The surface stability loss of the viscoelastic half-space covered with the stack of layers

It is usually assumed that one of the mechanisms causing the process of delamination andsubsequent fracture of laminated composite materials under compressive load is the stabilityloss in the material?s structure. In this case the surface and the internal instability are usuallydistinguished. In the first case the phenomenon is realized in the near-surface region of thematerial and attenuates with increasing distance from the surface. Therefore, the finding of thenear-surface stability loss characteristic of the laminated composites has a high significantimportance for the estimation of the strength of these materials in compression.In the present study, within the framework of the piecewise homogeneous bodies model byemploying the Three-dimensional Linearized Theory of Stability of Deformable Bodies(TLTSDB), the statement of the near-surface stability loss problems of the half-space coveredwith the finite number of elastic and viscoelastic layers in bi-axial compression and in plane-strain state are solved. The equations of the TLTSDB are obtained from the Three-dimensional Geometrically nonlinear Exact Equations of the Theory of Viscoelasticity by theuse of the boundary-form perturbation technique. By employing Laplace transform, themethod for the solution to these problems is developed. It is supposed that the layers in thestack have an insignificant periodic initial imperfection and as a stability loss criterion thecase is considered where this imperfection starts to increase and grows indefinitely.The developed method is employed for the investigation of concrete problems on the subjectof surface stability loss in bi-axial compression under both three-dimensional and plane-strainstate. As a result of these investigations the influence of the rheological parameters of thelayers and half-space materials on the values of the critical time and critical compressive forceare presented. The viscoelasticity of the materials is described by the fractional-exponentialoperator of Rabotnov.The algorithm and programmes which are used for obtaining numerous new numerical resultsare composed by the author in MATLAB.The presented investigations are the first attempts for the systems that consist of half-spacecovered with the finite number of elastic and viscoelastic layers in bi-axial compression underthree-dimensional strain state and in axial compression under plane-strain state.Keywords: Surface stability loss, composite, viscoelastic material, critical time, rheologicalparameter, stack of layers.JURY:1. Prof. Dr. Surkay D. AKBAROV (Supervisor) Date: 20.10.20062. Prof. Dr. Uğur GÜVEN Page: 1263. Prof. Dr. Esin İNAN4. Prof. Dr. Nazmiye YAHNİOĞLU5. Prof. Dr. Abdullah YILDIZ