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Modelling of Ceramic Mould Deformation in the Investment Casting Process

Modelling Ceramic Mould Deformation

 Researcher: Luke Swaina­,

Supervisor(s): Stuart Blackburna­­­, Roger Reedb­­­­­­

a. School of Chemical Engineering, University of Birmingham, Edgbaston B15 2TT

b. Department of Metallurgy and Materials, University of Birmingham, Edgbaston B15 2TT


The effect of mould deformation has been a concern in turbine blade manufacture since the use of single crystal turbine blades. Recrystallisation of nickel superalloys blades has been a related topic of study, as this phenomena arises from the differential thermal expansion between the nickel superalloy blade and the ceramic mould. However the primary appeal of modelling ceramic mould deformation is the possible environmental benefits that could result. Not only can this lead to an improvement in process capability and improve efficiency in the production of turbine blades, but this generalised model could be used as an aid in core and shell formulation development. Through a better understanding of how a ceramic will behave based on critical parameters such as composition of the ceramic and particle size, optimised formations can be obtained. Due to the required long exposure of moulds to high temperatures in furnaces a large amount of energy is consumed in experimental testing, which could be reduced through an appropriate numerical simulation.

 There are three significant phenomena which contribute to deformation of the ceramic mould.

            1. General thermal expansion

            2. Sintering

            3. Phase transformations

General thermal expansion is relatively straightforward in a modelling sense, described by (1)








However complexity is likely to arise in modelling the shell where the behaviour has been shown to be anisotropic.


There is a significant amount of literature on the phenomena of sintering, and although a few continuum sintering models have been constructed using finite element analysis[5]­, the majority of research seems to be more concerned with understanding sintering on a molecular level.










Figure 1: An illustration of the polymorphic transformations of concern in casting for silica.


A phase transformation of silica results from a natural drive to reduce the free energy of a structure. In this project, this is mainly dependent on temperature, impurities and particle size. The volume change resulting from a polymorphic transformation is significant in mould deformation. These polymorphic transformations are illustrate in figure 1 and are labelled in figure 2. A major aim of this project is to be able to replicate figure 2 for a number of different ceramic compositions, prior to dilatometry measurements.












Figure 2: A characteristic thermal expansion curve for originally amorphous silica.


Figure 3: A comparison between DFEM and experimental results[3].





A continuum model has been proposed due to a number of computational constraints[1].The complexity of interactions between individual molecules in both sintering and phase transformation, along with the large number of molecules that would need to be accounted for in a sizeable bulk structure such as a mould, restricts the use of promising modelling methods such as molecular dynamics simulation and multiscale modelling[2]­­­­­­. It has been proposed that a novel method of modelling sintering through densification data (DFEM) instead of  through the construction of a constitutive law produces comparable results and corresponds well in accordance with experimental results[3]­­­ as shown in figure 3. This is ideal for use in industrial applications due to considerably fewer parameters required to accurately model sintering deformation and its flexibility in producing sufficiently accurate results for a range of different sintering mechanisms[4]. It should be noted that the variability of associated material properties and obtaining properties at high temperatures makes property measurement a significant challenge.






[1] E.A. Olevsky. “Theory of sintering: from discrete to continuum” Mater. Sci. Eng. R23, pp. 41-100, 1998

[2] J. Pan. “Modelling sintering at different length scales” Int. Mater. Rev. 48, pp. 69-85, 2003

[3] S. Kiani, J. Pan, J.A. Yeomans, M. Barriere, P. Blanchart. “Finite element analysis of sintering deformation using densification data instead of a constitutive law” J. Eur. Ceram. Soc. 14, pp. 2377-2383, 2007

[4] R. Huang. J. Pan. “A further report on finite element analysis of sintering deformation using densification data—Error estimation and constrained sintering” J. Eur. Ceram. Soc. 28, pp. 1931-1939, 2008

[5] C.R. Reid. “Numerical simulation of free shrinkage using a continuum theory for sintering” Powder Technology 81, pp. 287-291, 1994

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