Validation of Novel Geometrically Necessary Dislocations Calculation Model Using Nanoindentation of the Metal Matrix Nan
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NTRODUCTION
THE reduced weight of structural elements is one of the prime requirements for aerospace, automotive, electric vehicle, biomedical, and tribological applications.[1,2] Metals are alloyed or reinforced with different phases to increase the strength and other characteristics. Understanding of strengthening mechanisms can reduce the experimental cost for engineering alloys/metal matrix nanocomposites (MMnCs). The presence of secondary phase particles impedes the motion of dislocation, leading to enhancement of yield strength. This phenomenon is known as Orowan strengthening.[3] Orowan looping can be overtaken by the shearing of obstructing particles by dislocations.[3] Further, the mismatch in the elastic modulus and the coefficient of thermal expansion (CTE) between the matrix and second phase can also lead to the gradient in deformation. In such cases, the development of geometrically necessary dislocations (GNDs) is essential for compatible deformation. These types of materials are known as plastically nonhomogeneous materials.[3,4] When the forest of dislocation significantly exceeds the statistically stored dislocations, this leads to enhancement in strength due to interaction between themselves.[5] Arsenault and Shi[6] developed a model by prismatic punching around cuboidal reinforcement equally on all
HARPRABHJOT SINGH and DEEPAK KUMAR are with the Centre for Automotive Research and Tribology, Indian Institute of Technology Delhi, Hauz Khas 110016, India. Contact email: [email protected]. Manuscript submitted April 28, 2020, accepted September 3, 2020.
METALLURGICAL AND MATERIALS TRANSACTIONS A
faces for mismatch in the CTE. Misfit strain due to differences in the CTE was calculated. They assumed the matrix to be isotropic. Dislocation density was calculated using the misfit strain, particle dimensions, bulk modulus, and Burgers vector. They found a considerable increase in dislocation density with a decrease in thickness beyond 5 lm and a drastic increase in dislocation density beyond 1 lm. They found their results were close to the experimental findings. Miller and Humphreys[7] proposed dislocation density for quench strengthening. However, they have not given details of the analysis. Ashby[4] discussed the formation of the dislocation array (shear loop and prismatic loop array) in a ductile matrix reinforced by a cube-shaped particle. They calculated dislocation generation around the particle under the shearing of the matrix. They used the shear strain, particle dimension, bulk modulus, and Burgers vector to calculate dislocation density. This approach answers noncompatible elastic deformation in the plastically nonhomogeneous system. Dai et al.[8] made a first attempt and proposed a numerical model for the calculation of GNDs generated around spherical particles in the compression mode. They proposed generation of a dislocation loop around the spherical particle in the cylindrical shape to accommodate the strain generated due to mismatch in the elastic modulus. Similarly, they proposed dislocati
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