= Favimat+ fibre testing machine
{c}
The <Favimat+ fibre testing machine> combines measurements on individual <material fibres>, including a <single-fibre tensile test> and vibroscopic estimation of <linear mass density>. Its useful feature is the association of the force-extension record with a measurement of the same strand, rather than with a batch-average geometry.
In the reported glass- and carbon-fibre study, a magazine held the prepared strands and a robotic device transferred each to the grips. The built-in <vibroscope> used acoustic excitation and a frequency sweep to identify <resonance>; a <load cell> measured tension and grip separation supplied the suspended length. Tensile measurements followed vibroscope measurements on the same still-gripped fibre.<Vibroscope method for determination of cross-sectional area of glass and carbon fibres – Experiments and analyses by Bo Madsen and others>[§§3.2–3.3, semi-automated handling, acoustic resonance measurement and same-fibre tensile sequence]{ref}
An original pairing example shows why strand identity matters. Suppose two strands have independently established material areas $50$ and $100\,\mathrm{\mu m^2}$, and each carries $0.050\,\mathrm N$. Their <engineering stresses> are
$$
\sigma_1=\frac{0.050}{50\times10^{-12}}=1.00\,\mathrm{GPa},\qquad
\sigma_2=\frac{0.050}{100\times10^{-12}}=0.50\,\mathrm{GPa}.
$$
Using the common mean area $75\,\mathrm{\mu m^2}$ would assign both $0.667\,\mathrm{GPa}$, concealing the difference. These are chosen values, not measured instrument data.
Frequency first supports a mass-per-length estimate under the vibration model; converting it into area also needs compatible <mass density> and deformation conventions. The <vibroscope area estimator> explains that inference and its limitations. Force and displacement readout resolution are likewise not complete statements of <measurement uncertainty> or specimen extension: <machine compliance> and grip motion must be assessed when extracting a modulus.
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