Analytical determination of the stress – strain field in an elastic half-space under high-intensity moving surface loading

Аuthors

Nguyen T. L.

Le Quy Don Technical University, 236 Hoang Quoc Viet, Ha Noi, Viet Nam

e-mail: kqvn.nguyenlong@gmail.com

Abstract

This study determines the stress–strain state of a metal powder composite during the selective laser melting of a half-space. To achieve this objective, an auxiliary boundary-value problem of transient heating of an isotropic elastic half-space is formulated and analytically investigated. The heating process is induced by a moving surface heat source characterized by prescribed kinematic and energy parameters. The Maxwell–Cattaneo theory uses a generalized heat conduction equation to account for the finite speed of thermal disturbance and include heat flux relaxation effects. Thermoelastic coupling is modelled because of the Lamé equations of linear elasticity with inclusion of thermal strains. A closed-form mathematical model is constructed, consisting of a system of coupled differential equations supplemented by the corresponding initial and boundary conditions. The analytical solution is obtained using the method of integral transforms: the Laplace transform with respect to time, and the two-dimensional Fourier transform with respect to spatial coordinates are applied, yielding explicit expressions for the temperature field and the components of the stress–strain state.

Keywords:

selective Laser Melting (SLM); metal powder composite; additive manufacturing; stress–strain state; thermoelectricity; transient heat conduction; Maxwell–Cattaneo theory; hyperbolic heat conduction equation; moving heat source; thermal stresses; residual stresses; heat flux relaxation; high-gradient heating

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