Buckled strips

Fig. 7 Sequential micrographs of the evolution of the damage in a SiO 4.5 wt.% P film deposited on an Al substrate subjected to a tensile test (system C, Figure 6). The black arrows show the tensile direction, (a) Networks of primary and secondary cracks perpendicular to the tensile axis (e = 11%). The white arrows show a secondary crack which stops when getting close to primary cracks, (b) decohesion and buckling of the strips of film. Slip lines are observed on the Al surface under the buckled strips, and (c) transverse rupture of the buckled zones along the directions of maximum shear of the substrate (e = 19%).

Fig. 8 Detailed views of decohesion and buckling among a cracked SiO 4.5 wt.% P film deposited on a scratched Al substrate. The white arrows show the scratches. The buckled strips of the film are perpendicular to the tensile direction.

Fig. 17 Schematic representation of the interfacial failure process which is induced by the transverse contraction of the substrate in the y direction. The system is submitted to uniaxial tension in the x direction, (a) the decohesion and buckling of a strip of the cracked film, defined by two consecutive transverse cracks, is decomposed in, (b) a decohesion stage, and (c) a buckling stage of the decohered part of the strip.

The interfacial debond occurs after the through-thickness cracking of the films. It is activated by transverse contraction of the substrate which induces the buckling of the strips of the cracked films. The analysis of this particular adhesion failure mechanism provides insights concerning the interfacial strength of... 

The uniaxial determination stretching of this sort of sample, produces transverse cracking of the film, until the saturation of the crack network. The debonding and buckling of the strips of a cracked film is induced by the transverse contraction of the substrate. 

We have already discussed confinement effects in the channel flow of colloidal glasses. Such effects are also seen in hard-sphere colloidal crystals sheared between parallel plates. Cohen et al. [103] found that when the plate separation was smaller than 11 particle diameters, commensurability effects became dominant, with the emergence of new crystalline orderings. In particular, the colloids organise into z-buckled" layers which show up in xy slices as one, two or three particle strips separated by fluid bands see Fig. 15. By comparing osmotic pressure and viscous stresses in the different particle configurations, tlie cross-over from buckled to non-buckled states could be accurately predicted. 

Most aerospace structures, such as wing and fuselage panels, are long compared with cross-sectional dimensions. Hence, strip models, making prismatic assumptions in the solution of Eqn (4.3), are computationally efficient in many applications. Approaches that find buckling loads by minimizing potential energy for assumed mode shapes have also been developed [3]. 

In this chapter we use a method that solves Eqn (4.3) using exact, periodic formulations [4]. Here, the eigenvalue analysis is executed on a transcendental stiffness matrix derived from the solution of the governing differential equations of the constituent strips, which are assumed to undergo a deformation that varies sinusoidally to infinity in the longitudinal direction. The out-of-plane buckling displacement w is assumed to be of the form... 

Dawe DJ, Craig TJ. Buckling and vibration of shear deformable prismatic plate structures by a complex finite strip method. Int J Mech Sci 1988 30(2) 77—99. http //dx.doi.org/ 10.1016/0020-7403(88)90063-X. 

Butler R, Liu W. Optimisation of stiffened panels using finite strip models. In Falzon BG, Aliabadi MH, editors. Buckling and postbuckling structures. London (UK) Imperial College Press 2008. pp. 225—57. 

Equation 8.23 expresses the theoretical or critical load per unit circumferential length of unit width of circumference. For a strip of unit widlli the critical load is the pressure at which buckling thet)retically cylindrical shell, the adjacent metal or either side of the ring will offer restraint t,o the longitudinal deformation of the strip. To allow for this restraint Eq. 8.23 may be divided by (1 — p ). (See Eejs. 6.1a and 6.12.) To expre.ss the criticsd stre.ss in terms of the shell thickness, a substitution for I may be made for a rectangular strip. 

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