PSI - Issue 32

Denis N. Sheydakov et al. / Procedia Structural Integrity 32 (2021) 313–320 Denis N. Sheydakov, Irina B. Mikhailova / Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 1 shows the dependencies of the critical axial compression of the rod on the relative initial extension compression of itscoating   .It should be clarified that the areas on the graphs that lie above and to the left of the constructed curves are regions of instability for the considered deformationof the rod with coating since they correspond to the values of the loading parameter  exceeding the critical axial compression. The results for rods of different size (scale) are presented. The relative radius of the rod withcoating r   has been used as the size parameter at a fixedlength-to-radius ratio l  and a fixed relative thickness of the coating h  . Micropolar rods with a sufficiently thin coating   0.05 h   and a coating of medium thickness   0.1 h   were considered.The ratio of the initial length of the rod with a coating to its diameter is 20   40 l   for all presentedgraphs.According to the results obtained, the preliminary extension of the coating   0    stabilizes the deformation of simple compression   = 0 p for the considered composite structure, while the influence of preliminary compression of the coating   0    is generally negative.Moreover, it is evident from Fig. 1 that with a sufficiently strong preliminary compression, the buckling of the rod is possible in the absence of its deformation   0   solely due to internal stresses in the coating. It should be noted that the described effects are more pronounced for rods with thicker coating. In the present paper, we also found that the stability of the micropolar rod with prestressed coatingincreases with a decrease in its overall size (scale).This effect is due to the influence of the material microstructure and is not observed in the classical elasticity.It is quite significant for small rods   5 r    , but negligible for large ones. 4.2. Combined loading case Next, the case of axial compression under external hydrostatic pressure was considered.By solving the linearized boundary value problem (12), (13), (15)again, the critical curves corresponding to the different buckling modes of the micropolar rod with prestressed coating were found, and the stability regions were constructed in the plane of loading parameters, which are the relative axial compression  and the relative external pressure p  .Fig. 2 and 3 show the boundaries of the stability regions for micropolar rods with preliminary compressed   0.04     and pre stretched   0.1    coatings.The stability regions themselves lie to the left of these curves.As with simple loading, micropolar rods of different sizes and coatings of different thicknesses were considered. According to the results obtained, in the considered case of combined loading, the preliminary extension of the coating   0    also stabilizes the deformation of circular rod, while the influence of preliminary compression of the coating   0    remains generally negative.Moreover, it isobvious from Fig. 2 that the application of external pressure in a certain range allows us to neutralize the effect described above, when internal stresses arising from strong preliminary compression of the coating provoke a buckling of the rod in the absence of its axial deformation   0   .

h = 0.05

h = 0.10

3.0 p

3.0 p

1.5

1.5

r * = 1 r * = 2 r * = 5 r * = 10

r * = 1 r * = 2 r * = 5 r * = 10

0

0.05

0.10

0

0.05

0.10





Fig. 2.Influence of initial compression of the coating 

 0.04

   

on the micropolar rod stability in the case of combinedloading.