PSI - Issue 45

Dylan Agius et al. / Procedia Structural Integrity 45 (2023) 4–11 Dylan Agius et al. / Structural Integrity Procedia 00 (2019) 000 – 000 = ∶ where is the Cauchy stress tensor. is the backstress which is defined as: = 0 2 curl(curl( )): where 0 and are material parameters with dimensions of stress and length respectively. From the analysis conducted by Marano, Gélébart et al. (2019) into the simulation of slip bands, to allow for these mechanisms to form, it is important a component of softening is added to the constitutive models. This is done through the constitutive equation defining the evolution of critical resolved shear stress ( ): = 0 − [1 − exp (− 0 )] ( 7 ) where ̇ = | ̇ | , 0 is the initial critical resolved shear stress, is the maximum softening, and 0 can be used to adjust the rate of softening. The higher order boundary condition applied in this work is the micro-free condition. In order to enforce this boundary condition, the approach used by Lebensohn and Needleman (2016) was utilised where the boundary voxels were assigned =0 , preventing the evolution of Geometrically Necessary Dislocation (GND) induced backstress in these voxels. 4. Simulation framework In the following sections, the simulation framework for both the calibration and EBSD reconstructed environment is presented. In both cases the numerical integration of the nonlocal model was implemented in the MFRONT code generator (Helfer, Michel et al. 2015). The simulations were then run using AMITEX_FFT (Gelebart, Derouillat et al. 2020). For simulations, the phase was modelled with three prismatic ( {101̅0}, 〈112̅0〉 ), three basal ( {0001}, 〈112̅0〉 ), and 12 pyramidal 〈 + 〉 ( {101̅1}, 〈112̅3〉 ) slip systems. It is important to note that some simplifications were made for the simulations. Firstly, 18 slip systems were considered. Application of this approach is due to crystal plasticity parameter availability in the literature. Since most parameters were selected directly from published work rather than calibration, it was deemed appropriate to conduct the analysis using available data. Additionally, only grains were used in the simulations. However from EBSD, there was a low amount of phase present in the microstructure (<1%). Future work will examine the influence of small amounts of phase on simulation accuracy. 4.1. Calibration simulations The calibration simulations were conducted on a three-dimensional representative volume element of 4×10 6 voxels, with the homogenised simulation results provided in Fig. 1 (a), along with the experimental monotonic tensile data. To generate the RVE representative of the -annealed Ti-6Al-4V microstructures, DREAM.3D (Groeber and Jackson 2014) was used to create the prior grains. A Python function based on the boundary vector calculator developed in (Agius, Mamun et al. 2022) was used to separate the prior grain voxels to form grains. The orientations assigned to the grains were determined based on the prior grain and orientation relationships ( {101} // {0001} and 〈111〉 // 〈2110〉 ). The final calibrated parameters are provided in Table 1. Table 1. Parameters used for the nonlocal model CP-FFT model. ( 6 ) 7 4 ( 5 )

E (GPa) 0 (MPa) (Prismatic,

(MPa) (Prismatic, Pyramidal 〈 + 〉 , Basal)

0 (MPa 1/

) 0

(MPa) (MPa)

Model

Pyramidal 〈 + 〉 , Basal) 315, 565, 325

0.0 0

Nonlocal (micro-free)

119

0.29

-59,-93,-62

0.05 7.41

20

200