Abstract
Two distinct length scale transition methodologies are developed to establish effective traction-separation relations for fracture in composite materials within a hierarchical multiscale framework. The two methodologies, one kinetics-based and the other kinematics-based, specify effective fracture properties that satisfy a surface-based Hill-Mandel consistency condition. Correspondingly, the total amount of energy dissipated is the same whether a crack is described in detail with micro quantities or in terms of an effective macroscopic crack. Though both methods guarantee consistency in terms of energy rates across length scales, they provide in general distinct effective traction-separation relations. Several representative samples of fiber reinforced composites are analyzed numerically, including the formation and propagation of cracks at mid-ply locations as well as (idealized) ply interfaces. Through post-processing of the microscale results, it is shown that the kinematics-based averaging method provides a macroscopic traction that is prone to rapid fluctuations while the kinetics-based averaging method shows a more smooth response but with openings that can deviate from the surface average of the microscale openings. The two methods are also compared with a previously-proposed scale transition methodology, which is a hybrid method that only satisfies the Hill-Mandel condition approximately. The suitability of the three methods is discussed in light of the results obtained from the simulations.
Highlights
With an ever increasing demand for more efficient lightweight composite materials in the transportation, infrastructure and energy conversion sectors, new types of composite materials are continuously being designed and tested
Through post-processing of the microscale results, it is shown that the kinematics-based averaging method provides a macroscopic traction that is prone to rapid fluctuations while the kinetics-based averaging method shows a more smooth response but with openings that can deviate from the surface average of the microscale openings
In order to satisfy the surface-based Hill-Mandel scale transition condition for fracture as given in (24), two distinct approaches are proposed namely a kinematics-based method where the crack opening rate is obtained from an average and the traction is adjusted in accordance with the scale transition and a kinetics-based methods where the traction is obtained from an average and the crack opening rate is adjusted from the scale transition
Summary
With an ever increasing demand for more efficient lightweight composite materials in the transportation, infrastructure and energy conversion sectors, new types of composite materials are continuously being designed and tested. Designers and certification authorities require a high degree of confidence on the performance of new materials, in particular their actual capacity to safely carry loads, a robust fracture theory is a critical aspect of material development In this context, advanced simulation methods provide a powerful approach to reduce experimental testing costs and shorten design cycle times (i.e., a virtual testing environment (Cox and Yang, 2006; Lopes et al, 2016)). Satisfaction of a surface-based Hill-Man del scale transition for fracture in general cannot be guaranteed a priori with a classical multiscale approach in which the effective properties are defined as volume or surface averages of the microscopic quantities.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
