Prediction of the Stress–Strain State and Failure Mechanism of the VT6 Titanium Alloy during Machining Using a Meshfree Numerical Method

Аuthors

Ahmed Soliman M. E.^*, Anisimov A. G.^**

Lavrentiev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia

*e-mail: ahmedsoliman@hydro.nsc.ru
**e-mail: anis@hydro.nsc.ru

Abstract

This work presents a numerical investigation of high-speed orthogonal cutting of the aerospace titanium alloy VT6 (Ti–6Al–4V) using the meshless Smoothed Particle Galerkin (SPG) method. The relevance of the study is driven by the increasing demand for reliable predictive tools capable of describing the stress–strain state and material separation mechanisms during the machining of titanium alloys, which are extensively used in aerospace and space engineering. The combination of high strength, low thermal conductivity, and pronounced tendency toward plastic strain localization makes these alloys particularly difficult to machine and requires advanced numerical approaches that can accurately capture large deformations and fracture processes.
The SPG method employed in this study is based on a variational Galerkin formulation of the governing equations of continuum mechanics and does not rely on a fixed computational mesh. This feature allows one to overcome numerical difficulties inherent in conventional mesh-based methods, such as severe mesh distortion and the need for remeshing under large plastic deformations. Contact interaction between the cutting tool, the workpiece, and the evolving chip is naturally described at the particle level, ensuring physically consistent material separation and chip formation without prescribing an a priori fracture path or geometrical failure criteria.
Particular attention is devoted to the numerical stability of Galerkin-type meshless formulations. The study considers physically motivated stabilization techniques based on local deformation smoothing and consistent treatment of kinematic relations in the vicinity of particles. This approach effectively suppresses nonphysical displacement modes, analogous to hourglass modes in reduced-integration finite element schemes, without introducing empirical stabilization parameters and while preserving the variational consistency of the numerical formulation.
The elastoplastic response of the titanium alloy is described using the Johnson–Cook constitutive model, which accounts for strain hardening, strain-rate sensitivity, and thermal softening effects characteristic of high-speed cutting conditions. Numerical simulations reproduce key features of high-speed orthogonal cutting of VT6 alloy, including the formation of the primary shear zone, strong localization of plastic deformation, and the development of segmented chip morphology. These results demonstrate the capability of the SPG method to capture the essential physical mechanisms governing material flow and chip formation under extreme deformation rates.
The findings contribute to the advancement of numerical technologies for the analysis of high-speed machining processes and provide a reliable computational framework for predicting the stress–strain state of the surface layer and chip formation conditions. From a practical standpoint, the proposed approach offers a foundation for optimizing cutting parameters, reducing the reliance on costly experimental trials, and improving material utilization efficiency in aerospace manufacturing and related high-technology industries.

Keywords:

numerical modeling of the cutting process, orthogonal cutting scheme, stress-strain state, fracture mechanism, Smoothed Particle Galerkin method, meshless methods, VT6 (Ti-6Al-4V) alloy, Johnson–Cook; segmented chips

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