Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles

Abstract

The mechanical characteristics of fibers (of various materials), as well as of fiber bundles, are of primary importance for the design and the mechanical behavior of textiles, or of fibrous and composite materials. These characteristics are classically determined from strain-rate controlled tensile testing, generally assuming a negligible role of thermal activation on damage and fracturing processes. Under this assumption, the distribution of individual fiber strengths can be deduced from a downscaling of the macroscopic mechanical behavior at the bundle scale. There are however many experimental evidences of strain-rate and temperature effects on the mechanical behavior of individual fibers or bundles, which can also creep under constant applied load. This indicates a strong role of thermal activation on these processes. Here, these effects are analyzed from a fiber-bundle model with equal-load-sharing, in which thermal activation of fiber breakings is introduced from a kinetic Monte-Carlo algorithm adapted for time-varying stresses. This allows to rationalize these rate or temperature effects, such as a decrease of bundle strength, strain at peak stress, and apparent Young's modulus with decreasing strain-rate and/or increasing temperature. This also shows that the classical downscaling procedure used to estimate the distribution of individual fiber strengths from the mechanical behavior at the bundle scale should be considered with caution. If mechanical testing of the bundle is performed under conditions favoring the role of thermal activation (e.g. low applied strain-rate), this procedure can strongly underestimate the intrinsic (athermal) Weibull's parameters of the fiber strengths distribution. The same model is used as well to explore size (number of fibers) effects on bundle mechanical response.

Figures (8)

• Figure 1: Macroscopic stress-strain curves of bundles, averaged over 50 realizations of disorder, for an intermediate strain-rate of $\dot{\varepsilon}=10^{-15}$, a vanishing temperature $\theta=2.76\times10^{-5}$ and a uniform distribution of individual fiber strengths. This is compared to expression (\ref{['eq:SScurveUniform']}) corresponding to athermal dynamics.
• Figure 2: Macroscopic stress-strain curves of bundles, averaged over 50 realizations of disorder, for an intermediate temperature $\theta=8.28\times10^{-3}$, varying strain-rates, and (a) a uniform or (b) a Weibull's distribution ($m=8$) of individual fiber strengths. This is respectively compared to (a) expression (\ref{['eq:SScurveUniform']}) or (b) expression (\ref{['eq:SScurve']}) corresponding to athermal dynamics.
• Figure 3: Evolution of the average bundle strength $\langle\sigma_f\rangle$ (closed symbols), as well as of the average strain at peak stress $\langle\varepsilon_f\rangle$ (open symbols), with increasing strain-rate for (a) a uniform and (b) a Weibull ($m=8$) distribution of fiber strengths, and a temperature $\theta=8.28\times10^{-3}$. The diagonal dashed-dotted lines represent the prediction of eq.(\ref{['eq:expectedStrength2']}) for the strength. The dashed horizontal line indicates the athermal value of the bundle strength, and the dotted horizontal line that of the strain at peak stress, both recovered at very large strain-rates. The error bars represent the strength variability among 50 realizations of disorder. When this variability is smaller than the symbol size, it is not represented.
• Figure 4: Macroscopic stress-strain curves of bundles for an intermediate strain-rate $\dot{\varepsilon}=10^{-15}$, varying temperatures, and a Weibull's distribution of individual fiber strengths ($m=8$). This is compared to expression (\ref{['eq:SScurve']}) corresponding to athermal dynamics.
• Figure 5: Evolution of the average bundle strength $\langle\sigma_f\rangle$ (closed symbols), as well as of the average strain at peak stress $\langle\varepsilon_f\rangle$ (open symbols), with increasing temperature $\theta$ for a Weibull ($m=8$) distribution of fiber strengths, and a strain-rate $\dot{\varepsilon}=10^{-15}$. The diagonal dashed-dotted line represents the prediction of eq.(\ref{['eq:expectedStrength2']}) for the strength. The dashed horizontal line indicates the athermal value of the bundle strength, and the dotted horizontal line that of the strain at peak stress, both recovered at very low temperature. The variability among 50 realizations of disorder was always smaller than the symbol size, and consequently not represented.