The standard method for tensile studies is the stress-strain measurement or, with-out the normalization by the fiber diameter, force-strain measurement in which the force is recorded versus elongation. Sometimes such curves are also referred to asε-σ-curves orε-σ-diagrams withε=strain andσ = stress. They characterize the sample’s response to an applied tensile strainεand allow the determination of important information such as elastic modulus, breaking strainσmax, breaking force, toughness (total energy per volume until breaking point) and the amount of energy dissipation. Figure 2.8 shows three materials which represent an ex-tremely stiff material (steel), a very extensible material (rubber) and an interme-diate, so-called viscoelastic, material (perlon / polyamide 6). The stress-strain curves of Nephila dragline at approximately 50% relative humidity (RH) is also shown. Spider silk lies in between the two extremes and is therefore also a vis-coelastic material. The unusual form of the stress-strain curve with two nearly lin-ear regions makes the difference to polyamide 6. From such simple stress-strain curves the following properties can directly be retrieved:
Initial elastic modulusE: Slope of the initial linear region;σ =Eε; UnitPa Yield point: Normally the stress at which a material begins to plastically deform.
For spider silk the point of the curve’s main inflection [39].
Tensile strength: Breaking stressσmaxat which the fiber tears.
Extensibility: Breaking strainεmax at which the fiber tears.
Toughness: Energy per unit volume a material can absorb before failure, repre-sented by the integral of stressσover strainσwhich corresponds to the area under the curve. Unit J/m3.
They are also shown in figure2.9. Stress-strain measurements can be performed with or without gauge force FG. Without a gauge force the measurement starts immediately. The stress-strain curves exhibit an initial region where the sample is not completely stretched and the force is nearly zero, see the region 0%≤ε ≤4%
in figure2.12, page18. A gauge force causes the measurement to start only when the preset force threshold is crossed. Therefore the measurements do not start at zero but with an offset which is also used to define l0 for the calculation of the relative elongation ε = [(l−l0)/l0]·100, see figure 2.10. Normally this offset is negligible but in hysteresis measurements it causes a shift in subsequent curves.
These errors can be corrected either by linear regression or renormalization. For dragline silk a gauge force ofFG= 1.5mNproved itself.
Figure 2.8: Stress-strain curves of steel, polyamide 6 (perlon), latex and NS dragline. Steel, polyamide 6 and dragline have a comparable maximum strain but different initial elastic moduli (slopes of the initial linear regimes), see also table2.1. The area under the curve which corresponds to the energy stored in the fiber, is maximal for dragline. The stress-strain curve of latex is upscaled otherwise it would be too close to the x-axis. Also only the beginning of the latex stress-strain curve is shown. Latex can be stretched up to 800% of its initial length.
Figure 2.9: Main properties which can be retrieved from a simple stress-strain measurement shown exemplary on NS dragline. Initial elastic modulus = slope of the initial linear region.
Yield point = position where the two linear regimes merge into each other. Tensile strength = breaking stress σmax. Extensibility = breaking strainεmax. Toughness (total energy per volume till breaking point) = area under the curve.
2.3.1 Hysteresis
The area under a force-strain curve resembles the integral of force over elonga-tion and therefore the stretching energy. Partly the stretching energy is stored in the fiber, partly it is dissipated. The percentage of energy dissipation is mea-sured by an advanced type of stress-strain experiments in which not only the fiber’s response to elongation but also to reduced extension is recorded. Such measurements are called hysteresis measurements or just hysteresis and consist of two curves, see figure 2.10. One for increasing strain, called ascent and one for decreasing strain (descent). While the area under the ascent curve resembles the total stretching energy necessary, the area under the descent gives the energy elastically stored in the fiber. The dissipated energy then is the area between these two curves. For Nephila dragline the dissipated energy is around 68% of the total stretching energy [52; 53] and approximately 32% is elastically stored.
Incidentally, this is the reason for the term viscoelastic, "viscous" like a fluid that dissipates energy and "elastic" for energy storage. Subsequent hysteresis mea-surements of the same sample indicate whether deformation and energy loss in the fiber are due to reversible or irreversible processes. No differences in subse-quent hysteresis cycles indicate reversible processes, see figure2.11, while signif-icant changes indicate irreversible processes. Depending on the material this is normally true for the first two to five cycles after which fatigue failure occurs.
Figure 2.10: A typical hysteresis curve forNS dragline. The area under the ascending curve corresponds to the total energy necessary to stretch the fiber, the area under the descending curve to the energy elastically stored in the fiber (checkered). The differences between the two areas correspond to the dissipated energy (streaked).
Figure 2.11: First and fifth hysteresis cycle of a latex sample. The different cycles are nearly indistinguishable. The energy loss per cycle is approximately 7% of the total stretching energy.
The sample was approximately15mm × 2mm × 0.125mm and is used e.g. for laboratory gloves.
Latex exhibits mainly entropic elasticity, the classical model for reversible processes.