, AIAA Member
∗∗
   Staff Engineer, Reliability and Materials Engineering, 6220 Culebra Road, 78238
†
  Staff Scientist, Mechanical and Materials Engineering, 6220 Culebra, 78238, AIAA Associate Fellow

                                                 1
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference




Figure 1. Dual-Axis containment vessel.                  Figure 2. Dual-Axis containment system.




            Figure 3. Containment vessel (left) and FE mesh used for the dynamic analysis (right).

The requirement for primary and secondary barriers is of utmost importance in blast containment design at
LANL, specifically as prevention against the expulsion of radioactive and hazardous materials. The US
Department of Energy (DOE) requirements are satisfied by the DACS system in mitigating explosion reaction
products and containing radioactive and hazardous particulates.

During explosion experiments the vessel walls and windows, Figure 4, are subject to impact from fragments.
Successful performance of the vessel is defined when a projectile penetrates less than half the thickness of the
outer window layer. The vessel design goal is to minimize window thickness to increase X-ray resolution while
mitigating fragment penetration.




                                                 2
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference




                                                        X-RAY
                                                    TUNGSTEN                                          X-RAY
                                                    SHIELDING                                         TUNGSTEN
                                                      PLATES                                          SHIELDING
                                                                                                      COVER PLATE

                                                 ROUGH X-RAY
                                                  COLLIMATOR




                                                      ENTRY                                           ENTRY LINE
                                                      COVER                                           OF SIGHT
                                                                                                      TUBE




                                                  CONFINEMENT
                                                  VESSEL ENTRY
                                                       NOZZLE



                                       Figure 4 – Radiographic window.


However, high velocity fragments that would potentially penetrate or perforate the beryllium radiographic
window and subsequently the safety vessel window, this would pose an environmental concern. As such, the
window design attempts to incorporate stacks of sacrificial B4C disks to mitigate penetration into the Be by
providing sufficient layers to break-up the fragments without compromising the radiographic quality necessary
for the experiments. This paper describes the computational effort in determining depth of penetration into the
beryllium windows for a series of possible fragment lengths. It should be stated that these fragments are
conservatively treated as long-rod penetrators to simplify the solution.


                                    VERIFICATION AND VALIDATION
In situations where full-scale experimental programs cannot be performed, the decision makers must rely on a
predictive strategy such as computational models. The key to establishing confidence, or credibility, in model
predictions is the development, implementation and practice of a process called model verification and validation
(V&V). Model V&V provides a systematic process for building and quantifying confidence in model
predictions through the logical combination of focused laboratory experimentation, hierarchical model building,
and uncertainty quantification (Thacker, 2005). Verification is the process of determining that a model
implementation accurately represents the developer’s conceptual description of the model and its solution.
Validation is the process of determining the degree to which a model is an accurate representation of the real
world from the perspective of the intended uses of the model (AIAA, 1998). In short, verification is a
mathematics issue, whereas validation is a physics issue.

Uncertainty quantification plays a key role in model V&V. Nondeterminism refers to existence of errors and
uncertainties in outputs of computational simulations due to inherent and subjective model uncertainties.
Likewise, measurements that are made to validate these simulation outputs also contain errors and uncertainties.
While experimental outcomes are used as reference for comparison, the V&V process does not presume the
experiment be more accurate than the simulation. Instead, the goal is to quantify uncertainties in both
experimental and numerical simulation results such that the model fidelity requirements can be assessed
(validation) and the predictive accuracy of the model quantified. The role of non-determinism in model V&V is
more fully discussed in Thacker et al., 2004.

For the DynEx project at LANL, V&V plays a leading role in the overall effort of testing and analysis. The
predictive tools and models utilized for both hydrodynamics and structural dynamics are rigorously exercised
through as complete a V&V process as possible. In certain instances it becomes prohibitively expensive to
conduct certain full-system experiments, and as such must rely on sub-system and component level test
providing a portion of the V&V effort.

                                                 3
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


                                       VALIDATION EXPERIMENTS
Validation experiments were performed to obtain the penetration depth of depleted uranium (DU) rods launched
into the window materials for several configurations in support of the vessel design (Mullin, et al. 2005). The
projectiles were 5mm in diameter and ranged from 10 to 50mm in length; ejected at impact velocity of 2.0 km/s.
Part I, of the two-part paper series presented at the 47th AIAA Structures, Structural Dynamics, and Materials
Conference (Mullins, et al. 2006) describes the test series developed and conducted at Southwest Research
Institute (SwRI).

         The task was to analyze the penetration threat from three different sizes of DU rod-shaped
projectiles. The rods were 5mm in diameter; three lengths were used: 10, 30, and 50mm. These
projectiles were manufactured by LANL, in the alloy designated U6Nb. For all tests the impact
velocities were nominally 2.0 km/s. The main concern from a confinement perspective is fragment
impact into the two X-ray windows made of Al 7050-T7451 and beryllium S-65C. In the tests the Al
target was a simple rectangular block 6.0 inches square and 2.0 inches thick, shown in Figures 3 and 4.
The Be target was more complex. The Be core was actually a truncated conical section, slightly larger
in diameter on the impact side (diameter = 1.75 inch) than the rear side (diameter = 1.64 inch), and
1.75 inches thick. It was press fit into the center of the 9-inch square, 1.9 inch thick steel support
assembly. Two rubber O-rings were placed into grooves cut into the center hole of the steel plate to
help hold the Be disk in place. On the impact side of the target a steel plate was screwed that helped
support the ceramic armor disks and the edge of the Be piece (Figure 5). On the rear side of the Be
target assembly an aluminum plate was placed that covered the rear of the Be disk. This aluminum
plate thickness directly behind the Be disk was 0.24 inches. The Be target assembly with this rear
aluminum plate removed can be seen in Figure 6.




Figure 5. View of the front of a Be target showing
                                                         Figure 6.   View of the rear of a Be target with the
          the stack of B4C armor tiles (above the
                                                                     rear aluminum plate removed, showing the
          impact side of the Be piece).
                                                                     back side of the Be disk.


                           ANALYTICAL AND COMPUTATIONAL MODELS

Analytical Model
An analytical model was developed along the lines of the Walker-Anderson penetration model, modified to
account for the two or three materials in the target assembly (Walker, et al, 2005). This model was integrated in
the NESSUS probabilistic analysis program (Riha, et al, 2004) to provide a deterministic and probabilistic design
tool and named the DynEx penetration model. The NESSUS probabilistic materials database is used to define
the two nominal test configurations. These test conditions assume a DU projectile and either a two or three-
layered target. The B4C-BeS65-Al7050 model is a three-layer target with boron carbide ceramic (B4C), a


                                                 4
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


beryllium (BeS65) layer, and aluminum (Al7059) backing. The B4C-Al7050 model is a two-layer target with
boron carbide ceramic (B4C) backed with aluminum (Al7059). For this paper, results for only the three-layer
target comprised of B4C-BeS65-Al7050 are presented. Tested configurations for the three-layer target are
analyzed deterministically using NESSUS and compared to the experimental results shown in Figure 5.




   Figure 5. NESSUS results visualization plot of the three L/D ratios using the B4C-BeS65-Al7050 model.



A probabilistic analysis was performed for the B4C, BeS65, Al7050 target using an L/D=10 for the DU
projectile. The random variables include the material strengths that are assumed lognormal with a COV of 5%
based on an engineering rule of thumb for metallic strength distributions. The density COV is assumed to be
2%. This small COV is based on the assumption of a common material lot for the target and projectile. The
uncertainty for the projectile velocity was estimated from the experimental data.

                                                                                       5.05 cm Al 7050
                                                   7.0


                                                                                                                                  -3u

                                                   6.0                                                                            +3u

                                                                                                                                  LD10

                                                                                                                                  LD6
                                                   5.0
               Residual Penetration into Be (cm)




                                                                                                                                  LD2


                                                   4.0
                                                                                                                     u=+3



                                                   3.0
                                                                                          PDF for 5.5 cm of
                                                                                          B4C


                                                   2.0




                                                   1.0
                                                                                                              u=-3


                                                   0.0
                                                         0.0     1.0     2.0     3.0             4.0          5.0    6.0    7.0          8.0
                                                                                         B4C Thickness (cm)




   Figure 6. NESSUS results visualization plot of the three L/D ratios using the B4C-BeS65-Al7050 model.

                                                                                       5
                                                               American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


Penetration depths corresponding to probability values of 0.00135 and 0.9987 (±3u respectively) were computed
using the AMV+ p-levels analysis method in NESSUS (10% error tolerance). The penetration depths
corresponding to these two probability levels for different composite thickness are used as bounds on the mean
value prediction using the DynEx penetration model. Computed mean value results and bounds are shown in
Figure 7 along with the experimental results. The solid line corresponds to the deterministic model response; the
dashed and dotted lines reflect the expected ±3u variation in response due to the input random variables.

The experimental results of the penetration depth for 5.7 and 6.5 cm of B4C fall fairly well within the bounds.
                                                                                                            B




However, the experimental results using the smaller thickness composite (4.9 cm) are outside the bounds. This
observation, as well as the trend indicated by the experimental results shown in Figure 7, suggests that there may
be missing random variables or incomplete physics in the model.

                                                               7

                                                                       Mean Prediction
                                                               6       -3u Bound
                           Residual Penetration into Be (cm)




                                                                       +3u Bound
                                                               5       Experimental Data


                                                               4


                                                               3


                                                               2


                                                               1


                                                               0
                                                                   0   2                   4        6           8
                                                                              B4C Thickness (cm )



        Figure 7. Mean penetration depth prediction with u=±3 bounds compared to experimental data.



Computational Model
A set of numerical analyses was conducted with a 2D hydrodynamics model, encompassing material strength
and equation-of-state (EOS) capability, of the multi-layer penetration process. This model can simulate the 2
dimensional characteristic of the target setup not achieved with the analytical model. The Sandia National
Laboratories (SNL) shock-wave physics code CTH (Bell et al, 2005) was used for the solution scheme primarily
because it incorporates viscoplastic material strength and EOS models. The numerical model, as shown in
Figure 8, is based on 2D cylindrical symmetry, applying “nominal” dimensions for all target materials (i.e., B4C,
beryllium, and aluminum). Viscoplastic material strength parameters using the Steinberg-Guinan-Lund model
(Steinberg, 1991) are used for U6Nb penetrator, beryllium (Be), and aluminum target materials. A Johnson-
Holmquist (Johnson and Holmquist, 1993) ceramic model is used for the B4C target for both strength and EOS.
                                                                                                        B




A Drucker-Prager model with pressure cutoff, as described by Walker et al. (2005), was also attempted with
CTH for the B4C target disks. Unfortunately depth-of-penetration results were indicative of a rather soft
material. Further numerical investigations are necessary with the Drucker-Prager model as it is widely believed
superior to the Johnson-Holmquist ceramic model.




                                                 6
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference




                            Aluminum Backing Plate




         Be Plug                HSLA-100 Door




                                      Steel Retainer Plate


                     B4C Disks


             U6Nb Rod




          Figure 8 – Schematic of radiographic window and computational model (without B4C disks).


Materials and materials models utilized in the CTH computations are shown in Table 1. A listing of material
properties is also shown in Table 2. Typical CTH results are shown in Figure 9 and 10 for a 4-cm long DU
projectile with three-layers, and four-layers, of B4C disks respectively. Penetration depths are listed in Table 3
for several computational models with varying projectile lengths. All computations utilized the same geometry
and the same projectile impact velocity, while increasing target thickness by addition of B4C disks.


                            Table 1 – Materials and Computational Material Models
           No.           Material        Component       Strength Model           EOS Model
            1              U6Nb              Rod             Steinberg          MieGruneisen
            2               B4C
                            B               Disks             JHCR2                JHCR2
            3             304SS           Retainer           Steinberg          MieGruneisen
            4            Be S65C          Window             Steinberg          MieGruneisen
            5           Al 7075-T6         Backing           Steinberg          MieGruneisen
            6           HSLA-100            Door          Johnson-Cook             Sesame



                                               Table 2 – Materials Properties
                                No.           Material       Density        Sound Speed
                                                             (g/cm3)           (km/s)
                                1               U6Nb          17.411            2.56
                                2                B4CB          2.51             8.885
                                3              304SS           7.896            5.22
                                4             Be S65C          1.85             7.92
                                5            Al 7075-T6        2.813            5.23
                                6            HSLA-100          7.85             4.85



                                                   7
                           American Institute of Aeronautics and Astronautics
      Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference




      Figure 9 - CTH penetration prediction for three-layer B4C target w/ 4-cm long DU rod.
                                                            B




      Figure 10 - CTH penetration prediction for four-layer B4C target w/ 4-cm long DU rod.

                                          8
                  American Institute of Aeronautics and Astronautics
            Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
      AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


                                      Table 3. CTH Predictions.
               B4C                                        Experimental
B4C Layers                  Rod Length   Beryllium DoP
                 B




             Thickness                                      Results          Notes on CTH Analysis
 B




                               (cm)           (cm)
               (cm)                                          (cm)
     0.0        0.0              1            2.73                 2.9    Good comparison
                                 2            5.06                -----   Back surface bulge; no perf.
                                 3            4.45                -----   Perforated Be
                                 4            4.45                -----   Perforated Be
                                 5            4.45                -----   Perforated Be
     1.0       0.8077            1            1.39                1.42    Good comparison
                                 2            3.19                -----
                                 3            4.45                -----   Perforated Be
                                 4            4.45                -----   Perforated Be
                                 5            4.45                -----   Perforated Be
     2.0       1.6154            1            0.22                -----
                                 2            1.75                -----
                                 3            3.58                -----
                                 4            4.45                -----   Perforated Be
                                 5            4.45                -----   Perforated Be
     3.0       2.423             1             0.0                -----   Perforated B4C w/o Be penet.
                                                                                      B




                                 2            0.52                -----
                                 3            2.22                -----
                                 4            4.06                -----
                                 5            4.45                -----   Perforated Be
     4.0       3.230             1             0.0                -----   Perforated B4C w/o Be penetration
                                                                                      B




                                 2             0.0                -----   Perforated B4C w/o Be penetration
                                                                                      B




                                 3            1.02                1.24    Good comparison
                                 4            2.72                -----
                                 5            4.72                -----   Back surface bulge; no perfor.
     5.0       4.039             1             0.0                -----   No perforation of B4C
                                 2             0.0                -----   No perforation of B4C
                                 3             0.0                0.20
                                 4            1.57                -----
                                 5            3.32                -----
                                 6            4.62                -----   Back surface bulge; no perfor.
     6.0       4.846             1             0.0                -----   No perforation of B4C
                                 2             0.0                -----   No perforation of B4C
                                 3             0.0                -----   No perforation of B4C
                                 4            0.27                -----
                                 5            1.87                2.13    Good comparison
                                 6            3.72                -----
     7.0       5.654             1             0.0                -----   No perforation of B4C
                                 2             0.0                -----   No perforation of B4C
                                 3             0.0                -----   No perforation of B4C
                                 4             0.0                -----   No perforation of B4C
                                 5            0.92                1.61
                                 6            2.42                -----
     8         6.462             1             0.0                -----   No perforation of B4C
                                 2             0.0                -----   No perforation of B4C
                                 3             0.0                -----   No perforation of B4C
                                 4             0.0                -----   No perforation of B4C
                                 5             0.1                0.84
                                 6            1.42                -----




                                                 9
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


Figure 11 shows a close-up view of the final depth-of-penetration for a 2-layer B4C disk stack-up and a 2-cm
long DU rod. Erosion of the U6Nb rod is shown with the bulk of remaining material being about 0.5 cm long.




       Figure 11 – Depth of penetration for 2-cm long DU rod with 2-layer of B4C, showing rod erosion.
                                                                               B




Figure 12 shows 2-cm long projectile, with no B4C sacrificial disks, having been eroded through the penetration
process, although not fully perforated the beryllium window, there is extensive back surface bulging. This
bulging is also well predicted by the Walker-Anderson analytical model embedded in the NESSUS code.




                                      Figure 12 – Back surface bulging.



                                                  SUMMARY
This paper described the analytical, computational, and probabilistic penetration model developed for the DynEx
vessel design and its role in the predictive model V&V process through a comparison with experimental data.
Refined numerical CTH model results are presented along with quantitative metrics for defining confidence in
the model prediction for application to the containment vessel design. Further numerical and probabilistic
analyses are required to provide additional data where gaps exists in experimental data.




                                                 10
                         American Institute of Aeronautics and Astronautics
          Submitted to the 1st Non-Deterministic Approaches (NDA) Conference, 47th
    AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference


                                                REFERENCES

AIAA, Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, American
Institute of Aeronautics and Astronautics, AIAA-G-077-1998, Reston, VA, 1998.

Bell, R.L., et al., “CTH Users Manual and Input Instructions, Ver. 7.0,” Sandia National Laboratories, April
2005.

Johnson, G. R. and Holmquist, T. J. “Development and Evaluation of Computational Constitutive Models for
Ceramics,” Technical Report for Contract MDA972-89-C-0094, 1993.

Mullin, S. A., Walker, J. D., Weiss, Leslie, P. O., “Impact and Penetration of B4C Ceramic, Aluminum, and
Berylium by Depleted Uranium Rods at 2 km/s,” Proc. International Symposium on Ballistics, Vancouver,
British Columbia, Canada, November 2005.

Riha, D. S., Thacker, B. H. Fitch, S. H. K. “NESSUS Capabilities for Ill-Behaved Performance Functions,”
Proc. AIAA/ASME/ASCE/AHS/ASC 45th Structures, Structural Dynamics, and Materials (SDM) Conf., Palm
Springs, CA, April 19-22, 2004.

Steinberg, D.J., “Equation of State and Strength Properties of Selected Materials,” Lawrence Livermore National
Laboratory report UCRL-MA-106439, 1991.

Thacker, B. H., Anderson, M. C., Senseny, P. E., and Rodriguez, E. A., “The Role of Nondeterminism in
Computational Model Verification and Validation,” Int. J of Vehicle Design, accepted for publication, 2004.

Thacker, B. H., “The Role of Nondeterminism in Computational Model Verification and Validation,” Proc.
AIAA/ASME/ASCE/AHS/ASC 46th Structures, Structural Dynamics, and Materials (SDM) Conf, Austin, TX,
April 2005.

Walker, J. D., Mullin, S. A., Weiss, Leslie, P. O., “Penetration of B4C Ceramic, Aluminum, and Berylium by
Depleted Uranium Rods: Modeling and Experimentation,” Proc. Hypervelocity Impact Symposium, Lake Tahoe,
CA, October 2005.

Mullins, S. A., Walker, J. D., Thacker, B. H., Rodriguez, E. A., Leslie, P. O., “Verification and Validation of a
Penetration Model for the Design of a Blast Containment Vessel, Part I: Validation Experiments,” Proceedings
AIAA/ASME/ASCE/AHS/ASC 47th Structures, Structural Dynamics, and Materials (SDM) Conf, Newport, RI,
May 2006.




                                                 11
                         American Institute of Aeronautics and Astronautics

				
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