Polymers and polymer composites are ubiquitous materials in our modern economy. They are present in the houses we live in, vehicles we drive, planes we fly, furniture we use, and many other things we don’t even think of. Thus, it is crucial to know when and how they resist external mechanical forces and, importantly, when and how they fail. It has been known for many decades that mechanical failure of polymer materials can be either “ductile” (slow yielding) or “brittle” (fast cracking). The transition between these two regimes (“brittle-ductile transition” or BDT) depends on the temperature (more brittle when it is cold), strain rate (more brittle when rate of deformation is high), and aging (the dependence here is non-trivial). Can we predict this transition as a function of these factors for any given material, either existing or one we are still designing?
There are many models explaining brittle fracture of polymers (see, e.g., Wang et al.1, Kinloch,2 and others). Those models start from the stress or energy balance near a crack tip and then look at the role of polymer chains, their entanglements, chain ends, and interactions. For amorphous thermoplastics (like PS, PMMA, PVC, PC), the BDT occurs at temperatures 10 – 100 °C below their glass transition,3 assuming that the strain rate is typical for conventional tensile/compressive tests (on the order of 1 /min). The accepted model is that “polymers in the plastic state are brittle because the underlying chain network breaks down before sufficient activation.”1 However, this model does not offer easy ways to generalize to other strain rates or to understand the effects of aging.
Experimentally, there have been multiple efforts aimed to measure and understand the dynamics of the brittle fracture in polymers (as well as other glasses). Baer et al.,4 Wu,5,6 and others noted that the BDT is often related to the secondary spectroscopic transition (“b-transition”). The b-transition is typically tens of degrees lower than the glass transition (aka “a-transition”). Both a- and b-transition temperatures are Arrhenius functions of the strain rate or frequency. Wu’s work, in particular, provided important predictive relationships between BDT and strain rate for many amorphous polymers. One big challenge, however, is that for many polymers, the nature of the b-transition is not fully understood – a specific dielectric peak may be related to some local dipole modes and thus be masking the “true” b-transition associated with BDT.
Recently, we have been investigating the dynamics of the glass transition and developed a theory labeled “two-state, two-(time)scale” (TS2) model.7–9 Within TS2, the b-transition is associated with the relaxation time of the pure supercooled liquid becoming comparable to the laboratory time (~ 1 min). Our “general TS2” scaling allows us to estimate the b-relaxation time as a function of temperature and compute its activation energy. By combining it with a relatively simple nonlinear visco-elasto-plastic model, we obtain BDT as the “point of instability”.10 In other words, when one increases the strain rate (at a given temperature) or reduces the temperature (at a given strain rate), a system that hitherto was flowing plastically finds itself no longer able to do so. The maximum possible rate of dissipation – set by the b-relaxation time – is smaller than the rate of energy absorption from the outside. Thus, material fails in a brittle fashion because it can no longer do it in a ductile one. The new theoretical results provide justification for the empirical rules developed by Wu.
This new framework should let us extend the BDT modeling to other systems, such as blends, semicrystalline polymers, and composites. We can also explore the impact of aging. We hope this new approach could be useful in material and system design.
References:
(1) Wang, S.-Q.; Fan, Z.; Gupta, C.; Siavoshani, A.; Smith, T. Fracture Behavior of Polymers in Plastic and Elastomeric States. Macromolecules 2024, 57 (9), 3875–3900.
(2) Kinloch, A. J. Fracture Behaviour of Polymers; Springer Science & Business Media, 2013.
(3) Wang, S.-Q.; Cheng, S.; Lin, P.; Li, X. A Phenomenological Molecular Model for Yielding and Brittle-Ductile Transition of Polymer Glasses. J. Chem. Phys. 2014, 141 (9).
(4) Matsushige, K.; Radcliffe, S. V; Baer, E. The Pressure and Temperature Effects on Brittle‐to‐ductile Transition in PS and PMMA. J. Appl. Polym. Sci. 1976, 20 (7), 1853–1866.
(5) Wu, S. Effects of Strain Rate and Comonomer on the Brittle–Ductile Transition of Polymers. J. Appl. Polym. Sci. 1976, 20 (2), 327–333. https://doi.org/10.1002/app.1976.070200204.
(6) Wu, S. Secondary Relaxation, Brittle–Ductile Transition Temperature, and Chain Structure. J. Appl. Polym. Sci. 1992, 46 (4), 619–624.
(7) Ginzburg, V. A Simple Mean-Field Model of Glassy Dynamics and Glass Transition. Soft Matter 2020, 16 (3), 810–825. https://doi.org/10.1039/c9sm01575b.
(8) Ginzburg, V. V; Zaccone, A.; Casalini, R. Combined Description of Pressure-Volume-Temperature and Dielectric Relaxation of Several Polymeric and Low-Molecular-Weight Organic Glass-Formers Using’SL-TS2’Mean-Field Approach. Soft Matter 2022, 18, 8456–8466.
(9) Ginzburg, V. V; Gendelman, O.; Casalini, R.; Zaccone, A. General Two-Parameter Model of Alpha-Relaxation in Glasses. Phys. Rev. E 2026. https://doi.org/10.1103/99c2-1znq. (10) Ginzburg, V. V.; Gendelman, O.; Zaccone, A. On Brittle-Ductile Transition in Polymers. (manuscript in preparation). 2026.
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