Evaluation of single crystal elastic stiffness coefficients of a nickel-based superalloy by electron backscatter diffraction and nanoindentation

Abstract

A new methodology was developed in order to obtain single crystal elastic coefficients from nanoindentation experiments on a cubic polycrystal. The method consists of locating grains that are oriented with a <100>, <110> or <111> direction near-parallel to the sample surface normal by means of electron backscattering diffraction. The reduced Young's moduli of the selected grains are then determined by nanoindentation. Finally, the average reduced modulus and Euler angles of each grain are used as input for a least-squares optimisation to calculate the three independent stiffness coefficients, which can then be used to obtain Young's modulus in any crystallographic direction. This technique, which was validated on a single crystal nickel-based superalloy (CMSX-4) with known elastic coefficients, was applied to a polycrystalline nickel-based superalloy (RR1000) with unknown elastic coefficients, resulting in a correct prediction of the general trend of increasing Young's modulus from the <100> to the <110> to the <111> direction. The stiffness coefficients C11, C12 and C44 were found to be 282, 121 and 108 GPa, respectively. These results, which are representative of the γ/γ' structure as a whole, are in good agreement with literature data on similar superalloys. By constructing a visual representation of the elastic anisotropy based on the crystallographic factor, it is shown that the observed anisotropy is lower compared to other alloys.

Identification of thermomechanical parameters based on the virtual fields method combined with the sampling moiré method

“…Ni-based superalloys are a class of materials that exhibit excellent mechanical properties at high temperatures; for example, their tensile strength can reach hundreds of MPa at 1000 C. Among them, NBPS has isotropic properties, whereas NBSCS is orthotropic because of its face-centred cubic structure. The NBSCS belongs to the cubic crystal system; therefore, the elastic stiffness matrix C of the NBSCS in the case of three dimensions (3D) can be given by [33][34][35][36] C ¼…”

Grain-to-Grain Interaction Effect in Polycrystalline Plain Low-Carbon Steel within Elastic Deformation Region

“…A grain is an important microstructural unit, and its Young’s modulus depends on its crystal orientation [ 2 , 3 , 4 , 5 ]. Grains in crystalline materials have different crystal orientations; correspondingly, they have different Young’s moduli.…”

“…The nanoindentation technique is a useful tool to measure the Young’s modulus of a local site. Its principle can be stated briefly as follows: a diamond indenter is pushed into the surface of the material, and the variation of load with the penetration depth of the indenter in the loading and unloading process is recorded; from the unloading curve, the Young’s modulus of the region where the indenter penetrated is obtained [ 2 , 3 , 4 , 5 ]. Many researchers have used the nanoindentation technique to measure the Young’s moduli of individual grains in polycrystals [ 2 , 3 , 4 , 5 ].…”

“…Its principle can be stated briefly as follows: a diamond indenter is pushed into the surface of the material, and the variation of load with the penetration depth of the indenter in the loading and unloading process is recorded; from the unloading curve, the Young’s modulus of the region where the indenter penetrated is obtained [ 2 , 3 , 4 , 5 ]. Many researchers have used the nanoindentation technique to measure the Young’s moduli of individual grains in polycrystals [ 2 , 3 , 4 , 5 ]. However, because the load–displacement curve in the nanoindentation test does not involve any information regarding grain-to-grain interaction, the obtained Young’s moduli were not the real ones of individual grains ( E 1 ) in the polycrystals, and they were close to the values of single crystals ( E 0 ) [ 5 ].…”

“…Many researchers have used the nanoindentation technique to measure the Young’s moduli of individual grains in polycrystals [ 2 , 3 , 4 , 5 ]. However, because the load–displacement curve in the nanoindentation test does not involve any information regarding grain-to-grain interaction, the obtained Young’s moduli were not the real ones of individual grains ( E 1 ) in the polycrystals, and they were close to the values of single crystals ( E 0 ) [ 5 ]. In addition to experimental measurements, E 0 is available from the theoretical calculation based on the elastic constants [ 18 ].…”