Parameter Optimisation of Johnson-Cook Constitutive Models for Single Abrasive Grain Micro-Cutting Simulation: A Novel Methodology Based on Lateral Material Displacement Analysis.

Abstract

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 (<i>B</i>, <i>n</i>) and strain rate sensitivity (<i>C</i>). 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 (<i>h</i>), width (<i>l</i>), and horizontal distance to the peak (<i>d</i>). 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 (<i>A</i> = 473 MPa, <i>B</i> = 80 MPa, <i>n</i> = 0.5, <i>C</i> = 0.001) achieved superior convergence, reducing the non-conformity criteria to Σ<i>k_A</i> = 0.46 and Σ<i>k_K</i> = 1.16, compared to 0.88 and 1.67 for the baseline model. Strain mapping revealed deformation values from <i>ε</i> = 0.8 to <i>ε</i> = 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.