Static response of asymmetrically damaged metallic strands: Experimental and numerical approach
Introduction
A strand can be a critical structural member in many engineering applications, including cranes, lifts, mine hoisting, bridges, cableways, electrical conductors, offshore mooring systems and so on. Different classes of strands, suited for different purposes, have a different number and arrangement of strand components within the strand cross-section in which the components can be made of different materials. Over the years, each field of strand application has developed a specific body of knowledge, based on extensive testing and field experience, leading to empirical rules for each particular application. Unifying these empirical rules under some general mathematical and mechanical theory would allow a better understanding, and in the long term, a better prediction of the mechanical behavior of strands as well as reduce the need for expensive tests under a variety of operating conditions. Thus, due to their extensive use and the need to predict their behavior, several researchers have presented analytical models that permit the calculation of rope response based on the strand component material and geometry [1].
Strands made of filaments drawn from ductile metals are widely used as structural components. In particular, the extensive use of steel wire strands for load bearing components is mainly due to the strength offered by steel coupled with the flexibility of strand construction, strand geometry and wire size that can be suited to the required application. On the other hand, aluminium-based strands are widely used in transmission lines (conductors) due to their high conductivity to weight ratio leading to reduce the size of the support structures. In any of the applications previously mentioned, strands are subjected to various loading conditions. Although a strand is essentially an element for transmitting a tensile load, its construction is such that the individual wires in a strand are subjected to bending and torsional moments, frictional and bearing loads, as well as tension. The magnitude and distribution of the stresses resulting from these loadings determine the overall strand/conductor response, which can be expressed in terms of the extension and rotation of the strand/conductor [2]. In the following, the descriptions given are valid for both steel strands and aluminium conductors unless otherwise specified; hence, just strand is used hereafter to avoid repetitive use of the term strand/conductor.
Strands experience damage throughout their loading history and from continued aggression of the environment (urban, industrial, marine, heat exposure, chemical, etc). The process by which damage occurs can be represented through a degradation of the properties of individual strand wires, and it can also include the complete rupture of one or more wires. The understanding of the interaction of the factors that induce damage to strand and their dependence on strand operational conditions are essential to estimate strand service life at the design stage and to establish the appropriate strand inspection methods and discard criteria. Hence, the service life of a strand can be greatly extended by following a planned program of installation, operation, maintenance, and inspection. In this context, damage-tolerance property (i.e., the ability of a strand to withstand damage) is an essential parameter for strand design, strand evaluation during operational service, and for developing discard criteria according to strand usage based on the residual strength and deformation capacity that the damaged strand can sustain [3].
Symptoms of strand degradation, which are related to the most common discard criteria utilized to remove damaged strands after inspections, are the number of broken wires, reduction in strand diameter, excessive corrosion, and strand deformation (waviness, birdcage, loops, loose wires, nodes, and kinks among others) [4], [5], [6]. Experimental [7], [8], [9], [10], [11] and numerical [12], [13], [14], [15] studies on metallic strands, mainly conducted on steel wire ropes, have intended to determinate the ability of particular types of strand constructions to withstand damage (i.e., damage-tolerance property). More precisely, considering a variety of wire breaks distribution, strands constructions, and loading conditions, aforementioned works have mainly focused on the determination of the residual strength [7], [8], [12] and axial strain field on strands cross-sections and along the length of the strands [9], [10], [13], [14]. Others have monitored damage evolution to establish reliable conditions of damaged strands use [10], [11], [15]. The results of previous studies have shown that, in particular, the impact of broken strand components on overall strand response (stiffness, residual strength, deformation capacity, and deformed configuration) depends on the length of the strand, number of broken strand components (degree of damage or damage level), type of strand construction, and their distributions throughout the strand cross-section (symmetric and asymmetric) and along the strand length. For the purpose of this study, damage is referred to the presence of fully ruptured wires in the strand cross-section.
In this paper, the effect of a particular damage distribution on metallic (steel and aluminium) strand static response is assessed through experimental tests and numerical simulations. The damage is asymmetrically distributed on the outermost strand layer to simulate surface damage (degradation due to corrosion, abrasive wear, and fatigue among others). To this end, a general mechanical model for multilayered strands asymmetrically damaged on their surfaces is presented, in which damaged strands are treated as a 1D nonlinear beam under uncoupled biaxial bending and axial load (NLBM). This proposed model is an extension of the model presented in [16], originally developed for single-layer ropes, to account for multilayered strand geometry, which is validated by comparisons with experimental data and 3D nonlinear finite element simulations. Experimental data are obtained from tensile tests conducted on galvanized steel and aluminium strands asymmetrically damaged on their surfaces. The validation process of the NLBM accounts for two strand constructions: 1 × 7 and 1 × 19, whose diameter values range from 3.5 mm to 22.2 mm and the damage levels from 5% to 43% relative to the virgin cross-section, in which damage is artificially inflicted at strands midspan by cutting a prescribed number of wires. The analyses performed validate the extended model which is used to interpret and extend the experimental data reported in this study. As such, a robust and computational efficient numerical tool to assess damage-tolerance property of metallic strand asymmetrically damaged on their surfaces is presented. This tool may assist in quantifying the variations in performance of damaged strands that should be anticipated when predicting service life and in evaluating the coupling of some of the discard criteria parameters used in strands that are built into many standards such as the number of broken wires, waviness, and residual strength.
Section snippets
Experimental set up and materials
Steel (ST) and aluminium (AL) strands are tested in this work. Steel strands cross-sections consist of six wires helically wrapped around a straight central wire (core)(ie., 1 × 7 = 1 + 6 strand). On the other hand, two types of cross-sections are considered for the aluminum strands specimens: (1) 1 × 7 strands and (2) a single straight wire (core) followed by six and twelve helically wound wires in two concentric layers (i.e, 1 × 19 = 1 + 6 + 12 conductor). Geometrical parameters and minimum
Numerical approach
In the particular case of ropes (metallic and synthetic fiber) asymmetrically damaged, some efforts have been made in order to numerically and analytically assess the impact of damage on their response [10], [12], [16], [17], [18]. This information could be later utilized to establish if the structural integrity of the damaged strands, and also the integrity of the structural system that they are part of, is compromised. In the current study, the model proposed by Beltran and De Vico [16],
Discussion of experimental results
In this section, the main results drawn from the experimental program conducted on asymmetrically damaged steel strands and aluminium conductors (hereafter referred as strands) are presented. In addition, the proposed model (NLBM) is used to extend and interpret the aforementioned experimental data along with performing an additional validation process of it.
Comparisons of the measured and predicted (by NLBM) capacity curves and axial strain distributions in the unbroken wires for some of the
Conclusions
In this paper, a robust and computational efficiency numerical model is proposed to estimate the static response of multilayered strands asymmetrically damaged on their surfaces. The proposed model relies on the assumption that a strand asymmetrically damaged on its surface behaves as a 1D nonlinear beam under uncoupled biaxial bending and axial load along with the fact that strand wires are mainly in radial contact. The proposed model is validated by comparisons with the results provided by 3D
Conflicts of interest statement
The authors of this manuscript confirm that there are no known conflicts of interest associated with this publication.
Acknowledgements
This work was supported by Fondecyt (Chile) Grant N° 1150409. The authors gratefully acknowledge this funding. The help of Mr. Pedro Soto and Victor Gonzalez during the experimental program is also deeply appreciated.
References (34)
- et al.
Steel wire ropes failure analysis: experimental study
Eng. Fail. Anal.
(2018) Wire recovery length in a helical strand under axial-fatigue loading
Int. J. Fatigue
(1991)- et al.
Static and dynamic response of elastic suspended cables with damage
Int. J. Solids Struct.
(2007) - et al.
Assessment of static rope behavior with asymmetric damage distribution
Eng Struct.
(2015) - et al.
Effect of broken rope components distribution throughout rope cross-section on polyester rope response: numerical approach
Int. J. Mech. Sci.
(2012) - et al.
Simplified analysis of the influence of strain localization and asymmetric damage distribution on static damaged polyester rope behavior
Ocean Eng.
(2017) - et al.
A concise finite element model for simple straight wire rope strand
Int. J. Mech. Sci.
(1999) - et al.
Full 3D finite element modelling of spiral strand cables
Constr. Build. Mater.
(2012) - et al.
finite element study of behavior and interface force conditions of seven-wire strand under axial and lateral loading
Constr. Build. Mater.
(2014) - et al.
Modeling of helically stranded cables using multiple beam finite elements and its application to torque balanced design
Constr. Build. Mater.
(2017)
An analytical approach to model the hysteresis bending behavior of spiral strands
Appl. Math. Model.
Modeling multilayered wire strands, a strategy based on 3D finite element beam-to-beam contact-Part I: model formulation and validation
Int. J. Mech. Sci.
Mechanical models of helical strands
Appl. Mech. Rev.
A survey literature on the behaviour of wire ropes
Wire Ind.
The fatigue and degradation mechanisms of hoisting ropes
Discard criteria for mine winder ropes, Report GAP502, Safety in Mines
Res. Advisory Committee
fourth edition
Cited by (11)
Hydroelastic analysis of an elastic thin-walled structure obliquely impacting a calm water surface
2024, Thin-Walled StructuresSimplified analysis of damage evolution in surface-damaged metallic strands: Uncoupled approach
2022, Engineering Failure AnalysisCitation Excerpt :At wire level, as damage index depends on the strain levels (Eq. (1)), it is expected that for the case of asymmetric initial surface damage distribution, for a given strand axial strain, a non-uniform damage evolution takes place within the strands cross-sections. This is due to the gradient in wires strain profile as a result of the induced bending for this type of initial damage pattern as reported in [22,24,37]. In this context, wires next to the inflicted damage (cut wires; Fig. 4a and d) start accumulating damage for lower strand axial plastic strain values than the opposite ones, and consequently, developing more damage.
Evaluation of the coupled effect of strain localization and asymmetric damage distribution on rope response: Numerical approach based on a nonlinear cable-beam element
2020, Engineering StructuresCitation Excerpt :Previous steps carried out are bed-in the ropes, inflict prescribed damage level at ropes midspan, and cycle the ropes to simulate storm loading. As in previous works ([13,20,21]), the degree of asymmetry of the damaged cross-section is captured by a scalar quantity termed the index of asymmetry (IA). This parameter accounts for the shift of the center of stiffness of the damaged cross-section relative to the intact rope cross-section due to the asymmetric distribution of damage.