Participating in the various forums on the technical aspects of fountain pens and specifically nibs, I found, there is a lack of knowledge of the technical, physical properties of metals, those of steel and gold in particular. The words used are elasticity, flexibility, smoothness, comfort and more in a way as if they were interchangeable. Some are technical expressions of physics, others are terms of common language which are imprecise if one talks ingeneering language.
When we want to change the characteristics of a nib, then, as an ingeneer, I want to know what the fundamental functional criteria of a nib are and where to apply my tools most efficiently. I also like to have a sense of what to expect.
I present here a condensed general ingeneering knowledge on the measurement and determination of the physical properties of metals. A more elaborate version can be found at Wikipedia => Deformation
The Stress-Strain Diagram
Diagram 1 shows a fundamental piece of ingeneering information and learning to read it, gives a good sense of a material’s behaviour and properties. It helps to explain the essential behaviours of many metals.
The two coordinates of the diagram are stress along the vertical axis and strain along the horizontal. Force applied across an area is called stress (Newton or pound per area), while strain is caused inside a material due to deformation when an outer force is applied. Therefore, the same curve (stress-strain) also relates to the relationship of a force applied to a component and the consequential deflection.
The curve shows the typical shape of a ductile material such as soft steel. It can sustain significant plastic deformation prior to fracture. A brittle material, besides being often harder and needing higher loads for deformation, hardly enters the yield area, thus shows hardly any plastic deformation before fracture.
Diagram 1
For easier understanding, I added
- Force to strain
- Deformation to stress
Before getting carried away too far, let me travel along the curve and explain what happens. Initially, it rises in a straight line. Deflection increases proportionally with the force applied to the component or material sample. This ratio, the steepness of the slope, is called the Modulus of Elasticity, E-Modulus or Young’s Modulus. A high number indicates a stiff or strong material; a small number tells that the material is easy to bend.
This straight line depicts the range of elasticity, meaning, a certain force can be applied to a component and after the force is removed the component returns to its original shape, this proceeding is called “elastic deflection”. When a force is applied to a component it always goes first through the phase of elastic deflection.
If the applied force deforms the component beyond the Yield Strength (wriggly section), the material begins to yield; the component changes its shape without an increase of force. After that, the stress-strain ratio is no longer constant. Moreover, the component will not return to the original zero point but somewhere right, along the deformation axes. This residual change of shape is called “plastic deformation”. This deformation is needed for work or stress hardening.
The highest stress a material can take is called the ultimate strength. This is usually an unsteady area in which a small increase in load can cause a significant change in shape. A test sample would reduce its cross-section, called necking and the material yields further without an increase of load (it may reduce) until the test sample breaks.
Elasticity and Elastic Deformation
I am aware of repeating myself in sections, it’s done on purpose and is an emphasised indication for the importance of this information. Here we go:
When a material returns to its original shape after deformation, then this deformation had remained within the range of its elasticity. Most common, elastic deflection is applied to springs.
Diagram 2 — The green line demonstrates elastic deformation
In diagram 2, I show the range of elastic deflection as the green straight line, starting at the zero point a and ending at an arbitrary point b, it could go up to just below the wriggly bit, however, it is good ingeneering practice to stay well away from this section when calculating the dimensions of a component because it can change and its tolerances vary even within the same material specifications.
The material can be loaded and unloaded repeatedly and always returns to the zero point. Many materials and most steels behave in this proportional way of elasticity.
There is a possible fracture due to fatigue, a fascinating topic, however, since this would not occur in a fountain pen situation, I will restrain myself and not write about it. There is plenty of information on the internet.
Plastic Deformation
When a component is stressed with a load to a point beyond the range of elastic deflection, beyond the yield strength (the wriggly section), where it can’t yield anymore and a change of shape occurs on the component, then, after the load is taken away, this change of shape remains. In ingeneering terms, it’s called plastic deformation.
Diagram 2 the second time — The purple line demonstrates plastic deformation
I drew up this progress with a purple line. It starts at the zero point e (same as a). As the load increases, it passes point b, wiggles its way through the area of the yield strength, up to point f.
The stretching that happens between Yield Strength and point f is used in the process of work-hardening.
As the load decreases the curve does not follow the virgin line (with the bit green line) down to the zero point but slides down the purple line from f to g. This line runs parallel to the virgin line. The properties of the material have been altered through work-hardening, the deflection beyond the yield strength to point f. The distance between the original zero point e and the new baseline point g is called residual or plastic deformation. The latter can be visualised as a force contained inside the component, like a tension coil spring. It doesn’t show the force it stores, the force only reveals itself when one tries to pull the coil apart. The same applies to the tines of a nib which only separate after a certain writing pressure is applied.
The process of work hardening finds application during the shaping or bending of components when we want components to retain the shape into which we have formed them. You may have noticed that you need to over-bend a part to some degree, and then it springs back: that’s your elastic deflection. Yes, when making coins or nibs and dents in your car… it’s the same process but certainly not very desired.
Let’s pass on to the next topic, we have already started.
Prestress
This internal force is called prestress. Any psychologists reading this? Yes, you are absolutely correct; it’s just like with humans. It is a force that has been taken on board which had no opportunity to be released. In the mechanical world, a component is heated up, several hundred degrees and the stress relaxes, annealing it’s called.
We have learned already about one way of imposing residual stress onto a component: plastic deformation. A similar situation is obtained, when two components are held together under load. According to Mr Newton: “Actio est reactio!” – the force in each component is/must be the same, otherwise, they would move until equilibrium is obtained. Applications are electrical contacts, the wheel suspension of a car as well as the tines on a nib. One wants to make sure that at the balanced position, the components have definitely reached the predetermined point, for example: if the tines have received different preloads, the nib point will end up somewhere off the central axis.
The nib would work, but what an unpleasant sight. The nib containing prestress means, to widen the line of writing, we need to apply pressure and overcome the force, which holds the tines together.
Diagram 2 — Stress-Strain diagram showing Pre-Stress
The prestress or preload is indicated in the diagram as the distance between h and m. Before any deflection can occur, the acting force must climb beyond this load. Then the deflection follows the straight orange line up to point k (arbitrary). In this example, the process shown is the elastic deflection. After the load is reduced to the preload value, the deflection returns to point m, or, if taken off completely, to point h alternatively.
The prestress can be reduced by applying a load above the point k, into or beyond the yield strength (the wriggly bit). When the load is released, the curve will end at a point below point m. This is the process of adjusting preloads; the tricky part is developing a feeling for the required over-bending.
PS: You may notice that the force levels of the yield strength remain within the diagram of one component remains constant.
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With regard to nibs, the preload of the tines is set or altered by applying this technique. Increasing the load makes the nib feel harder, reducing the load makes it more responsive, thus feel softer. If all nibs were handset at the end of production, then this force would be individually applied and this way many tolerances could be compensated. Then the preload can be kept at a minimum.
Most nibs (99.99% or several 9s more) are mass-produced, and tolerances must be compensated for during assembly. The stamping pressure for the setting of the tines (see Nib Manufacturing in the section setting) must be high enough to close the tines at the tip even at unfavourable tolerance combinations. Therefore, the preload at the tines varies between nibs and thus, their responsiveness to writing pressure alters. The range of variation is mainly affected by the inconsistency of the raw material properties, the precision of the manufacturing process as well as the level of rejects established by the quality assurance department.
I could write a long chapter on this topic. Tell me if you are interested.
Work or Stress Hardening
I give this topic more attention because it is of great significance in the manufacturing of nibs. Work-hardening is a process where through rolling or impacting forces the material is deformed plastically and its structure is altered. For each progressive manufacturing step, a higher load will need to be applied to change this newly attained shape.
This happens at several stages during the manufacturing of a nib. As an example, I describe the initial rolling process. Prior to rolling the strips were cut from sheets (of gold) while stainless steel, which comes in rolls, is cut to a length of about 3/4 of a meter length for ease of handling (in my days!).
Sketch 1 — Notched strip of metal
Before rolling the profile, notches were stamped into the strip to reduce its bending shown as the blue outline in sketch 1. The grey area in sketch 1 is produced in a second stamping process after which the individual nibs are separated.
Sketch 2 — Rolled profile of nib before bending
The profile has a thin section where the deformation, hence the work-hardening is strong thus the material becomes quite hard. From this section, the seat of the nib will be formed. See sketch 2. The thick section will be the tines, the thickness will prevent their bending which therefore will rather happen across the thinner part, the location of the hole. More about this in the chapter Design of Fountain Pen Nibs.
The stainless steel strip is thinner than the gold strip; it does not need as much work-hardening, luckily, because it also requires 4-5 times higher forces during rolling. Gold needs more hardening therefore the necessary deformation is higher. A further issue for the final profiles to be identical in their inner shape, they must fit the same tools for the subsequent processes. And, last but not least: both nibs must fit the same feed.
Once a component is work-hardened, one could say, it is made from a new, more brittle material. Often, the range of elasticity increases, but the range of deformation reduces.
Allow me to remind you, one of gold’s incredible characteristics is: generally, it does not work-harden. However, gold nibs are made from a particular 14-carat alloy with a higher content of nickel which makes it work-hardenable, see Nib Materials.
Annealing
As a thinking model one could say, work-hardening moves the material fibres closer together (aligns the fibres or increases adhesion, etc) and therefore makes the material harder, keeps the formed component in its new shape and holds the internal stress, the preload. If the forming process has achieved the desired final shape of the component, all is good.
However, in some situations, the hardening of the final component is not desired. In another case, the achieved shape may not be the final, and further forming is required. What to do if the material is now too hard or brittle for permitting additional modifications.
During annealing, the component is heated to a point, where the material fibres can move apart again, slide and reorientate, and the internal stress is released. Unfortunately, with annealing, the shape of the component relaxes to some degree, as well unless it’s held in a jig.
For each component, the annealing temperature needs to be found experimentally, a compromise between the degree of material softening and the relaxation of the shape. If at least some stress can be released without too much reformation, another production step can follow.
Stainless Steel versus Gold
Diagram 4 — Stress/Strain curves comparing gold and stainless steel
In my experience, both materials allow the production of excellent nibs, even their material properties are worlds apart. Diagram 4 demonstrates this in proportion.
How can this be achieved? Let me take away one problem, immediately. What you see, is the complete scope of behaviour of those materials, their complete stress-strain diagrams in one graph. The range of operation for nibs, which is the minute spreading and closing of the tines, happens only in the small section of the bottom left corner, inside the red circle.
How are the two materials to be made useful for nibs? Most obviously, the answer lays in the difference in their construction. Since in many cases the overall shape of the nib for stainless and gold must be compatible with the same feed, this is not the only solution. It has been done, hence, there must be others. We have talked about the “means and ways!”.
If the nibs of either material must have at least almost the same shape, one change in material characteristics is achieved through work-hardening, the other, through the application of different prestresses. Surely you know now what this means. In the chapter Design of Fountain Pen Nibs you will find more information on this topic.
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The next chapter is on Nib Materials where we talk about the movement of the nib and why the tines open with increasing writing pressure.
Above all: Enjoy!
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23 May 2016
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