The theory of thermoelastic stress analysis is reviewed and the implications of some theoretical developments are assessed. Available instrumentation is described and techniques available for separation of individual stress values are summarized. The scope of the technique is illustrated with reference to a number of applications covering crack-tip stress studies, stress analysis and damage assessment in composite materials, and ‘field’ work on a traffic-loaded road bridge.

Development and applications of thermoelastic stress analysis

Thermoelastic stress analysis has been developed in recent years as a direct method of investigating the crack tip stresses in a structure under cyclic loading. This is a consequence of the fact that stress intensity factors obtained from thermoelastic experiments are determined from the cyclic stress field ahead of a fatigue crack, rather than inferred from measurement of the crack length and load range. In the present paper the results of fatigue crack growth tests performed on welded ferritic steel plates are reported. From the results it can be observed that the technique is sensitive to the effects of crack closure and the presence of tensile and compressive residual stresses due to welding.

Measuring stress intensity factors during fatigue crack growth using thermoelasticity

A generalized approach for determining the stress intensity factors (SIFs) K-I and K-II for any mode mixity directly from displacement fields obtained by digital image correlation is presented using a centre fatigue cracked aluminium plate as an example problem. It was found that the crack-tip position could be determined on average to within 50 per cent of the displacement vector spacing (60 mu m). The approach has been shown to be fairly robust, both in terms of the stability of the SIFs thus obtained and their sensitivity (less than 0.07 MPa root m) to the above uncertainty in the crack-tip location. Differences between the nominal and experimentally determined K-I and K-II values were found to be comparable (around 1.0 MPa root m) for values of K-I ranging from 0 to 15 MPa root m and K-II from 15 to 0 MPa root m, and may have arisen because the nominal values are not representative of those acting at the real crack tip.

The stress intensity of mixed mode cracks determined by digital image correlation

The enormously enhanced power of photoelasticity resulting from adoption of digital technologies is highlighted and discussed. An overview of the principal techniques of digital fringe processing is provided within a single theoretical framework. The practical application of the new technologies using both conventional instruments and novel optical devices is discussed. Experiments involving more I x 10 6 quantitative fringe order measurements are possible and practical on a routine basis using the current technology. Products based on this research are beginning to appear on the market so that many new application areas are opening up for photoelasticity, such as dynamic events, real-time fatigue crack analysis, monitoring polarisation changes at a microscopic level in materials; detailed validation of numerical simulations, particularly of complex geometry and loading; and in-service monitoring using reflection photoelasticity of damage in both homogeneous and heterogeneous materials, such as composites.

Digital photoelasticity: Principles, practice and potential

Some improvements in the analysis of fatigue cracks using thermoelasticity

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.

Full-field automated photoelasticity by use of a three-wavelength approach to phase stepping

— 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.

On determining stress intensity factors for mixed mode cracks from thermoelastic data

The new approach to phase-stepping photoelasticity known as ‘‘load stepping’’ is used to determine automatically the isochromatic parameter a and the isoclinic angle ?. There is no need for the user to calibrate the results other than to convert the isochromatic parameter into a principal stress difference using the material fringe constant. Four phase-stepped images are collected using a circular polariscope for each of three load steps, which differ by small equal increments. A ramped phase map for the isochromatic parameter is produced in the range -?<??? that can be unwrapped using conventional techniques. Calibrated values of a can then be calculated using the phase map of ??, which is the incremental change in the isochromatic value between the different steps. The value of the isoclinic angle is automatically determined in the correct range -?/2<?????/2 without unwrapping. The results obtained from experimental testing of a disk-in-compression specimen using transmission photoelasticity presented in comparison with theoretical solutions demonstrate the accuracy of the new approach. In another test performed on a bar in torsion using reflection photoelasticity we demonstrate how determination of the isoclinic angle in the range -?/2<???/2 gives results superior to those obtained if the isoclinic angle is determined in the wrapped range -?/4<???/4 .

Andrew D. Nurse

Papers

Full-field automated photoelasticity by use of a three-wavelength approach to phase stepping

On determining stress intensity factors for mixed mode cracks from thermoelastic data

Completely automated determination of two-dimensional photoelastic parameters using load stepping

Identification of subsurface delaminations in composite laminates

Ultrasonic cutting : a fracture mechanics model