In this paper, the problem of the circular orthotropic bars with multiple cracks is investigated based on the Saint-Venant torsion theory. The solution to the problem of an orthotropic bar weakened by a Volterra-type screw dislocation is first obtained by means of the finite Fourier sine transform. In this research, the bar is assumed to be subjected to an axial net torsion when finding the dislocation solution. The closed form solution is then derived for displacement and stress fields in the bar. At the next step, the dislocation solution is employed to derive a set of Cauchy singular integral equations for analysis of the circular bar with curved cracks. The solution to these equations is used to determine the torsional rigidity of the bar and the stress intensity factors of the tips of the cracks. The paper is furnished with several examples of a single crack and multiple cracks.

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In this article, the viscoelastic behavior of fabric yarns is modeled by a new means of fractional calculus. First, the constitutive relation of the fractional “Poynting-Thomson” model is developed to investigate the behavior of yarns. The proposed material constitutive relation is a differential equation of fractional order, where the response to a unit step of stress (for determination of creep compliance), or a unit step of strain (for stress relaxation modulus) can be readily found in the literature. Here, focusing on the stress relaxation, the response function is fitted to the experimental data of yarns in a typical woven fabric prepreg, at both dry and partially consolidated conditions. The yarns were made of E-glass fibers comingled with polypropylene fibers. The results showed a significant agreement with experimental data along with improved predictions of the new fractional modeling approach when compared to other approaches such as the integer order model and Prony series. For early relaxation times, especially for [Formula: see text] a considerable discrepancy was observed between the values of relaxation modulus obtained by the experiments and that by the integer-order derivative model. However, the results extracted via the fractional derivatives were in close agreement with experimental results at all relaxation times. Using the fractional properties of the yarns, the variation of storage and loss moduli of the yarns with external frequency loading was also predicted, capturing both the rubbery and glassy regions of the material frequency response.

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