Isochromatic Loops Research Articles

Isochromatic patterns in a plate with a rigid fibre inclusion

A thorough analysis of the isochromatic fringe patterns developed in the vicinity of the end point of a rigid fibre inclusion embedded in an elastic plate was carried out. The general characteristics properties of these patterns and their dependence on the Poisson's ratio of the plate were analysed for the case of an infinite plate subjected to a uniaxial uniform stress at infinity. The stress field distribution in the local neighbourhood of the fibre end was used for the determination of stress intensity factors k 1 and k 2 for any form of geometry and loading of the plate. The relationship between the ratio ( k 2/k 1 ) and the angle θ m formed by the fibre axis and the line connecting the fibre end with the farthest point on a given isochromatic loop was established. Nomograms based on measurements on the isochromatic pattern for the direct determination of k 1, k 2 were constructed.

Notch effects on photoelastic determination of mixed-mode stress intensity factors

An investigation into the notch effect on the photoelastic determination of the mixed mode stress intensity factors is presented. This accomplished by comparing the isochromatic loops generated for a crack and an ellipse in an infinite plate. The generated mathematical loops are based on the exact solutions. A method of analysis is proposed and used to correct the distorted maximum angle θ m and maximum shear stress τ max due to the notch effect. The results obtained from the photoelastic measurements based on the proposed method compare favourably with those by an earlier investigation.

A three-parameter method for determining stress intensity factors from isochromatic fringe loops

Methods for determining the stress intensity factor, K, from isochromatic fringe loops obtained from photoelastic models with sharp cracks are briefly reviewed. A new three-parameter method is introduced which follows the two-parameter approach developed previously by Irwin. In the three-parameter method, three different terms in an analytical solution are adjusted to obtain a suitable match between the theoretical and experimental isochromatic loops. The three parameters are: K/√2πz, which describes the crack-tip singularity, ( b) β K/√z, to account for variations in the stress field removed from the crack tip and ( c) σoa = α1 K/√2πa, which is added to the σ x component of the stres field to account for the biaxiality of the far-field stresses. A relationship is derived for the maximum shear stress, τm, in terms of the three fitting parameters ( K, α, and β) and the two geometric parameters ( rm and θm) associated with the isochromatic fringe loops. A method of solution based on measurements of rm and θm from any two independent fringe loops is given. The accuracy of the three-parameter method was determined by using exact results from the central crack problem for a standard. It was found that the error was within ± 1 per cent for 69° < θm < 145°. Comparison with the two-parameter method shows that the three-parameter method is more accurate and is applicable over a wider range of θm.

A new method of determining the stress intensity factor K from isochromatic fringe loops

This paper describes the four parameter method of analysis for determining the stress intensity factor K. Dynamic photoelastic isochromatic fringe patterns associated with cracks propagating in centerpin loaded, eccentric-pin-loaded and crack-line-loaded SEN specimens of Homalite 100 were recorded. Data was obtained for tests over a range of crack velocities from arrest to the terminal velocity of 14,900 in. sec (378 m sec). Six measurements describing the size and shape of the experimental isochromatic loops were used to determine the stress intensity factor K by employing a comparison function to match analytical and experimental results. The analytical isochromatic loops were generated with a Westergaard stress function of the form Z(z) = K √2πz {1 + β( z a}) and a superimposed normal stress σ Ox = αK|√2 πz which acts parallel to the direction of crack extension. Results were obtained by the computer program (FRACTURE) for different values of the four parameters to give 8925 analytical fringe loops. Another computer program (SEARCH) was used to find a small group of solution which given very low values of the comparison function f c . The final solution which contains the value of K was obtained from the small group by selecting the most consistent solution. The results obtained for Homalite 100 show that K min and K k are nearly the same and that ȧ increases abruptly from 0 to about 10,000 in./sec (254 msec) for modest increases in K above 400 psi √in. (4.4 × 10 5 Nm 3 2 ). Further increases in crack velocity require significant increases in K until terminal velocity is