Optimization and Evaluation of Crucial Properties for Stainless Steel Wire Used as Guitar Strings

M A S T E R’S T H E S I S

2005:264 CIV

SINA VOSOUGH

Optimization and Evaluation of Crucial Properties for Stainless Steel Wire Used as Guitar Strings

MASTER OF SCIENCE PROGRAMME Physics

Luleå University of Technology

Department of Applied Physics and Mechanical Engineering

Division of Physics

Master’s Thesis

“Optimization and Evaluation of Crucial Properties for Stainless Steel Wire Used as Guitar Strings”

Sina Vosough

CONFIDENTIAL INFORMATION

Division of Physics Lulea University of Technology

SE-97187 Lulea Sweden

© Copyright by Sina Vosough, 2005

Abstract

The musical wire is a topic not well explored and almost no earlier reports could be found about it. Therefore, many experimental methods and testing machines had to be invented. One of them being the unusual relaxation machine built from scratch. Many different experiments have been carried out for the understanding of a good guitar string, few of which showed to be of little or no interest.

An ordinary guitar string is made of regular high carbon steel alloy drawn to different wire diameters. Carbon steel has many good qualities but also some major drawbacks. The corrosion properties of carbon steels are not as good as stainless steels’, on the other hand it is easier to draw carbon steels to higher tensile and yield strengths without encountering brittleness.

The result of this project shows that Audioflex and SAF2205SH two of many Sandvik stainless steels tested, are well suited for the musical wire application. Although they have quite different properties in many ways, both can be used as guitar strings. The former for electric guitars and the latter as acoustic guitar strings.

These stainless steels are very likely in the soon future to be a big revolution for the guitar string

business.

Acknowledgements

First of all I would like to thank my parents Shahla Soltanieh and Manouchehr Vosough for their guidance and never ending support. Without you I wouldn’t have found the interest and ever lasting passion for physics.

I am also very thankful to Dr. Johan Hansson for many mind opening discussions and his pedagogical support throughout my time at Lulea University of Technology. And also I would like to express thanks to Prof. Sverker Fredriksson for his openness and educational guidance throughout my time as a student.

I also thank Anders Söderman, my thesis advisor, for giving me the most interesting project of all and his endless support throughout the Master’s Thesis.

I would like to thank my fellow student Erik Setterqvist both for his help and support, but also for all the exciting conversations and interesting exchange of ideas throughout our time as

classmates.

Finally, a word of gratitude goes to the following people for their support throughout my time as a student:

Prof. Lech Melagrande, Dr. Nils Almqvist, Dr. Marta-Lena Antti, Reinhold Näslund, Jan Andersson and Viola Nilsson.

Thank you all,

Sina Vosough

Sandviken

October 11, 2005

“There are two things that are infinite. The stupidity of man and the universe...

- and I'm not sure about the universe!”

Albert Einstein

Contents

CHAPTER 1 INTRODUCTION ... 7

1.1.BACKGROUND... 7

1.1.1. Master’s Thesis: ... 7

1.1.2. A Presentation of Sandvik: ... 7

1.2.PURPOSE... 8

1.3.METHOD... 8

CHAPTER 2 THEORETICAL BACKGROUND ... 9

2.1.THE PHYSICS OF MUSICAL SOUND... 9

2.1.1. Background: ... 9

2.1.2. Historical Background: ... 9

2.1.3. Sound Waves: ... 9

2.1.4. Transverse Vibrations in Musical Instruments:... 10

2.1.5. The Wave Equation: ... 12

2.1.6. The Relation between Frequency and Tension in a String: ... 14

2.1.7. The Human Hearing:... 16

2.2.THE GUITAR... 17

2.2.1. History of the Guitar: ... 17

2.2.2. The Modern Acoustic Guitar: ... 18

2.2.3. Electric Guitars: ... 19

2.2.4. Strings, Frets and Compensation: ... 20

2.3.STAINLESS WIRE PRODUCTS... 22

2.3.1. Presentation of Sandvik Wire: ... 22

2.3.2. Stainless Steel:... 23

2.3.3. SAF2205SH: ... 24

2.3.4. 1RK91 Nanoflex: ... 24

CHAPTER 3 EXPERIMENTS ... 25

3.1.EXPERIMENTAL BACKGROUND... 25

3.2.HEAT TREATMENT AND SURFACE FINISHING... 25

3.2.1. Heat treatment of 1RK91 versus time:... 26

3.3.YIELD AND TENSILE STRENGTH... 26

3.4.SPECTRAL ANALYSIS (ACOUSTIC SPECTRUM)... 27

3.5.MAGNETIC RESONANCE... 27

3.6.RELAXATION... 29

3.7.CHEMICAL COMPOSITION AND SURFACE ANALYSIS (SEM)... 31

3.8.CORROSION... 32

3.9.MICROSTRUCTURE... 33

3.10.GDOES... 33

3.11.SOUND CHECK... 34

CHAPTER 4 RESULTS ... 35

4.1.HEAT TREATMENT OF 1RK91 VERSUS TIME... 35

1RK91 ∅ 0,254 mm ... 35

1RK91 ∅ 0,43 mm ... 36

4.2.YIELD AND TENSILE STRENGTH... 37

4.3.MAGNETIC RESONANCE... 38

4.4.RELAXATION... 39

4.5.CHEMICAL COMPOSITION (SEM) ... 42

4.6.SURFACE ANALYSIS (SEM) ... 42

4.7.MICROSTRUCTURE... 42

4.8.GDOES... 42

4.9.SOUND CHECK... 49

CHAPTER 5 CONCLUSION ... 50

CHAPTER 6 DISCUSSION... 51

SYMBOLS ... 52

APPENDIX ... 53

I.MAGNETIC RESONANCE RESULTS... 54

II.CHEMICAL COMPOSITION (SEM) ... 61

Sample 1. Elixir Plain Steel ... 62

Sample 2. Fender Stainless Steel 350s ... 63

Sample 4. GHS Plain Steel ... 64

Sample 5. D’Addario PL017 Plain Steel ... 65

Sample 6.1. D’Addario EXLS510 Stainless Steel ... 66

Sample 6.2. D’Addario EXL110 Plain Steel... 67

Sample 7. Ernie Ball Custom Gauge 1017 Plain Steel ... 68

Sample 8. D’Aquisto Electric/Acoustic 0.13 Plain Steel ... 69

III.SURFACE ANALYSIS (SEM) ... 70

Elixir... 71

Fender 350s ... 72

GHS ... 73

D'Addario PL... 74

D'Addario EXLS510 ... 75

D'Addario EXL110 ... 76

Ernie Ball ... 77

D'Aquisto ... 78

SAF2205SH ... 79

1RK91 Audioflex... 80

IV.MICROSTRUCTURE... 81

Elixir... 81

GHS ... 81

D'Addario PL... 82

Ernie Ball ... 82

1RK91 Audioflex... 82

SAF2205SH ... 83

V.SAMPLE NAMES AND NUMBERS: ... 84

VI.MATHEMATICAL CALCULATION OF A GUITAR STRING: ... 85

VII.WIRE DRAWING:... 88

BIBLIOGRAPHY... 90

Verbal Contacts:... 90

Literature: ... 90

Chapter 1

Introduction 1.1. Background 1.1.1. Master’s Thesis:

An ordinary guitar string is made of regular high carbon steel alloy drawn to different wire diameters. Carbon steel has many good qualities but also some major drawbacks. The corrosion properties of carbon steels are not as good as stainless steels’, on the other hand it is easier to draw carbon steels to higher tensile and yield strengths without encountering brittleness. Sandvik produces mostly stainless steel and would like to broaden their market in the wire manufacturing field. Due to the fact that stainless alloys have high corrosion resistance and often better surface finishing and good relaxation properties, they could be a good choice for many string

instrumentalists worldwide. With the properties that a stainless steel alloy have, one can get longer lasting strings that rarely need tuning. The biggest drawback on using stainless steels for musical instruments are their low yield and tensile strength properties compared to that of carbon steels. Another important drawback is the insufficient magnetic properties of stainless steels, whereas the carbon steels are almost 100% ferromagnetic. The loading of the high E guitar string is about 1500 MPa, and lower for the lower strings. High carbon steel music wire is drawn typically in the 2700 - 3000 MPa range. An average stainless steel wire is drawn to about 1500 - 2200 MPa. This means that a regular stainless steel can not be used as a guitar string. Therefore, a better and reinforced alloy is needed if one wants to use stainless steel as an option.

Sandvik have earlier been evaluating stainless wires used for piano. After a long evaluation process, a stainless steel alloy patented by Sandvik 1RK91, also known as Nanoflex but for the guitar application named Audioflex, was earlier tested for the piano application. Nanoflex is highly complex mar-aging steel. It met all the strength demands but according to the piano manufacturer the sound of the string was “different”. And this was enough for the piano maker not to use these strings, because in the long run it would lead to an undesirable modification of the piano.

The background of this Master’s Thesis derives from a growing interest, both from Sandvik as a steel manufacturer and from the guitar string manufacturers, of finding an alternative to the carbon based wire used on musical instruments today. Sandvik have been contacted many times from different manufacturers on the market throughout the years, regarding stainless wires used for string instruments such as piano, violins and guitars, but have never had the time to evaluate the possibility of meeting those demands. Based on these premises this project was launched.

1.1.2. A Presentation of Sandvik:

Sandvik is a high-technology, engineering group with advanced products and a world-leading position within selected areas. Worldwide business activities are conducted through

representation in 130 countries. The Group has 38 000 employees and annual sales of

approximately SEK 55 billion. The Sandvik Group is firmly committed to research. In 2004, SEK

1,900 M (4% of annual sales) was invested in research and development and quality assurance, an area which employs more than 2,200 persons. The Sandvik Group is concentrated to three core areas.

1. The Tooling business area focuses mainly on tools and tooling systems for metalworking applications. Major customers include companies in the automotive and aerospace industries.

2. Mining and Construction specializes in rock-working equipment and tools used in mining and civil engineering worldwide.

3. Materials Technology develops mainly products in stainless steel, special alloys and resistance heating materials as well as process systems. Customers are to be found in most industrial

segments.

1.2. Purpose

The purpose of this Master’s Thesis is to optimize the existing stainless steel alloys Sandvik produces for a forthcoming guitar application, and also to find the crucial properties for defining a good guitar string. Another purpose was to do a comparison between already established strings on the market for widening the understanding of guitar strings as a whole.

1.3. Method

During my literature study I noticed that the area of musical wire was not well explored. A lot

could be found on guitar bodies and violin constructions but not on the strings themselves. This

made the approach much harder, due to the fact that I could not find any other earlier research

done on the subject. Many of the experiments carried out were based on pure intuition with an

engineering approach. The main approach was to map the guitar strings behavior in all aspects,

everything from plucking the string to its corrosion properties and overall lifetime. To find all the

important parameters and properties for the string was also of big importance.

Chapter 2

Theoretical Background 2.1. The Physics of Musical Sound 2.1.1. Background:

This Master’s Thesis will concern mainly the guitar string. But still the physics involved is of a wider use, therefore, it is necessary to explain the background.

2.1.2. Historical Background:

Musical sound or acoustics as known nowadays, is a word that entered the English language in the seventeenth century, the century which Galileo wrote about musical sound. Today papers in the Journal of the Acoustical Society of America are divided into categories, some of which have little relation to music, such as “Underwater Sound”, or “Ultrasonic, Quantum Acoustics, and Physical Effects of Sound”. In the Greek and Roman worlds music, including whatever was known about musical acoustics, held a high place in science and philosophy. Quadrivium, the higher division of the seven liberal arts in the Middle Ages, composed of geometry, astronomy, arithmetic, and music. The place of music in the liberal arts was above that of grammar, rhetoric, and logic, which constituted the lower trivium that dealt with words rather than numbers. As time passed music’s status became more complicated. Through the nineteenth century scientists studied music and musical sound with insight as well as aesthetic appreciation. In this century as well as the twentieth century some musicians have looked to science and technology for new directions in music. The greatest influence of science on music has come through the

development of means for recording and reproducing the sounds of music played on conventional music instruments. Today the computer and digital technology in general are working fantastic changes in the recording and transmission of sound, and in the generation of musical sound. The musical instruments have also been improved greatly in both range and quality. In part, this improvement resulted from (1) the development of better, more easily playable instruments; (2) the increasing skill of instrumentalists; and (3) an expansion of the range of musical sound.

2.1.3. Sound Waves:

The definition of a wave is an energy-carrying disturbance propagated through a medium by a progressive local disturbance of the medium but without any overall movement of matter. Waves can be found in many different forms such as water waves, sound waves or electromagnetic waves. Although the physical mechanism may be different for each of these waves, they all have a common feature: they are physical disturbances that are produced at one point in space,

propagated through space, and produce an effect later at another point. Naturally this Master’s Thesis will concern the sound wave. The propagation of sound is similar to the propagation of

1The Science of Musical Sound by J.R Pierce pp 1-5

ripples that move outward when a raindrop falls into a quiet pool. However, sound waves do not travel merely on a surface, but through the air in all directions. The air in a sound wave does not move bodily but locally. This means that when sound waves propagate the air imparts motion to the air ahead and so on. This distribution of disturbance leads to the propagation of sound waves in the air. Thus, we can think of a single sound wave as an expanding shell of compression.

Successive layers of air are compressed and decompressed as a wave moves outward from the source of disturbance, but each individual air molecule moves only a little distance out and back.

A vibrating string sends out a series of expanding shells of compression. If the string vibrates fast enough and with enough force, we can hear the succession of shells as a tone. There are two basic types of wave motion: longitudinal waves and transverse waves. A wave in which the vibrations are in the direction of propagation of the wave is called longitudinal, whereas for transverse waves vibrations are perpendicular to the propagation of the wave. Examples of transverse waves are those seen on a vibrating string such as a guitar string, water waves, and electromagnetic waves including visible light. The guitar string and water waves vibrate in one direction and thus are called linear waves. Electromagnetic waves vibrate in all directions.

2.1.4. Transverse Vibrations in Musical Instruments:

In the case of musical instruments such as guitars the transverse vibrations are of interest. All waves in a guitar string travel with the same speed (v = constant), so the waves with different wavelengths have different frequencies. The mode with the lowest frequency (f

) is called the fundamental, and the nth mode has frequency n times that of the fundamental. The term harmonics refer to modes of vibration of a system that are whole-number multiples of the fundamental mode, and also to the sounds they generate. The frequencies f, 2f, 3f, 4f etc are called the harmonic series. This series is familiar to most musicians. The relationships among the frequencies of these modes are explained in Fig. 2-2. For a wave, the frequency is the ratio between the speed of the wave to the wavelength, hence:

λ

f = (2.1) v

The strings on musical instruments are fixed at the ends and the stable, controlled vibration is produced by a standing wave. Standing waves are produced whenever two waves of identical frequency interfere with one another while traveling opposite directions along the same medium.

Standing wave patterns are characterized by certain fixed points along the medium which undergo no displacement. These points of no displacement are called nodes. If a force is applied to pull the string to the left, the kink that travels away to the left will come back as a kink to the right - the reflection is inverted. This effect is important not only in string instruments, but in winds and percussion as well. When a wave encounters a boundary with something that won't move or change (or that doesn't change easily), the reflection is inverted. A guitar string behaves in this fashion. You pull the string out at one point, and then release it as shown in Fig. 2-1. If

2The Science of Musical Sound by J.R Pierce pp 24-38

you look carefully, you will see the shape traced out by the kink (indicated by the thin line in Fig.

2-1) as it moves along the string in both directions.

Fig 2-1. A sketch of the reflection of traveling kinks caused by plucking a string. The bold line represents the string, and the thin line is the path traced out by the kink. At the instants represented by (d) and (j), the string is straight so it has lost the potential energy associated with

pulling it sideways, but it has a maximum kinetic energy. Note that, at the reflections, the phase of the kink is changed by 180°: from up to down or vice versa.

As said earlier the string on a musical instrument is fixed at both ends, so any vibration of the string must have nodes at each end. That limits the possible vibrations. For instance the string with length L could have a standing wave with wavelength twice as long as the string

(wavelength λ = 2L) as shown in Fig. 2-2. This gives a node at both ends and an antinode in the middle. This is one of the modes of vibration of the string ("mode of vibration" just means style or way of vibrating).

Fig. 2-2. A sketch of the first four modes of vibration of an idealized stretched string with a fixed length.

Compared to the string length L, you can see that these waves have lengths 2L, L, 2L/3, L/2. We could write this as 2L/n, where n is the number of the harmonic. By using equation (2.1) we can get the following formulas for a fixed string at both ends.

3http://www.phys.unsw.edu.au/~jw/strings.html

The fundamental or first mode has frequency f

= v/ λ = v/2L, The second harmonic has frequency f

= v/ λ

= 2v/2L = 2f

The third harmonic has frequency f

= v/ λ

= 3v/2L = 3f

,

The fourth harmonic has frequency f

= v/ λ

= 4v/2L = 4f

, and, to generalize, The nth harmonic has frequency f

= v/ λ

= nv/2L = nf

.

So for the nth harmonic we have the following expression

L n v f

= 2 (2.2)

The rest of this chapter will only concern the frequency of the first harmonic on a guitar string which is for n = 1

L f v

= 2 (2.3)

2.1.5. The Wave Equation:

The relation between frequency and tension in a string can be derived in many ways. But the most fundamental derivation is probably from the famous wave equation.

2

0

2 2 2 2

∂ =

− ∂

∂

∂

x v y t

y (2.4)

Where the displacement y(x,t) of the string depends on both the time t and the position of the string x, v is the propagation velocity of the transverse string. The general solution of Eq. (2.4) is

) ( ) ( ) ,

( x t f

x vt f

x vt

y = − + + (2.5)

This can be easily proved by applying the change rule for derivatives. Consider next a wave in a string subject to a tension T. Under equilibrium conditions the string is straight (Fig. 2-3).

Suppose now that the string is displaced sidewise or perpendicular to its length by an amount small relative to the length as shown in Fig. 2-4

Fig. 2-3. A guitar string under equilibrium conditions, no displacement of the string, therefore,

the string is straight.

Fig. 2-4. A section of the string, of length dx that have been displaced a distance y from equilibrium position.

Consider a section AB of the string, of length dx, that has been displaced a distance y from the equilibrium position. On each end of section AB, a tangential force T is acting: the one at B is produced by pull of the string on the right: and the one at A, by the pull of the string on the left.

Because of the curvature of the string, the two forces are not directly opposed. The vertical or Y- component of each force is T´

= T sin θ

and T

= - T sin θ

. The resultant normal force on section AB of the string is

) sin (sin θ

− θ

= T

F

(2.6)

If the curvature of the string is not very large, the angels θ

and θ

are small; and the sines can be replaced by tangents. So the normal or transverse force in the upward direction is

) tan (tan θ

− θ

= T

F

(2.7)

this may also be written as

x dx T Td

F

(tan θ

) (tan θ

)

∂

= ∂

= (2.8)

where the partial derivative is used because tan θ

depends not only on the position x but also on the time t. However, tan θ

is the slope of the string; and by definition the slope is equal to ∂y/∂x.

Then

x dx T y x dx y T x

F

2

)

( ∂

= ∂

∂

∂

∂

= ∂ (2.9)

This force must be equal to the mass of the section AB times its upward acceleration which is

∂

y/ ∂t

. Given that µ is the linear density of the string, or mass per unit length, expressed in kg/m,

the mass of the section AB is µ dx; and based on Newton II, the equation of motion of this

section of the string may be written as

x dx T y t

dx y

2 2

2

)

( ∂

= ∂

∂

µ ∂ ^(2.10)

we rewrite this expression to

2 2 2

2

x T y t

y

∂

= ∂

∂

∂

µ ^(2.11)

And here we se the wave equation (2.4), verifying that a transverse disturbance in a string propagates along the string with a velocity

µ

v = T (2.12)

where µ, as said earlier, is mass per unit length

L

= m

µ ^(2.13)

Note that Eq. (2.11) takes into account only transverse motion of the string because there is essentially no motion along the string. To se this point, consider the resultant force parallel to the X-axis

) cos (cos

cos

cos θ

− θ

= θ

− θ

= T T T

F

(2.14)

For a very small angel cosine is essentially one. Therefore we can approximate cos θ

≈cos θ

≈ 1.

Thus we get F

= 0 so that there is no net force parallel to the X-axis and therefore no resultant motion of the string in the x-direction.

2.1.6. The Relation between Frequency and Tension in a String:

By combining the equation (2.2) with (2.12) and (2.13) we get the final relation between the frequency ƒ and the tension T for a transverse vibrating string.

L L m n T f

= 2 (2.15)

4The Eq. (2.11) can be as said earlier derived in other ways, for more information please se “Physics for Scientists and Engineers by Lawrence S.

Lerner. p569-573”

This is the equation for transverse vibrating strings. All stringed instruments are tuned by adjusting the tension T of the string. If T is increased the frequency will increase. On the other hand one sees easily that a shorter string with length < L gives a higher frequency ƒ if same tension is applied. When a guitar string is depressed on one side of a fret, the string does not vibrate on that side; the rest of the string, being shorter than the whole, then produces a higher note when it is plucked.

If we now rewrite the equation (2.15) (n = 1, for the first harmonic) to obtain the expression for the tension T

( ) L Lf m

T = 2

(2.16)

We know that mass is equal to density ρ multiplied by volume V V

m = ρ (2.17)

The volume V for a long cylindrical wire is

4

* *

2

2

d L

L r

V = π = π (2.18)

Combining equation (2.16) (2.17) (2.18) we get an expression for the tension T in a guitar string

( ) ^Lfd

πρ

T = (2.19)

rewrite

Ld T

f ₌ πρ _(2.20)

Because of the fact that guitar string manufacturers use the tension of the strings in kg we must divide equation (2.19) by the constant g according to Newton II.

fLd g

T

= ( )

πρ (2.21)

Now we have the final expression for the tension T [kg] related to the frequency ƒ, the total

length L of the string, the diameter of the guitar string d and the density ρ of the specific material

used.

2.1.7. The Human Hearing:

The human auditory system is complex in structure and remarkable in function. Not only does it respond to a wide range of stimuli, but it precisely identifies the pitch and the timbre (quality) of a sound and even the direction of the source. The range of pressure stimuli to which the ear responds represents a variation of over a million times. The energy content of an extremely loud sound is about 10

times greater than of the weakest sound that can be heard. At some

frequencies, the vibrations of the eardrum may be as small as 10

mm, about one tenth of the diameter of the hydrogen atom.

Usually "sound" is used to mean sound which can be perceived by the human ear, i.e., "sound" refers to audible sound unless otherwise classified. A reasonably standard definition of audible sound is that it is a pressure wave with frequency between 20 Hz and 20,000 Hz. The normal human ear can detect the difference between 440 Hz and 441 Hz.

5The Science of Sound, Second Edition, Thomas D. Rossing, Chapter 5.1 6http://hyperphysics.phy-astr.gsu.edu/hbase/sound/earsens.html

2.2. The Guitar 2.2.1. History of the Guitar:

The guitar is an ancient and noble instrument, whose history can be traced back over 4000 years.

Many theories have been advanced about the instrument's ancestry, but the most probable one is that the guitar has its roots from the ancient Persian instrument setar.

It has often been claimed that the guitar is a development of the lute, or even of the ancient Greek kithara. Research done by Dr. Michael Kasha in the 1960's showed these claims to be without merit. He showed that the lute is a result of a separate line of development, sharing common ancestors with the guitar, but having had no influence on its evolution.

The name "guitar" comes from the ancient Sanskrit word for "string" - "tar". (This is the

language from which the languages of central Asia and northern India developed.) Many stringed folk instruments exist in Central Asia to this day which has been used in almost unchanged form for several thousand years, as shown by archaeological finds in the area. Many have names that end in "tar", with a prefix indicating the number of strings:

Two = modern Persian "do"

dotar, two-string instrument found in Turkistan, Three = modern Persian "se"

setar, 3-string instrument, found in Persia (Iran),

The Indian sitar almost certainly took its name from the Persian setar, but over the centuries the Indians developed it into a completely new instrument, following their own aesthetic and cultural ideals.

Four = modern Persian "char"

chartar, 4-string instrument, Persia (most commonly known as "tar" in modern usage) (cf. quitarra, early Spanish 4-string guitar, modern Arabic qithara, Italian chitarra, etc) Five = modern Persian "panj"

panjtar, 5 strings, Afghanistan

The four-stringed Persian chartar arrived in Spain, where it was changed somewhat in form and construction and became known as the quitarra. The old Spanish quitarra originally had four pairs of strings. This was increased to 5, and later 6 pairs of strings, the pairs becoming single strings along the way. By this time the Spanish name had also mutated to guitarra.

7This information is widely known in the Middle Eastern countries but for some reason it is not known in the western cultures.

8http://www.guyguitars.com/eng/handbook/BriefHistory.html

2.2.2. The Modern Acoustic Guitar:

The establishment of the guitar as a concert instrument took place largely in the nineteenth century. Fernando Sor (1778-1839) was the first of a long line of Spanish virtuosos and composers for the guitar. The Spanish luthier (craftsman who makes stringed instruments) Antonio de Torres (1817-1892) contributed much to the development of the modern classical guitar. Francisco Tarrega (1852-1909), perhaps the greatest of all nineteenth century players, introduced the apoyando stroke and generally extended the expressive capabilities of the guitar.

The modern guitar, shown in Fig. 2-5, has 6 strings, about 65 cm in length, tuned to low E, A, D, G, B and the high E (ƒ = 82, 110, 147, 196, 247 and 330 Hz). The top is usually cut from spruce or redwood, planed to a thickness of about 2,5 mm. The back, also about 2,5 mm thick, is usually a hardwood, such as rosewood, mahogany or maple. Both the top and back plates are braced where the bracing of the top plate being one of the critical design parameters. Acoustic guitars generally fall into one of four families of design: classical, flamenco, flat top and arch top.

Classical and flamenco guitars have nylon strings; flat top and arch top guitars have steel strings.

A certain type of bracing called fan bracing is shown in Fig. 2-6.

Fig. 2-5. These two pictures show the anatomy of two types of acoustic guitars. The picture to the left shows a classical nylon-stringed guitar, the one to the right is a steel-stringed acoustic

guitar.

Fig. 2-6. There are various designs for bracing a guitar soundboard. This is a traditional fan bracing. Bracing is important for the sound of the guitar.

2.2.3. Electric Guitars:

Although it is possible to attach a contact microphone or some other type of pickup to an acoustic

guitar, the electric guitar has developed as a distinctly different instrument. Most electric guitars

employ electromagnetic pickups, although piezoelectric pickups are also used. Electric guitars

may have either a solid wood body or a hollow body. The vibrations of the body are relatively

unimportant, and since the strings transfer relatively little energy to the body, electric guitars are

characterized by a long sustain time. The solid-body electric guitar is less susceptible to acoustic

feedback than an amplified acoustic guitar or a hollow-body electric guitar. The electromagnetic

pickup consists of a coil with a permanent magnet. The vibrating steel strings cause changes in

the magnetic flux through the coil, thus inducing electrical signals in the coil. The signals are

then transferred to a guitar amplifier where the signal is processed and amplified. Most pickups

provide a separate magnet pole piece for each string. The pole pieces, which are adjustable in

height, are usually set to be about 1,5 mm below the vibrating string.

Fig. 2-7. Here is a schematic picture of the different parts of electric guitars. The electric guitar is very thin compared to an acoustic guitar, this is because no resonating body is needed for the

production of the sound. The magnetic pickups transfer the vibration of the strings to an amplifier who amplifies the sound.

Most electric guitars have two or three pickups mounted at various positions along the strings that favor various harmonics. The front pickup (nearest the fingerboard) provides the strongest

fundamental, whereas the rear pickup (nearest the bridge) is more sensitive to higher harmonics.

Switches or individual gain controls allow the guitarist to mix the signals from the pickups as desired.

2.2.4. Strings, Frets and Compensation:

Strings for the modern classical and flamenco guitars are made of nylon, replacing the gut strings used in the past. The three highest strings are usually monofilament nylon, while the three lowest strings have nylon cores wrapped with a metal winding. Flat top or folk guitars use steel wire for the highest two strings and sometimes the third, whereas the remaining strings have steel cores wrapped with steel (carbon steel), nickel-steel, bronze or stainless steel. Usually the wrapping is composed of a fine wire of circular cross section (“round-wound” strings), but sometimes a flat ribbon of stainless steel is used for the wrapping (“flat-wound” strings). Other variations are the

“flat-ground” string (wound with round wire that is then ground flat), and compound strings with a winding of silk between the steel core and metal outer windings.

The major disadvantage of steel (carbon steel) strings is corrosion, and many attempts to arrest corrosion have been done with no success. Ideas of coating the steel strings with different materials such as natural and

9The Science of Sound, Second Edition, Thomas D. Rossing, Chapter 10.15

synthetic polymers have been done. Unfortunately any form of coating decreases the strings vibrations leading to reduced brightness and deteriorated sound quality.

Spacing the frets on the fretboard presents some interesting design problems. Semitone intervals on the scale of equal temperament correspond to frequency ratios of 1,05946. This is very near the ratio 18/17, which has led to the well-known rule of eighteenth. This rule states that each fret should be placed 1/18 of the remaining distance from the specific fret to the bridge. Therefore the fret spacing decreases as one moves down the fretboard. Since the ratio 18/17 equals 1,05882 rather than 1,05946 (an error of about 0,0690), each semitone interval will be slightly flat if the rule of eighteenth is used to locate the frets. By the time the twelfth fret is reached, the octave will be 12 cents (12/100 semitone) flat, which is noticeable to the ear. Thus, for bets tuning, the more exact figure 17,817 should be used in place of 18; in other words, each fret should be placed 0,05613 of the remaining distance to the bridge.

Another problem in guitar design is the fact that pressing down a fret increases the tension slightly. This effect is much greater in steel strings than nylon, since a much greater force is required to produce the same elongation. Fretted notes will tend to be sharp compared to open ones. The greater the clearance between strings and frets is the greater this sharpening effect will be. To compensate this change in tension in fingering fretted notes, the actual distance from the nut to the saddle is made slightly greater than the scale length used to determine the fret spacings.

This small extra length is called the string compensation, and it usually ranges from 1 to 5 mm on acoustic guitars bur may be greater on electric guitars. Some electric guitars have bridges that allow easy adjustment of compensation for each individual string.

10The information in chapter 2.2. The guitar, has mainly been taken from the book ”The Physics of Musical Instruments” by N.H. Fletcher T.D.

Rossing Chapter 9. Guitars and Lutes.

2.3. Stainless Wire Products 2.3.1. Presentation of Sandvik Wire:

Sandvik’s wire business is primarily concerned with the development, manufacture and distribution of wire in stainless steels and high-alloyed materials. Sandvik is one of the largest producers in the world of stainless wire, and for some products they are world leaders. The standard diameter range for drawn wire is 0.10 – 12 mm. However, production is flexible and upon agreement sizes outside this range, closer tolerances and a wide range of special steel grades can be delivered. Sandvik concentrate on niche products where their long experience and know-how can be fully utilized.

Spring wire:

Springs are the wire product we encounter every day. Under each button – on the computer keyboard, the ball pen or pencil, the telephone, the radio, the aerosol can or in the car – there is a spring. But springs are also used for thousands of other applications. We deliver spring wire in a number of stainless grades, both standard and special. Our standard size range is 0.15 – 10 mm.

From this wire our customers coil springs, which can be divided into 4 groups depending on the function and use of the spring: Compression springs, Tension springs, Torsion springs and Formed springs. These springs need high elasticity to fulfill their tasks, and therefore we supply the wire with suitable mechanical properties. We offer different surface finishes and delivery forms according to the spring manufacturers’ requirements.

Welding wire:

Our products are being used either for joining two pieces of metal – with the same or different composition – or for surfacing, i.e. providing a construction (often of carbon steel) with a corrosion- or wear-resistant layer, which imparts improved properties to the construction.

The size range comprises all commonly used dimensions, and we offer suitable delivery forms for all type of welding, including mechanized and robot-operated, within all types of industry.

Welding is used in nearly every sector of industry. We have a comprehensive range of round wire, and some bought products (sourced from outside the company), which cover most applications where stainless steels and high-alloyed grades are concerned.

Precision wire:

Precision wire covers all types of drawn, round wire. By this we mean products that are not classified as spring wire or welding wire. This is where you find all the new, exciting applications requiring special attention from the mills. The precision-wire factory is therefore set up to be as flexible as possible in order to satisfy the requirements prescribed for the customers’ applications.

The requirements involved in precision-wire applications vary. They can be on mechanical or corrosion properties, physical properties such as thermal or magnetic, machining or cold-heading properties. If necessary, we can manufacture to the customer’s specification upon special

agreement.

These wires are used in a wide variety of applications, for instance, medical (surgical needles), in the petrochemical industry, as free cutting steel and flat products just to mention few.

2.3.2. Stainless Steel:

The stainless steel was invented in 1913, at the research laboratory of Brown-Firth, Sheffield, England by Harry Bradley. He had been investigating ways to reduce corrosion in gun barrels, when it was noticed that a discarded sample was not rusting.

A stainless steel is defined as steel that has at least 12% chromium in its composition. The chromium makes the steel both resistant to oxidation (rust) and corrosion, hence the name

“stainless” steel. The corrosion resistant property derives from the fact that the chromium produces a thin oxide layer which prohibits further corrosion. An alloy with a composition of 12- 13% chromium can resist normal corrosion attacks from fresh water and diluted nitric acid (in room temperature). A higher composition of chromium makes the corrosion resistant stronger and more durable against corrosive attacks from more aggressive environments.

As said high oxidation resistance in air at ambient temperature is normally achieved with additions of more than 12% (by weight) chromium. The chromium forms a layer of chromium (III) oxide (Cr

O

) when exposed to oxygen. The layer is too thin to be visible, meaning the metal stays shiny. It is, however, impervious to water and air, protecting the metal beneath. Also, when the surface is scratched this layer quickly reforms. When stainless steel parts such as nuts and bolts are forced together, the oxide layer can be scraped off causing the parts to weld together.

This effect is known as galling.

There are different types of stainless steels: when nickel, for instance is added the austenite structure of iron is stabilized and these steels become non-magnetic. For higher hardness and strength, carbon is added. When subjected to adequate heat treatment these steels are used as razor blades, cutlery, tools etc. In recent decades, significant quantities of manganese have come to be used in many stainless steel recipes. Manganese imparts similar qualities to the steel as doe’s nickel, but at a lower cost. Stainless steels are also classified by their crystalline structure:

Austenitic stainless steels comprise over 70% of total stainless steel production. They contain a maximum of 0.15% carbon, a minimum of 16% chromium and sufficient nickel and/or

manganese to retain an austenitic structure at all temperatures from the cryogenic region to the melting point of the alloy. A typical composition is 18% chromium and 8% nickel, commonly known as 18/8 stainless. Ferritic stainless steels are highly corrosion resistant, but far less durable than austenitic grades and cannot be hardened by heat treatment. They contain between 10.5%

and 27% chromium and very little nickel, if any. Most recipes include molybdenum; some, aluminum or titanium. Common Ferritic grades include 18Cr-2Mo, 26Cr-1Mo, 29Cr-4Mo, and 29Cr-4Mo-2Ni. Martensitic stainless steels are not as corrosion resistant as the other two classes, but are extremely strong and tough as well as highly machineable, and can be hardened by heat treatment. They contain 11.5 to 18% chromium and significant amounts of carbon. Some grades include additional alloying elements in small quantities.

11 Rostfria stål SIS handbook, chapter 4 ”Allmänt om rostfria stål”

12 http://encyclopedia.laborlawtalk.com/Stainless_steel

2.3.3. SAF2205SH:

Austenitic-Ferritic (duplex), stainless ELC (= Extremely Low Carbon) steel with 22Cr, 5.5Ni, 3.2Mo and N. Because of the duplex structure, it is fairly magnetic. The grade is characterized by its excellent corrosion resistance, especially to pitting and chloride-induced stress corrosion cracking (SCC), and its high mechanical strength. The grade is approved according to NACE up to a H

S partial pressure of 1.5 psi. SAF2205SH can be used in the temperature range -100 to +300°C.

The fatigue strength is at the level of ordinary stainless steels. The relaxation resistance is good.

At elevated temperature relaxation resistance is even better.

This steel grade is a good choice when a material with excellent mechanical properties combined with high corrosion resistance is required. It is used for e.g. wirelines, rig rods and emission filters.

2.3.4. 1RK91 Nanoflex:

Austenitic-Martensitic, modern mar-aging ELC steel of 12Cr-9Ni type, alloyed with 4Mo, 2Cu plus Ti and Al. It is highly magnetic due to its Martensitic structure. The steel is developed and patented by Sandvik. Mar-aging is a heat treatment, which is in fact a precipitation hardening or age hardening. However, the effect is much stronger than in normal precipitation-hardenable steels and, therefore, it is generally referred to as mar-aging (= martensite ageing) in order to emphasize a difference. In mar-aging steels the strength can be raised by up to 1000 MPa, i.e.

about 3 times as much as in normal precipitation-hardenable steels. This means that a tensile strength of exceptional 3000 MPa can be reached.

The high obtainable tensile strength in 1RK91 is taken advantage of in its main application:

needles for heart and eye surgery. It is thus possible to decrease the needle diameter and still get a ductile, high-tensile product. This grade is also used as dental files and reamers.

The steel can be used within the temperature range -200 to +350°C, its relaxation properties at elevated temperatures and fatigue strength are better than most stainless steels on the market today.

13 Sandvik database on patented materials, SAF 2205.

14 Sandvik database on patented materials, 1RK91.

Chapter 3

Experiments

3.1. Experimental Background

The experiments carried out are all based on the data that I have collected throughout my studies of the guitar strings. After many different tests the experiments presented below have showed to be the most important ones for the understanding physics of a good guitar string or musical wire;

the heat treatment and surface finishing (the history of the steel), yield and tensile strengths, corrosion resistance, acoustic sound, electromagnetic properties and relaxation resistibility (tuning stability).

Some preparations had to be done on the Sandvik material that was tested. 1RK91 existed only in 0,43 mm and 0,254 mm diameter, not in 0,33 mm. A redrawing from 0,43 mm to 0,33 mm had to be done. This was done by a three step reduction process where the 0,43 mm 1RK91 passed 3 smaller diamond dies until it was reduced to 0,33 mm. The SAF2205SH original diameter was 0,5 mm so it had to be reduced to 0,43 mm. Then the 0,33 mm diameter wire had to be reduced by yet another three reduction dies. SAF2205SH was already so cold drawn so it was not possible to reduce it to any lower diameters than 0,33 mm, therefore, the high E string was not made out of SAF2205SH.

Each of the cold drawing processes gives a rise of deformation martensite which leads to brittleness, but at the same time stronger and more magnetic material. The amount of cold deformation is important depending on the desired magnetic and strength specifications needed.

A series of twist tests were also carried out but with no reliable results. No data from the twist tests and torsion tests have been presented.

3.2. Heat Treatment and Surface Finishing

The Sandvik materials 1RK91 and SAF2205SH have both been tested in their cold-drawn and heat treated (aged) forms. The ageing process is done by placing the samples in a furnace with the temperature of 475

C for approximately 10 min. This process called precipitation hardening mentioned earlier strengthens the material. The samples are “dirty” oxidized after this heat treatment, therefore, a surface “cleaning” operation is needed to restore the original metallic surface and luster. This is done by placing the material in a chemical bath. The samples were treated for 30 min in 90°C AVFKA-bath. This bath consists of KMnO

(potassium

permanganate) 5% and NaOH (Sodium hydroxide) 5% diluted in water.

3.2.1. Heat treatment of 1RK91 versus time:

The 1RK91 has quite astonishing characteristics when aged, and the time of the ageing process is very important. The longer the samples are aged the higher yield and tensile strengths are

achieved. Naturally the perfect balance between the shortest ageing time and the desired yield/tensile strength is of interest. Therefore, a test was carried out to see where precisely one could find a suitable ageing time for the desired strengths. 1RK91 was drawn to two different diameters 0,43 mm and 0,254 mm, then the samples were aged in 475

C for 0, 60, 180, 600 seconds. After the ageing process a tensile test was done on each wire. The results are presented in chapter 4.1.

3.3. Yield and Tensile Strength

Tensile tests measure the force required to break a specimen and the extent to which the specimen stretches or elongates to that breaking point. Tensile tests produce a stress-strain diagram, which is used to determine tensile modulus. The data is often used to specify a material, to design parts to withstand application force and as a quality control check of materials. Since the physical properties of many materials (especially thermoplastics) can vary depending on ambient temperature, it is sometimes appropriate to test materials at temperatures that simulate the intended end use environment. Wires of the same gauge, but made of different metals typically support different loads (masses) before going through the point at which they change from being elastic to being plastic. Elastic deformation is recoverable after the load is removed.

Plastic deformation is not recoverable. Specimens are placed in the grips of the testing machine at a specified grip separation and pulled until failure. An extensometer is used to determine

elongation and tensile modulus.

3.4. Spectral Analysis (Acoustic Spectrum)

The spectral analyses were done in Stockholm at KTH in an acoustic laboratory. These tests are usually done on regular nylon strings. By connecting a simple magnet to an oscilloscope the vibrations of the string could be measured. I used this test only to get an idea of how I could transfer the tests done on regular nylon strings to steel strings. As a result the data from these tests are not of any significance.

Fig. 3-1. These pictures are from the visit at KTH, Mr. Jansson shows how the testing is done.

3.5. Magnetic Resonance

To see how well the different steel guitar strings sounded and how good electromagnetic properties they had, a magnetic resonance test was done. The vibrating steel strings cause changes in the magnetic flux through the coil, thus inducing electrical signals in the coil. The actual disturbance that the different guitar strings did on the electromagnetic pickup was monitored. The fluctuations made from the vibration of the string, in the magnetic field of the pickup produces a current. Therefore, the more magnetic the string is the higher voltage will be produced, hence a louder sound. By connecting the guitar to an oscilloscope this produced current could be measured. The pickup’s ability to “pick up” the vibration of the string is seen as voltage fluctuations on the oscilloscope.

The entire magnetic resonance tests were done in the following way (Fig 3-2). By plucking the

string on a distance of 10 cm from the bridge and applying a force corresponding to the shear-

breaking point of a 0,10 mm copper wire, the same force was applied on all the strings. The

copper wire was looped around perpendicular to the plucked string and then pulled until breaking

point. In this way the same force was applied for every test run. The breaking point of the copper

wire must also be at the point of contact with the plucked string. If the copper wire broke at any

other point the procedure explained earlier was repeated. Five approved tests were done on each

string and the data was gathered. All five individual tests on each string were put together and

presented as graphs in Appendix I “Magnetic Resonance”. The test time from the plucking of the string to stopping the measurement was 9 seconds.

Fig. 3-2. The left picture shows the oscilloscope connected to the guitar, and me plucking the string. The right picture shows the plucking point of the string (right above the middle pickup)

using a thin copper wire to obtain the same force for each test.

Some of the samples were also magnetically weighed, these data are presented under chapter 4.3.

3.6. Relaxation

Relaxation is basically how good the guitar string will maintain its tune. Relaxation test is mainly done on springs, therefore I had to invent a new method for testing the relaxation on a simple wire (Fig. 3-4). The basic idea for relaxation in a spring is that, if a spring is kept loaded for a certain length of time, it will lose part of its original force. This load loss or relaxation, as it is called, proceeds rapidly at first but then becomes considerably slower. See the diagram below Fig. 3-3.

Fig. 3-3. This is a typical relaxation diagram, here we can see the relaxation versus the load time diagram.

The load loss is most pronounced at elevated temperatures. The temperature during testing was 24

C (room temperature) and the load time 24 h. The loads of the strings are set as follows below:

Diameter [mm]

Load Weight [kg]

Tension [N]

Frequency [Hz]

Engineering stress [MPa]

0,254 7,35 72,1 330 1423

0,33 6,98 68,5 247 801

0,43 7,53 73,9 196 509

A force loss of 1 N on a test wire of diameter 0,33 mm corresponds to a drop of 2 Hz in frequency. The normal human ear can detect the difference between 440 Hz and 441 Hz, this means that a force loss of approximately 1 N will give an out of tune frequency of 2 Hz that is well hearable for the human ear. If a drop like this occurs, the guitarist must then retune the string to get the desired frequency and tone.

The relaxation tests have been done in the following way, see Fig 3-4. A pick connected to a drilling machine plucks the string with approximately 250 rpm. The plucking point of the pick is set at 18 cm below the top force sensor which is connected to a computer. The total length of the string is 0,65 m and it rests on two plastic pieces at each end point. The distance between each end point and its corresponding force sensor is 5 cm.

I faced many problems when I started building the relaxation testing machine. The first test runs

did not work at all, the samples tested broke all the time after a few seconds of testing. I used

another slower motor (6 rpm) at first but because nothing happened to the samples at those low plucking rates, the motor was changed to the drilling machine. The drilling machine has some drawbacks, one is that the speed of the plucking changes. These changes can easily be seen from the data, when the string is plucked the force on it raises and that is monitored by the logger connected to the force sensors. By locking at the periodicity of the raise of force one can calculate the plucking velocity. The average speed throughout the entire 24 hour period is 200 rpm.

Fig. 3-4. The rig for the relaxation testing. The whole length of the string is 0,65 m and the plucking point is set at 18 cm from the top. The pick is connected to a drilling machine and hits the string with approximately 100 rpm. The string is connected to force sensors at the end points

which are connected to a computer for monitoring.

The data gathered from the force sensors are in Volts. To get the relation between Volts and

Newton we used a 2 kg (19,6 N) weight and hung it on one of the sensors that corresponded to

0,65 V. This gives that 1 V = 30 N. The values presented in chapter 4.4 are multiplied by a factor

of 30 to show the actual load in Newton.

3.7. Chemical Composition and Surface Analysis (SEM)

SEM, Scanning Electron Microscope, can give the composition of the elements in an alloy.

Images on the scanning electron microscope are generated as a fine electron beam scans across a sample. This interaction results in release of energy as electrons, X-rays, and light, which are recorded by various detectors inside the microscope.

The chemical compositions of the materials used for guitar strings can tell us whether the steel is stainless or not. An examination was done by SEM to find what different composition each string manufacturer used. The SEM is not capable of showing any elements bellow 0,5 weight%, therefore the results show us only if the steel is stainless or not. To obtain the exact amount of each element other measurements must be done. In our case the exact composition is of no interest.

The samples were inserted in a rubber block and then ground, to get a smooth surface. The diameter of the strings tested were all 0,43 mm except for sample 8. (D’Aquisto) which was 0,33 mm.

For the chemical composition the cross section of the wires were examined, but for the surface analysis the profile of the wires were tested.

The chemical composition results are presented in Appendix II “Chemical Composition”.

3.8. Corrosion

The corrosion resistance of stainless steels such as 1RK91 and SAF2205SH are superior to regular carbon strings such as D’Addario EXLS510 or EXL110. The whole idea of a stainless steel is its corrosion resistance whereas for carbon steels which have none. No corrosion tests were carried out for this project since the results could be found in quite many earlier works at Sandvik, so I will only use their data to confirm 1RK91 and SAF2205SH’s extremely outstanding corrosion resistance. Their CPT (Critical Pitting Temperature) values and PRE (Pitting Resistant Equilibrant) are presented below. The CPT value show the temperature when the stainless material is corroded in a Cl

solution. PRE is a theoretical equation (PRE = %Cr + 3,3% Mo +16% N), this equation shows that the higher the rates of chromium, molybdenum or nitrogen are the better is the corrosion resistant properties of the material.

Corrosion properties

35

26

19 85

40

28

0 10 20 30 40 50 60 70 80 90

PRE CPT °C

PRE 35 26 19

CPT °C 85 40 28

SAF2205SH 1RK91 AISI 304 (Standard

Stainless)

3.9. Microstructure

During microstructure test a cross section of the sample is investigated in a Light Optical Microscope (LOM). The test shows whether the string is symmetrical and homogenous or deformed in some way. The surface of the string can also be seen. If the outer edges of the samples are jagged or deformed in any way it can easily be observed, in the LOM. The pictures from these tests are presented in Appendix IV “Microstructure”.

3.10. GDOES

GDOES (Glow Discharge Optical Emission Spectroscope) is a technique that makes it possible to measure the chemical composition as a function of the distance from the surface. This technique is very sensitive for low concentrations and it has an excellent depth resolution. These factors make it suitable for analyzing very thin surface layers. During the analysis, the sample is eroded by ion etching (also called sputtering) using Argon ions. The atoms that are removed from the surface will be exitated and therefore unstable. Then they will emit a photon to get stable and these photons can then be detected and recorded in an optical spectrometer. This process Sputtering->Exitation->Emission->Detection is continuous and will result in a qualitative depth profile. If the instrument is properly calibrated it is easy to calculate quantitative depth profiles from the intensity profiles.

Normally the instrument is used for flat surfaces and in this case the samples were thin wires, Ø 0,56 mm. The wires were analyzed over a length of about 8 mm and the sputtering takes place around the whole area of this length of the wire. The quantification model is not applicable for this kind of samples, mainly because of the geometrical differences and different electrical parameters, and therefore, we have to make some corrections of the quantifications. The quantitative presentation of the results is therefore very approximate.

In this investigation, a Spectruma GDA750-HP, GDOES instrument was used to study concentration variations on the surface.

GDOES was used to see if the guitar strings were coated. Some guitar manufacturers use coating for corrosion protection but usually this leads to a dampening effect on the strings. The coating is usually a thin plastic cover but can also be a thin layer of tin. Even though the GDOES can detect non-metallic surfaces, no traces of any coatings could be found on any of the samples tested except two.

A thin layer of tin coating was found on the D’Addario EXLS510 and EXL110 samples. The tin

acts as a corrosion resistance enhancer.

3.11. Sound Check

The most important property for a musical wire is its sound, and it is probably the most difficult parameter to measure. It is up to the individual musician to decide whether the string sounds good or not. At the start of this Master’s Thesis a sound check was done (by author) to see if the

different steels were of any interest for further evaluation. Many different stainless steel alloys

were tested and sorted out due to a bad sound quality. But in my opinion the samples left 1RK91

and SAF2205SH have excellent sound. I have had contact with several professional musicians

and they have all shared the same opinion with me. The sound check that was carried out was

only on the three highest strings on a guitar that is the high E-string, B-string and G-string. None

of the wound strings were sound tested based simply on the fact that Sandvik did not have any

string winding machines. The strings that are wound will still have the same characteristics in

sound due to the fact that their cores consist of the three highest strings.

Chapter 4

Results

4.1. Heat Treatment of 1RK91 versus Time The samples tested are aged in 475

C for 0, 60, 180 and 600 seconds.

1RK91 ∅ 0,254 mm

Pnr. Diameter d0 Load Rp 0.2 Rm

Legends mm N N/mm² N/mm²

“ 0a 0,253 91 1539 1808

“ 3 min 0,253 124 2441 2473

“ 1 min 0,253 116 2295 2314

“ 10 min 0,253 131 2574 2604

“ 1 min retry 0,253 115 2267 2289

“ 3 min retry 0,253 121 2406 2412

0,0 0,5 1,0 1,5 2,0

0 500 1000 1500 2000 2500

Strain in %

Stress in N/mm²

0,25 E-Modulus Rp 0.2 Rm Load

n = 6 N/mm² N/mm² N/mm² N

x 174754 2254 2317 116

min. 167095 1539 1808 91

max. 177713 2574 2604 131

1RK91 ∅ ^{0,43 mm}

Pnr. Diameter d0 Load Rp 0.2 Rm

Legends mm N N/mm² N/mm²

“ 0a 0,43 241 1481 1660

“ 3 min 0,43 332 2281 2284

“ 1 min 0,43 308 2104 2122

“ 10 min 0,43 354 2407 2441

“ 1 min retry 0,43 306 - 2106

“ 3 min retry 0,43 332 2246 2287

0,0 0,5 1,0 1,5 2,0

0 500 1000 1500 2000 2500

Strain in %

Stress in N/mm²

0,43 E-Modulus Rp 0.2 Rm Load

n = 6 N/mm² N/mm² N/mm² N

x 166904 2104 2150 312

min. 158761 1481 1660 241

max. 170517 2407 2441 354

Here we can see how the ageing affects the mar-ageing 1RK91’s yield and tensile strength. After

only 1 min of ageing the tensile strength is improved by 500 MPa.