In the present research, two stress-based failure criteria were proposed to predict brittle fracture in components containing V-notches with end holes (VO-notches) under mixed mode I/II loading. The first criterion, called VO-MTS, was an extension of the maximum tangential stress (MTS) criterion, and the second one, called VO-MS, was developed based on the mean stress (MS) failure concept. Two different groups of critical distances were utilized in the predictions. The first group was equal to the critical distances for sharp crack, and the second one was computed by using the mode I fracture test results on notched specimens. To verify the criteria, the theoretical fracture curves were compared with numerous experimental results gathered from 108 new brittle fracture tests performed on the Brazilian disk specimens weakened by central V-notches with end holes and made of PMMA under mode I and mixed mode I/II loadings. It was found that both the criteria provide very good predictions to the experimental results for different mode mixity ratios. Also, found in this research was that the curves are almost independent of the critical distance groups, meaning that one can simply utilize the critical distances of sharp crack in both the VO-MTS and the VO-MS criteria without requiring performing mode I VO-notch fracture experiments.
List of symbolsCTSN Compact-tension-shear-notch CZM Cohesive zone model d Total slit length in the VO-BD specimen D Diameter of the VO-BD specimen d c Critical distance of the MS criterion for sharp cracks d c,vo Critical distance of the MS criterion for VO-notch E Young's modulus ERNFT Effective relative notch fracture toughness FE Finite element FFM Finite fracture mechanics FNR Fictitious notch radius K vo eff Effective relative notch fracture toughness K IC Plane-strain fracture toughness of material K vo I Mode I notch stress intensity factor
To investigate the effects of flow rate, diameter and offset of secondary fuel injection on combustor noise level, pressure fluctuation and NOx emission, four types of injectors were examined in a swirl-stabilized combustor for overall equivalence ratio (φ) of 0.7 ~ 0.9 and flow rate of secondary fuel (Q sec ) from 0.6 to 4.2 L/min. As for the reference injector used in previous related studies, secondary fuel injection of 3.0 L/min is the best condition for the reduction of pressure fluctuation and combustion noise with tolerable NOx emission. For lower secondary fuel rate of 1.8 L/min, reduction of the injection diameter of reference injector results in a better performance in terms of combustion noise and pressure fluctuation reduction. By the secondary fuel injection with offset, NOx emission shows lower values than those of the injections without offset for the whole range of equivalence ratios. Spectral analysis of pressure fluctuations revealed that larger amount of secondary fuel (Q sec ≥ 3.0 L/min) by the injectors with injection offset induce a lot of new modes in the wide range of frequency. For near stoichiometric operating condition (φ ≥ 0.85) by higher amount of secondary fuel injection with offset (Q sec = 4.2 L/min), the flame lifts over the swirl injector, NOx emission decreases and instability modes appear in a frequency range lower than those of the injection without offset. The results also suggest that the emission index is deeply related to flame lift-off and the dominant mode of instability.
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