On Determining Stress Intensity Factors for Mixed Mode Cracks From Thermoelastic Data

Abstract

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.

T-stress determination using thermoelastic stress analysis

“…Two different Fig. 1 Stress state ahead of a crack tip mathematical descriptions have been used to determine the SIFs from TSA data: Williams's equations and the Muskhelishvili solutions [15]. However, since the Muskhelishvili approach makes it only possible to determine the SIFs, the only applicable model to determine the T-stress and SIF is Williams's formulation.…”

“…In recent years, thermoelastic stress analysis (TSA) has proved to be an ideal technique for the determination of mode I, mode II, and mixed SIFs [11][12][13][14][15]. Therefore the aim of this work was to develop these methodologies to determine the Tstress in addition to the SIF.…”

Thermoelastic investigations for fatigue life assessment

“…The approach which was used in the current experiments was developed by Tomlinson et al 4 . A Newton-Raphson iteration combined with a least squares approach is used to fit the equations describing the stress field around the crack tip, based on Mushkelishvili's approach, to the experimental data.…”

Thermoelastic Investigations for Fatigue Life Assessment

“…No reasons could be given for the unusually large differences and plans for further investigation were indicated. The majority of the published data have been for cracks under predominantly mode I loading and the only data for predominantly mode II loading showed a difference between theory and experiment of up to 40% 4 . It was suggested that the theoretical solution may not be reliable at this extreme notch geometry for which there was only one numerical and no other experimental study in support.…”

“…Although accurate analyses have been performed for opening mode cracks and slots, only limited progress has been made for the determination of stress intensity factors for mixed-mode cracks using thermoelastic techniques 4,5,6,7,8 . Recently published data on the subject 5 show good agreement between theory and experiment for both K I and K II for central slots and cracks, and edge slots.…”