A new approach to the solution of stress intensity factors from isochromatic data has been developed and is based on complex Fourier analysis. Solutions are shown to be accurate when the loading of the crack tip is predominantly Mode I1 and also for cases that are generally mixed-mode. The new method and its application to a four-point-bend test is described in this paper. Tests on angled-edge-cracked specimens have also been performed to show the validity of the method for a range of mixed-mode loadings.

An alternative methodology is presented for determining stress intensity factors for cracks subject to mixed-mode displacements. The methodology involves thermoelastic data generated from a SPATE (Stress Pattern Analysis by Thermal Emission) system and has been adapted from one used successfully in photoelasticity. The thermoelastic data is collected throughout the elastic stress field dominated by the crack tip singularity. The stress field is described using a Fourier series within Muskhelishvili's approach. This method allows different applied stress fields to be described which may include transient or non-uniform stress fields. The results obtained using the new methodology are at least as good as those obtained previously for pure mode I cases, and generally better for mixed mode displacement conditions. NOMENCLATURE a = crack length or crack half length A = SPATE calibration factor AN, BN, h, b. = series coefficients of the stress field equations cg = specific heat for constant deformation E = Young's modulus m = shape of the mapped circle M = mass r, 0 = polar co-ordinates in mapping plane R = arbitrary length parameter S = SPATE signal T = temperature V = volume W = panel width x, y = rectangular co-ordinates in the physical plane z = x + iy = complex variable in the physical plane a = thermal expansion coefficient [ = r(cos 0 + i sin 0) = complex variable in mapping plane p = crack tip radius ol, n2, a, = principal stress 5 = shear stress v = Poisson's ratio @, !P= analytical stress functions of a complex variable 4 = cos 0 + i sin 0 = complex variable in mapping plane defining unit circle w = mapping function Z = conjugate of complex variable (2) Complex notation Superscript (') = denotes differentiation 217 218 R. A. TOMLINSON et al.

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An overdeterministic least-squares phase-stepping method for automated photoelasticity is described. Problems associated with isochromatic-isoclinic interaction are solved by use of a three-wavelength method to calculate the value of the isochromatic parameter and the isoclinic angle. The ramped isoclinic phase map can now be unwrapped to give the orientation of the principal stresses with respect to a reference axis of the polariscope unambiguously. A three-wavelength approach to determination of the absolute value of the isochromatic parameter is shown to give reliable results also.

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ABSTRACT--A new approach to full-field automated photoelasticity is presented in which a circular polariscope is used to enable the isochromatic phase value (c 0 to be determined unambiguously and without input of a known isochromatic value obtained using an auxiliary technique. Values of cosc~ are obtained from light-field and dark-field images for three loads of small incremental steps. Using a relatively straightforward procedure, ramped phase maps for c~ are produced which can be unwrapped using conventional techniques. The resulting distribution of cl is then found absolutely using information provided by which Oct is the incremental change in the isochromatic phase value between the load steps. The results obtained for disk-in,compression tests presented here in comparison with theoretical solutions demonstrate that the technique is both simple to use and very accurate. A similar approach may be adopted using three wavelengths instead of three load steps.

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Transmission and reflection photoelasticity has been used to determine the stress intensity factors for artificial cracks emanating from a hole in two-dimensional tensile plates. Three geometries were investigated, namely a free hole, a pin-loaded hole and a hole with an interference-fit pin. All these cases relate to situations commonly found in aircraft structures. The results have been compared where possible with analytical data and a good correlation was found for these cases.