Coarsening of self-stressed plates

• Published in: Scripta materialia Vol. 43; no. 11; pp. 1027 - 1032
• Main Authors: Johnson, William C., Leo, Perry H.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Ltd 13.11.2000; Elsevier Science
• Subjects: Constant-composition solid-solid phase transformations: polymorphic, massive, and order-disorder; Cross-disciplinary physics: materials science; rheology; diffusion; Exact sciences and technology; Materials science; Phase diagrams and microstructures developed by solidification and solid-solid phase transformations; Phase transformations (spinodal decomposition); Physics; Theory and modeling (kinetics; Thin films; transport; Thin films; Phase transformations (spinodal decomposition); diffusion; transport; Theory and modeling (kinetics; Phase transformations; Spinodal decomposition; Prestressed plate; Thin sheet; Theoretical study; Modelling; Transport processes; Coalescence; Diffusion; Sheets
• ISSN: 1359-6462; 1872-8456
• DOI: 10.1016/S1359-6462(00)00534-0

In recent work, Cahn and Kobayashi examined one-dimensional spinodal decomposition in coherently self-stressed thin plates. In this letter, we employ a simple approxiamtion to derive an expression for the time rate-of-change of the thickness of the surface phase, which we call the coarsening rate. We present some results from numerical simulations for different compositional strains and film thicknesses which show good agreement with the analytic predictions. Cahn and Kobayashi elegantly showed that the composition moment mu sub 1 increases exponentially in time during the early stages of the coarsening regime. We have extended this result to show that the coarsening rate, tau sub c , defined by the time rate-of-change of the thickness of the outer phase is approximately constant at long times, indicating that the coarsening proceeds as a linear function of time. The coarsening rate is predicted to be proportional to the square of the compositional strain and inversely proportional to the film thickness. These results are in good agreement with numerical simulations of coarsening for film thicknesses 100 < = lambda < =500 and compositional strains 0.1 < = alpha sub 1 < =0.25. (Example material: isotropic binary alloy.)