Mechanical Behavior of Ni-based superalloys having γ/γ’ Interface: A first-principles study

Abstract

The process of fracture of solid materials is still not fully understood in many aspects, and thus lot of research both experimentally and theoretically is carried out to address this issue. The mechanism by which most of the fracture process occurs involves crack nucleation and its propagation. Until now, numerous efforts in understanding mechanical properties of materials have been based mainly on phenomenological and empirical concepts and approaches. This is mainly because the problem of addressing the mechanism of fracture involves the length scales from macroscopic dimensions to the atomistic length scale. This thesis is aimed at gaining the theoretical understanding of the γ - γ’ system and more specifically γ/γ’ interface in Ni-based single crystals superalloys for pure and alloyed condition in terms of the two modes of fracture, namely cleavage as mode I and shear as mode II, at atomic length scale. This study has been performed within the framework of first-principles calculations using density functional theory (DFT). The thesis is divided into five chapters. The first chapter provides a brief introduction to Ni-based superalloys and fracture mechanics. Here a brief introduction of Ni-based single crystal superalloys, their development and their usefulness over conventional alloys and areas of application are described. A brief introduction to the fracture mechanism covering brittle and ductile fracture and various modes is also provided. A brief overview of the different atomistic simulation techniques with their pros and cons is also described. In the second chapter, a detailed description of the simulation techniques (firstprinciples calculations based DFT) used in the present study along with the assumptions involved and the limitations of the techniques is provided. The computational details used in the present thesis along with the calculated lattice parameters of γ, γ’ and γ-γ’ systems are also described in this chapter. The third chapter provides our study related to mode I cleavage fracture. Here abinitio calculations have been used to calculate the fracture strength in terms of Griffith’s work (Gc) or ideal brittle cleavage energy. Gc is defined as the work needed to cleave a crystal along a plane. Briefly stated, we calculate Gc for adjacent atomic layers which are displaced (x) (sufficiently large such that the interaction between the interfaces ceases) from their interlayer spacing of the crystal into two semi-infinite parts. This is represented as Gc = (1/A).[Etot(x=0) - Etot(x=)] where, A is the area of the cleaved plane, Etot(x=0) and Etot(x=) are the total energy, after complete relaxation, of the pure and cleaved system respectively. We determine x when the total energy of the system as a function of separation (x) between adjacent layers converges to a narrow margin (<0.02 J/m2 ).In the present work, Gc is calculated for bulk γ –Ni, γ’-Ni3Al and γ – γ’ systems. Results of cleavage energies suggest that γ has a higher cohesive strength than the ordered γ’. For γ – γ’ systems, Gc as a function of distance away from the γ/γ’ interface ((002)||(001)’) towards γ and γ’ for (001) plane with 20 atomic planes (with 2 atoms per plane) was calculated. The results suggest that for pure γ-γ’ system the cleavage energy is always higher (by about 6%) within γ than within γ’. This demonstrates that the matrix phase (γ) is stronger as compared to the precipitates (γ’) under tensile deformation. Our study could establish that the effect of the interface on the cleavage strength is not appreciable beyond a distance of 4 – 5 Å.