Parameter Optimisation of Johnson-Cook Constitutive Models for Single Abrasive Grain Micro-Cutting Simulation: A...

The accurate modelling of material removal mechanisms in grinding processes requires precise constitutive equations describing dynamic material behaviour under extreme strain rates and large deformations. This study presents a novel methodology for optimising the Johnson-Cook (J-C) constitutive model parameters for micro-grinding applications, addressing the limitations of conventional mechanical testing at strain rates exceeding 10⁵ s^-1. The research employed single abrasive grain micro-cutting experiments using a diamond Vickers indenter on aluminium alloy 7075-T6 specimens. High-resolution topographic measurements (130 nm lateral resolution) were used to analyse the scratch geometry and lateral material displacement patterns. Ten modified J-C model variants (A1-A10) were systematically evaluated through finite element simulations, focusing on parameters governing plastic strengthening (B, n) and strain rate sensitivity (C). Quantitative non-conformity criteria assessed agreement between experimental and simulated results for cross-sectional areas and geometric shapes of material pile-ups and grooves. These criteria enable an objective evaluation by comparing the pile-up height (h), width (l), and horizontal distance to the peak (d). The results demonstrate that conventional J-C parameters from Hopkinson bar testing exhibit significant discrepancies in grinding conditions, with unrealistic stress values (17,000 MPa). The optimised model A3 (A = 473 MPa, B = 80 MPa, n = 0.5, C = 0.001) achieved superior convergence, reducing the non-conformity criteria to Σk_A = 0.46 and Σk_K = 1.16, compared to 0.88 and 1.67 for the baseline model. Strain mapping revealed deformation values from ε = 0.8 to ε = 11 in lateral pile-up regions, confirming the necessity of constitutive models describing material behaviour across wide strain ranges. The methodology successfully identified optimal parameter combinations, with convergence errors of 1-14% and 7-60% on the left and right scratch sides, respectively. The approach provides a cost-effective alternative to expensive dynamic testing methods, with applicability extending to other ductile materials in precision manufacturing.