Measurement of scratch-induced residual stress within SiC grains in ZrB₂–SiC composite using micro-Raman spectroscopy

Abstract

An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB₂–SiC composite is developed. Using a “secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB₂ and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB₂–SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith theory.

Introduction

Ultra-high-temperature materials with low density, good mechanical strength and high oxidation resistance at elevated temperatures (>2000 °C) are potential candidates for applications in future hypersonic vehicles, kinetic energy interceptor missiles, reusable launch vehicles, etc. [1], [2], [3], [4], [5], [6]. Specific examples include wing leading edges, engine cowl inlets, nose-caps, etc. These components have sharp aero-surfaces that are subjected to reactive environments at temperatures >2000 °C. Currently, materials used in high-temperature aerospace structural components are mostly carbon–carbon composites and silicon carbide-based composites [4]. Although, these composites have high-temperature structural capabilities, their oxidation resistance is known to be poor. Ultra-high-temperature ceramics (UHTC) such as borides of transition metals (e.g., zirconium (Zr) and hafnium (Hf)) and their composites are identified as the next generation materials for high-temperature aerospace applications [1], [2], [3], [4]. Among UHTC, zirconium diboride–silicon carbide (ZrB₂–SiC) composites have been receiving significant attention in recent years [3], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] owing to their low density (∼6.0 g cm⁻³), high melting point (>3000 °C) and good oxidation resistance >1500 °C.

In the above-mentioned aerospace applications, the UHTC may be subjected to impact by atmospheric debris that can lead to wear of the structural components. This abrasive action of the atmospheric debris particles causes inelastic deformation within the material. Therefore, it is important to study the wear behavior and the associated damage mechanisms in UHTC subjected to such loads. However, most of the available literature on ZrB₂–SiC composites is focused on processing and their oxidation behavior [3], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]; knowledge on wear behavior of these materials is literally non-existent.

Indentation and scratch experiments have been used effectively to model deformation and damage mechanisms that evolve in ceramics during an abrasion process [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. In scratch experiments, both normal and tangential point loads are applied whereas, in indentation experiments, only a normal point load is applied on the surface [24], [26], [27], [28], [29]. Experimental and theoretical studies have shown that the loading phase of the scratch process (or indentation) causes elastic–plastic deformation within a brittle material, resulting in accumulation of mechanical residual stress upon unloading [24], [27], [28]. The loading phase also causes evolution of radial and median cracks during indentation and scratch experiments [24], [27], [28]. Upon unloading, the accumulated deformation-induced residual stress causes lateral cracking. Initiation of such damage and consequent material removal from the surface due to these contact processes may result in lower mechanical reliability of the components made out of UHTC. Therefore, quantification of mechanical residual stress due to scratch or abrasion phenomena is necessary for a fundamental understanding of the material removal process and for design of abrasion-resistant materials.

The authors have recently investigated scratch-induced deformation and damage patterns in a ZrB₂–5 wt.% SiC composite in the load range 50–250 mN [29]. Microstructural studies of the scratch grooves revealed microplasticity (in the form of slip lines) and microcracks within the ZrB₂ phase. The present paper describes the results of scratch-induced mechanical residual stress measurements within the SiC grains of the ZrB₂–SiC composite using micro-Raman spectroscopy (MRS).

Raman spectroscopy has emerged as a useful non-destructive tool for residual stress measurements. The sensitivity of a Raman peak to mechanical stress (or more precisely the strain) was first reported by Anastassakis et al. [30]. In particular, MRS is useful in determining local residual stress owing to its high spatial resolution (of the order of 1 μm) [30], [31], [32], [33], [34], [35], [36], [37]. For example, in thin films and micro electro-mechanical systems devices, MRS is largely used for residual stress determination arising as a result of coefficient of thermal expansion (CTE) mismatch between the substrate and the film materials [31], [33], [36], [37]. Indentation- and scratch-induced residual stress analyses are also conducted using MRS [34], [35]. In crystalline materials, the atomic vibrational frequencies depend on the interatomic force constants [36]. In strain-free crystalline materials, interatomic force constants as well as the vibrational frequencies correspond to the equilibrium atomic spacing. Residual stress resulting from either thermal process (such as sintering) or mechanical deformation (such as indentation, scratch, etc.) causes a definitive residual strain, which in turn changes the equilibrium atomic spacing within a material and thus the interatomic force constants. As a result, Raman scattering wave numbers are also perturbed. Depending upon the tensile or compressive nature of the residual stress, bond lengths and force constants either increase or decrease compared with the equilibrium values. Accordingly, a Raman peak shifts to lower or higher frequency for tensile or compressive residual stress, respectively [30], [31], [36], [37], though there is no unique general relationship between the Raman spectrum parameters (particularly the wave number shift) and the residual stress state. One way to establish such relationships is by the calibration procedure, which correlates Raman peak shift in a material with the known applied stress. Then, using the calibration curve, unknown residual stresses can be determined from the changes in Raman peak positions for that particular material. However, the resultant calibration curve also depends on the applied stress state and, therefore, there is no unique relationship between residual stress and Raman peak shift for a given material. In contrast, explicit expressions relating Raman peak shift and residual stress have been derived for simple situations such as uniaxial stress state, hydrostatic or equi-biaxial stress state which can also approximate the residual stresses [31], [36], [38]. Therefore, expressions for appropriate scenarios must be developed to estimate residual stress within Raman active materials using MRS.

Although ZrB₂ is not Raman active, SiC is known to be Raman active, and its characteristic Raman peaks, particularly for cubic SiC, are sensitive to residual stress [38], [39], [40]. Therefore, it is possible to determine the magnitude of the residual stresses from the stress/strain sensitive Raman peaks of SiC material. In the current study, the changes in Raman peak positions of SiC grains located within the scratch grooves of a ZrB₂–5 wt.% SiC composite were measured as a function of scratch load. Then, from these Raman measurements a mechanics-based expression was derived to estimate scratch-induced mechanical residual stress within the SiC grains in the composite.