Random Grid-Based DIC Analysis of Plastic Flow Near Interfaces in Deformation Processing

Digital Image Correlation (DIC), an in situ analysis technique, has gained widespread popularity within the mechanics community over the past two decades. Despite this, accurate computation of strain and displacement fields, especially at interfaces and free surfaces, remains a central challenge. This problem is particularly acute since material flow near free surfaces and interfaces is paramount for understanding the mechanics of several deformation processing configurations, such as machining and forming. Two common DIC implementations exist, and they exploit either local or global information about the deformation. Local techniques suffer from a lack of continuity across subsets, while global methods, despite ensuring continuity, fail to estimate fields at interfaces accurately. Furthermore, global DIC necessitates grid refinement to capture heterogeneous deformation and can often be computationally expensive. Both local and global methods finally use interpolation schemes to obtain continuous displacement fields, along with a finite difference scheme to compute strains. However, these present additional limitations, such as spurious strains at interfaces and loss of experimental data. In this work, we present a random grid-based scheme that uses local correlation search, while simultaneously exploiting global information. Our algorithm is based on a forward 6-parameter (displacement and its first order derivatives) Newton-Raphson (N-R) search. An underlying random grid is first generated and serves to locate subset centers for the correlation scheme. Second derivatives are then computed using a triangulation method. Multiple random grid realizations enable averaging with minimal data loss, thereby eliminating the need for post-processing. The use of second-order derivatives ensures continuous strain fields, which will otherwise need a twelve-parameter (displacement, its first and second derivatives) based correlation search. We establish the validity of our scheme using standard test cases derived from synthetic non-homogeneous displacement fields and demonstrate its utility in practical machining and deformation processing applications.