Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

Investigation of Fringe Pattern Distribution in Circular Disk by Reflection Polariscope Technique

In this study, the fringe pattern distribution of various loads on circular disk of homogeneous acrylic in different thicknesses by using reflection polariscope technique was carried out. The load was pressed at the top and the bottom to produce the fringe patterns, which were recorded by digital camera. Then the results were analyzed. The number of isochromatic fringe pattern depends on the magnitude of force acting on the circular disk and these relation is linearly. The application of these research is used to predict stress distribution on the transparent material in the case of different dimension of the circular disk shape.

Numerical Computation of Complex Stress Intensity Factors of Interface Cracks in Bi-Materials Based on Photoelastic Theory

This paper presents a new numerical method for obtaining the complex stress intensity factor with an interface crack in bi-materials using photoelastic isochromatic fringe numbers N. The theoretical solution of stress field at the crack tip was deduced from Muskhelishvilis stress function and an undetermined term σ0 which is a function of material properties was added to this theoretical solution. A partial differential iterative equation with fast convergence was formed by applying the photoelastic theory. The complex stress intensity factor K=K1+iK2 and σ0 were obtained by Newton-Raphson iteration method and K domain was discussed. The simulant photoelastic isochromatic fringe pattern could be generated through image processing and numerical calculation according to K and σ0. The simulant isochromatic fringe pattern accords with experimental photoelastic isochromatic fringe pattern, so it is practicable for this numerical method of obtaining the complex stress intensity factor.

Complete Two-Dimensional Principal Stress Separation by the Photoelastic Oblique Incidence Method

The oblique incidence method of photoelastic principal stress separation is reconsidered and presented in a form that allows the existence of negative fringe orders to be identified. The normal incidence isoclinic angle, two oblique incidence isoclinic angles and two oblique incidence isochromatic fringe orders are required for the new method. However, by allowing negative fringe orders to be identified, significant uncertainty relating to the separated principal stresses is removed and confidence in the calculated results may be improved