Engineering Failure Analysis 91 (2018) 234–242
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Engineering Failure Analysis
journal homepage: www.elsevier.com/locate/engfailanal
Steel wire ropes failure analysis: Experimental study
⁎
T
Houda Mouradi , Abdellah El Barkany, Ahmed El Biyaali
Mechanical Engineering Laboratory, Faculty of Science and Technology, University Sidi Mohammed Ben Abdellah, Fez, Immouzer Road, B.P.2202 Fez,
Morocco
A R T IC LE I N F O
ABS TRA CT
Keywords:
Non-rotating rope
Damage
Fraction of life
Static tests
Ultimate residual forces
Steel wire ropes are structural elements which occupy central functions in the industrial, maritime and civil engineering domain. They consist of several steel wires twisted together to make a
structure with huge mechanical properties combining axial strength and stiffness with bending
flexibility. In the great majority of applications, steel wire ropes are subjected to several mechanisms of damage. These mechanisms can lead to the premature break of the rope components
causing its sudden and unexpected failure. In this context, the aim of this paper is to characterize
the mechanical behavior of the wire rope in service along with monitoring the evolution of its
damage in order to facilitate the determination of the conditions of use reliably. For this, an
experimental study was presented in order to trace the evolution of the non-rotating rope 19 × 7
damage and to define its different stages as well as the critical fraction of life which can lead to
sudden failure of this wire rope. The adopted approach is proactive and facilitates the prediction
of the rope failure based solely on static tests and without doing any dynamic tests. Indeed, this
approach is based on the application of two models of damage: The static damage which consists
in tracking the evolution of the residual ultimate forces taken at different percentages of the life
of the test specimen. The second model of damage is that which is based on the reduction of the
strength and the endurance limit of damaged wire rope according to the unified theory. This
technique is highly desirable in the industrial field so as to establish a rigorous maintenance
system as well as to ensure the ability to work in a safe reliable environment.
1. Introduction
The effective use of steel wire ropes goes back to 1836 thanks to Wilhelm Albert engineer. Ever since, the use of these ropes has
known tremendous growth and has had significant effects on several industrial applications, such as lifting loads, suspended bridges,
elevators, boat caching… They have enormous mechanical properties combining a capacity to support important axial loads, a
torsional stiffness and a bending flexibility [1]. Moreover, unlike other structures such as bars, wire ropes consist of several elements;
their composition offers the advantage of not breaking suddenly [2]. Thus, they can fulfill their task in spite of the breaking of one
component or more. This point is very important in order to ensure that the wire rope is tough in a sense that it is tolerable to having
local damages that take the form of, mainly, broken wires or strands.
However, in spite of the advantages offered by these cables, they ought to be considered as elements of wear with limited lifespan.
On a factual point, cables in service are subjected to several mechanical solicitations which can cause local deformations or degradations along with environmental ones causing corrosion of steel wires [3]. Consequently, companies very often have recourse to
reducing the probability of unexpected failure of such a structure so as to guarantee a smooth running of their activities but most
⁎
Corresponding author.
E-mail address: houda.mouradi@gmail.com (H. Mouradi).
https://doi.org/10.1016/j.engfailanal.2018.04.019
Received 10 October 2017; Received in revised form 6 April 2018; Accepted 12 April 2018
Available online 19 April 2018
1350-6307/ © 2018 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 91 (2018) 234–242
H. Mouradi et al.
Nomenclature
Ds
Fu
Fur
Fa
β
n
Nf
Δσ
σ0
σu
F0
D
Static damage
Value of the ultimate force in the initial state
Value of the ultimate force for different percentages of damage
Value of the breaking force of the last strand of the
outer layer
Fraction of life
Instantaneous number of cycles under an applied
ni
N
stress
Number of cumulated cycles at breaking
Amplitude of solicitation
Endurance limit of the virgin material
Ultimate stress
Endurance limit of the virgin cable
Damage which is equal to 0 for neat material and 1
for complete damage
Number of broken strands in the outer layer
Total number of the outer strands
importantly, ensure the staff security. In fact, this is the role of the preventive maintenance which takes place before the probable
date of occurrence of any critical damage.
In this context, several experimental studies have recently been carried out to characterize and predict the mechanical behavior of
lifting steel wire ropes. Meksem [4] presented works on the reliability of a wire rope damaged by fatigue at different percentages of
its wires. Then, Mouhib [5] carried out experimental tests on a strand extracted from a wire rope and artificially damaged at different
levels of its wires. In the comparative study done by Boudlal et al. [6], the residual strength of the central core strand was evaluated in
relation to that of the outer strands. In addition, Meknassi et al. [7] was interested in the corrosion of the wires constituting the wire
rope. Following this study, Tijani et al. [8] compared the residual force of an artificially damaged strand with that of another
damaged by corrosion.
Otherwise, the aim of this work is to characterize the mechanical behavior of the entire wire rope in service. Indeed, the evolution
of the non-rotating rope 19 × 7 damage is monitored according to the number of broken strands as well as the evaluation of its
gravity. This technique is highly sought by the industrials so as to predict the useful lifespan of this structure and to be able to deposit
it at the appropriate time.
For this, an experimental study was carried out to trace the evolution of the non-rotating rope 19 × 7 damage and to define its
different stages as well as the critical fraction of life which can lead to the failure of this wire rope. This study was based on tensile
tests that were performed on virgin specimens and others that are artificially damaged at different levels of their strands.
2. Experimental procedure
The examined cable is the 19 × 7 non-rotating rope type of 7 mm diameter, with a metallic central core strand and crossed to the
right (Fig. 1). This structure consists of two layers of strands wired in opposite directions, which makes it possible to avoid the
rotation of the suspended load under important hoisting heights. Generally, the geometric composition of non-rotating ropes is
chosen so that the turning torque of the steel core and the outer strands cancel each other in a wide load range. It avoids in this way
Fig. 1. Non-rotating wire rope of 19 × 7 type (1 × 7 + 6 × 7 + 12 × 7).
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H. Mouradi et al.
the kinking of the ropes. This cable construction is robust in nature and widely used in the industrial field, mainly, in lifting applications.
The main geometrical and mechanical characteristics of the studied wire rope are presented in Table 1.
The objective of this experimental study is to track the mechanical behavior of the non-rotating rope 19 × 7 in service. Thus,
static tests have been performed on virgin samples of cables and others that are artificially damaged at different levels of their
strands. This damage was realized by means of cutting a well-defined number of strands constituting the sample as illustrated in the
Fig. 2. According to ISO 3108, a length of 600 mm was taken as the test length for all cable samples.
The experiment consists in subjecting cable samples to tensile tests according to the ISO 3108 international standard prescriptions. The samples were tested with imposed displacement corresponding to a deformation rate of 2 mm/min; that is under ambient
conditions of air and temperature. These tests were realized by fixing firmly the sample in the MTS 64.106 tensile machine with a
capacity of 1000 kN as illustrated in Fig. 3. Also, the mobile cylinder shifts with a constant velocity (2 mm/min) until the end of the
test which coincides with the breaking of the sample.
3. Theory
3.1. Residual force loss ratio
The virgin wire rope supports an ultimate static force Fu. As the number of broken strands increases, this force decreases progressively and receives different values Fur (Table 2). Thus, the residual force loss ratio is given by the following expression [9]:
Residual force loss ratio =
|Fur − Fu |
∗100
Fu
(1)
In what follows, we will use two models of damage: The static damage which consists in tracking the evolution of the residual
ultimate force taken at different percentages of the life of the test specimen. The second model of damage is that which is based on the
reduction of the strength and endurance limit of damaged wire rope according to the unified theory.
3.2. Static damage
The static damage model consists in tracking the evolution of the residual ultimate force which varies according to the level of
damage. The static damage is presented by the variable Ds expressed in terms of the following relationship [5]:
F
Ds =
1 − Fur
u
F
1 − Fa
(2)
u
3.3. Damage according to unified theory
The various theories representatives of damage are initiated by a linear model called Miner's law [10], according to which the
damage is independent of the loading levels and evolves linearly according to the fraction of life β. This is the most common and used
model adopted by the international codes like ASME and ISO. This law is expressed as below:
D = β = n/ Nf
(3)
This approach overestimates the damage and says that the material failure occurs when the history of solicitations it underwent,
caused partial damage such that their sum is equal to one.
p
D=∑
i=1
ni
=1
Ni
(4)
Table 1
Principal geometrical and mechanical characteristics of the 19 × 7 non-rotating rope.
Nominal cable diameter
Construction
Wiring direction
Core nature
Young modulus
Poisson coefficient
Category of material
Mass per unit length
Minimum breaking force
Dn = 7 mm
- Strands construction: 1 + 6
- Cable construction: 19 × 7 (1 × 7 + 6 × 7 + 12 × 7)
- Left wiring in the inner layer
- Right wiring in the outer layer
Metallic
200 GPa
v = 0.3
Galvanized
0.27 Kg/m
33 kN
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Fig. 2. Artificial cutting of a strand constituting the cable sample.
Fig. 3. Assembly of the cable sample in the MTS 64.106 tensile machine.
Table 2
Values of ultimate forces and endurance limits of damaged cables.
Number of broken strands
Residual ultimate forces (kN)
Endurance limit (kN)
0
33.94
5.65
2
30.54
5.09
4
25.69
4.28
6
22.15
3.69
8
19.01
3.16
10
15.03
2.5
12
13.08
2.18
Moreover, several models have been developed to show the nonlinear character of damage. Among these nonlinear models, is the
unified theory [11] which synthesizes the works of Sorensen [12], Valluri [13] and Shanley [14]. This theory is based on the
reduction of the strength and endurance limit of the material during the process of damage. It evaluates the impact of cumulative
damage at different loading levels. It is a theory that was employed in different research works to study the materials strength,
namely: Steel wire ropes [5–9], high density polyethylene pipes [15] and polypropylene random copolymer [16]. The expression of
damage according to this theory is given as follows:
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D=
β
γ
m
⎛ γ − ⎛ γu ⎞ ⎞
β + (1 − β ) ⎜ γ⎝− 1⎠ ⎟
⎜
⎟
⎝
⎠
(5)
with β = n/Nf, γ = Δσ/σ0, γu = σu/σ0 and m = 8 for metallic materials.
By analogy with this theory, an empirical relation describing the damage based on the reduction of the residual ultimate forces
and the endurance limit is proposed, given by:
D=
β
m
( )
δ
⎛δ −
⎞
β + (1 − β ) ⎜ δ −δu1 ⎟
⎝
⎠
(6)
n
with: β = Ni , δ = Fur/F0, δu = Fu/F0 and m = 8 for metallic materials.
4. Results and discussions
4.1. Characterization of the mechanical behavior of artificially damaged cables
After subjecting the test samples to the static tensile tests, we obtained the curves presented in the Fig. 4. This later shows the
superposition of the tensile curves of the virgin samples of cables and others that are damaged at different levels of their outer
strands.
The tensile curves depicted in Fig. 4 indicate the drop of the supported load caused by the damage of the test specimens showing
thus residual ultimate forces Fur. In fact, the virgin cable has an ultimate force of Fu = 33.94 kN that gradually decreases, as the
number of broken strands increases, until reaching Fur12 = 13.08 kN; a value corresponding to the total damage of the outer layer
strands of the test sample.
The Fig. 5 shows the loss of the residual ultimate force (in percentages) caused by the artificial damage of the test specimens,
ranging from 1 up to 12 broken strands constituting the outer layer.
After a graphical reading of Fig. 5, we can notice that the residual force loss ratio increases gradually as the number of broken
strands increases. Indeed, the total damage of the outer strands results in a loss of 61% of the ultimate force supported by the cable.
As a result, the damaged cable will no longer be operational and must be removed immediately.
Generally, the outer layer of the wire rope is that which is the most exposed to environmental and mechanical external aggression.
It is thus subjected to wear, abrasion, corrosion, etc. In fact, it is for this reason that we have confined our next study to the damage of
the outer layer of the cable so as to study its mechanical behavior.
Nevertheless, compared to the external strands, internal ones can be quickly affected. This phenomenon cannot be easily perceived due to its discrete nature. Therefore, it is assumed that the layers remain intact; the outer layers not being included.
4.2. Evolution of the residual ultimate force and endurance limit in static tensile testing
The virgin wire rope supports an ultimate static force Fu. This force decreases progressively and receives different values (Fur) as
the number of broken strands increases. Finally, it receives a critical value Fa which corresponds to the force just before the breaking.
Fig. 4. Superposition of the tensile curves of virgin and artificially damaged cable samples.
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Fig. 5. Loss of the ultimate residual force caused by the damage of test specimens.
The wire rope has also an endurance limit F0, this limit decreases as the number of broken strands increases. Finally, upon
breaking, it eventually receives a critical value called the critical endurance limit F0*.
Note that the endurance limit is equal to the ultimate force multiplied by the α coefficient equivalent to the inverse of the rope
safety coefficient. The coefficient of use of the wire ropes that are intended for our experimentation is equal to 6 [17]. This gives
α = 0.16.
Hence
(7)
F0 = α. Fu
The values of the residual ultimate forces taken from Fig. 4 and the corresponding endurance limits calculated from Eq. (7) are
given in Table 2:
The decrease in both the residual force and the endurance limit of the damaged cables are schematically illustrated in Fig. 6,
according to the fraction of life β = ni/N corresponding to the proportion of the number of broken strands in the outer layer (ni) and
the total number of the outer strands (N).
The curves in this figure describe the decrease of the residual ultimate force in static tensile testing and that of the endurance limit
according to the fraction of life β. Actually, the virgin cable has an ultimate force Fu = 33.94 kN and an endurance limit F0 = 5.63 kN
which gradually decrease, as the number of broken strands increases, until reaching critical values Fa = 13.08 kN and F0* = 2.18 kN,
corresponding to the total damage of the outer strands of the cable.
4.3. Quantification of static damage
The static damage evolution is monitored for various levels of degradation starting with the virgin state up until the last strand of
the outer layer breaks (Eq. (2)). The evolution of the static damage according to the percentages of broken outer strands is depicted in
Fig. 7.
The observed increase in damage implies the loss of the samples strength in static tensile test. This loss becomes more relevant as
Fig. 6. The diminution of the ultimate force and the decrease of the endurance limit for pre-damaged cables at different levels of their outer strands.
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Fig. 7. Evolution of static damage according to the percentages of broken strands in the outer layer of the test samples.
the percentage of broken strands in the outer layer increases.
According to Fig. 7, we can identify three damage stages by dint of the change of curve. The first stage corresponds to its
initiation; up to β = 25% of damage of the external layer (which is the equivalent of three broken strands), the damage increases
slowly. Then, stage II is achieved and is located in the interval β = [25%, 67%]. In this zone, the damage becomes progressive and
predictive maintenance is imposed on the industrialist. Finally, we find stage III which is characterized by a critical fraction of life
βc = 67% of damage of the external layer, corresponding to eight broken strands. Beyond this point, the progressive damage suddenly accelerates and the rupture of the sample can be brutal.
4.4. Quantification of damage by unified theory
By analogy with the unified theory, an empirical relation Eq. (6) based on the reduction of the residual ultimate forces and
endurance limit is used for describing the damage of the wire rope. The results of the damage calculated by this theory according to
the fraction of life β for different loading levels δ are presented in Fig. 8.
It is noted that the concavity of the damage curves is accentuated for low loading levels. However, they tend gradually towards
linearity (Miner rule) for higher loadings. This proves that the Miner rule overestimates the damage. This may justify the simplicity
and the safety in the use of Miner's law in comparison with other theories.
4.5. Comparison of the two damage models
Fig. 9 illustrates the comparison of the static damage calculated from Eq. (2) and that according to the unified theory Eq. (6) for
pre-damaged cables samples at different levels of their outer strands.
This comparative study of the two methods of damage calculation shows that the curve of static damage coincides with that of
Miner rule throughout Stage I. However, it takes off in Stage II and Stage III to settle beyond Miner curve. In general, the average gap
Fig. 8. Variation of the damage according to the unified theory for different loading levels δ.
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Fig. 9. Comparison of the damage according to the unified theory with the static damage.
of damage remains remarkably negligible and is equal to about 0.067. This deviation can be explained by the fact that the damage
accelerates at the expense of reliability in these two latter stages. Moreover, it is clear that Miner curve lies between that of the static
damage and those of the unified theory. This is the reason for that the Miner rule is the most common and used model adopted by the
international codes like ASME and ISO.
5. Conclusion
In order to reduce the probability of sudden failure of steel wire ropes in service, we have been brought to characterize their
mechanical behavior along with monitoring the evolution of their damage in order to facilitate the determination of the conditions of
use reliably. For this, an experimental study was carried out to trace the evolution of the non-rotating rope 19 × 7 damage. Then,
based on the two damage models, we were able to define the different stages of this wire rope damage as well as the critical fraction
of life which can lead to critical damage of such a rope. The first stage I, corresponding to its initiation, up to β = 25% of damage of
the outer strands (which is equal to three broken strands), the damage grows slowly. Then, at stage II, which is in the interval
β = [25%, 67%], the damage becomes progressive until stage III is initiated. This latter is characterized by a critical fraction of life
βc = 67% of damage of the outer layer, corresponding to eight broken strands. Beyond this point, the rupture of the sample can be
sudden and the removal criteria shall intervene. This technique is widely sought in the industrial field so as to predict the useful
lifespan of this structure and to be able to deposit it at the appropriate time.
In the next work, we will compare these experimental results with our analytical model developed previously [18] that estimates
the reliability of the non-rotating rope 18 × 7 at various levels of damage of its strands.
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