Issue 48

V. M. G. Gomes et alii, Frattura ed Integrità Strutturale, 48 (2019) 304-317; DOI: 10.3221/IGF-ESIS.48.30 311 low; however, computation results are more accurate and local contact stress can be obtained. Results by Zhang [11] showed that the pretension element method is enough and can reproduce good numerical results taken into account its simplicity. For these reasons, this method will be used to model the clamping torque on bolts. Displacements application The imposed displacement values are very important because these values should be chosen in order to cover the joint behaviour until ultimate loads are achieved. The adopted displacement values were about 17 and 12 mm for single and multiple connections, respectively. The displacements were defined in the longitudinal axis, X. Also displacements were applied in Z direction on the free nodes of the clamping grips of the testing machine, as signalized in red line/arrows in Fig. 4. The imposed displacements together with the symmetry boundary conditions impeded any rotation of the specimen ends as occurred in the gripping provided by the machine. R ESULTS AND DISCUSSION nitially and due a lack of knowledge about mechanical behaviour of the two steel grades, preliminary tensile tests were performed in order to obtain more information that will be very useful for correct modelling of the joints and to explain some differences between the two steel grades. Fig. 5 (left) illustrates uniaxial engineering stress-strain curves for S355MC (blue) and S350GD (red); Fig. 5 (right) shows the final aspect of the tested specimens. Regarding to the experimental curves, they show that the S350GD has some differences in comparison with S355MC steel. Firstly, S350GD has an ultimate strength lower than S355MC however the S350GD showed greater ductility. Zinc coated steel does not present yield plateau like S355MC. The yield plateau is a typical characteristic of the hot-rolled steels, while the transition from elastic to plastic behaviour without a perfectly defined point is characteristic of the cold-formed steels [12, 13]. As regards the failure modes of tensile specimens, Fig. 5 (right), both steels show a typical mild-steels failure behaviour with necking followed by final perpendicular to slightly inclined to loading direction cracking. Regarding the slip tests, sliding forces ( slip F ) measured between plates with LVDTs were used to compute the slip factor values ( slip µ ). Slip factors for each test were calculated using Eqn. (1). In addition, the characteristic values of the slip factors were also calculated according to Eqn. (2), taken into account the average and standard deviation of the slip factors calculated previously. Tab. 4 shows the sliding forces, slip factors and their correspondent coefficient of variations, CoV , for the three tested surface treatments. Results showed that zinc and zinc plus paint coatings resulted in the greatest and the lowest slip factors, respectively. From Tab. 4 is also possible to verify that the coefficient of variations were relatively high. Steel Grade Surface Treatment Sliding Force Slip Factor CoV [%] F slip AVG [kN] µ slip AVG µ c S355MC Without coating 97.06 0.28 0.16 21.65 S350GD Zinc coating 107.90 0.31 0.20 18.77 S350GD Zinc plus paint coating 47.28 0.14 0.09 15.56 Table 4 : Average sliding forces ( F slip AVG ), average slip factors ( µ slip AVG ), characteristic slip values ( µ c ) and respective coefficient of variations ( CoV ) obtained from the slip tests, for the three investigated surface treatments. Friction coefficients were also evaluated from static monotonic tests. Static friction coefficients were estimated from load- displacement (load-disp.) curves. The method consisted in detecting the load peak or the curve slope variation, the latter being useful for load-disp. curves with abrupt slope variation. In other cases, the slope variation was softer or for some cases some vibration occurred and therefore the correct detection of peak load was not possible. In these cases, the minimum values were considered to identify the starting of sliding. Tab. 5 shows the results and can be verified that the slip factor according the slip tests is very different when compared with average friction coefficients according to the static/monotonic tests. However, according to Picard [14] for steels without special treatment, the average slip coefficient is 0.33 for most of steels, being able to occur values around 0.23. These slip factor values are characteristic of steels provided by clean mills. In addition, for surfaces as rolled, the slip factors could be 0.20, according to EN 1090-2 [8]. As regards the steel submitted to hot-dip galvanizing process (zinc coating), the average slip values from slip and static tests are within the interval from 0.08 to 0.36 [14], validating the approach assumed initially. The friction coefficient values I