PSI - Issue 39

Riccardo Cappello et al. / Procedia Structural Integrity 39 (2022) 179–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

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DIC), commonly used for evaluating crack tip stress, strain or displacement fields [12]–[18], TSA presents different advantages, such as the capability of following dynamic fatigue loading, easiness of sample preparation, portability of the setup (thus allowing in-situ evaluations) and speed of data processing [2]–[4], [11]. In particular, TSA has proven to be a powerful tool in the analysis of different fatigue and fracture related problems: crack growth monitoring [5], [11], evaluation of fracture parameters [2], [3], [5], [9], and quantitative analyses, also by means of low-cost setups [2], [11], [19]. Since the first introduction of the concept of plasticity induced crack closure in the early 1970s [20], several researchers [3], [5], [17], [21], [6], [8], [9], [12]–[16] conducted analytical, experimental, and numerical investigations to evaluate the influence of crack-closure phenomena during crack propagation. A part of them evaluated the crack opening loads and the effective Stress Intensity Factor (SIF) range measuring the strains in the crack tip region using strain gauges and applying the compliance method [12], [13], [22]. The methods that rely on the evaluation of the strain fields benefited from the development of Digital Image Correlation (DIC), given its non-contact full-field nature [15]–[17]. Some other authors [9], [14], [23] exploited experimental techniques capable of directly retrieving information about the stress field (i.e., photoelasticity and TSA) combined with a Least Squares Fitting of analytical solutions to evaluate an effective stress intensity factor range, where the stress measurements are in part affected by the presence of the crack closure. A thorough analysis of the thermoelastic amplitude and phase at different harmonics, with a special focus on what happens on the wake of the crack, has been carried out in [3], [5], [6], [8]. In particular, some typical crack-closure related features have been detected by a second harmonic thermoelastic analysis: (i) the amplitude maps show a signal in the wake of the crack that has been associated to rubbing effects [8] or material plasticization [6], but is more likely due to the thermoelastic effect associated to the compression forces between the crack flanks on the wake of the crack tip, that arise for a certain portion of the applied load cycle [3]; (ii) a 180° phase shift ahead and behind the physical crack tip on the phase map [3], [5], [8]. In this work, an experimental thermographic procedure is proposed and employed to detect plasticity induced crack closure in a Single Edge Notched Tension (SENT) AISI 304L stainless steel specimen, allowing real time monitoring by means of an Infrared camera as the crack grows. The structure is analysed under fatigue loading with near zero R ratios and a pure Mode I opening. Two cases are analyzed: one with no initial residual stresses, and one where the sample is initially overloaded to generate a residual compression stress zone at the notch tip, to highlight the different crack closure behavior when the cracked structure is subject to an overload. The analysis of the harmonics at the loading frequency allows to determine an effective stress intensity factor and evaluate the crack length, thus allowing the evaluation of the Paris’ law. The analysis of the signal at twice the loading frequency demonstrates that both amplitude and phase of the Second Harmonic are correlated to the onset and influence of crack closure on the local stress field. The work explains the mechanisms that generate typical amplitude and phase signatures of crack closure ahead and behind the crack tip.

Nomenclature A n n

th Williams’ series coefficient

Paris’ law coefficients

C, m

FH K th

Harmonic of temperature at the angular frequency ω

Thermoelastic constant [1/MPa] Number of Williams’ series terms

Ν w

Load ratio

R

Value of the external radius of the fitting area [mm] Value of the internal radius of the fitting area [mm] Harmonic of temperature at the angular frequency 2 ω

r max r min SH

Mean body temperature [K]

Τ ο ∆ K ∆ T 1 ∆ T 2

Stress Intensity Factor range [Μ Pa √m ]

Temperature variation at the angular frequency ω [Κ] Temperature variation at the angular frequency 2 ω [Κ]

Phase of the First Harmonic FH [°]

φ 1