Determining Stress Intensity Factors Using Hybrid Thermoelastic Analysis
This paper presents and discusses a technique suited for the determination of mode I Stress Intensity Factors (SIF) of fatigue-initiated and propagated cracks at the keyhole of polycarbonate specimens. A hybrid approach combined Thermoelastic Stress Analy
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Determining Stress Intensity Factors Using Hybrid Thermoelastic Analysis R.B. Vieira, G.L.G. Gonza´les, and J.L.F. Freire Abstract This paper presents and discusses a technique suited for the determination of mode I Stress Intensity Factors (SIF) of fatigue-initiated and propagated cracks at the keyhole of polycarbonate specimens. A hybrid approach combined Thermoelastic Stress Analysis (TSA) results with Linear Elastic Fracture Mechanics solutions using Westergaard’s stress function to describe the stress field near the crack tip. The TSA results used an experimental approach that does not require an infrared camera with lock-in capability. The experiments used a micro-bolometer camera A655sc from FLIR Inc. and a data processing software DeltaTherm2 from StressPhotonics Inc. Two distinct data fitting methods are presented. The first method measures the crack length, which makes the problem become linear, allowing for a simple Least Squares Method (LSM) approach. The second method, highlighting the true power of TSA as a fatigue analysis technique, uses the crack tip position as an adjustable parameter, making the problem non-linear and solvable by a complex numerical algorithm known as the Downhill Simplex Method (Nelder-Mead). The paper describes automated methodologies for making good initial estimates for the position of the crack, required by the non-linear approach, as well as for selecting data points to be fitted, both based on the loss of linearity of the TSA data due to non-adiabatic conditions. Keywords Thermoelastic Stress Analysis • Micro-bolometer detector • Fatigue • Stress Intensity Factor • Polycarbonate
6.1
Introduction
Thermoelastic Stress Analysis (TSA) is a non-contact experimental technique that measures full-field stress maps for the surface of a component. It is based on the thermoelastic effect [1], which states that a cyclic loaded body experiences small temperature variations (ΔT), and that, if adiabatic conditions are satisfied, this variation is proportional to the first stress invariant. Practical applications of TSA use infrared thermography to measure the very small pixel-by-pixel temperature variations. With these variations having been measured, Eq. (6.1) describes how the stress invariant is determined. Δ ðσ 1 þ σ 2 Þ ¼ A S
ð6:1Þ
where Δσ1 and Δσ2 are the principal stress ranges acting on the observed point located at the surface, A is the thermoelastic calibration coefficient, and S is the magnitude of the TSA signal. Combining the experimental data for the first stress invariant range, obtained through TSA, with an analytical solution for the crack tip stress-field, such as Westergaard stress function, the stress intensity factor (SIF) can be estimated. Infrared detectors with enough sensitivity to measure such small temperature variations were very expensive in the past, but with recent advancements in micro-bolometer technology, the cost is going down quickly. The camera used to gather the experimental data presented in this paper is the A655sc from FLIR Inc., which has a
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