Chapter 1 Interface Mechanical Strength and Elastic Constants Calculations via Nano Impact and Nanomechanical Raman Spectroscopy Devendra Verma and Vikas Tomar Abstract Interfaces are ubiquitous in important natural and manmade materials. Research evidence has shown that interface chemistry, structure, and thickness together strongly influence material microstructure and mechanical properties. The focus of the present work is on presenting an experiment based theoretic advancement to predict thickness dependent elastic properties of materials interfaces by treating the interfaces and the area around them in a material as an elastic continuum. The experiments are based on the nanomechanical Raman spectroscopy (NMRS) developed by authors earlier with a capability to simultaneously measure stress components in orthogonal directions during an in-situ nanomechanical loading. An analytical model is developed based on boundary conditions of interface to predict thickness dependent interface elastic constants. The interface elastic constants are compared with the relations provided in literature. Keywords Nanomechanical Raman spectroscopy • In-situ interface deformation • In-situ nanomechanical measurements • Interface thickness • Interface elastic constants The first ever mention of interfaces is in the work of Gibbs [1] where he formulated thermodynamic foundations of interface excess energy. Gibbs definition of interfaces was a zero thickness mathematical entity. The focus of the present work is different from interface thermodynamics, interface chemistry, and interface structure characterization work available in literature. The interface in this study is considered to be of finite thickness with a non-zero volume. Emphasis is on deducing the influence of interfaces on mechanical deformation using a classical approach that incorporates interface multi-axial properties. The present work uses a nanomechanical Raman spectroscopy (NMRS) [2–7] based experimental framework to measure direct in-situ interface deformation properties. In the classical work by Dingreville and Qu [8–10] the interfacial mismatch stress was related to the in-plane strain and applied stress in the case of a zero thickness interface. These formulations provide a way to calculate interfacial elastic properties based on the contribution of interfacial coherent surface stress, incoherent surface stress and transverse excess strain. The role of transverse direction properties of interfaces is accounted for mathematically. In an another formation, the interface is explicitly considered as a finite thickness entity to calculate the interface elastic constants in the case of heterogeneous thin interfaces by Ustinov et al. [11] showing the interface stiffness dependence on their thickness. The present work focuses on using NMRS based direct observations of multiaxial interface deformation to develop a theoretical framework for predicting interface elastic constants as a function of interface thickness. Interfaces in composite materials are considered as a material phase confined between two separate grains or phases. In this experimental work, the interface elastic constants are measured in the case of an idealized epoxy interface between two glass plates. Single interface samples of glass and epoxy were prepared with an epoxy interface sandwiched between two glass plates. The thickness of the interface in samples was measured with a microscope to make sure that it was in the error margin of 10 ˙0.5 m. Considering different stiffness for the interface and the bulk phases, this boundary condition leads to a jump in the stresses. It has continuous strain distribution for the component in indentation direction while the stresses perpendicular to the interface must fulfill the condition of equilibrium. To solve this problem, a fictitious homogeneous isotropic elastic half space is assumed which for a given applied load through the indenter exhibits the same normal surface displacement as the material with interface. Figure 1.1 shows the schematic of solution procedure for this case. The key assumption of the analytical approach presented here is that the classical strain solution and the solution for the layered half space are similar for the applied loads. The assumptions for these components are therefore: D. Verma • V. Tomar ( ) School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, 47907, USA e-mail: vermad@purdue.edu; tomar@purdue.edu © The Society for Experimental Mechanics, Inc. 2018 J. Carroll et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-62831-8_1 1
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