Issue 27

L. Mardavina et alii, Frattura ed Integrità Strutturale, 27 (2014) 13-20 ; DOI: 10.3221/IGF-ESIS.27.02 14 The stress intensity factor value obtained from thermoelastic analysis is equal to the range of the stress intensity factor, Δ K , which occurs at the crack tip due to the applied cyclic load. This allows the actual crack driving force to be experimentally determined rather than being inferred from maximum and minimum stress intensity factors, which is the case with other experimental techniques. The direct determination of Δ K makes the technique ideal for use in structural integrity assessment. Further advantages over other experimental methods are that thermoelasticity is a non-contacting method, with minimal surface preparation required, which may be used to study cracks in both real components and models. This paper will review the advances made in thermoelastic fracture mechanics in recent years. An outline of the experimental issues which need to be considered for determining stress intensity factors using thermoelasticity was presented by Tomlinson and Olden [2] and this paper adds to that. Methods to determine the stress intensity factor at crack tips using thermoelastic stress analysis are explored, starting from selected line techniques using the Westergaard equations to the most recent methods which utilise the full array of data available together with complex stress field equations. Crack path analysis and interaction of cracks will be explored in addition to fracture mechanics investigation of a range of materials. In order to obtain accurate results a number of areas of experimental procedure need to be considered and these are discussed in detail. The paper will present the progress made on determination of stress intensity factors for fatigue cracks, tracking the location of the crack tip during propagation under cyclic loading, and also in investigating the crack closure effect. Recently, Risitano et al. [3], utilizing the thermographic method, made an estimations very close of the real values of stress concentration factor and fatigue-stress concentration factor. T HE DETERMINATION OF STRESS INTENSITY FACTORS FOR SHARP NOTCHES Evaluation of mode I Stress Intensity Factors for sharp notches here are primarily five methods available to determine the stress intensity factor of a crack using thermoelastic equipment. The techniques proposed by Stanley and Chan [4], Stanley and Dulieu-Smith [5], Lesniak [6], Tomlinson et al. [7] and Lin et al. [8] are detailed in the following sections. In 1986 the thermoelastic technique was first used to determine  K I , the opening mode stress intensity factor, by Stanley and Chan [4] who used a SPATE (Stress Pattern Analysis by Thermal Emission) system to record the thermoelastic signal, S . Using the first two terms of the Westergaard equations for the elastic stresses in the vicinity of a crack under mode I and mode II loading it was shown that the stress intensity factor of a crack could be related to the SPATE signal recorded using the following relationship: 2 2 cos sin 2 2 2 2 I II K K AS r r         (2) Thus the SPATE signal around the crack tip, S , when multiplied by a calibration factor, A , could be used to calculate stress intensity factors from points located at distances ( r,  ) from the crack tip. This equation provides the basis of determining both single-mode stress intensity factors, and also mixed-mode. For the latter case it was explained that  K I would first be generated from data along the line  = 0, before  K II could be calculated from a general line. Emphasis was placed by the authors on the likelihood of large errors if a single point value were used, as it would not be clear whether data had been recorded from the region of validity for the Westergaard equations, and also it would be necessary to know the exact location of the crack tip. The region of validity of the Westergaard equations is discussed in a later section. Stanley and Chan [4] also describe a graphical method to determine the opening mode stress intensity factor of a fatigue crack. This used a series of line scans either perpendicular or parallel to the crack line. In the parallel case the stress intensity factor is determined using: 2 4 3 3 I A Gr K    (3) where Gr . is the gradient of the linear region from a graph of 1/ S max 2 against distance y . Typical data points from which the gradient was obtained are shown in Fig. 2. The non-linearity observed close to the crack tip and also at the extremities was attributed to crack tip plasticity and finite plate size respectively. Remote stresses in a finite width specimen are higher than in an infinite specimen, for which the Westergaard equations were derived. For the fatigue cracks studied all experimental results were found to be within 10 % of the theoretical solutions. T