Engineering Failure Analysis 14 (2007) 1224–1232
www.elsevier.com/locate/engfailanal
Investigation of service failures of steel music wire
Andrew V. Olver *, Daniel Wilson, P. Shaun J. Crofton
Department of Mechanical Engineering, Imperial College, London, UK
Received 14 July 2006; accepted 20 November 2006
Available online 11 January 2007
Abstract
An investigation of a number of service failures of the hard steel strings of plucked musical instruments is reported. All
the failed strings were found to contain transverse fatigue cracks, mostly located near the end of the vibrating length (e.g.
at the ‘‘bridge’’ of the instrument) and extending to about one third of the section thickness. One wire had corroded
severely before failing in fatigue. Final failure occurred by ductile fracture.
An analysis of the service stresses showed that the strings are subjected to high mean tensile stresses resulting principally
from elastoplastic bending opposite the failure location. It is shown that a small cyclic axial tension arises from repeated
plucking during playing and this can lead to fatigue initiation and propagation over a large proportion of the wire cross
section.
Neither surface nor bulk defects, wear nor contact stresses were found to be factors of importance in the cases examined, contrary to some speculation.
2006 Elsevier Ltd. All rights reserved.
Keywords: Music wire; Fatigue; Plastic bending; SEM
1. Introduction
Many modern musical instruments use high carbon, hard drawn steel wire (‘‘music wire’’). This includes
pianos, harpsichords and many types of fretted instruments such as electric, acoustic and bass guitars, the
mandolin family, banjos and bouzoukis. Still other instruments have strings of nylon or natural products.
At first sight it perhaps seems surprising, from an engineering materials perspective, that very hard steel
and polymers could be used in such similar applications. However, it is easy to show (see later) that the flexural stiffness, even of steel strings, (and hence the importance of the Young’s modulus) is negligible, so the
choice of material is probably determined by acoustic properties (accuracy of pitch, low internal damping),
cost and durability rather than by mechanical properties.
Steel strings, despite their widespread use in popular instruments are moderately prone to in-service breakage, sometimes having only short useful lives. This seems to be a particular problem with guitars and other
*
Corresponding author. Tel.: +44 20 7594 7066.
E-mail address: [email protected] (A.V. Olver).
1350-6307/$ - see front matter 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.engfailanal.2006.11.014
A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
1225
Nomenclature
c
d
e
E
f
l
r
T
y
y 1, y 2
Y
l
r
r0
rz
clearance
diameter of string
strain
Young’s modulus
frequency of vibration (Hz)
scale length (vibrating length of string)
radius of curvature
tensile force
distance co-ordinate, origin at neutral axis
distance of neutral axis from top and bottom of string section, defined in Fig. 7.
yield stress
mass per unit length of string
direct stress
mean tensile stress in wire
axial direct stress
hand-plucked instruments [1]. It was therefore decided to investigate the causes of music string fracture using
techniques of engineering failure analysis, with the objective of establishing the cause(s) of failure and seeking
rational strategies for prevention or life extension.
2. Background
Music wire is high carbon, hard drawn steel wire [2]. Typical treatment involves ‘‘patenting’’ in which the
wire is austenitised and quenched in molten metal or salt [3] leading to an approximately isothermal transformation to a fine pearlite. This is then followed by wire drawing.
In musical instrument strings the wire, used as the central load-bearing element of the string is typically
silver or nickel plated for corrosion resistance and/or wound with secondary (often bronze) wires in order
to achieve the desired mass per unit length. A key requirement is that the string be uniform so that stopped
or fretted notes have frequencies precisely related to the stopped length; wire drawing achieves this for plain
(unwound) strings, as well as providing good surface finish and static strength. Plain strings are usually circular in section but wound strings often use hexagonal core wires. This has the effect of localising the contact
and increasing the local pressure between the core and winding so that stick occurs during use – in turn this
ensures that the structure is stable and minimises frictional damping and fretting damage.
Music wire is also used for spring manufacture and, in lighter gauges, for construction of reinforced elastomer products such as timing belts and automotive tyres. For this reason it is available with closely controlled
static mechanical and fatigue-related properties such as surface finish. ASTM A228 (0.80–0.9% carbon)
requires a minimum UTS of 2600 MPa for 0.3 mm diameter wire [2].
Fretted instruments have the strings stretched over a fingerboard of fixed length, defined by a ‘‘bridge’’
located at the plucked end of the instrument and by a ‘‘nut’’ at the fingerboard end. The bridge and nut
may be metal, bone or polymer and both often contain shallow grooves to locate the string laterally. The
vibrating length, l, of the string between bridge and nut varies typically from 360 mm (mandolin) to
890 mm (long scale bass guitar). Axial tension, T, is applied to the string by means of a machine head and
a variety of end fittings. Fig. 1 shows a typical construction.
In the current investigation, we examined ten failed strings from a variety of instruments by scanning electron microscopy and carried out static tensile tests and metallography on some new strings. We also analysed
service stresses in the strings and considered how they might lead to failure. Results showed that fatigue cracking leading to final ductile fracture was primarily responsible.
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A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
Fig. 1. Schematic of generic fretted instrument, showing location of string, bridge and nut.
3. Experimental investigation
Details of the ten failed strings examined are given in Table 1. Initial examination using an optical microscope showed that many of the strings had fractured in a similar manner with a smooth transverse fracture
surface evident over part of the failed section. The fractures were then examined using a scanning electron
microscope. Typical secondary electron images are shown in Figs. 2–4. All show relatively smooth transgranular fatigue fractures extending to a depth of about one third of the section with origins at the wire surface.
There was evidence of several faint beachmarks (crack arrests) on the fatigue fracture surface (Fig. 2). Beyond
the fatigue crack, there was an area of fibrous fracture with numerous secondary cracks (Fig. 2) and regions of
final fracture (identified as B in Figs. 2 and 3). These showed ductile dimpling typical of ductile fracture by
Table 1
The identities and source of the broken guitar, bass and mandolin strings examined
String no.
(Core) wire diameter
(mm) W = wound
Instrument
Musical note
of open string
Fundamental
frequency (Hz)
Location of fracture
1
2
3
4
5
6
7
8
9
10
0.37 W
0.35 W
0.36 W
0.32
0.17
0.32
0.48 W
0.32
0.17
0.30
Guitar
Guitar
Guitar
Mandolin
Mandolin
Guitar
Bass guitar
Mandolin
Mandolin
Guitar
A
D
A
A
E
B
A
A
E
B
110.0
146.8
110.0
440.0
659.2
246.9
55.00
440.0
659.2
246.9
Bridge
Bridge
Nut
Bridge
Bridge
Nut
Bridge
Nut
Bridge
Bridge
Fig. 2. Secondary electron SEM image of string No. 2. Note the fatigue crack with origin near A and the shear lip at B. The bronze wire
used for the outer winding and the rounded hexagonal form of the core wire are also evident.
A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
1227
Fig. 3. Secondary electron image of string No. 8. The fatigue crack is at top right (probable origin near A) and shear lip below (B). The
feature at C, which is charging strongly in the electron beam, is believed to be a contaminating dust particle. The fatigue crack is on the
outer surface of the lengthwise curve formed where the string has been bent across the bridge. The inset shows ductile dimples in region B
(scale length = 10 lm).
Fig. 4. Fracture surface of string 5. Despite extensive corrosion pitting, there appears to be a region of fatigue fracture with origin (A) at
the outer wire surface.
microvoid coalescence. (Fig. 3, inset) One string showed severe corrosion on the outer surface (Fig. 4) but also
contained a region of flat transverse fracture which had the appearance of fatigue.
A number of new guitar strings were also examined. Static tensile tests were carried out; results are shown
in Table 2. The heavier gauges tested (plain G strings) failed to meet the minimum ultimate tensile stress (UTS)
Table 2
Results of tensile tests on unused strings
Manufacturer
(designation)
Diameter,
mm
Measured UTS,
MPa
ASTM A228 minimum UTS,
MPa
ASTM A228 maximum UTS,
MPa
1
1
1
1
2
2
2
2
0.432
0.254
0.406
0.222
0.421
0.254
0.406
0.230
2221
2755
2333
2892
2353
2754
2095
2852
2450
2650
2450
2680
2450
2650
2450
2680
2700
2950
2700
2980
2700
2950
2700
2980
(G, medium)
(E, medium)
(G, light)
(E, light)
(G, medium)
(E, medium)
(G, light)
(E, light)
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A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
Fig. 5. Microstructure of wire, left: longitudinal section, right: transverse, ·37.
Fig. 6. SEM fractograph of string subjected to tensile test, showing necked ductile fracture.
requirement of ASTM A228. The results were extremely similar for both suppliers, suggesting a common
source of wire.
A scanning electron micrograph of a fractured tensile test wire is shown in Fig. 5. Its appearance is markedly distinct from the service failures having a cup-and-cone appearance typical of ductile fracture and there is
considerable necking and plasticity.
Longitudinal and transverse microsections were prepared of the 0.254 mm diameter wire; the optical microstructures are shown in Fig. 6. They show a fine, probably pearlitic, structure with highly elongated prior austenite grains. These are perhaps reflected in the fibrous region of fracture in the failed wire (Fig. 2), suggesting
a region of microstructurally controlled growth.
4. Analysis
The lowest natural frequency (the fundamental) of a uniform vibrating string with negligible flexural stiffness is dependent only on the axial tension, T, the length, l, and the mass per unit length, l:
f2 ¼
T
4l2 l
ð1Þ
In some electric guitars with low tension steel strings, the flexural stiffness becomes significant. The effect is
first noticeable in the higher harmonics, which show an increased frequency (they become ‘‘sharp’’) due to
the increased stiffness caused by the flexural moments [4]. The fundamental is hardly affected but the ‘‘twangy’’
effect of sharp harmonics is important in some musical genres. In the present instance, we are justified in using
Eq. (1) to find the axial tensile stress.
Since all the failed strings were used in known instruments, f and l were available and l was measured using
a laboratory balance so that T and the mean axial tensile stress, r0 could be found. Results of these calculations are shown in Table 3.
A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
1229
Table 3
Tensile loads and stresses in failed strings
String
no.
(Core) wire diameter
(mm) W = wound
Fundamental
frequency, f (Hz)
Mass per unit
length, l (g/m)
Scale length,
l (mm)
Axial
tension, T
(N)
Axial tensile
stress, r0 (MPa)
1
2
3
4
5
6
7
8
9
10
0.37 W
0.35 W
0.36 W
0.32
0.17
0.32
0.48 W
0.32
0.17
0.30
110.0
146.8
110.0
440.0
659.2
246.9
55.00
440.0
659.2
246.9
3.890
2.010
3.870
0.627
0.477
0.627
8.0 (est)
0.627
0.477
0.551
646.5
646
646.5
362.5
361.5
640
850
362.5
361.5
644.5
78.7
72.3
78.3
63.8
108.3
62.7
69.9
63.8
108.3
55.8
731.9
751.5
769.1
793.7
1771.8
779.0
386.5
793.7
1771.8
790.0
The axial tensile loads do not vary greatly on each instrument since they would otherwise affect the manual
effort needed to fret each string and would cause bending moments on the instrument neck and body. However the tensile stresses are appreciably greater for treble (high frequency) than for bass strings of a given construction and vary from 15% to 65% of the UTS. For a given application and string construction, the tensile
stress does not depend on the diameter of wire selected since the cross-sectional area and the mass per unit
length both vary with the square of the diameter.
Since many of the strings failed near the bridge, at a location where they are bent, apparently plastically
(Fig. 3) the stresses arising from plastic bending were also evaluated. For this purpose it was assumed that
the strings were bent to a known radius, r, dependent upon that of the bridge at the point of contact. The
radius r was measured by inspecting a number of instruments; it varied considerably for different instruments
but a typical value for an electric guitar with a metal bridge was 5.0 mm. Some acoustic instruments had very
sharply curved bridges, with radii perhaps as low as 1.0 mm.
The stresses due to elastoplastic bending of a beam are given for example by Chakrabarty [5]. They consist of regions of compressive and tensile plastic yielding (±Y) each side of an elastic region in which the
stress varies linearly with depth. The actual distribution may be found by considering compatibility with
E
the imposed radius, which yields the slope r
y ¼ r in the elastic region, together with equilibrium of the axial
forces:
Z y2
T ¼
rz ðyÞbðyÞdy
ð2Þ
y 1
Here, b(y) is the width at depth, y, of the circular section and rz(y) is the corresponding axial stress at the same
location. The integral must be evaluated over the range of depths y1 to y2 from the neutral axis. Since the
position of the neutral axis is not known in advance, it is necessary to solve the integral Eq. (2) to find the
unknown depths y1 and y2 for each, known, value of T.
Taking typical values for a treble guitar string, T = 70.9 N, r = 5 mm, Y = 2270 MPa (yield stress, assumed
constant, i.e. perfectly plastic) we find, for d = y1 + y2 = 0.254 mm, that y1 = 0.196 mm and y2 = 0.058 mm.
The width of the elastic zone is 0.114 mm. This stress distribution is plotted in Fig. 7 where it is seen that
around 55% of the wire periphery is subjected to yield magnitude tension.
The forgoing stresses are all predominantly steady so they do not account for the observed fatigue. However, there are two possible sources of cyclic stress. The first is the plucking of the string and subsequent vibration. This is difficult to quantify but it is known that the initial vibration rapidly reduces in magnitude
(‘‘attack’’) and that the maximum displacement during plucking must be less than the clearance, c, between
the string and its neighbours. A typical value of the clearance for a guitar is c = 10 mm; this value would presumably be much less for a mandolin where the strings are in close pairs. As the string shows no flexural stiffness, the bending moment is negligible and the effect of the displacement will be to increase the axial strain, e,
by an amount:
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A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
Fig. 7. Stress distribution in typical treble guitar string at the bridge. (d = 0.254 mm,T = 70.9 N, r = 5 mm, Y = 2270 MPa). A large
portion of the string surface is exposed to yield magnitude tensile stress. The contact with the bridge is at the right. The width of the
compressive plastic zone is slightly exaggerated for clarity.
e ¼ ð2=lÞ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðl2 =4 þ c2 Þ 1 ¼ 2:5 104
ð3Þ
and hence the vibratory axial stress is 49 MPa.
A second source of low cycle vibration is perhaps repeated tuning and detuning of the instrument. This is
again difficult to quantify but it is not impossible that some tens of cycles of 10% of the axial tension are
involved. Many musicians initially apply higher axial tensions to stabilise the attachment of the string at
the machine (tuning) head prior to reducing to the required value (relaxation tuning). This may slightly
increase the effective cyclic stress amplitude and reduce the maximum tensile stress at the bridge. In any case,
it is clear that the vibratory stresses are likely to be small in comparison with the steady mean stress.
Fig. 8 shows a schematic Goodman diagram for a typical fretted instrument string. The allowable stresses
are determined from the (R = 0) fatigue tests on ASTM A228 wire reported in [6] and the Goodman law. The
applied stresses are those calculated for the main portion of the string and those at the bridge.
Finally, we investigate the critical flaw size for rapid fracture in order to investigate the transition from fatigue to final failure. The stress intensity factor for a circular section containing a transverse crack has been
given by James and Mills [7] for a straight-edged crack and by Shih and Chen [8] for an elliptical crack.
Fig. 8. Schematic Goodman diagram for A228 music wire, showing typical operating conditions for treble guitar string.
A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
1231
Fig. 9. Calculated stress intensity factor for typical treble guitar string (0.254 mm diameter) containing a straight-edged transverse fatigue
crack. Fracture is expected when the crack extends to about 1/3 of the wire diameter.
We may adapt this (elastic) analysis to the present case where (at the bridge) there has been yielding by choosing yield magnitude values of tensile stress reduced by a factor of 0.95 to account for relaxation tuning. The
results are shown in Fig. 9; despite the idealisation, the results are sufficient to show why the strings can
accommodate cracks through one third of their section before failure despite the high tensile mean stress.
5. Discussion
The present study shows that the service failures of steel musical instrument strings were due to transverse
fatigue cracks propagating through about one third of the section, followed by ductile fracture. The one failure (Fig. 4) in which there was corrosion also seemed to have fatigue present – indeed it seems that the failure
could have been caused by the external corrosion in the fingerboard region reducing the cross-section and
roughnening the surface. This then acted as a stress concentration and led to fatigue initiation – in other
words, it was corrosion initiated fatigue. However, the absence of intergranular fracture near the origin in
any of the failures shows that stress corrosion was most probably not involved.
The simple analysis carried out suffers from some obvious shortcomings. In the first place, it was extremely
difficult to quantify the cyclic component of stress since this is dependent on playing style and on the stiffness
of pick used for playing the instrument. In addition, the analysis of the plastic bending at the bridge used simple bending theory together with a radius which was both difficult to estimate and potentially comparable with
the string section. It was also not possible to account for residual stresses from wire drawing or other manufacturing process. (One might suppose these to be removed during plastic bending, in any case.) Nevertheless,
the results show why bridge and nut failures predominate. The fracture mechanics analysis is also highly simplified since in reality the section is at or near yield. However it may be argued that the results show why fatigue propagation extends to such a large proportion of the cross section in all the failures despite the very high
axial stress. The fibrous region of fracture arising from the elongated microstructure probably also contributes
to the high effective toughness.
All the wires examined had very good surface quality and no specific surface (or other) defects could be
associated with the fatigue origin. Nor was there any evidence that friction or contact at the bridge relevant
since the failures were on the tensile side of the bend, well away from the contact. Many of the wires had thin
(few lm) surface coatings of silver, nickel or tin (core wires of wound strings [1]) and these may have acted to
reduce fatigue strength or affect mechanical properties but the effect is probably marginal for thin coatings,
correctly applied.
In addition to the often repeated call for musicians to play softly (and minimise the cyclic stresses!) two
features stand out as possible remedies. One is that the strength of the thicker wire was quite low compared
to ASTM A228 requirements. In general, the thicker strings are lower stressed over the majority of their length
than are the thinner ones (Table 2) but this conclusion does not apply to the bridge location where, as we have
seen, plastic bending occurs. The cyclic stresses are also just as high in thicker strings and the Goodman diagram suggests that strength level is potentially critical. It may be of benefit if all wires were made to A228
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A.V. Olver et al. / Engineering Failure Analysis 14 (2007) 1224–1232
strength levels – experience in other applications (springs) suggests this would be optimum for fatigue
properties.
Secondly, the musicians’ practice of relaxation tuning, where new strings are initially overtightened and
allowed to relax may be beneficial. In principle, this will reduce the mean stress in the tensile plastic region
where initiation occurs. A snag is that often, axial displacements of the string occur due to settling-in of
the attachment points so that the pre-stressed and relaxed region may no longer be near the bridge. A cautious
over-tightening, of say 10–20%, after the tuning has stabilised but before fatigue cracking has started, may be
beneficial for string durability. This could be achieved by tuning to a few semitones sharp and relaxing back to
concert pitch.
6. Conclusions
Examination of a number of service failures of guitar, electric bass and mandolin, steel (music wire) strings
by SEM show that fatigue was the main cause of failure. The failures were associated with plastic bending at
the bridge or nut of the instruments. Analysis showed that the fatigue occured at very high mean stress
although the small diameter meant that fatigue cracks occupied a high proportion of the fractured cross-section. One example may have failed by a corrosion fatigue initiation mechanism.
Possible remedies include increasing strength levels for the thicker wires and careful use of relaxation tuning. Contact or friction properties did not seem to be important in the failure process.
References
[1] Fields G. Myths and Misconceptions about Strings, Ozark Steel Guitar Association Newsletter No. 19, GFI Musical Products,
reprinted www.GFIMusicalProducts.com, viewed July 2006.
[2] Dove AB. Steel Wire, in ASM Handbook, vol1, Properties and selection: irons, steels, and high performance alloys, http://
products.ASMinternational.org, viewed July 2006.
[3] ASTM committee A1 on steel stainless steel and related alloys, standard specification for steel wire, Music Spring Quality, ASTM
A228/A 228M – 90, ASTM, West Conshohocken, 2000.
[4] Braddick HJJ. Vibrations, waves and diffraction. Maidenhead: McGraw-Hill; 1965. p. 143.
[5] Chakrabarty J. Theory of plasticity. New York: McGraw-Hill 1987, ISBN 0-07-010392-5.
[6] Godfrey L. Steel Springs, in ASM Handbook, as Ref. [3].
[7] James LA, Mills WJ. Review and synthesis of stress intensity factor solutions applied to cracks in bolts. Engineering Fracture
Mechanics 1998;30:641–54.
[8] Shih Y-S, Chen J-J. The stress intensity factor of an elliptical[ly] cracked shaft. Nuclear Engineering and Design 2002;214:137–45.