Mechanistic Modeling of Strain Hardening in Ni-Based Superalloys
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INTRODUCTION
IN recent years, several physics-based yield strength models have been developed for predicting the onset of plastic flow in polycrystalline Ni-based superalloys.[1–4] These yield strength models consider interactions of dislocations with the microstructure to assess the material’s resistance against plastic deformation. Individual hardening mechanisms such as Hall–Petch hardening, solid solution hardening, and precipitation hardening were treated. For precipitation hardening, shearing of c¢ (Ni3Al, L12 structure) precipitates, cross-slip-induced anomalous hardening, and dislocation bowing around c¢ particles were considered in the development of the yield strength models, since Ni-based superalloys are generally strengthened by ordered c¢ precipitates with the L12 crystal structure. Most of these constitutive models treated the onset of yielding only, while one model also considered the strain hardening response beyond yielding. The yield strength models were successful in predicting the variability of yield strength due to microstructural variations in Ni-based superalloys.[1,2] The Ramberg–Osgood equation[5] is a constitutive model that is commonly used for structural analysis and KWAI S. CHAN is with the MESI Technologies LLC, San Antonio, TX 78250. Contact e-mail: [email protected] Manuscript submitted April 6, 2020.
METALLURGICAL AND MATERIALS TRANSACTIONS A
life prediction applications of gas turbine engine components. According to this model, the total strain is comprised of an elastic strain component and a plastic strain component. The stress, r, is governed by a power law of the plastic strain, as described by r ¼ kenp ;
½1
where ep is the plastic strain, k is the strength coefficient, and n is the strain hardening exponent. Both k and n are empirical constants which are considered to be independent of plastic strains and are evaluated by fitting to experimental data. By itself, Eq. [1] provides little information on the underlying dislocation mechanisms or microstructural parameters responsible for the strain hardening behavior. However, the influence of microstructure factors on the strength coefficient and the strain hardening exponent can be correlated with the grain size of the c matrix, and the size and volume fraction of c¢. Such an approach was applied to IN 100[4] and low solvus high refractory (LSHR) Ni-based superalloys.[6] Complex correlations and expressions were observed between these microstructural parameters and yield strength and the strength coefficient, but no clear correlation was obtained for the strain hardening exponent n.[4] While Eq. [1] is well known and has been shown to be applicable for a variety of engineering alloys and metals, there have been reports that the linear relation between log r and log ep implied by Eq. [1] does not occur over
the entire plastic strain range, but occurs in two distinct stages: (1) a lower strain hardening exponent, n1, in the low plastic strain regime, and (2) a higher strain exponent, n2, in the higher plastic strain regime. The
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