A chemo-thermo-mechanically coupled theory for elastic–viscoplastic deformation, diffusion, and volumetric swelling due to a chemical reaction

Abstract Thermal barrier coatings (TBCs) are applied to superalloy turbine blades to provide thermal insulation and oxidation protection. A TBC consists of an oxide/metal bilayer: the outer oxide layer (top-coat) imparts thermal insulation, while the metallic layer (bond-coat) affords oxidation protection through the formation of a thermally-grown-oxide (TGO) at elevated temperatures. The TGO layer possesses significantly different elastic, thermal expansion, and creep properties than the surrounding top-coat and bond-coat layers. An intrinsic mechanism which controls the long-term stability and mechanical integrity of a TBC is the volumetric change accompanying the oxide formation, and the attendant locally large stresses that can arise due to the geometrically uneven development of the TGO layer. In this paper we focus on modeling the response of the bond-coat material and its oxidation, and present a new continuum-level thermodynamically-consistent, large-deformation, fully three-dimensional theory which couples high-temperature elastic–viscoplastic deformation of the material with diffusion of oxygen, eventually leading to an oxidation reaction in which the reaction-product causes permanent swelling. The theory is chemo-thermo-mechanically coupled and complex, and at this point in time the list of material parameters appearing in the theory are not fully known. Once the material parameters in our theory are calibrated from suitable experiments, and the theory is numerically-implemented and validated, then the numerical simulation capability should provide an important ingredient for analyzing the evolution of the local stress and strain states which are important ingredients for the life-prediction and performance-improvement of TBCs.

[1]  E. Busso,et al.  A mechanistic study of microcracking in transversely isotropic ceramic–metal systems , 2006 .

[2]  John W. Hutchinson,et al.  Simulation of stresses and delamination in a plasma-sprayed thermal barrier system upon thermal cycling , 2003 .

[3]  Carlos G. Levi,et al.  The influence of oxides on the performance of advanced gas turbines , 2008 .

[4]  E. Jordan,et al.  Damage evolution in an electron beam physical vapor deposited thermal barrier coating as a function of cycle temperature and time , 2005 .

[5]  G. Cailletaud,et al.  Comparison of Oxidation-Growth Stresses in NiO Film Measured by Deflection and Calculated Using Creep Analysis or Finite-Element Modeling , 2002 .

[6]  Zhenguo Yang,et al.  Recent advances in metallic interconnects for solid oxide fuel cells , 2008 .

[7]  Lallit Anand,et al.  Moderate deformations in extension-torsion of incompressible isotropic elastic materials , 1986 .

[8]  M. Cherkaoui,et al.  Stress-induced roughness development during oxide scale growth on a metallic alloy for SOFC interconnects , 2010 .

[9]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[10]  Carlos G. Levi,et al.  MATERIALS DESIGN FOR THE NEXT GENERATION THERMAL BARRIER COATINGS , 2003 .

[11]  A. Evans,et al.  The mechanics of coating delamination in thermal gradients , 2007 .

[12]  Lallit Anand,et al.  A theory of amorphous solids undergoing large deformations, with application to polymeric glasses , 2003 .

[13]  W. Porter,et al.  Characterization of Alumina Scales Formed During Isothermal and Cyclic Oxidation of Plasma-Sprayed TBC Systems at 1150°C , 1999 .

[14]  A. Evans,et al.  A numerical assessment of the durability of thermal barrier systems that fail by ratcheting of the thermally grown oxide , 2003 .

[15]  A. Evans,et al.  Influence of thermal cycle on surface evolution and oxide formation in a superalloy system with a NiCoCrAlY bond coat , 2008 .

[16]  J. Stringer,et al.  The effect of reactive element additions on the selective oxidation, growth and adhesion of chromia scales , 1995 .

[17]  E. Jordan,et al.  Thermal Barrier Coatings for Gas-Turbine Engine Applications , 2002, Science.

[18]  E. Kröner,et al.  Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen , 1959 .

[19]  D. Clarke,et al.  Competition Between Stress Generation and Relaxation During Oxidation of an Fe-Cr-Al-Y Alloy , 1998 .

[20]  D. Clarke.  The lateral growth strain accompanying the formation of a thermally grown oxide , 2003 .

[21]  Ernst Rank,et al.  A simulation system for diffusive oxidation of silicon: a two-dimensional finite element approach , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[22]  Lallit Anand,et al.  On H. Hencky’s Approximate Strain-Energy Function for Moderate Deformations , 1979 .

[23]  A. Evans,et al.  Effects of bond coat misfit strains on the rumpling of thermally grown oxides , 2006 .

[24]  E. Busso,et al.  Effects of breakaway oxidation on local stresses in thermal barrier coatings , 2010 .

[25]  A. Evans,et al.  The effect of the thermal barrier coating on the displacement instability in thermal barrier systems , 2002 .

[26]  Ann Bolcavage,et al.  Technical and Economical Aspects of Current Thermal Barrier Coating Systems for Gas Turbine Engines by Thermal Spray and EBPVD: A Review , 2008 .

[27]  E. Jordan,et al.  Stress variation with thermal cycling in the thermally grown oxide of an EB-PVD thermal barrier coating , 2004 .

[28]  W. Moore.  Oxidation of Metals at High Temperatures , 1953 .

[29]  M. Cherkaoui,et al.  Stress influence on high temperature oxide scale growth: Modeling and investigation on a thermal barrier coating system , 2010 .

[30]  Olivier Coussy,et al.  Thermo-chemo-mechanics of ASR expansion in concrete structures , 2000 .

[31]  Jianguo Lin,et al.  A mechanistic study of oxidation-induced degradation in a plasma-sprayed thermal barrier coating system.: Part II: Life prediction model , 2001 .

[32]  T. Besmann.  Interface science of thermal barrier coatings , 2009 .

[33]  A. Evans,et al.  On the Role of Imperfections in The Failure of a Thermal Barrier Coating Made by Electron Beam Deposition , 2000 .

[34]  M. Gurtin,et al.  The Mechanics and Thermodynamics of Continua , 2010 .

[35]  E. Busso,et al.  The influence of bondcoat and topcoat mechanical properties on stress development in thermal barrier coating systems , 2009 .

[36]  Lallit Anand,et al.  The decomposition F = FeFp, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous , 2005 .

[37]  Anthony G. Evans,et al.  Mechanisms controlling the durability of thermal barrier coatings , 2001 .