A hybrid deterministic-probabilistic approach to model the mechanical response of helically arranged hierarchical strands

Abstract

This is the author's final version of the contribution published as:[M. Fraldi, G. Perrella, M. Ciervo, F. Bosia, N.M. Pugno, A hybrid deterministicprobabilistic approach to model the mechanical response of helically arranged hierarchical strands, Journal of the Mechanics AbstractVery recently, a Weibull-based probabilistic strategy has been successfully applied to bundles of wires to determine their overall stress-strain behaviour, also capturing previously unpredicted nonlinear and post-elastic features of hierarchical strands. This approach is based on the so-called "Equal Load Sharing (ELS)" hypothesis by virtue of which, when a wire breaks, the load acting on the strand is homogeneously redistributed among the surviving wires. Despite the overall effectiveness of the method, some discrepancies between theoretical predictions and in silico Finite Element-based simulations or experimental findings might arise when more complex bundle structures are analysed, e.g. helically arranged bundles. To overcome these limitations, an enhanced hybrid approach is proposed in which the probability of rupture is combined with a deterministic mechanical model of a strand constituted by helically-arranged and hierarchically-organized wires. The results show that generalized stress-strain responses -incorporating tensile/torsion couplingare naturally found and, once one or more elements break, the competition between geometry and mechanics of the strand microstructure, i.e. the different cross sections and helical angles of the wires belonging to the different hierarchical levels of the strand, determines the no longer homogeneous stress redistribution among the surviving wires whose fate is hence governed by an "Unequal Load Sharing" criterion.

Unveiling a new shear stress transfer mechanism in composites with helically wound hierarchical fibres

“…Following the recent work by Fraldi et al [38], in which the general characterization of hierarchical multi-layer strands was extensively reported, here we investigate the mechanics of a specific structure, namely the simple straight strand constituted by a central core surrounded by one layer of helically wound wires. Let us consider a global coordinate system { } 3 1 2 3 , , x x x ∈ R , with 3…”

“…This result is implicit for the vast majority of the approaches based on Costello's model as well as on other similar models [19,41,25], and is related to the constitutive aspect that links the radial stress to the in-plane shear displacement, although more recent works show the possibility of extending the Argatov-based approach by directly deriving a symmetric stiffness matrix [27]. The constitutive equations ( 12) can easily be generalised to strands with more complex hierarchical arrangements, such as multi-layer and multi-core strands illustrated in Figure 3 [38]. In fact, the particular structure of the stiffness matrix in Eq.…”

“…In the local helical reference system 1 2 3 { , , } e e e (see Figure 1), the unstrained curvatures of the wires in the strand outer layer can be defined as follows [38] As the strand is loaded, each wire deforms by assuming a helical configuration coaxial with the initial helix. The updated curvatures and twist can be expressed as…”

“…Once the closed-form solutions are obtained, we essentially solve a system of algebraic equations to finally establish a direct one-to-one identification of the elastic moduli of the homogenized stiffness matrix of the monoclinic/trigonal composite cylinder with the stiffness coefficients obtained following Argatov [25], thus deriving explicit expressions of the elasticity tensor as a function of wire configuration and geometrical and elastic parameters of the single wires of which the strand is made. Numerical Finite Element (FE) simulations are then performed to highlight the fact that competition between geometry and mechanics of the strand microstructure -affecting the strand rupture probability [38] -if projected at the continuum level and implemented in much less expensive calculations than those required by computational models describing the wires in detail. Further, this interaction also plays a non negligible role in the mechanics of composites reinforced with helical fibres at any scale, influencing magnitude and distribution of shear stresses across the material interfaces in a relevant manner, producing unexpected stress intensifications, triggering the onset of possible failure phenomena and thus determining the mechanical performance of the composites.…”

Finite Element Modeling of Fatigue Life of Steel Wire

“…In addition, some other mechanical characteristics could be obtained. FE modeling is based on dividing any object into very tiny parts called elements, and then each element can be studied separately to determine the applied forces, displacements and other internal and external factors that could affect its mechanical properties [9][10][11][12].…”