A Direct Approach to In-Plane Stress Separation using Photoelastic Ptychography.

Nicholas Anthony,Eric Huwald,Henry Kirkwood,Brian Abbey,Keith Nugent,Guido Cadenazzi

doi:10.1038/srep30541

Abstract

The elastic properties of materials, either under external load or in a relaxed state, influence their mechanical behaviour. Conventional optical approaches based on techniques such as photoelasticity or thermoelasticity can be used for full-field analysis of the stress distribution within a specimen. The circular polariscope in combination with holographic photoelasticity allows the sum and difference of principal stress components to be determined by exploiting the temporary birefringent properties of materials under load. Phase stepping and interferometric techniques have been proposed as a method for separating the in-plane stress components in two-dimensional photoelasticity experiments. In this paper we describe and demonstrate an alternative approach based on photoelastic ptychography which is able to obtain quantitative stress information from far fewer measurements than is required for interferometric based approaches. The complex light intensity equations based on Jones calculus for this setup are derived. We then apply this approach to the problem of a disc under diametrical compression. The experimental results are validated against the analytical solution derived by Hertz for the theoretical displacement fields for an elastic disc subject to point loading.

Highlights

Determining stresses in solids is crucial for evaluating and predicting mechanical behaviour
In this paper we demonstrate that a straightforward approach to quantitative in-plane stress determination can be achieved by combining the circular polariscope with ptychographic coherent diffractive imaging (CDI)
The combination of a circular polariscope and the imaging geometry described by Fresnel Coherent Diffractive Imaging (FCDI) Ptychography[18,19,20,21] was used for the optical measurements (Fig. 1a)

Summary

Introduction

Determining stresses in solids is crucial for evaluating and predicting mechanical behaviour. The drive for new methods to measure stress in optically transparent materials, e.g. thin films, has led to the development of a variety of approaches including photoelasticity and thermoelasticity. Such full-field techniques are routinely used to obtain images of fringe patterns that qualitatively relate to the samples’ stress distribution. Both Lei et al.[9] and Yoneyama et al.[10] have demonstrated stress separation in two-dimensions by combining circular polarimetry and interferometric photoelasticity In their approach the phase values of the isochromatics and isoclinics are determined using a circular polariscope, whilst the phase of the isopachics is obtained using interferometry. In addition to the ease of the optical set up, ptychography offers a number of other advantages when compared to previous interferometric based approaches:

Methods

Results

Conclusion