Bayesian calibration of strength parameters using hydrocode simulations of symmetric impact shock experiments of Al-5083

Predictive modeling of materials requires accurately parameterized constitutive models. Parameterizing models that describe dynamic strength and plasticity require experimentally probing materials in a variety of strain rate regimes. Some experimental protocols (e.g., plate impact) probe the constitutive response of a material using indirect measures such as free surface velocimetry. Manual efforts to parameterize constitutive models using indirect experimental measures often lead to non-unique optimizations without quantification of parameter uncertainty. This study uses a Bayesian statistical approach to find model parameters and to quantify the uncertainty of the resulting parameters. The technique is demonstrated by parameterizing the Johnson-Cook strength model for aluminum alloy 5083 by coupling hydrocode simulations and velocimetry measurements of a series of plate impact experiments. Simulation inputs and outputs are used to calibrate an emulator that mimics the outputs of the computationally intensive simulations. Varying the amount of experimental data available for emulator calibration showed clear differences in the degree of uncertainty and uniqueness of the resulting optimized Johnson-Cook parameters for Al-5083. The results of the optimization provided a numerical evaluation of the degree of confidence in model parameters and model performance. Given an understanding of the physical effects of certain model parameters, individual parameter uncertainty can be leveraged to quickly identify gaps in the physical domains covered by completed experiments.Predictive modeling of materials requires accurately parameterized constitutive models. Parameterizing models that describe dynamic strength and plasticity require experimentally probing materials in a variety of strain rate regimes. Some experimental protocols (e.g., plate impact) probe the constitutive response of a material using indirect measures such as free surface velocimetry. Manual efforts to parameterize constitutive models using indirect experimental measures often lead to non-unique optimizations without quantification of parameter uncertainty. This study uses a Bayesian statistical approach to find model parameters and to quantify the uncertainty of the resulting parameters. The technique is demonstrated by parameterizing the Johnson-Cook strength model for aluminum alloy 5083 by coupling hydrocode simulations and velocimetry measurements of a series of plate impact experiments. Simulation inputs and outputs are used to calibrate an emulator that mimics the outputs of the computationally inte...

[1]  J. G. Williams,et al.  Determination of the Constitutive Constants of Non-Linear Viscoelastic Materials , 2004 .

[2]  T. Børvik,et al.  Influence of yield-surface shape in simulation of ballistic impact , 2017 .

[3]  D. McDowell,et al.  A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates , 2011 .

[4]  U. F. Kocks,et al.  Kinetics of flow and strain-hardening☆ , 1981 .

[5]  Y. Estrin,et al.  On the “threshold stress” for creep of particle-strengthened materials , 1985 .

[6]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[7]  M. Langseth,et al.  Ballistic penetration of steel plates , 1999 .

[8]  Marc J. Cawkwell,et al.  A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine , 2017 .

[9]  Douglas J. Bammann,et al.  Modeling Temperature and Strain Rate Dependent Large Deformations of Metals , 1990 .

[10]  Stefan M. Wild,et al.  Uncertainty quantification for nuclear density functional theory and information content of new measurements. , 2015, Physical review letters.

[11]  J. L. Brown,et al.  Estimating material properties under extreme conditions by using Bayesian model calibration with functional outputs , 2018 .

[12]  C. Greeff,et al.  Analytic model of the shear modulus at all temperatures and densities , 2002, cond-mat/0208585.

[13]  M. Shashkov,et al.  The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy , 1998 .

[14]  Kamel Fezzaa,et al.  In situ investigation of the dynamic response of energetic materials using IMPULSE at the Advanced Photon Source , 2014 .

[15]  S. R. Rodner.  Constitutive equations for metals at high strain rates , 1986 .

[16]  Jerome Sacks,et al.  Choosing the Sample Size of a Computer Experiment: A Practical Guide , 2009, Technometrics.

[17]  J. B. Stone,et al.  Estimation of Metal Strength at Very High Rates Using Free-Surface Richtmyer–Meshkov Instabilities , 2017, Journal of Dynamic Behavior of Materials.

[18]  L. M. Barker,et al.  Laser interferometer for measuring high velocities of any reflecting surface , 1972 .

[19]  U. F. Kocks,et al.  A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable , 1988 .

[20]  David L. McDowell,et al.  Parameterization of a rate-dependent model of shock-induced plasticity for copper, nickel, and aluminum , 2012 .

[21]  X. Kong,et al.  Hemispherical nosed steel projectile high-speed penetration into aluminum target , 2017 .

[22]  Dattatraya P. Dandekar,et al.  Dynamic response of two strain-hardened aluminum alloys , 2006 .

[23]  Y. Gupta,et al.  Anisotropic material model and wave propagation simulations for shocked pentaerythritol tetranitrate single crystals , 2010 .

[24]  M. Cawkwell,et al.  A single-crystal model for the high-strain rate deformation of cyclotrimethylene trinitramine including phase transformations and plastic slip , 2017 .

[25]  T. Børvik,et al.  A computational model of viscoplasticity and ductile damage for impact and penetration , 2001 .

[26]  C. Bronkhorst,et al.  A computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialities , 2018 .

[27]  Y. Gupta,et al.  Nonlinear anisotropic description for the thermomechanical response of shocked single crystals: Inelastic deformation , 2006 .

[28]  Jon H. Eggert,et al.  An iterative forward analysis technique to determine the equation of state of dynamically compressed materials , 2017 .

[29]  Edgar Weckert,et al.  The potential of future light sources to explore the structure and function of matter , 2014, IUCrJ.

[30]  Dean L. Preston,et al.  Model of plastic deformation for extreme loading conditions , 2003 .

[31]  Dominik Kraus,et al.  Conceptual Design Report: Dynamic Laser Compression Experiments at the HED Instrument of European XFEL , 2017 .

[32]  Yuri Estrin,et al.  A unified phenomenological description of work hardening and creep based on one-parameter models , 1984 .

[33]  R. Armstrong,et al.  Dislocation-mechanics-based constitutive relations for material dynamics calculations , 1987 .

[34]  G. R. Fowles.  Shock Wave Compression of Hardened and Annealed 2024 Aluminum , 1961 .