Abstract
Existing mathematical models for the process of HIP porous blanks are based on the solution of approximately differential equations of the equilibrium of quasi-continuous medium. The continual approach is used for computer modeling of the compressible body HIP process. Partial differential equations of motion for a quasi-continuous packing medium and physical equations for a viscous-plastic isotropic porous material subjected to work hardening are taken as the basis for the mathematical model by means of these simultaneous equations. Besides the equations of motion and the rheological equation, the equation of continuity deformation and the equation of heat flow are used. Numerical calculations for additional packing of a high-speed steel powder billet preliminary pressed in the hydrostat are performed. Numerical calculation of the problem for hardening the cylindrical high-speed steel billet with a mild steel shell is done using Lagrange’s method by means of the difference scheme of continuous calculation of the Wilkins’ type. Computer modeling allows to control the process of hardening and changing the form of a porous body during the HIP process.
Highlights
Hot isostatic pressing (HIP) is one of the most suitable techniques for producing the high-speed steel cemented carbide, superalloys, soft ferrites and composites at a simultaneous application of high-pressure and high temperature [1–3]
Results of numerical calculations In numerical calculations the HIP process of a porous compressible high speed steel billet pressed in the hydrostat was modeled
The initial density of the porous body at HIP is assumed to be equal to 0.93ρc, where ρc is the density of non-porous high speed steel, and the process temperature being as high as 1300, 1400 and 1500 °C
Summary
Existing mathematical models for the process of HIP porous blanks are based on the solution of approximately differential equations of the equilibrium of quasi-continuous medium. The continual approach is used for computer modeling of the compressible body HIP process. Partial differential equations of motion for a quasi-continuous packing medium and physical equations for a viscous-plastic isotropic porous material subjected to work hardening are taken as the basis for the mathematical model by means of these simultaneous equations. Numerical calculations for additional packing of a high-speed steel powder billet preliminary pressed in the hydrostat are performed. Numerical calculation of the problem for hardening the cylindrical high-speed steel billet with a mild steel shell is done using Lagrange’s method by means of the difference scheme of continuous calculation of the Wilkins’ type.
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