Nondestructive Evaluation of Solids Based on Deformation Wave Theory

Sanichiro Yoshida,Tomohiro Sasaki,Conor Mcgibboney

doi:10.3390/app10165524

Sanichiro Yoshida, Tomohiro Sasaki + Show 1 more

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https://doi.org/10.3390/app10165524

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Abstract

The application of a recent field theory of deformation and fracture to nondestructive testing (NDT) is discussed. Based on the principle known as the symmetry of physical laws, the present field theory formulates all stages of deformation including the fracturing stage on the same theoretical basis. The formalism derives wave equations that govern the spatiotemporal characteristics of the differential displacement field of solids under deformation. The evolution from the elastic to the plastic stage of deformation is characterized by a transition from longitudinal (compression) wave to decaying longitudinal/transverse wave characteristics. The evolution from the plastic to the fracturing stage is characterized by transition from continuous wave to solitary wave characteristics. Further, the evolution from the pre-fracturing to the final fracturing stage is characterized by transition from the traveling solitary wave to stationary solitary wave characteristics. In accordance with these transitions, the criterion for deformation stage is defined as specific spatiotemporal characteristics of the differential displacement field. The optical interferometric technique, known as Electronic Speckle-Pattern Interferometry (ESPI), is discussed as an experimental tool to visualize those wave characteristics and the associated deformation-stage criteria. The wave equations are numerically solved for the elastoplastic stages, and the resultant spatiotemporal behavior of the differential displacement field is compared with the experimental results obtained by ESPI. Agreement between the experimental and numerical results validates the present methodology at least for the elastoplastic stages. The solitary wave characteristics in the fracturing stages is discussed based on the experimental results and dislocation theory.

Highlights

We propose that the application of a recent field theory [9] of deformation and fracture can be a solution to the problem
In refs. [31,32], we demonstrated the deformation stage criteria based on these qualitative features of the displacement field
Fringe patterns obtained from Electronic Speckle-Pattern Interferometry (ESPI) for a tensile experiment are analyzed in detail based on the field theoretical criteria of deformation stages

Summary

Introduction

Continuous application of external loads, even if their strength is considerably lower than the ultimate strength of the material, causes fractures. The current load level observed or associated deformation data is not reliable information to predict fracture. It is known that fracture is led by a defect and that defects grow in the scale level from the atomistic to macroscopic. Dislocations [1] are typical atomistic defects and their propagation is responsible for the deformation to evolve from the elastic to plastic regime. It is known that in the plastic regime the dislocations react to the stress field and lead to the generation of macroscopic defects. It is difficult to connect dislocation behaviors and macroscopically observable phenomena. On the one hand we know that the propagation of dislocation initiates plastic deformation.

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