POROUS SINGLE CRYSTAL UNIT-CELL SIMULATION DATABASE FOR DUCTILE FRACTURE THROUGH VOID GROWTH AND COALESCENCE Cédric Sénac, Jean-Michel Scherer and Jérémy Hure Version v1.0 - 18/10/2021 *** DESCRIPTION *** Ductile fracture through void growth to coalescence occurs at the grain scale in numerous metallic alloys encountered in engineering applications. In order to perform mechanical homogenization of porous single crystals, a database of porous single crystal unit-cell simulation results has been gathered through Finite Element Modeling and Fast-Fourrier Transform simulations, respectively performed on Z-set [1] and Amitex_FFTP [2]. In these simulations, a cubic unit-cell with a unique central spherical void undergo axisymmetric mechanical loading. Mechanical simulations are performed within finite strain theory. Input parameters of interest are stress triaxiality, crystallographic orientation, initial porosity and strain hardening law type; results include macroscopic stress, macroscopic deformation gradient, porosity, void aspect ratio, ligament size and cell aspect ratio. *** DATABASE FIELDS *** Results are stored in the subgroup "Axisymmetric Loading" of the HDF5 file "PorousSingleCrystalUnitCellResults.hdf5". Each simulation can be found in a subgroup whose title is "Simulation_X". X does not cover a full interval: some simulations have been removed for various issues. Input parameters of interest are recorded in the subgroup attributes: * Method: simulation method chosen, 'FEM' for Finite Element Modeling (Z-set) or 'FFT' for Fast-Fourrier Transform (Amitex_FFTP). Initial critical stresses differ according to the method: tau_0 = 88 (FEM) and tau_0 = 100 (FFT). * Stress Triaxiality: 1, 1.5, 2 or 3; Lode parameter is kept equal to -1 (axisymmetric loading). * Crystallographic orientation: matrix of the crystal orthotropy axes in the axisymmetric loading frame of reference. * Crystallographic orientation number: crystallographic orientation are numbered for convenience; regular orientations (both FEM and FFT) range from '0' to '7', random orientations (only FFT) range from to 'r1' to 'r5'. * Elasticity: elasticity parameters (cubic orthotropy), same for every simulation. * Hardening law: strain hardening law chosen and the value of the associated material hardening parameters. * Hardening law number: hardening laws are numbered for convenience; '0' is no hardening, '1a' is Franciosi-Berveiller-Zaoui hardening [3], '2X' is Peirce-Asaro-Needleman hardening [4], for which various set of parameters X are tested. * Number of elements: number of FEM elements or FFT voxels used in the unit cell simulation mesh. *** SIMULATION OUTPUTS *** * Time: 1_time * Macroscopic deformation gradient: 2_F11 / 3_F22 / 4_F33 / 5_F12 / 6_F23 / 7_F31 / 8_F21 / 9_F32 / 10_F13 * Macroscopic stress: 11_S11 / 12_S22 / 13_S33 / 14_S12 / 15_S23 / 16_S31 * Porosity: 17_f * Void aspect ratio (only FEM): 18_W * Ligament size (only FEM): 19_chi * Cell aspect ratio (only FEM): 20_lambda Figure "UnitCellGeometry.png" has been provided for additional reference on the unit cell geometry and definition of microstructural parameters. *** APPENDIX *** Stress triaxility T: T = S_m/S_eq where S_m = trace(S)/3 is the hydrostatic stress and S_eq = sqrt((3/2)*dev(S):dev(S)) is von Mises equivalent stress. S denotes the Cauchy stress tensor, and dev(S) is its deviator. Imposed stress tensor (axisymmetric loading in the simulation frame): S = [ S_11 0 0 ] [ 0 a*S_11 0 ] [ 0 0 a*S_11 ] a = (3T - 1)/(3T + 2); T = (2a + 1)/(3 - 3a) Direction 1 is the main loading direction. Cubic elasticity coefficients (in the crystal orthotropy frame of reference): y1111 = 198600 / y1122 = 136200 / y1212 = 104700 Franciosi-Berveiller-Zaoui hardening (1a) parameters: tau_0 = 88 / mu = 65615 / G0 = 10.4 / K_rho = 42.8 / r_0 = 5.38e-11 / n = 15 / K = 10 / loading speed = 1.e-4 rho is a dislocation density normalised by b**2 where b is the norm of Burgers verctor. Peirce-Asaro-Needleman hardening (2) parameters: 2a - tau_0 = 100 / tau_s = 150 / h0 = 250 / q = 1.00 / n = 15 / K = 10 2b - tau_0 = 100 / tau_s = 150 / h0 = 500 / q = 1.00 / n = 15 / K = 10 2c - tau_0 = 100 / tau_s = 200 / h0 = 250 / q = 1.00 / n = 15 / K = 10 2d - tau_0 = 100 / tau_s = 200 / h0 = 500 / q = 1.00 / n = 15 / K = 10 2e - tau_0 = 100 / tau_s = 150 / h0 = 250 / q = 0.75 / n = 15 / K = 10 2f - tau_0 = 100 / tau_s = 150 / h0 = 500 / q = 0.75 / n = 15 / K = 10 2g - tau_0 = 100 / tau_s = 200 / h0 = 250 / q = 0.75 / n = 15 / K = 10 2h - tau_0 = 100 / tau_s = 200 / h0 = 500 / q = 0.75 / n = 15 / K = 10 Regular orientation Miller indexes (axisymmetric loading axes in the crystal orthotropy frame of reference): 0 -- [ 1 1 1] - [-2 1 1] - [ 0 -1 1] 1 -- [ 2 1 0] - [-1 2 0] - [ 0 0 1] 2 -- [-1 2 5] - [ 1 -2 1] - [ 2 1 0] 3 -- [-1 2 5] - [ 0 -5 2] - [29 2 5] 4 -- [ 1 0 0] - [ 0 1 0] - [ 0 0 1] 5 -- [ 1 0 0] - [ 0 1 -1] - [ 0 1 1] 6 -- [ 1 0 0] - [ 0 2 -1] - [ 0 1 2] 7 -- [ 1 1 0] - [-1 1 0] - [ 0 0 1] Random orientation (axisymmetric loading axes in the crystal orthotropy frame of reference): r1 - 1 = [ 7.0626193e-01, -5.3500109e-01, 4.6364634e-01], 3 = [-5.6110449e-01, -2.3668627e-02, 8.2740652e-01] r2 - 1 = [ 5.8424883e-02, 5.3305586e-01, 8.4406041e-01], 3 = [ 8.7723319e-01, 3.7615512e-01, -2.9827715e-01] r3 - 1 = [-6.2808146e-01, 4.8505426e-01, 6.0847025e-01], 3 = [ 4.7797317e-01, 8.5753037e-01, -1.9021911e-01] r4 - 1 = [ 2.7905403e-01, -9.3069605e-01, 2.3650309e-01], 3 = [ 7.3322339e-01, 3.6554768e-01, 5.7337453e-01] r5 - 1 = [-8.7037512e-01, 7.5615728e-02, 4.8654847e-01], 3 = [ 3.9426297e-01, 6.9896640e-01, 5.9665961e-01] *** REFERENCES *** [1] J. Besson, R. Foerch, Object-oriented programming applied to the finite element method: Part I - General concepts, Revue Européenne des Eléments Finis 7 (1998) 535–566. [2] CEA, AMITEX FFTP, www.maisondelasimulation.fr/projects/amitex/html/ (2020). [3] P. Franciosi, M. Berveiller, A. Zaoui, Latent hardening in copper and aluminium single crystals, Acta Metallurgica 28 (3) (1980) 273–283. [4] D. Peirce, R. J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta metallurgica 31 (12) (1983) 375 1951–1976.