Any assembly of wires spun into a helical formation (either as a strand or a wire rope), when subjected to a tensile load, can extend in three seperate phases, depending on the magnitude of the applied load:

    Phase 1: initial extension
    Phase 2: elastic extension
    Phase 3: permanent extension (thermal elongation and contraction, rotation, wear and corrosion)

Phase 1 and 2 are very important because they are a normal part of the rope bedding in and working of the rope. Phase 3, on the other hand, can be caused by the wrong choice of rope or lack of rope inspection. The phases occure in sequence in all ropes that are exposed to a gradual increased load. Due to this a new rope, when overloaded, will go through phase 1 and 2 before the third phase (permanent extension) begins.

Phase 1: Initial or permanent extension
This phase of extension of the rope depends on the construction of the rope and can be explained as follows:

When loading a new product, extension is created by the bedding down of the assembled wires with a corresponding reduction in overall diameter. This reduction in diameter creates an excess length of wire which is accommodated by a lengthening of the helical lay.

When sufficientely large bearing areas have been generated on adjacent wires, to withstand the circumferential compressive loads, this mechanically created extension ceases and the extension in phase 2 commences.

The initial extention can not be accurately determined and depends on, apart from the strand or the rope construction, the various loads and the current load frequency.

It is not possible to quote any exact values for various constructions but the following approximate values can be used to give reasonably accurate results.

Load

Safety Factor Extension in % of the total length of rope
    Rope with Fibre core Rope with steel core
Lightly loaded 8 0.25 0.125
Normally loaded 5 0.5 0.25
Heavily loaded 3 0.75 0.5
Heavily loaded with many "bends" 2 Up to 2 Up to 1

 

Phase 2: Elastic extension (elongation)
Following Phase 1, the rope extends in a manner which complies approximately with Hookes Law, i.e. stress is proportional to strain. 

The proportionality factor normally is a material constant called Modulus of Elasticity (E-modulus). To steel wire ropes the E-modulus is more of a construction constant than a material constant. 

The elastic extension can be calculated as follows (Hookes law): 

Elastic extension (mm) = (W x L) / (E x A)

W = applied load (kg)
L = rope length (mm)
E = elastic modulus (kg/mm2)
A = area of rope - circumscribed circle (mm2)

The modulus of elasticity varies with different rope constructions. Due to  specific manufacturing factors, wire dimensions and other factors, the E-modulus varies between different wire ropes of the same construction and dimension. If the exact E-modulus value of a certain rope is necessary a specific modulus test needs to be done for that rope.

The elastic extension is valid until the proportionality or elasticity limit is reached. Once the load exceeds this limit , extension according to phase 3 takes place. The elasticity limit is defined as the largest force where the rope returns to its original length when unloaded.

General E-module of the rope construction

Type of steel wire rope E-Module
  kp/mm2
Spiral strand, type 1x7 12600
Spiral strand, type COMPACTED 1x7 14000
Spiral strand, type 1x19 10900
Spiral strand, type COMPACTED 1x19 13600
6-part single constructions with fibre core, e.g. 6x7 FC 6300
6-part single constructions with steel core, e.g. 6x7-WRC 7000
6-part assemblies with fibre core, e.g. 6x36-FC 5000
6-part assemblies with steel core, e.g. 6x36-IWRC

 

6000
Compacted constructions with steel core, e.g. ROPETEX 6 6400
Compacted constructions with steel core, e.g. DSC-DYFORM 7900
Multi strand, rotation resistant constructions, e.g. 18x7 4200
Multi strand, rotation resistant constructions, e.g. 35x7 6900
Multi strand, rotating resistant compacted constructions, e.g. ROPETEX 88 7200
Elevator rope TRULIFT 8F (8x19S-FC) 4000
Elevator rope TRULIFT 8SPC (8x19S-SPC) 

4300

Elevator rope TRULIFT 8S (8X19S-IWRC)/TRULIFT 9S (9X 19S-IWRC) 6000

 

These values are valid for ropes operating with a safety factor of 5:1. With  lower safety factors the modulus of elasticity indicated are increased and for higher safety factors they reduce.

Phase 3: Permanent extension
The permanent, non-elastic extension of the steel caused by tensile loads exceeding the yield point of the material. If the load exceeds the Limit of Proportionality, the rate of extension will accelerate as the load is increased, until a loading is reached at which continuous extension will commence, causing the wire rope to fracture without any further increase of load.

Thermal Expansion and Contraction
The coefficient of linear expansion (∝) of steel wire rope is 0.0000125 = (12.5 x10-6) per o C and therefore the change in length of 1 metre of rope produced by a temperature change of t o C would be;
Change in length Δ| = ∝ |o t
where:
∝ = coefficient of linear expansion
|o = original length of rope (m)
t = temperature change (o C)
The change will be an increase in length if the temperature rises and a decrease in length if the temperature falls.

Extension due to Rotation
The elongation caused by a free rope end being allowed to rotate.

Extension due to Wear
The elongation due to inter-wire wear which reduces the cross-sectional area of steel and produces extra constructional extension.

Example:
The total elongation of a 200 m length of steel wire rope type 28 mm 265-wires (6x36-IWRC) at a tension of 10 tonnes (safety factor 5:1) and with an increase in temperature of 20°C.

According to phase 1:
Permanent constructional extension = 0,25% x total rope length = 0,25% x 200 m = 500 mm.

According to phase 2:
Elastic extension = (W x L) / (E x A) = (10000 x 200000) / (6000 x 615,4) = 540 mm.

According to phase 3:
Thermal expansion = 0,0000125 x L x t = 0,0000125 x 200 x 20 = 50 mm.

Total extension = 500 mm + 540 mm + 5+ mm = 1090 mm.