Full in-plane strain tensor analysis using the microscale ring-core FIB milling and DIC approach

Abstract

Full In-plane Strain Tensor (FIST) analysis at the micro-scale is crucial for improving the evaluation of residual stress and the understanding of the origins of mechanical failure in many applications ranging from civil structures to energy systems and micro-electronics. This study presents the analytical background and experimental implementation of a Focused Ion Beam (FIB) milling and Digital Image Correlation (DIC) based technique that uses material removal and strain relief monitoring to perform precise, reliable and rapid quantification of micro-scale residual stress.The nature of semi-destructive FIB milling overcomes the main limitations of X-Ray Diffraction (XRD) strain tensor quantification: unstrained lattice parameter estimates are not required, analysis is performed in within a precisely defined 3D microscale volume, both amorphous and crystalline materials can be studied and access to X-ray/neutron facilities is not required.The FIST FIB milling and DIC experimental technique is based on extending the interpretation of strain relief observed for the ring-core milling geometry to quantify the strain variation with azimuthal angle. The approach benefits from the high magnitude of strain relief, excellent precision and the simplicity of the analytical approach associated with this method. In-plane strain analysis is reported for a sample of commercial interest: a porcelain veneered Yttria Partially Stabilised Zirconia (YPSZ) dental prosthesis, for which the results were also compared with micro-beam synchrotron X-ray diffraction. Since the two methods sample different gauge volumes and mechanical states (approaching plane stress for ring-core milling and through-thickness averaging that approaches plane strain for XRD), the important matter of correlating the two sets of measurements arises and requires addressing. Complex variable and Finite Element (FE) methods are used to connect the two states, demonstrating that valid comparisons can be drawn. The analysis revealed excellent agreement between the principal stress orientation and values, led to realistic residual stress estimates which closely matched literature measurements ( ≈ 460 MPa) and produced upper and lower bounds for the (101) interplanar crystal lattice spacing of YPSZ in the range 2.9586 − 2.9596 Å, closely matching published values. Highlights• Full in-plane strain tensor measured by ring-core Focused Ion Beam (FIB) milling• Absolute strain measurement at the μm-scale for amorphous & crystalline materials• Comparative X-ray diffraction study validates experimental FIB results• Lattice parameter and stress state in Zr prosthesis sample match literature values• Surface vs bulk residual stress state relationships was identified and validated

Investigations into the interface failure of yttria partially stabilised zirconia - porcelain dental prostheses through microscale residual stress and phase quantification

“…A transmission setup similar to that previously successfully implemented by Lunt et al [26] was used for this study. Samples were mounted onto two crossed Newport 25 mm linear translation stages in order to facilitate 2D translation in a direction perpendicular to the beam at a precision better than ±0.1 μm.…”

“…In order to improve the surface contrast and thereby facilitate improved DIC, a single pass of the FIB was applied to the sample surface prior to milling. This approach generates a stable, random surface pattern (as shown in Figure 1) which has been shown to aid effective marker tracking while minimising residual stresses induced in the surface [26,28].…”

“…A comprehensive overview of in-plane strain tensor analysis of YPSZ prostheses has previously been published, and the following analysis is based on this work [26]. Azimuthal integration of the 2D diffraction data was performed over 10° sectors to provide 1D profiles of average intensity against 2 scattering angle for 36 orientations within the sample plane (normal to the incident beam).…”

Digital Image Correlation of 2D X-ray Powder Diffraction Data for Lattice Strain Evaluation

“…This approach is easier and more straightforward, since ‘caking’ typically performs binning and averaging within an entire sector (‘slice’ of the ‘cake’), whilst XRD-DIC only seeks to interpret information about the immediate vicinity of the selected markers, and is therefore more convenient and even potentially more precise in this sense. Furthermore, full in-plane strain analysis can be readily accomplished [ 40 ] in one DIC analysis by selecting as many ring segments as necessary and calculating strains, from which principal directions and principal strains can be determined. In principle, XRD-DIC is likely to have the capability to measure lattice strains at the accuracy that can reach ∼ .…”

A procedure for high residual stresses measurement using the ring‐core method

“…The ring‐core method is more sensitive than the hole‐drilling method, involving almost complete relief of the surface strain. Recently, capabilities and application of this method have been expanded by development of milling techniques and using new strain sensing methods . However, in conventional use, the size of the annular groove is relatively large, causing much more damage than the hole‐drilling method, which allows more localised residual stress measurement …”