X-Ray Rocking Curve Measurements of Dislocation Density and Creep Strain Evolution in Gamma Prime-Strengthened Ni-Base S
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INTRODUCTION
A. Dislocation Density vs Creep Strain In their 1983 publication on creep in Ni-base superalloys, Dyson and Mclean proposed that mobile dislocation density increases linearly with creep strain with no dependence on stress or temperature.[1] Subsequently, Dyson[2] and Zhu et al.[3] used a linear relationship between dislocation density and creep strain in physically based models for creep of superalloys. e ¼ fðq; M; r; TÞ;
½1
q ¼ gðeÞ:
½2
Equation [1] relates the creep rate to dislocation density (q), c¢ characteristics (M), stress, and temperature, and Eq. [2] relates the dislocation density to creep strain. The same broad philosophy was adopted by Manonukul et al.[4] though with more elaborate reasoning. In the last three decades, there has not been any serious effort to verify the assumption of a linear
K.G.V. SIVA KUMAR and RAMKUMAR ORUGANTI are with the John F Welch Technology Centre, GE Global Research, Bangalore 560066, India. Contact e-mail: [email protected] PARTHA CHATTERJEE is with the Department of Physics and Electronics, Vivekananda Mahavidyalaya, Haripal, Hooghly 712405, India. Manuscript submitted November 24, 2017. Article published online October 24, 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A
relationship between dislocation density and creep strain. The current study aims to address this gap using X-ray rocking curve measurements of dislocation density on test bars crept to varying levels of creep strain. B. X-Ray Diffraction for Measurement of Dislocation Density X-ray diffraction has been widely used for ascertaining strain induced by plastic deformation in both polycrystalline and single-crystal metallic systems. Plastic deformation is accompanied by the movement and multiplication of dislocations, whose arrangement within the grains is dependent on stress, temperature, and the magnitude of accumulated strain. The strain field of a dislocation scales as 1/r and therefore spans a larger distance compared to that of a point defect.[5,6] In reciprocal/diffraction space, this effect manifests itself as peak broadening around the Bragg reflection, whose severity is indicated by the full-width-at-half-maximum (FWHM) of the measured peak. In polycrystalline metals where diffraction is from an ensemble of grains, FWHM averaged over this collection of grains is measured by an x 2h scan of the chosen Bragg reflection. Regions within a grain where dislocations are present are distorted which results in a local change of the interplanar spacing dhkl relative to undeformed regions of the grain. X-ray line broadening is a direct consequence of this spread in dhkl. Here, the measured broadening (FWHM) is along the diffraction vector g as explained by Zilahi et al.[7] Line broadening due to crystal defects such as dislocations was first VOLUME 50A, JANUARY 2019—191
proposed by Warren and Averbach,[8] albeit phenomenologically. They showed that diffraction line broadening, more specifically strain broadening, scales as the spatial average of mean-squared microstrain he2 i: In additio
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