Theoretical Considerations for Transitioning the Grid Method Technique to the Microscale

Abstract

As new applications demand the synthesis and validation of materials with specific mechanical performance targets, there is a need for improved characterization and understanding of reduced length-scale deformation processes which govern mechanical behavior (i.e., dislocation slip and twinning). The heterogeneous nature of deformation in polycrystalline materials makes it essential to employ length-scale-independent and material agnostic full-field measurement techniques during mechanics of materials studies. The intention of the current work is to demonstrate the fundamental steps of transitioning the Grid Method (GM), a macro-scale full-field measurement technique used in mechanics of materials studies, to the microscale. Two obstacles overcame when transitioning the technique are reported. The first is the deposition of ultra-fine grids with a pitch of 500nm using a focused ion beam. The second is the characterization and correction of equipment-dependent raster-based image distortions inherent to scanning electron microscope (SEM) image acquisition. The SEM-induced distortions are simulated using a closed-form model which more accurately represents the Fast Fourier Transform modulus obtained from SEM micrographs. The proposed model is validated against synthetic deformation cases, specifically uniaxial tension, uniaxial compression, pure shear, simple shear, and heterogeneous deformation. A two-step filtering procedure informed by the newly introduced closed-form model, consisting of a notch and frame filter is proposed in order to remove distortions observed in SEM micrographs. After correcting the SEM-induced distortions on the stationary microgrid micrographs using the proposed two-step filtering, the extracted strain distortion level is reduced from 0.02 to 0.005 strain. Combined, the efforts presented in the current work demonstrate the initial development and promise of the microscale scanning electron microscope grid method (SEM-GM) to capture distortion corrected strain maps in reduced length-scale.