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A Lattice-Misfit-Dependent Damage Model for Non-linear Damage Accumulations Under Monotonous Creep in Single Crystal Superalloys J.-B. LE GRAVEREND A lattice-misfit-dependent damage density function is developed to predict the non-linear accumulation of damage when a thermal jump from 1050 C to 1200 C is introduced somewhere in the creep life. Furthermore, a phenomenological model aimed at describing the evolution of the constrained lattice misfit during monotonous creep load is also formulated. The response of the lattice-misfit-dependent plasticity-coupled damage model is compared with the experimental results obtained at 140 and 160 MPa on the first generation Ni-based single crystal superalloy MC2. The comparison reveals that the damage model is well suited at 160 MPa and less at 140 MPa because the transfer of stress to the c¢ phase occurs for stresses above 150 MPa which leads to larger variations and, therefore, larger effects of the constrained lattice misfit on the lifetime during thermo-mechanical loading. https://doi.org/10.1007/s11661-018-4681-5  The Minerals, Metals & Materials Society and ASM International 2018

I.

INTRODUCTION

MONOCRYSTALLINE nickel-based superalloys are widely used in the hottest parts of aeroengines or industrial gas turbines[1] and, therefore, should withstand temperatures as high as 1100 C for thousands of hours.[2] These alloys are particularly resistant to creep load which makes them suited for uncooled components such as high pressure turbine blades of turboshaft engines for helicopters or small industrial gas turbines. These interesting properties result from the precipitation of a high volume fraction (close to 70 pct up to 975 C) of the long-range ordered L12 c¢ phase which appears as cubes coherently embedded in a face-centered cubic (fcc) solid solution c matrix (see Figure 1(a)) and evolves into platelets, also known as rafts, by directional coarsening during high temperature mechanical testing (T > 850 C).[3] The orientation of the rafts, as well as the distribution of internal stresses within the initial non-deformed material, depends on the sign and amplitude of the natural c/c¢ lattice misfit between both phases defined as ac 0  ac ; ½1 d¼2 ac 0 þ ac

J.-B. LE GRAVEREND is with the Aerospace Engineering and Materials Science Engineering Departments, Texas A&M University, College Station, TX, 77843. Contact e-mail: jblgpublications@ gmail.com Manuscript submitted March 9, 2018.

METALLURGICAL AND MATERIALS TRANSACTIONS A

where ac¢ and ac are respectively the free lattice parameters of the c¢ and c phases. Some authors have already studied the temperature dependence of the natural lattice misfit by X-ray[4,5] and neutron diffraction.[6,7] They found that the lattice misfit considerably changes above around 700 C. The constrained lattice misfit d? is defined in a similar fashion than the natural lattice misfit, but it uses the lattice parameters in the plane perpendicular to the loading axis. However, contrary to the natural lattice misfit, a few studies exist on the conti