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Fatigue behaviour of a PET-Geogrid under cyclic loading

Abstract

The lines of 'damage-begin' and 'specimen-break' for dynamic loading of a geogrid were determined in a series of Iaboratory testing. The cyclic Ioad ratio was set to R = 0.5, loading frequency f = 10Hz and

f = 3Hz. The test results show clearly that the chosen procedure for the determination and analysis of the beginning of damage and break is reproducible and allow for safe extrapolation for lower Ioad Ievels. Furthem1ore the method chosen enables explicit decrease of the required testing time. The assumption of linear damage accumulation was examined in two-step-trials. The number of Ioad cycles to 'break' evaluated in 'one-step-tests' compared with those of 'two-step-loading' are practically the same. The existence of 'damage-lines' for the examined geogrid under a dynamic pulsating Ioad of 10Hz and 3 Hz and a R-value of0.5 could be verified. Damage of the specimens occurs only for load-cycles lying between the 'damage-line' and the 'stress-cycle-diagram' ('Woehler-curve'). When it comes to dimensioning against 'damage-beginning' or 'break', higher loading frequencies present the critical case.

Conclusion

ln an extensive testing program, samples of PET-geogrid Fortrac R 560/115-15 T were subjected to cyclic tensile loading. The test conditions were chosen for frequencies of 10Hz and 3 Hz under a Ioad ratio of R = 0.5 as it is believed to represent the dynamic loading for both goods and high speed trains. A Ioad ratio of /~ = 0.67 would be the typical situation but a Ioad ratio of R = 0.5 covers all situations. The test data with R = 0.5 will be on the safe side in comparison with higher R-values. Such high dynamic Ioads can occur in applications where the geosynthetic reinforcement is installed in a shallow position under the rail tracks. The used Ioad Ievels of the cyclic loading have been chosen in such a way to reach failures within acceptable test durations. This eans for e.g. 107 cycles at a frequency of 10Hz, a test runs for two weeks. As the results of dynamic loading tests have a scattering, a statistical evaluation is absolutely necessa1y. Therefore many tests (2': 10 tests per Ioad Ievel) are needed. As the tests are ve1y time consuming, testing at high Ioad Ievels are meaningful. ln the case of the tested geogrid, the maximum Ioads in the tests correspond to 43 till 58% of the short-tcrm tensile strength of 560 kN/m. With regard to the question in how the material behaviour of the tested geogrid would be representative for the same family of geogrid (i.e. same raw-material and production technology but different ultimate strength) it is to be noted that definite answers to this question would require additional testing. However, from a comparison of the static behaviour of different grades of this material (e.g. short term tensile testing, creep behaviour, durability) it can be assumed that the performance of this geogrid is basically related to its raw material. Therefore, significantly different behaviour should not be expected even under cyclic loading. The results indicate that the dynamic performance of the material can be characterized by two significant events which depend on the number of applied Ioad cycles, the 'beginning of damage' and 'fatigue failure'. On account of statistical analyses, the test results clearly show the reproducibility of the method employed. The existence of the 'damage-begin' parameter which can be quantified renders additional safety for dimensioning of the geogrid against operational dynamic loading. The loading Ievels were selected in such a way that on one hand no temperature dependent changes in material properties would influence the tests, on the other hand statistically weil established loading Ievels could be executed without increasing the required numbers of individual tests inan unjustified manner. Furthermore the differences between the Ioad Ievels should be sufficient (about 10% of the maximum cyclic Ioad), and the differences between the average numbers of Ioad cycles to fatigue failure should also be not too large, This approach facilitates the determination of 'lifetime curves' by means of regression analyses. Accounting for elementary methods of mathematical modelling, the 'life-time-curves' appear as straight lines with inclinations determined with good statistical safety. The extrapolation towards lower Ioad Ievels is easy and well secured. This extrapolation is in each case conse1vative. so it always Ieads to results on the safe side. However, if the regression functions are used for extrapolations considerably beyond 50 years, respectively for Ioad cycles considerably in excess of e.g. 108 then it has to be taken into account that synthetic plastic material is ageing and becomes brittle with time. This phenomenon is known in principle. That kind of changes in material properties depends on operational loading, temperature or temperature variations, and possibly on actions of media (chemical, biological). The evaluation of the tests clearly showed that specimens tested at 3 Hz possess a Ionger lifetime than specimens tested at 10Hz. The difference in lifetime increases with decreasing maximum values of cyclic Ioad. Therefore, in dimensioning against beginning of damage or against fatigue failure, the higher frequencies are more critical. For the tested geogrid, the existence of the 'damage-line' had to be verified by two-steps tests. The results of the two-steps tests and the comparison with one-step tests can be summarized as follows:

- Measurement and recording of specimen temperature, lass work, dynamic modulus (stiffness) and extensometer amplitude during the tests Iead to convincing, reproducible criteria for determination of the damage-beginning when evaluated simultaneously.

- With respect to distribution and magnitude, the numbers of Ioad cycles to fat igue failure of two-steps tests show good agreement with those of one-step tests.

- The results could be presented visually as well as qualitatively in diagrams and quantitatively after statistical analysis.

- The assumed linear damage accumulation (linear Miner rule) was examined in practice by two-steps tests in both directions. Very good agreement was observed, independent of the question whether the second Ioad step was defined by increasing or decreasing the Ioad, and independent of the question how many Ioad steps were skipped between the two applied Ioad steps.

-lt was demonstrated statistically that in case of one-step tests and in case of two-steps tests for the second step, fatigue failure events follow a logarithmic normal distribution. Depending on the Ioad Ievel. The widths of the distributions differ only slightly.

- Comprising alt test results and the items mentioned before, it can be concluded that for the tested geogrid under dynamic tensile cyclic loading at 10 Hz and U = 0.5, a 'damage-line' exists. This means that there is a region ofload cycles below the 'Woehler-curve' in which no specimen damage occurs. Damage is initiated for numbers of Ioad cycles only, which plot between the 'damage-line' and the 'Woehler-curve'.

- The method presented here for the determination of the 'Woehler-curve' and the 'damage-line' has enormous advantages in time-saving combined with cost reduction for testing.