Improved Maxwell Model Approach and its Applicability toward Lifetime Prediction of Biobased Viscoelastic Fibers

Abstract

The evaluation of relaxation measurements is a well‐established technique for predicting the lifetime of polymer materials, with research primarily focusing on increasing prediction accuracy and minimizing material testing time. The current study presents a novel approach toward describing the long‐term behavior of viscoelastic polymers based on the Maxwell model. It assumes a mean relaxation time of the polymer chains in conjunction with a dimensionless number that accounts for averaged polymer chain inhomogeneities. This coefficient is analogous to the dimensionless number, which successfully describes the asymmetry of both the Weibull distribution and of particle size distribution according to the Rosin, Rammler, Sperling and Bennet model. In comparison to earlier models based on time‐superposition principles, the current approach enables lifetime prediction using a single short‐term measurement, which must be taken at a properly chosen applied strain. The applicability of the new model in predicting the long‐term behavior has been demonstrated by the analysis of the relaxation behavior of semi‐crystalline bio‐based fibers.

Revisiting the Contribution of Additives to the Long-Term Mechanical Stability and Hydrolytic Resistance of Highly Crystalline Polylactide Fibers

“…As seen in Figure 7b,c, the relaxation coefficient n behaves almost ideally independent of the strain ε i while the relaxation time λ̅ i shows a linear decrease, as expected. As described earlier, 54 the high standard deviation of λ i at low strains ε ̅ i suggest a better applicability of the model for the relaxation measurement at high strains.…”

“…The initial modulus E 0 shows a slight tendency to decrease with the increasing strain ε i , which is attributed to the measurement uncertainty (Figure 7a). 54 The expected invariance of the initial modulus E 0 as well as of the final modulus E ∞ is therefore verified. As seen in Figure 7b,c, the relaxation coefficient n behaves almost ideally independent of the strain ε i while the relaxation time λ̅ i shows a linear decrease, as expected.…”

“…To elucidate the effect of the assumed inner heterogeneity of the morphology of the blends, despite similar degree of crystallinity for all fibers, on the long-term mechanical performance and hydrolytic resistivity, we applied a relaxation model, 54 which earlier proved to be successful in lifetime prediction of artificially aged semicrystalline PLA fibers. 16 Validation of Lifetime Prediction Model for Semicrystalline PLA-Blended Fibers.…”

“…This relaxation model allows the evaluation of the modulus E depending on time t. In contrast to several established algorithms on time superposition principles, this model enables the construction of the long-term RMC from a single (experimental) relaxation curve. 54 The relaxation time is determined via the vertex of the parabola, which is obtained from the derivative of the modulus plotted against the modulus. Furthermore, since the model does not require a time shift, the construction of the long-term RMC relies on a single measured curve, which is recorded over a short period.…”

“…In this case, the existing relaxation models have to be adapted to the individual characteristics of the material to account for possible differences in the relaxation behavior of the structural domains. Recently Schippers et al 54 presented a new approach based on the generalized Maxwell model. This model enables the construction of the long-term relaxation master curve (RMC) from a single (experimental) relaxation curve recorded over a short period.…”