Finite element simulation of a steel cable - rubber composite under bending loading: Influence of rubber penetration on the stress distribution in wires

• Published in: International journal of solids and structures 2019-03, Vol.160, p.158-167
• Main Authors: Bonneric, Matthieu, Aubin, Véronique, Durville, Damien
• Format: Article
• Language: English
• Subjects: Adhesive bonding; Bending loading; Cable simulation; Computer simulation; Elastoplasticity; Engineering Sciences; Finite element method; Materials and structures in mechanics; Mathematical analysis; Mathematical models; Mechanics; Multiscale approach; Penetration; Rubber; Rubber penetration; Shearing; Steel cables; Steel cord - rubber composite; Stiffness; Stress concentration; Stress distribution; Three dimensional models; Wire
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2018.10.023

Fatigue design of cables requires to assess the stresses of individual wires during in-service loadings. Specific applications need steel cables to be embedded in a rubber matrix. In such cases, the adhesive bonding between wires and matrix might impact the stress distribution in wires. This paper presents a finite element model of cable coated with a rubber matrix subjected to a bending loading. Wires are represented with a strain beam model taking into account for non linear phenomena, such as contact friction between wires and elastoplastic behavior. A 3D model for the matrix surrounding the cable is coupled with the beam model. The impact of matrix penetration inside the cable is also studied. This work proposes a multi-scale approach to account for local interactions between infiltrated matrix and wires under bending loading in the coated cable model. The behavior of infiltrated matrix subjected to a shearing loading induced by longitudinal inter-wire displacements is investigated using both analytical calculations and local FE simulations with ABAQUS software. Based on the results at the microscopic scale, “junction” elements are introduced in the coated cable model to account for matrix penetration, by coupling neighbor wires’ displacements. The model is compared with experimental measurements of cables slightly and fully penetrated by matrix. The influence of matrix penetration on the stress distribution is eventually discussed. It is found that the limitation of inter-wire motions due infiltrated matrix induces tensions in wires, which are responsible for increases of the bending stiffness and of the maximum stresses in wires.