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Notes: Abstract A theoretical model was introduced for the evaluation of the boundary layer developed between the main phases during the preparation of unidirectional fiber composites. It has been shown that this thin layer influences considerably the physical properties of the composite. It was assumed that the physical properties of themesophase unfold from those of the hard-core fibers to those of the softer matrix. Thus, a multicylinder model was assumed improving the classical two-cylinder model introduced by Hashin and Rosen for the representative volume element of the composite. Based on thermodynamic phenomena appearing at the glass transition temperatures of the composite and concerning the positions and the sizes of the heat-capacity jumps there, as well as on the experimental values of the longitudinal elastic modulus of the composite, the extent of the mesophase and the mechanical properties of the composite may be accurately evaluated. This version of the model is based on a previous one concerning a multilayer model, but it is considerably improved in order to take into consideration, in a realistic manner, the physical phenomena developed in fiber reinforced composites.

Notes: Abstract The size of the mesophase, which constitutes a boundary layer between fillers and matrix in composites, has been efficiently evaluated by the modified two-term unfolding model, which was based on delicate DSC measurements of the heat capacity jumps at the glass transitions of the composite and its constituent phases [1,2]. This model is now used to evaluate the mesophase along the whole viscoelastic spectrum of the composite, by making measurements of the storage and loss compliances or moduli of the composite and matrix and without making recourse to any other type of special measurement at the glass transition temperature of the substances. By applying this model the following important results were derived: i) Lipatov's empirical formula for defining the mesophase atT g was shown to yield reasonable results and ii) the evaluation of the size of mesophase over the entire viscoelastic spectrum was shown to remain almost constant and in conformity with the values defined by the other versions of the model. Extensive application of the experimental results of the literature indicated the mutual proof of the validity of these affine models.

Notes: Abstract A slow crack growth was achieved in initially edge-cracked specimens made of a high-molecular weight PMMA by regulating the cross-head speed of loading by a computer-driven testing machine. The strain rate $$\dot \varepsilon $$ used during the tests varied between $$\dot \varepsilon $$ =1× l0−6 s−1 and 1×10−4 s−1. It was shown that, in this zone of slow quasi-static loading of brittle polymethylmethacrylate specimens under conditions of plane stress, the crack initiated for a critical value of loading, at some characteristic zone of strain-rate variation at the crack tip. It was established that for strain rate between $$\dot \varepsilon $$ =0.18×10−5 s−1 and $$\dot \varepsilon $$ =0.45×10−4 s−1 brittle cracks were propagating always slowly with velocities in the range ofc=3 to 5×10−2 m/s. For values ofv s outside this transition zone fracture was typically brittle with high crack-propagation velocities. As the strain rate was varying beyond the stable low-velocity region, a two-step crack velocity pattern was operative, where the one step took always low values, and the other step corresponded to crack-propagation velocities significantly higher than these limits, tending to typical brittle-fracture velocities of the material. Oscillations of the velocityc at the transition zones, or, in many cases all over the zone of slow propagation of the crack, indicated the unstable character of crack propagation, influenced by different stress raisers and especially by the opposite longitudinal boundary of the specimen. Stress intensity factor values during crack propagation, evaluated from the front (cuspoid) and the rear (external) caustic, which remained alwaysk g-dominant, were following similar trends as the variation of the crack propagation velocity.

Notes: Abstract The degree of adhesion developed between matrix and inclusions in composites is among the main factors characterizing their mechanical and physical behavior. The quality of adhesion depends mainly on the boundary layer created between inclusions and matrix because of chemisorption, physisorption and mechanical constraint phenomena developed between the main phases in the RVE of a composite. The extent of this boundary layer, which is called mesophase or interphase, may be a potential means for defining the quality of adhesion. While almost all previous models describing the mechanical and physical properties of composites are based on the concept of mathematical and smooth interfaces constituting the boundaries of the phases, a series of recent models developed by the author and his collaborators consider a more pragmatic situation at the interfaces between phases assuming the existence of boundary layers between phases ensuring a continuous transition of the properties of adjacent phases, which should be accepted as being in conformity with the physical and chemical procedures happening at these boundaries. The unfolding type of models introduced by the author aims to fill the gap by trying to accommodate the properties of neighbouring phases by transition boundary layers with varying properties between the bounds of the limiting phases. Thus, the unfolding models constitute a powerful means, where the notion of mesophase was introduced for defininig the RVE of a composite. The RVE was considered as consisting of the two main phases (the reinforcement and the matrix), coupled together by the intermediate phase, whose variable mechanical properties unfold from those of the reinforcement to those of the matrix. The extent of mesophase was evaluated by the three different and alternate methods, that is: i) by considering the variations in the heat capacity jumps,ΔC p , of the matrix material and the respective composite, appearing at the respective glass-transition temperatures of both substances. Based on thermodynamic measurements with differential scanning calorimetry, the extents of these jumps were accurately measured and these defined the thickness of the mesophase. It was further assumed that the steep variations of the mechanical properties in the mesophase follows negative-power laws, whose exponents were derived by measuring the moduli of the matrix, inclusions and the composite and assuming the validity of an improved law of mixtures. § ii) by evaluating the extent of mesophase along the whole range of temperature by using exclusively the mechanical properties of the storage and loss compliances and moduli of the composite and the matrix, without making recourse to thermal or other types of measurements and without limitations at the glass transition temperatures, and § iii) by defining the extent of the mesophase by the same method, but evaluating the properties of the mesophase or mesophases by methods based on diffusion laws of mutually soluble phases or impregnations. This method is convenient for studying polymer-polymer composites and composites with encapsulated or sized phases. By applying all three variations of the unfolding model it was shown that all three possibilities of defining the extent and the variable properties of mesophases are equivalent and, furthermore, they yield reasonable results. Moreover, experimental evidence with either particulates, or fiber composites indicated clearly that the introduction of the mesophase yields a better and more flexible model for interpreting in a realistic manner the complicated phenomena appearing in all composites used in engineering applications.

Notes: A simple two-step corrective technique is presented in this paper for evaluating stress intensity factors in crack problems. In the first step an approximate evaluation of the stress intensity factor was made by considering the cracked plate to be of infinite size. The stresses of the problem were relaxed by the stresses of the infinite body which corresponds to the approximate value of the stress intensity factor. The expected discrepancy in the value of SIF by the infinite plate approximation was corrected in the second step where the existing residual stresses are equilibrated at the cracked plate by using any of the conventional finite element techniques and the corrective value of the stress intensity factor is calculated by using an appropriate collocation formula. The method was applied to three typical plane problems of cracked plates with satisfactory results.

Notes: A new technique for the solution of singular integral equations is proposed, where the unknown function may have a particular singular behaviour, different from the one defined by the dominant part of the singular integral equation. In this case the integral equation may be discretized by two different quadratures defined in such a way that the collocation points of the one correspond to the integration points of the other. In this manner the system is reduced to a n × n system of discrete equations and the method preserves, for the same number of equations, the same polynomial accuracy. The main advantage of the method is that it can proceed without using special collocation points. This new technique was tested in a series of typical examples and yielded results which are in good agreement with already existing solutions.

Notes: A modification of the collocation method for the numerical solution of Cauchy-type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A(x - c)α + B(x - c)β, where α 〈 0, 0 〈 β - α 〈 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.

Notes: A modification of the numerical techniques of solution of Cauchy-type singular integral equations and determination of stress intensity factors at crack tips in plane elastic media is proposed. This technique presents some advantages under appropriate geometry conditions.

Notes: A method which combines the finite element technique and the singular-integral equation method is presented. The association of the two methods is obtained with the help of Schwarz's alternating method (SAM). The method was applied with satisfactory results to the solution of a series of problems of a circular arc crack lying inside a finite thin plate for various lengths of the circular arc and for various dimensions of the rectangular cracked sheet.