Sintering Mackenzie-Shuttleworth model

Diffusion models have been developed by Coble (1970) for initial, intermediate and final stages of pressure sintering including both the applied pressure and the surface energy as driving forces. The Mackenzie-Shuttleworth model is considered suitable for Newtonian viscous materials. 

Relative density (p/p versus reduced time for Mackenzie-Shuttleworth model (solid curve) and cylinder model (dashed curve). For p/p > 0.942, the MS model applies. The curves have been shifted to coincide at the time t when sintering is complete. From Scherer 128). 

Figure 8.21 Finite element simulation of viscous sintering of two rigid particles coated with an amorphous layer (a) Rigid particles of radius a coated with a viscous layer of thickness s and showing the finite element mesh (b) predictions for the relative density versus reduced time for different coating thicknesses, and for the Mackenzie and Shuttleworth (M-S) model. (From Ref. 33.)...

Because the effects become less difficult to predict than the more realistic case of constant heating rate sintaing, we shall limit our discussion to isothermal sintering. The linear densification rate of the free matrix (i.e., the glass) can be found from the models for viscous sintaing described in Chapter 8. The Mackenzie and Shuttleworth equation is used because of its simple form, giving... 

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