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

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2. Experimental analysis 2.1. Sample preparation

Samples were machined from an extra low interstitial (ELI) -annealed Ti-6Al-4V plate into a flat subsize tensile specimen geometry (oriented in the rolling direction). Tensile specimens had a dog bone geometry with a gauge length, width, and thickness of 12mm, 5mm, and 3mm respectively. One side of the tensile specimen surface was first ground up to a 2500 grit finish using SiC paper and then polished to a mirror finish using a solution of 90% OPS and 10% hydrogen peroxide. Various micro-hardness indents in a grid-like pattern were made over the samples to help locate a ROI. Using a novel patterning process described in (Yan, Tasan et al. 2015), silicon oxide (SiO 2 ) particles from OPS solution were deposited over the sample to create a fine speckle pattern suitable for μ -DIC. The quality of the speckle pattern (density and distribution) was checked using a JEOL 7001F FEG Scanning Electron Microscope (SEM). To stabilise the SiO 2 particles from the electron beam a 2nm carbon coating was applied. 2.2. Local strain measurements Prior to deforming the specimen, an initial EBSD map (0.8 μm step size) and low voltage secondary electron imaging (SEM-SEI) capturing the SiO2 particle distribution was undergone of the select area. The tensile test was then conducted on an Instron 5982 using a crosshead speed of 0.02mm/s and 10mm extensometer. The specimen was loaded to 2.5% strain. The EBSD map and SEM imaging was repeated over the selected area. The local strain map was then generated by mapping the SiO 2 markers between the unstrained and strained images using Ncorr (v1.2) (Blaber, Adair et al. 2015). 3. Strain gradient crystal plasticity FFT (CP-FFT) model 3.1. Formulation For this work, the crystal plasticity theory was applied in the context of small deformations. Additionally, only the governing equations for this work are provided. A more complete description of the theory being applied can be found in Gurtin (2002), and Marano, Gélébart et al. (2021). The underlying concept of the work proposed by Gurtin (2002) is that the local rotations (and in this case rotations due to the displacement field) contribute to the kinematic description of deformation (Abu Al-Rub, Voyiadjis et al. 2007). The total displacement gradient can be decomposed into elastic (which represents stretching and rotation of the lattice) and plastic (which is the plastic distortion due to slip) parts: = + (1) The lattice strain is given by the symmetric part of : = 1 2 ( + ) (2 ) The plastic deformation rate evolves according to the following: ̇ =∑ ̇ (3 ) where = ⨂ is the Schmid tensor, is the slip direction and is the slip plane normal of slip system . The flow rule evolves according to the classical Norton flow rule: ̇ = ⟨ | − |− ⟩ sign( − ) ( 4 ) where 〈 〉 are Macaulay brackets, and and are the Norton law exponent and coefficient. is the resolved shear stress: