Abstract
In this paper is presented a new single crystal elastic/plastic constitutive model for tetragonal crystals. This new single-crystal anisotropic yield criterion has been developed using representation theorems for anisotropic tensor functions. It is defined for any type of loadings and depends on the characteristics of the tetragonal lattice (c/a ratio). It involves three independent plastic anisotropy parameters that can be expressed analytically in terms of the uniaxial yield stresses along four crystallographic directions. Illustration of the capabilities of this model is done for a pentaerythritol tetranitrate (PETN) crystal. Moreover, we present finite-element meso-scale simulations of the thermo-mechanical response under impact of a polymer bonded explosive for which the behavior of the constituent energetic molecular crystals is described with a constitutive model with yielding governed by the new single-crystal yield criterion. The simulation results provide insights into the role played by the anisotropic crystalline plasticity and the interactions between crystals on the thermo-mechanical response under dynamic compression of the PETN-based polymer bonded explosive aggregate.
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References
Abaqus (2014) Abaqus–version 6.14–1. Dassault systemes simulia Corp., Providence, RI
Asaro R, Lubarda V (2006) Mechanics of solids and materials. Cambridge University Press
Boehler JP (1987) Representations for isotropic and anisotropic non-polynomial tensor functions. In: Boehler JP (eds) applications of tensor functions in solid mechanics. International centre for mechanical sciences (courses and lectures), vol 292. Springer, Vienna.
Cady HH, Larson AC (1975) Pentaerythritol tetranitrate II: its crystal structure and transformation to PETN I; an algorithm for refinement of crystal structures with poor data. Acta Crystallogr Sect B: Struct Crystallogr Cryst Chem 31:1864–1869
Cazacu O, Revil-Baudard B, Chandola N (2019) Plasticity-damage couplings: from single crystal to polycrystalline materials. Springer
Clayton JD, Becker R (2012) Elastic-plastic behavior of cyclotrimethylene trinitramine single crystals under spherical indentation: modeling and simulation. J Appl Phys 111:063512
Conroy M, Oleynik II, Zybin SV, White CT (2007) December. Anisotropic constitutive relationships in energetic materials: PETN and HMX. In AIP Conf Proc 955:361–364
Dick JJ (1984) Effect of crystal orientation on shock initiation sensitivity of pentaerythritol tetranitrate explosive. Appl Phys Lett 44:859–861
Handley CA, Lambourn BD, Whitworth NJ, James HR, Belfield WJ (2018) Understanding the shock and detonation response of high explosives at the continuum and meso scales. Appl Phys Rev 5:011303
Hardin DB, Rimoli JJ, Zhou M (2014) Analysis of thermomechanical response of polycrystalline HMX under impact loading through mesoscale simulations. AIP Adv 4:097136
Hooks DE, Ramos KJ, Bolme CA, Cawkwell MJ (2015) Elasticity of crystalline molecular explosives. Propellants, Explos, Pyrotech 40:333–350
Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the 7th international symposium on ballistics: pp. 541–547.
Mohan VK, Bhasu VJ, Field JE (1989) Role of adiabatic shear bands in initiation of explosives by drop-weight impact. In Ninth symposium on detonation. Office of the chief of naval research, Arlington, Virginia, pp. 1276–1283.
Schmid E, Boas W (1950) Plasticity of crystals.
Spencer AJM (1987) Anisotropic invariants and additional results for invariant and tensor representations. In: Boehler JP (eds) Applications of tensor functions in solid mechanics. International centre for mechanical sciences (courses and lectures), vol 292. Springer, Vienna.
Sun B, Winey JM, Hemmi N, Dreger ZA, Zimmerman KA, Gupta YM, Torchinsky DH, Nelson KA (2008) Second-order elastic constants of pentaerythritol tetranitrate and cyclotrimethylene trinitramine using impulsive stimulated thermal scattering. J Appl Phys 104:073517
Teodosiu C (1982) Elastic models of crystal defects. Springer
Peirce D, Asaro R J, Needleman A (1982) An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metallurgica 30(6):1087–1119
Acknowledgements
BRB gratefully appreciates and acknowledges the partial support for this work from the Air Force Office of Scientific Research (AFOSR) under contracts FA9550-22-1-0242.
Funding
This study was partially funded by the Air Force Office of Scientific Research (AFOSR) grants FA9550-22-1-0242.
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Revil-Baudard, B. A new constitutive model for tetragonal crystals. Meccanica 58, 233–244 (2023). https://doi.org/10.1007/s11012-022-01634-1
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DOI: https://doi.org/10.1007/s11012-022-01634-1