Mathematical Modelling of Stress-Strain State of Multilayer Shell Molds

Abstract

The analysis of the trends for development of technological processes to form shell molds shows that the accuracy and purity of the surface of shaped castings are one of the main criteria for the level of development of the science and technology of foundry engineering. The equations of continuum mechanics and thermal conductivity and the numerical method were used to build a mathematical model of SSS of multilayer shell mold to determine the temperature fields in a shell mold and solidifying casting, thickness of solidified layer of the casting, stress, strain, and displacement of shell layers against each other, as well as ferrostatic pressure on the metal form. The calculation results show that at metal casting, the highest temperature differences occur between the first and second layers of a shell mold, and the maximum values of the stresses and strains are typical for the first layer of a shell mold. The mechanism of the effect of temperature difference between the layers of the shell mold on fracture toughness of the shells and its critical value are determined, above which either a decomposition of a shell mold occur, or through-thickness cracking occur, which lead to the destruction of a shell mold. The ignition process of shell molds in the control filler has no significant influence on the formation of cracks, since the temperature difference between the shell layers does not reach critical values.

Numerical Modeling of the Process of Filling the CCM Mold With Metal

“…Покажем, что система уравнений (4) -(6) эквива-лентна системе (1), (2). Выразим из уравнений (5) зна-чения σ ij = σδ ij + 2μξ ij и подставим их в уравнение дви-жения (4) …”

Numerical Modeling of Thermal Stress State of "Shell Mold-Casting" System with Phase Change when Inverstment Casting

“…Crack formation in SM is related to temperature impact arising during filling the molds with melt and thermoplastic stress state arising as result of no uniform heating as well as to low ceramic strength. Theoretical researches of these processes carried out by using numerical method are presented in works [1,2,3].…”

“…Porous layer created using the above-mentioned technology will act as a damper under the temperature impact. Research results of the stress-strain state of these SMs were presented in works [7,8,9,10,11].…”

“…Thus, usage of these multilayer SMs having heterogeneous layers and different variants of these layer combinations over SM thickness will make it possible to model required macro and micro structure of SM, its properties and variants of layer combination over the shell thickness [12] at the stage of process designing.…”

Theoretical Prediction of Crack Formation in Axisymmetric Multilayer Shell Molds

“…Stress-strain state (SSS) of cylindrical shells is studied in papers [1,2], and papers [3,4] describe features of technology of electrophoretic process. Paper [5] uses the mathematical modeling to study SSS of multilayer shell molds. It is shown that during casting of metal, the greatest temperature differences occur between the first and second layers of the shell mold, and the maximum values of stresses and strains are typical for the first layer.…”