Steady-state creep analysis of polymer matrix composites using complex variable method

Abstract

A new analytical formulation is presented to study the steady-state creep in short fiber composites using complex variable method. In this new approach, both the fiber and matrix creep at low stresses and temperatures. To analyze the crept fiber, a plane stress model was used. Important novelties of the present analytical method are determination of displacement rates with proper boundary conditions in the crept fibers and also using the complex variable method in creep analyzing. It is noteworthy that the method can be useful to study the creep behavior in polymeric matrix composites due to their high capability of creep. Moreover, another significant application of the present method is to study on the creep or elastic behavior of carbon nanotube polymer composites. Finally, the results obtained from the present analytical method (complex variable method) show a good agreement with the existing experimental results.

Review on Creep Analysis and Solved Problems

“…In addition, many investigations were carried out concerning the creep of the fibrous composites and applications by different methods theoretically [19][20][21][22][23][24]. Some investigators have employed different methods in place of the shear-lag model to solve the problems like Eshelby'st h o u g h t experiment with a formulation based on the Schapery model [19] and variational approach [21].…”

“…To study the creeping fiber, a plane stress model has been employed. Significant novelties of the research work of Monfared et al [23] are determination of the displacement rates with suitable boundary conditions in the creeping fibers and also utilizing the complex variable method in the creep analyzing. It is important that the model and method may be helpful to investigate the creep behavior in polymeric matrix composites.…”

“…The unknowns may be obtained employing the appropriate boundary conditions. As the major benefit of the method and formulation of [23], Eq. (3) will be able to analyze and solve the improper integrals [23].…”

“…As the major benefit of the method and formulation of [23], Eq. (3) will be able to analyze and solve the improper integrals [23]. Moreover, displacement rates _ w 1 and _ w 2 are obtained utilizing different boundary conditions in the crept matrix, distinctive geometric relations and same procedures.…”

“…In above equations, (u 1 ,u 2 ) and (w 1 ,w 2 ) are displacement fields in the fiber and matrix, respectively. Also, subscripts 1 and 2 are related to x 1 and x 2 directions [23].…”