PSI - Issue 44

Laura Giovanna Guidi et al. / Procedia Structural Integrity 44 (2023) 1284–1291 Laura Giovanna Guidi et al. / Structural Integrity Procedia 00 (2022) 000–000

1289

6

Stability issues for rubber devices: discussion on the experimental results and comparison with codes requirements In view of the analytical formulations form literature, the limit condition for buckling is given by V crit =V: theoretically, instability occurs when the applied vertical force corresponds to the value of the critical load, V crit = V crit (d H ), at a certain shear deformation. To avoid buckling failure the ratio V cri t/V has to be greater than one. On the other side, design recommendations for rubber devices indicate a buckling ration at least greater than 2. To evaluate stability issues for the abovementioned full-scale devices, in Table 3data from four sets of static shear tests are compared, varying γ for 175% to 250%, while the applied vertical stress grows from 6MPa to 14MPa. The table includes: the factor γ /S 2 = d H / ɸ , corresponding to dimensionless horizontal displacement; the ratio A r /A, that expresses the reduced area as percentage of the plan area of device; the buckling ratio, V crit /V. The dimensionless horizontal displacement, marked with an asterisk (*) indicate the experimental instability occurrence. On the contrary, in the column of the buckling ratio, values lower than one indicate the theoretical instability occurrence. As visible in Table 3, for HDRB500 (S 1 ·S 2 = 64,52) the buckling ratio is always lower than one, excepted for the first shear test, at γ =175%with σ v = 6MPa. Matching analytical formulations with the experimental results, it is visible that bearing instability occurs more rarely than expected from theoretical evaluations. Results for the slenderest device, HDRB600 (S 1 ·S 2 = 59,11) are synthetized in the second column of Table 3. To avoid bearing failure, tests at γ = 250% have not been performed. From a theoretical point of view, buckling instability should always occur. On the contrary, full scale tests show device unstable behaviour only at large deformations ( γ = 220%) when the highest values of vertical stress are applied ( σ v = 10 - 14MPa). Finally, the third column of Table 3 indicates the experimental results for the squattest device, HDRB700 (S 1 ·S 2 = 65,70), the only one having S 2 >3. In this case, for shear strain γ < 250% at σ v = 6MPa theoretical instability never happens, while the increase of vertical stress leads to buckling occurrence also at low shear deformations. On the contrary, experimental results evidence this phenomenon only for the last shear test, at γ =250% with σ v = 14MPa. Matching results from different devices, it clear that the theoretical limit condition for buckling instability works on the side of safety, considering that the effective buckling phenomena can be seen for horizontal displacement greater than half of device diameter.

Table 3. Theoretical evaluation of critical load based on full-scale-tests SI-S-500-176 SI-S-600-217

SI-S-700-207

No.

σ v [MPa]

γ max [%]

γ /S 2 62% 62% 62% 70% 70%

Ar/A 27% 27% 27% 19% 19% 37% 12% 12%

V crit /V

γ /S 2 63% 63% 63% 72% 72% 58% 80%

Ar/A 25% 25% 25% 17% 17% 31% 10% 23% 36%

V crit /V

γ /S 2 53% 53% 53% 59% 59% 59% 64% 64% 64% 71% 71%

Ar/A 36% 36% 36% 30% 30% 30% 24% 24% 24% 18% 18% 18%

V crit /V

7 8 9

6

175% 175% 175% 200% 200% 200% 220% 220% 220% 250% 250% 250%

1,16 0,69 0,50 0,82 0,48 0,68 0,52 0,31

0,99 0,59 0,42 0,66 0,40 0,52 0,41 0,55 0,61

1,58 0,95 0,68 1,31 0,79 0,56 1,06 0,64 0,45 0,77 0,46 0,33

10 14

10 11 12 13 14 15 17 18 19

6

10 14

52%(*) 78% (*) 78% (*) no done. 88% (*) no done no done

6

10 14

65% (*) 53% (*)

-

-

6

5%

0,21

- - -

no done

- - -

10 14

- -

- -

-

no done

71% (*)

(*) experimental instability occurrence

In the following Table 4 the experimental data are compared to the codes’ requirement for the design of such bearings. Considering that the European Standards allow a maximum compressive force equal to one half of the critical load, the maximum horizontal displacement have been defined for each σ v -level, assuming a limit value for the buckling ratio equal to 2. In this case, V is function of the maximum vertical stress (6 – 10 -14 MPa), while V crit results from the fixed buckling ratio. The reduced area, A r , derives from the value of critical load, while, through the