You are here

Uncertainty Quantification for Modeling and Testing of Carbon-Carbon (C-C) Materials


TECHNOLOGY AREA(S): Info Systems, Materials, Weapons 

OBJECTIVE: Develop an innovative methodology that will enable hydro-code tools (e.g. Dyna, Paradyn, Zapotec, Velodyne, etc.) that model C-C materials at high temperature with high-rate loadings, to be used as a predictive tool for analysis of energetic events like high-velocity impacts or explosive loadings. 

DESCRIPTION: This topic seeks innovative methodologies that estimate C-C modeling uncertainties in hydro-code results in a predictive tool that does not depend on being able to interpolate between known test results. Due to limitations of test venues available for system-level tests that can only partly cover the range of operational conditions for aerospace systems, high costs, and challenging data collection, the ability of hydro-codes to simulate load cases of interest exceeds the capability of test venues to perform high-fidelity experiments. Thus, uncertainty quantification methodologies for hydro-codes and C-C materials is of interest as they would serve as a bridge for uncertainty comparisons between test data, hydro-code tools, and engineering tools. In order to perform meaningful hydro-code analysis for cases outside the parameter space of interpolation between test data points, uncertainty quantification is critical. When extrapolating beyond known benchmarking tests, uncertainty quantification makes the difference between a tool that can assess trends, and a tool that can be predictive. The typical approach for reconciling computational models with test data is to use tunable parameters in the system model to give the best agreement with the measured test response of the system. It may be possible to look at a variety of test responses, and tune model parameters for the best over-all fit to multiple sets of data. Goodness-of-fit parameters in the statistics can be used to estimate the uncertainty. Some uncertainty will be due to assumptions and approximations in the code itself, some will be due to assumptions in construction of the model, and some will be due to input parameters like material properties. For this topic, the uncertainty in material property test data for C-C due to manufacturing process variability should be characterized in terms of the material response. For meaningful comparisons with data, the measurement uncertainty must be quantified as well, and meaningful metrics must be chosen for fracture and failure of the C-C material and the overall structure. In the case of C-C materials, the variability in manufacturing processes is a key driver of the variability in material properties. Thus, the proposed methodology should address both the C-C and hydro-code model uncertainties as well as the uncertainty present in the input parameters (uncertainties in the measurements of material properties). Load cases of interest will be for high-strain-rate and high-temperature loadings of structural systems.  

PHASE I: Formulate an innovative methodology for uncertainty quantification of hydro-code predictions using C-C models that are based on material characteristics from uncertain test data. Include the effects of manufacturing process variability, such as phase transformations, cloth wrap types, weave changes, shrinkage, and residual stresses. Characterize test data in terms of material response. Demonstrate feasibility using a representative structural model with high strain-rate loadings (e.g. high-velocity impact or explosive loading that would cause strain-rates of 10^7 sec^-1 and above over a range of temperatures from 25 degrees C up to well above 1,000 degrees C. Consider relevant cases where experimental data sets are available. 

PHASE II: Perform further demonstration of the Phase I methodology with more complex, larger-scale models of interest to the government, and use of a broader range of experimental data sets. Include additional sources of uncertainty and show the relative importance of the various error sources for full-scale testing, such as flight test, sled test, or arena test. Demonstrate an interface with missile defense application engineering level tools, and hydro-codes. 

PHASE III: Transition the uncertainty quantification capability for first-principle physics-based modeling capability developed under this program to target lethality and debris prediction efforts. Fully integrate the uncertainty quantification tool with an appropriate hydro-code and execute model runs for design and analysis cases of interest to the government. 


1: Roy and Oberkampf, "A comprehensive framework for verification, validation and uncertainty quantification in scientific computing," Comput. Methods Appl. Mech. Engrg. 200 (2011) 2131-2144

2:  Dimitrienko, "Modeling of carbon-carbon composite manufacturing processes," Composites Part A: Applied Science and Manufacturing, Vol. 30, No. 3, 221-230, 1999.

3:  Center for Applied Scientific Computing, "The PSUADE Uncertainty Quantification Project," Lawrence Livermore National Laboratory, US Department of Energy,

4:  "DAKOTA – Explore and predict with Confidence," National Technology and Engineering solutions of Sandia, LLC, Sandia National Laboratories, US Department of Energy,


6:  Zucas, J.A., "Introduction to hydrocodes (Studies in Applied Mechanics)," Elsevier, New York, NY, 2004.

7:  McGlaun, J.M., Tompson, S.L., Elrick, M.G., "CTH: A three-dimensional shock wave physics code," International Journal of Impact Engineering, Vol. 10, Issue 1, 1990, 351-360.

8:  Melis, et al., "Reinforced Carbon-Carbon Subcomponent Flat Plate Impact Testing for Space Shuttle Orbiter Return to Flight," NASA/TM 2007-214384, September 2007.

9:  Carney, et al., "A Heterogeneous Constitutive Model for Reinforced Carbon-Carbon using LS-DYNA, 10th International LS-DYNA User’s Conference – Material Modeling, 2008.

KEYWORDS: Uncertainty Quantification, Hydro-codes, Hydro-structural Codes, Carbon-Carbon Composites, High-strain-rate Material Properties, High-temperature Material Properties 

US Flag An Official Website of the United States Government