What Controls the Character of Glassy-Polymeric Cavitation: Entanglement Topology, Strain Hardening, Temperature, and Stress State

Glassy polymers fail either brittly, through runaway void growth and coalescence into crazes, or in a ductile manner in which many small voids nucleate but grow slowly. Molecular-dynamics work (Nan, Abritta and Hoy, Macromolecules 54, 7347, 2021) showed that at the athermal limit, tightly entangled, semiflexible glasses generate far more but far smaller voids than loosely entangled glasses at the same strain and imposed Poisson ratio, but could not decide whether entanglements suppress void growth directly through topological constraints or indirectly by raising the strain-hardening modulus, and left the finite-temperature regime, the connection to craze-front void nucleation seen in experiments, and the role of evolving elastic heterogeneity unexplored. The problem is to give a predictive, mechanism-level account of which cavitation character emerges as a function of entanglement density, strain hardening, chain stiffness, imposed Poisson ratio, and temperature. The comparison the authors proposed for separating the two mechanisms — glasses with matched strain-hardening modulus and flow stress but different entanglement density — has not been performed in the source or in its follow-ups, so the mechanistic core remains open.

Background

A glassy polymer is an amorphous polymer cooled below its glass transition temperature $T_{\mathrm{g}}$, where it deforms plastically through localized rearrangements rather than viscous flow. Under tensile loading, glassy polymers develop nanoscale voids (cavitation). Two fates are possible: 'ductile' cavitation, in which many small voids nucleate but grow slowly and never coalesce, and 'runaway' cavitation, in which voids grow and coalesce into fibril-bridged planar crack precursors called crazes, leading to brittle fracture. Classical crazing theory (Kramer and coworkers) attributes craze stability to the entanglement network: entangled chain strands, segments of chain between consecutive entanglements (topological constraints where chains cannot pass through each other), are drawn out into fibrils and resist further drawing. The entanglement density $\rho_{\mathrm{e}}$ (entanglements per unit volume) also sets, in classical rubber-elasticity-based formulas, the strain-hardening modulus $G_{\mathrm{R}}$ (the slope of the rising stress-strain branch at large strain, with $G_{\mathrm{R}} \propto \rho_{\mathrm{e}}$), while the flow stress $\sigma_{\mathrm{flow}}$ is the roughly constant post-yield stress plateau. Which of these coupled factors — entanglement topology or strain hardening — actually stabilizes voids against growth is a long-standing, unresolved question, since $G_{\mathrm{R}} \propto \rho_{\mathrm{e}}$ makes the two hard to vary independently.

Nan, Abritta and Hoy (Macromolecules 54, 7347–7353, 2021) studied this with molecular-dynamics simulations of generic bead-spring polymer glasses in which chain stiffness $\kappa$ (the energetic cost of bond bending, which tunes the entanglement length and the packing) and the imposed Poisson ratio $\nu$ were varied systematically. Here $\nu$ is a property of the deformation protocol, not the material: strain-controlled extension at fixed $\nu$ (the ratio of transverse contraction to axial extension) prescribes the volumetric expansion (triaxiality) at a given axial strain, which uniaxial-deformation and uniaxial-stress protocols cannot do independently. Their central finding: for $0.125 \lesssim \nu \lesssim 0.45$, tightly entangled semiflexible glasses have a significantly lower void volume fraction $f_{\mathrm{v}}(\epsilon,\nu)$ (but far more voids) at the same strain and volumetric expansion than loosely entangled flexible glasses; voids in loosely entangled glasses coalesce more often and grow faster, while tightly entangled glasses keep nucleating new voids well into the strain-hardening regime. Ultrasmall-angle X-ray scattering experiments on moderately ductile glasses (Charvet et al., Macromolecules 52, 6613, 2019; Djukic et al., Macromolecules 53, 5538, 2020) had found precisely this signature — homogeneous void nucleation just ahead of craze fronts, where the pressure $P$ is most negative — and argued from mechanistic models that strain hardening, not entanglement per se, is the proximate cause of suppressed void growth, while earlier simulations suggested entanglements act directly as topological blockers only near the final hardening regime. The simulation study was performed in the athermal $T \to 0$ limit, where cavitation is purely stress-activated (voids form only when local energy barriers vanish), and in small periodic representative volume elements (RVEs), and it quantified initial packing heterogeneity only through the dispersion of Voronoi cell volumes (the spread of nearest-neighbor cage sizes, a standard local-packing measure) — leaving open how spatially heterogeneous local elastic moduli evolve with strain and steer where voids form.

Problem Statement

The problem, posed by Nan, Abritta and Hoy (Macromolecules 54, 7347, 2021) and still unresolved, is to determine what controls the character of cavitation in glassy polymers — ductile cavitation (many small, slowly growing, non-coalescing voids) versus runaway void growth and coalescence leading to crazing and brittle fracture — as a jointly coherent function of entanglement density, strain hardening, chain stiffness, imposed Poisson ratio, and temperature. Its four linked facets, which jointly support this single objective — facet 1 is the open question the source explicitly labels as remaining, and facets 2–4 are the follow-up directions it proposes toward that same objective — are:

1. Mechanistic decoupling (the core). Determine whether entanglements suppress void growth directly, through topological constraints on chain strands spanning a void, or indirectly, by raising the strain-hardening modulus $G_{\mathrm{R}}$ and thereby the local stress and pressure fields that stabilize voids.

2. Finite-temperature extension. Extend from the athermal $T \to 0$ limit, where cavitation is purely stress-activated, to finite temperature up to the room-temperature-relevant $T \simeq 3T_{\mathrm{g}}/4$ regime, determining how the reported $\nu$- and $\kappa$-dependencies of cavitation character change when thermal activation over (and lowering of) cavitation energy barriers is allowed.

3. Connection between simulations and craze-front experiments. Establish whether the homogeneous void nucleation and suppressed void growth observed in small periodic representative volume elements are responsible for the experimentally observed void nucleation ahead of craze fronts and for precursors to fracture.

4. Elastic heterogeneity. Quantify how spatially resolved elastic heterogeneity (local moduli) evolves with increasing strain and how that evolution depends on chain stiffness $\kappa$ and Poisson ratio $\nu$, connecting initial packing heterogeneity (Voronoi-volume dispersion) to preferential cavitation sites and to the continued void nucleation observed in tightly entangled glasses.

A complete answer identifies, with evidence at the molecular or microstructural level, which factor(s) stabilize voids against growth under which conditions, and thereby when each cavitation character — ductile or runaway — is expected. A resolution requires facets 1 and 2 — the mechanistic decoupling, carried out over the chain-stiffness values used by the source and $0.125 \lesssim \nu \lesssim 0.45$, together with its finite-temperature extension; facets 3 and 4 are encouraged extensions that deepen the account rather than separate requirements.

References

1. Kai Nan, Pedro Abritta, and Robert S. Hoy, "How Does the Character of Glassy-Polymeric Cavitation Depend on Entanglement Density and the Local Poisson Ratio?", Macromolecules 54(16), 7347–7353 (2021). DOI 10.1021/acs.macromol.1c01128, https://doi.org/10.1021/acs.macromol.1c01128
2. Joseph D. Dietz, Kai Nan, and Robert S. Hoy, "Unexpected Ductility in Semiflexible Polymer Glasses with Entanglement Length Equal to Their Kuhn Length", Physical Review Letters 129, 127801 (2022). DOI 10.1103/physrevlett.129.127801, arXiv:2205.12060, https://doi.org/10.1103/physrevlett.129.127801
3. Kai Nan and Robert S. Hoy, "Craze Extension Ratio of Semiflexible Polymer Glasses", Macromolecules 56(20), 8369–8375 (2023). DOI 10.1021/acs.macromol.3c01608, https://doi.org/10.1021/acs.macromol.3c01608
4. Robert S. Hoy, "Glassy polymers' strain-hardening moduli scale with their statistical-segment volumes", Physical Review Materials 10, 045603 (2026). DOI 10.1103/6qn6-9zrz, arXiv:2511.16833 (2025 preprint), https://doi.org/10.1103/6qn6-9zrz
5. Tobias Laschuetza, Ting Ge, Thomas Seelig, and Joerg Rottler, "Molecular Simulations of Crazes in Glassy Polymers under Cyclic Loading", Macromolecules 57(23), 10894–10902 (2024). DOI 10.1021/acs.macromol.4c01445, https://doi.org/10.1021/acs.macromol.4c01445
6. Shanshan Xu, Grégory Stoclet, Jean-François Tahon, Isabelle de Waele, and Valérie Gaucher, "Microscopic Origin of the Brittle-to-Ductile Transition Induced by Macromolecular Orientation in Glassy Polymers: From Crazes to Shear Bands", Macromolecules 58(17), 9272–9284 (2025). DOI 10.1021/acs.macromol.5c00607, https://doi.org/10.1021/acs.macromol.5c00607
7. Maximilian Ries, Lukas Laubert, Paul Steinmann, and Sebastian Pfaller, "Impact of the unimodal molar mass distribution on the mechanical behavior of polymer nanocomposites below the glass transition temperature: A generic, coarse-grained molecular dynamics study", European Journal of Mechanics – A/Solids 107, 105379 (2024). DOI 10.1016/j.euromechsol.2024.105379, https://doi.org/10.1016/j.euromechsol.2024.105379
8. Ruibin Ma, Wenfeng Zhang, Yimin Wang, Haoxiang Li, Xiuying Zhao, Xiaolin Li, Liqun Zhang, and Yangyang Gao, "Manipulating the Void Nucleation and Propagation in Silica Nanoparticle/Polyisoprene Nanocomposites via Grafted Chains: A Multiscale Simulation", Macromolecules 56(21), 8448–8460 (2023). DOI 10.1021/acs.macromol.3c01387, https://doi.org/10.1021/acs.macromol.3c01387
9. A. Charvet, C. Vergelati, P. Sotta, and D. R. Long, "Damage Mechanisms of Plasticized Cellulose Acetate under Tensile Deformation Studied by Ultrasmall-Angle X-ray Scattering", Macromolecules 52(17), 6613–6632 (2019). DOI 10.1021/acs.macromol.9b00858, https://doi.org/10.1021/acs.macromol.9b00858
10. S. Djukic, A. Bocahut, J. Bikard, and D. R. Long, "Study of Damage Mechanisms of Amorphous and Low Semicrystalline Polymers under Tensile Deformation by Ultrasmall-Angle X-ray Scattering", Macromolecules 53(13), 5538–5559 (2020). DOI 10.1021/acs.macromol.0c00534, https://doi.org/10.1021/acs.macromol.0c00534