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Notes: Summary The present paper studies the influence of adhesives on the behaviour of cracks in two-dimensional linear elastic bodies. Especially the delamination and debonding effects are studied. The adhesive material is assumed to introduce non-monotone, possibly multivalued laws which can be described via non-convex superpotentials. The direct boundary integral equation method is extended for this problem. It gives rise to two equivalent multivalued integral equations holding on each crack. Numerical examples concerning the resulting stress intensity factors illustrate the theory.

Notes: Summary The optical method of reflected caustics was applied to beam buckling problems. The reflected rays of a light beam (either parallel, or convergent, or divergent) on the flanks of the strut create caustics which consist of two strongly illuminated straight lines, confining the luminous region of the strut. By measuring the distance between the extremities of the caustics, the perturbation parameters of the buckled beam can be defined. The accurate experimental evaluation ofs allows the solution of the respective Euler expansion equations for the critical buckling load and its higher order terms in the post-buckling state of the strut. The method is a versatile and sensitive technique for experimentally defining the mode of elastic buckling of struts and can be extended to study plastic buckling cases.

Notes: Summary The elastic problem of an infinite orthotropic plate with different roots of its characteristic equation, when the fibers are oriented perpendicularly to an internal crack, and is weakened by an elliptic hole, is solved using Lekhnitskii's theory. The plate is subjected to prescribed stresses at infinity, while the boundary conditions are given at the flanks of the crack, at the rim of the perforation and at infinity. Using the complex-variable method, the solution of the problem is reduced to the evaluation of Cauchy-type integrals concerning the analytic functions of the problem. The numerical solution of the problem revealed an intense variation of mode-I stress intensity factors (SIF) at the crack tips due to the increase of either the crack length, or the distance of the near-by rack tip from the center of the hole. Furthermore, it was found that orthotropy strongly influences the intensity of stresses at the crack tips. These findings are in complete agreement with results given in a previous work by the authors, concerning a similar problem for an orthotropic plate, which, however, constitutes a special case, where the material presents equal roots for its characteristic equation [1].

Notes: Abstract Ductile blunting and fracture under conditions of plane stress in metals are described by two main phases: static crack growth, and slow crack propagation. In the first phase the crack tip is deformed in an elastic-plastic mode, the main characteristics of which are the formation of the plastic enclave around the crack tip, and the evolution of blunting. In the second phase the crack propagates through expansion and coalescence of microvoids and microdefects developed at the vicinity of and in front of the crack tip. Ductile blunting under plane-stress conditions in metallic plates was studied, and the influence of the geometry and the mode of loading specimens was defined. This was achieved by interrelating the amount of crack opening displacement at its tip, and its comparable effect of the crack tip advance displacement. The experimental study was executed in a scanning electron microscope with thin specimens under dominating plane-stress conditions. The mechanism of development of ductile blunting up to the point of initiation of slow crack propagation was interrelated with these characteristic quantities.

Notes: Summary It is shown that the necessary parameters for an invariant description of the elastic behaviour of a transversely isotropic medium in terms of the spectral decomposition of its compliance tensor are the four eigenvalues of it and a dimensionless parameter, appropriately defined, the eigenangle ω. A study of the variational bounds imposed by thermodynamic restrictions on the values of the eigenangle ω is presented. It is further proposed that the eigenangle ω can be successfully used as a single parameter characterizing qualitatively both elasticity and toughness of transversely isotropic media.

Notes: Summary The behavior of the two main types of flows encountered in materials such as rocks, i.e., cracks and slits, under compressive and shear stresses has been examined. It was shown that the existence of a gap between the edges of a slit is allowing the inward movement, causing the development of a negativeK I -SIF at its cornered extremities. On the other hand, for a slant ideal crack additional compressive stresses should develop because of the noncongruent deformation of its lips thus opposing the incompatible interpenetration of the crack flanks and causing an openingK I -SIF. Finally, for an ideal crack normal to the global stresses in the plate the cracked body behaves as a continuum without any singularity. In order to verify the validity of the above arguments the method of caustics has been used. After developing the appropriate equations of the caustics a series of experiments were executed giving results which support the already developed theory.

Notes: Summary The failure strengths of anisotropic bodies and especially those of fiber reinforced materials are generally studied at the principal directions of their strength and loading of the bodies. For the most reliable criteria, based on failure functions having the form of a general tensorial polynomial, the modes of failure of anisotropic (orthotropic, transversely isotropic) bodies were studied primarily on the principal stress (σ1, σ2, σ3). The elliptic paraboloid failure surface, (EPFS), being one of them, was based on the phenomenological assumption that even the anisotropic media do not fail under the influence of any hydrostatic pressure superimposed with an elementary loading, taking care of the anisotropy. Modes of failure of orthotropic media under the influence of shear loading, which are very important especially for the transfer of loading between fibers and matrix in a single lamina, as well as in the theory of failure of laminates, was up-to-now neglected. In this paper the effect of shear is studied for transversely isotropic and orthotropic materials. The dependence of the pure shear loading on the sign of shear, as well as on the parameters of anisotropy of the medium, is established. Interesting results are revealed, having a direct application on a well-founded theory of strength of laminates.

Notes: Summary Cellular solids and brittle foams are increasingly finding application in constructions mainly as core materials for loaded sandwich structures where the loading of the structure generates multiaxial stress states on them. It has been established that the principal mechanism of deformation is based on the cell-wall bending and closed-cell as well as open-cell foams present similar stiffnesses. Therefore simple relations are found for their tensile, compressive and shear strengths and their elastic properties. It has been established in this paper that the modes of failure of such materials can be satisfactorily described by the elliptic paraboloid failure criterion for the general orthotropic body. Then, as soon as the yield or failure stresses in simple tension and compression are measured along the three principal stress directions of the material the failure locus is unequivocally defined and all the properties of the material under any complicated load can be accurately established. However, since these materials fail in the compression-compression-compression octant of the principal stress space by elastic buckling, the EPFS-criterion is cut-off by an ellipsoid surface, with intercepts along the principal axes the respective compressive failure stresses. The criterion thus established yields satisfactory results. It has been tested among others in a reticulated vitreous carbon foam as well as in an aluminium foam. The experimental results for these foams existing in the literature are fitting better with this universal criterion than any other considered, thus indicating the validity of the elliptic paraboloid failure criterion also for this type of materials.

Notes: Summary It has been recently shown [1] that the stress concentrations in anisotropic materials with distinct complex or imaginary roots of the respective characteristic function are much higher than in materials with equal roots. It was further shown [2] that anisotropic materials with equal roots behave like quasi-isotropic materials. Modern carbon-carbon and metal-ceramic composites are intuitively using these facts to create much stronger materials by reinforcing the matrix properties. A theory is presented in this paper where the coupling of strongly anisotropic fibers along their axis with strongly anisotropic matrices along either the fiber direction or the transverse plane to the direction of the fibers, either deteriorates, or improves perceptibly the mechanical behavior of the composites. It was shown that anisotropy of the matrix, increasing its mechanical properties on the transverse isotropic plane of the composite, increased the transverse Poisson's ratio, whereas decreased the longitudinal shear modulusG LC . This resulted in values of the eigenangleω c receding from the corresponding valueω ic for the respective isotropic, case. This resulted in a deterioration of the mechanical performance of the composite since the material now has the tendency to develop higher stress concentrations for equivalent loadings. On the contrary, a strong anisotropic matrix along the direction of the fibers yielded the inverse results for the various moduli of the anisotropic composite. The most important result is the increase of the longitudinal shear modulusG L , so that the ratioE L /2G L is consistently decreasing, thus yielding values of the eigenangleω c tending to approach the critical valueω c for the isotropic material. This decrease ofω c indicates the improvement of the quality of the composite, which develops relatively lower stress concentration factors approaching their respective isotropic values. This fact makes the anisotropic composite material to approach an equivalent state of quasi-isotropy and thus to improve the strength of the material by reducing considerably the eventual, anisotropic stress concentration factors of the respective structural elements. Examples with T300/N5208 Graphite-Epoxy composites and Borsic-1100 Aluminum metal-metal composites indicate clearly the beneficial effect of the anisotropy of their matrices.