Chapter 1 Diagnosis of Deformation Stages with Optical Interferometric Technique and Comprehensive Theory of Deformation and Fracture Sanichiro Yoshida and Tomohiro Sasaki Abstract A method to diagnose the stages of deformation nondestructively, quickly and as full-field information is discussed. In-plane sensitive Electronic Speckle-Pattern Interferometry is used in the subtraction mode to form the fringe pattern representing the differential displacement occurring during a short-time interval. The dark fringes in a fringe pattern exhibit the contours of the differential displacement field. The interferometer keeps forming such fringe patterns continuously. The change in the fringe pattern with the development of the deformation is interpreted based on a field theory of deformation and fracture. Based on a fundamental principle of physics, this theory describes all stages of deformation and fracture on the same theoretical basis. It does not need to use phenomenology or empirical formulation of the phenomenon. The transition from one stage to another, e.g., the elastic to plastic stage or the plastic to fracturing stage, of given deformation is diagnosed based on specific features of the fringe patterns and the field theoretical interpretation of the features. The transition from the elastic to plastic stage is characterized by the generation of shear instability that triggers the initiation of a large-scale rotation wave. The transition from the plastic to fracturing stage is characterized by the immobility of the rotation wave that causes the generation of material discontinuity. Keywords Deformation theory · Electronic Speckle-Pattern Interferometry · Nondestructive testing · Field theory 1.1 Introduction For nondestructive evaluations of solid objects, diagnosis of transition from one stage to another is important. Generally, the transition from the elastic to plastic regime is identified as the change from the linear to nonlinear behavior of the stressstrain characteristics. In field applications, it is unrealistic to measure stress-strain characteristics. While various techniques are available for deformation (strain) measurement [1–3], stress is hard to measure in the field. It is desirable to diagnose the current deformation status from the spatiotemporal characteristics of strain. A challenge for this approach is the lack of theory that describes all stages of deformation comprehensively. Prevailing practice is to use stage-specific theories: theories of elasticity [4], plasticity [5], and fracture mechanics [6] in the respective regimes. This is mainly because these theories are based on phenomenology. The application of a recent field theory [7] of deformation and fracture can be a solution to the problem. Being based on the physical principle known as the local symmetry of theory [8], this theory has a mechanism to describe all stages of deformation on the same theoretical basis without relying on phenomenology. It formulates deformation as dynamics of mechanical waves that carry stress energy through the material. Fracture is characterized as the final stage of deformation where the mechanical wave is unable to carry the stress energy, and consequently, the stress becomes stationary at a certain location of the material. At this stage of deformation, the only mechanism for the material to establish energy balance becomes the generation of discontinuity, which causes the fracture. Previously various experimental studies [9–14] exhibit evidence that evolution of deformation can be characterized by different forms of the displacement wave as explained by S. Yoshida ( ) Department of Chemistry and Physics, Southeastern Louisiana University, Hammond, LA, USA e-mail: syoshida@selu.edu T. Sasaki Department of Mechanical Engineering, Niigata University, Niigata-shi, Niigata, Japan e-mail: tomodx@eng.niigata-u.ac.jp © The Society for Experimental Mechanics, Inc. 2021 M.-T. Lin et al. (eds.), Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59773-3_1 1
RkJQdWJsaXNoZXIy MTMzNzEzMQ==