Generalised residual stress depth profiling at the nanoscale using focused ion beam milling

Abstract

The study of Residual Stress is gaining more and more attention due to its importance in design for structural integrity. At present a lot of emphasis is placed on understanding the origins of mechanical failure that lie at the nano-/micron-scale. This leads to the evident need for evaluating residual stress distributions at increasingly smaller scales, and the search for modern tools capable of accomplishing this task. Prior state-of-the-art methodologies mostly required expensive and time-consuming sample preparation and examination processes to evaluate residual stress, e.g. the study of thin TEM lamellae. The recent advent of Focused Ion Beam methods opened up methods suitable for direct application at sample surface, yet allowing the observation and quantification of stress relief phenomena at the nano-scale. In the last decade, technical aspects of FIB-based method(s) have seen significant development. On the other hand, the calculation framework employed to analyse the experimental outcome remained largely conventional, in most inconvenient for high precision analysis of challenging problems. In the present paper, the eigenstrain-based method previously presented by the authors for the depthresolved evaluation of equi-biaxial residual stress, is generalised to non-equi-biaxial distributions of residual stress. This extends the applicability of the method to a much wider class of problems. The use of cylindrical ring-core shape in FIB-DIC analysis allows reconstructing the full in-plane residual stress tensor as a function of milling depth. We report formulae for calibrated influence functions that have very broad applicability, and can be used in the overwhelming majority of cases. Their derivation is based on an extensive set of FEM simulations that allowed reliable identification of the limitations of this approach, and highlight the importance of making appropriate selection of ring-core diameter(s). Finally, experimental validation of the method is presented that involves the reconstruction a known non-equibiaxial residual stress depth profile, confirming the validity and reliability of the present approach.

Study on Local Residual Stress in a Nanocrystalline Cr2O3 Coating by Micro-Raman Spectroscopy

“…Therefore, the stress in such local areas should be fully understood. This goal can be achieved by the Focused Ion Beam (FIB)-Digital Image Correlation (DIC) method [20]. Unfortunately, the fundamental aspect of the FIB-DIC method lies in the use of FIB for the material removal process, which determines the destructive nature of this method.…”

Nanoscale Depth Profiling of Residual Stresses Due to Fine Surface Finishing

“…The displacements of the DIC markers, with 12 pixel grid spacing, were averaged over the five images per milling step, and subjected to the appropriate image drift correction and outlier removal procedures . The relief strain data were used to evaluate the in‐plane residual stress profiles as a function of depth after the different polishing steps using the nonintegral method for an equi‐biaxial stress state described by Korsunsky et al The sensitivity of this method extends to a depth of maximum 30% of the diameter of the micropillar (i.e., 1.5 µm for a 5 µm micropillar, 3 µm for a 10 µm micropillar, etc.). For this reason, larger micropillar diameters were used when it was necessary to obtain information at larger depths.…”

“…The lack of data on polishing‐induced residual stresses can be attributed to the fact that it is challenging to measure near‐surface residual stress at such a fine scale. However, very recent developments in the ring‐core “Focused Ion Beam‐Digital Image Correlation” (FIB‐DIC) technique have opened up the possibility to obtain depth‐resolved residual stress information with sub‐micrometer resolution . This method utilizes focused ion beam (FIB) to perform an incremental milling of a circular trench, as shown in Figure , thereby creating a cylindrical micropillar that is gradually being relieved from residual stress .…”

Nano-Scale Residual Stress Profiling in Thin Multilayer Films with Non-Equibiaxial Stress State

“…In this way, the non-equibiaxial relaxation strain was calculated using three components of strain in the 0 • , 45 • , and 90 • directions. In the general case, the three components of the incremental strain relief were used to calculate the two in-plane principal stress depth profiles and their orientation with the respect to the reference coordinate system, according to the procedure as reported in a previous paper by Salvati et al [21].…”