Why Plastic 'Glass' Snaps or Bends: New Model Predicts the Brittle-Ductile Switch Within 5 Kelvin

Glasses are mostly brittle. Metals can bend. Liquids flow. Polymers are strange because they can do all three, depending on their chemistry, their temperature and how fast they are deformed. A new theoretical model aims to explain exactly when a polymer glass will snap and when it will bend, and it matches experiments for three common plastics.

The work comes from Valeriy Ginzburg, a visiting professor at Michigan State University and a former Dow Chemical researcher, working with Prof. Oleg Gendelman of the Technion in Israel and Prof. Alessio Zaccone of the University of Milan. Ginzburg described the approach in a Phys.org feature.

The puzzle is easy to state. If a polymer cannot crystallize, its low-temperature state is glassy, hard and transparent. A familiar example is poly(methylmethacrylate), or PMMA, used as artificial glass since the early 20th century. Yet such polymer glasses can deform plastically at temperatures well below their glass transition temperature. A "glass" would be expected to be brittle, but often it is not.

The team started with a simple model that reproduces three types of stress-strain behavior: brittle (Type I), ductile with a stress overshoot (Type II), and ductile with no overshoot (Type III). It builds on the Maxwell element, a century-old representation of viscoelastic materials as a spring and a dashpot in series, with two changes. The spring is no longer linear but follows a sinusoidal function of elastic strain, reflecting an energy landscape with many minima. And the dashpot's viscosity drops at large strains, as the Eyring-Long model predicts.

From this, the researchers calculate the yield strain at each strain rate. At small rates the yield strain is small and the curve is Type III. At intermediate rates the yield strain is larger and the curve is Type II. At high rates the model has no solution, the material cannot flow, and the curve is brittle Type I.

That leads to a different way of seeing the brittle-ductile transition. A polymer glass can yield uniformly if the strain rate is below a temperature-dependent threshold, and must break in a brittle fashion if the rate is above it. The team's hypothesis is that the threshold is inversely proportional to the Johari-Goldstein beta-relaxation time. Ginzburg noted that S. Wu of DuPont had proposed the idea empirically in the 1970s, and that the new work supplies a theoretical justification.

Aging matters too. The alpha-relaxation time in glassy polymers depends on how old the sample is, since far below the glass transition the material seldom reaches equilibrium. Analyzing the transition therefore requires knowing the sample's age, a fact experimentalists know but theorists often underappreciate, Ginzburg wrote.

The model produces a "universal" map separating the three behaviors. Using known relaxation times, the team converted it into polymer-specific predictions for PMMA, PVC and polystyrene. For all three, the fit was within 5 kelvin of the experimental data.

Open questions remain. The model's "relaxation time floor" depends on network structure, entanglements, crosslinks and pretreatment, and a full theory is still elusive. Predicting failure also needs the yield or fracture stress, which the team is addressing with molecular simulations and experiments to forecast full stress-strain curves and help design better plastics.