PSI - Issue 1

Luca Susmel / Procedia Structural Integrity 1 (2016) 002–009 Author name / Structural Integrity Procedia 00 (2016) 000–000

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Table 1. Overall accuracy of the TCD in estimating the high-cycle fatigue strength of the tested notched concrete.

Error [%]

Batch A

Batch B

Notch type

K t

PM 8.8 12.7

LM -14.1 -13.9 -15.3

AM 12.6 16.6 10.8

PM 0.4 4.9 0.0

LM -20.8 -19.9 -18.7

AM

Blunt

1.47 1.84 4.32

3.7 8.5 6.3

Intermediate

Sharp

0.0

As shown in Figure 4, the PM was seen to be highly accurate in estimating the high-cycle fatigue strength of the samples containing not only the intermediate (K t =1.47), but also the blunt notches (K t =1.84). Table 1 summarises the overall accuracy obtained by apply the TCD in the form of the PM, LM, and AM, the error being calculated as:







eff ,max

0,MAX

Error



[%]

(10)



0,MAX

To conclude, it can be pointed out that, according to Table 1, the use of both the PM and AM resulted in estimates falling within an error interval of ±15%, whereas the use of the LM in predictions falling, on the non-conservative side, within an error interval of ±20%. The obtained level of accuracy is certainly satisfactory since, in the presence of stress concentration phenomena, it is not possible to distinguish between an error of ±20% and an error of 0% as a consequence of those problems that are usually encountered when performing the testing as well as the numerical analyses (Susmel, 2009; Taylor and Wang, 2000). 6. Conclusions  Both the PM and AM were seen to be highly accurate in estimating the high-cycle fatigue strength of the tested notched concrete. This strongly supports the idea that these two formalisations of the TCD can be used in situations of practical interest to efficiently design notched plain concrete against fatigue.  The use of the LM to estimate the generated notch endurance limits resulted in non-conservative predictions falling within an error interval of ±20%.  The TCD critical distance was seen to be the same for both batches. This suggests that, in plain concrete, L is a microstructural length scale parameter whose value is mainly related to the microstructural features of the material being assessed. References Dixon, W. J., 1965. The up-and-down method for small samples. Journal of the American Statistical Association 60(312), 967-978. Jadallah, O., Bagni, C., Askes, H., Susmel, L, 2016. Microstructural length scale parameters to model the high-cycle fatigue behaviour of notched plain concrete. International Journal of Fatigue 82, pp. 708-720. Ohlsson, U., Daerga, P. A., Elfgren, L., 1990 Fracture energy and fatigue strength of unreinforced concrete beams at normal and low temperatures. Engineering Fracture Mechanics 35 l/2/3, 195-203. Plizzari, G. A., Cangiano, S., Alleruzzo, S., 1997. The fatigue behaviour of cracked concrete. Fatigue and Fracture of Engineering Materials and Structures 20(8), 1195-1206. Spindel, J. E., Haibach, E., 1981. Some considerations in the statistical determination of the shape of S-N curves, in: “Statistical Analysis of Fatigue Data” . In: Little, R. E., Ekvall, J. C. (Ed.). ASTM STP 744, pp. 89. Susmel, L., 2009. Multiaxial Notch Fatigue: from nominal to local stress-strain quantities. Woodhead & CRC, Cambridge, UK. Susmel, L., 2014. A unifying methodology to design un-notched plain and short-fibre/particle reinforced concretes against fatigue. International Journal Fatigue 61, 226–243. Taylor, D., 2007. The Theory of Critical Distances: A new perspective in fracture mechanics. Elsevier, Oxford, UK. Taylor, D., Wang, G., 2000. The validation of some methods of notch fatigue analysis. Fatigue Fract. Engng Mater. Struct., 23, 387–394. Thun, H., Ohlsson, U., Elfgren, L., 2011. A deformation criterion for fatigue of concrete in tension. Structural Concrete 12(3), 187-197.

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