Determination of residual stress distributions in polycrystalline alumina using fluorescence microscopy

Abstract

Maps of residual stress distributions arising from anisotropic thermal expansion effects in a polycrystalline alumina are generated using fluorescence microscopy. The shifts of both the R1 and R2 ruby fluorescence lines of Cr in alumina are used to create maps with sub-µm resolution of either the local mean and shear stresses or local crystallographic a- and c-stresses in the material, with approximately ± 1 MPa stress resolution. The use of single crystal control materials and explicit correction for temperature and composition effects on line shifts enabled determination of the absolute values and distributions of values of stresses. Temperature correction is shown to be critical in absolute stress determination. Experimental determinations of average stress parameters in the mapped structure are consistent with assumed equilibrium conditions and with integrated large-area measurements. Average crystallographic stresses of order hundreds of MPa are determined with characteristic distribution widths of tens of MPa. The stress distributions reflect contributions from individual clusters of stress in the structure; the cluster size is somewhat larger than the grain size. An example application of the use of stress maps is shown in the calculation of stress-intensity factors for fracture in the residual stress field.

Review: Coefficients for Stress, Temperature, and Composition Effects in Fluorescence Measurements of Alumina

“…Hence, the linear variation of shift with applied stress (up to a few hundred megapascals; one unverified exception) and the numerical agreement with the non-polycrystal coefficient determinations surveyed above further support the observations. It is noted that the applied stress range of the polycrystal experiments was about an order of magnitude less than the single-crystal or fiber experiments (previous sections) and comparable to the intrinsic microstructural stresses expected and observed in bulk polycrystals [38][39][40][41][42][58][59][60][61][62][63][64][65][66][67]. Table 3 gives the first author, year published, citation, R-line coefficients (R1 or R2), and notes for original works that (experimentally) determined the temperature coefficients β (1) and β (2) ; see Eq.…”

“…Typical large values are Δ (1) = −0.80 cm −1 and Δ (2) = −0.60 cm −1 [67]. A typical value for T is 21 °C = 294.15 K. A typical value for C for alumina is 0.0001.…”

“…where the second line emphasizes that the shift in energy arises from a mean stress contribution (σM) plus a shear stress contribution (σS) [67]:…”

“…At least part of the motivation for the polycrystalline research was to investigate the stress fields arising in polycrystalline alumina responsible for microcracking-the spontaneous localized cracking that occurs in polycrystalline alumina on cooling as a consequence of the anisotropic structure and thermal expansion of corundum [39][40][41]. From the 1990s onward, although there were many notable fundamental studies of the phenomenon [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58], the shift in energy of R lines with stress was largely confined to the applied domain, detailed in numerous works, such as: measurement of stress in bulk Al2O3 polycrystals [42,[58][59][60][61][62][63][64][65][66][67]; in bulk Al2O3-ZrO2 composites [68][69][70][71][72][73][74][75][76][77][78]; in sapphire or composite fibers, free or in matrices [79][80]…”

“…This was the approach taken in two recent papers [66,67] regarding stress measurement in polycrystalline alumina. It was emphasized in those papers and elsewhere that the corrections of Eq.…”