Machine Learning Meets Ballistics: Predicting How PEEK Plates Deflect High-Speed Impacts

When a steel sphere slams into a plastic plate at several hundred meters per second, the outcome unfolds in fractions of a millisecond. Whether the projectile punches through, ricochets, or grinds out a crater depends on a delicate interplay of speed, angle, and the material’s internal character. A team of researchers from Southwest Jiaotong University, The Peac Institute of Multiscale Sciences, Ningbo University, and the Chinese Academy of Sciences has now mapped that interplay for one of engineering’s most prized polymers, polyether ether ketone, better known as PEEK. Their study, published in the Journal of Materials Science, combines high-speed ballistic experiments, detailed finite element simulations, and a neural network trained to predict how obliquely struck PEEK plates will respond.

PEEK occupies a special niche in the materials world. This semi-crystalline thermoplastic boasts an unusual combination of strength, toughness, chemical resistance, and thermal stability, which explains its popularity in aerospace structures, biomedical implants, and high-performance bearings. Yet precisely because it is increasingly used in applications where foreign object debris and high-velocity impacts threaten structural integrity, engineers need to know how it behaves when struck at angles rather than head-on. Most ballistic studies focus on normal incidence, where the projectile travels perpendicular to the target surface. Oblique impact, by contrast, is far more common in the real world, from runway debris kicked up at shallow angles to micrometeoroids grazing spacecraft panels, and it produces fundamentally different failure patterns.

The research team, led by J. Y. Hua and S. N. Luo, fired spherical stainless steel projectiles at PEEK plates at an incident angle of 60 degrees, with velocities ranging from roughly 100 to 450 meters per second. This velocity window spans the transition from low-speed denting to high-speed penetration, making it an ideal regime for probing how the material’s response evolves. High-speed imaging and post-impact examination of the targets revealed the dominant failure mode: wear-induced ductile damage. Rather than shattering brittly, the PEEK deformed plastically, material accumulated and smeared along the crater path, and the surface failed through a process reminiscent of erosive wear, consistent with earlier impact and erosion studies of the polymer dating back decades.

Central to the study is a new dynamic constitutive model for PEEK, built from uniaxial compression tests conducted across an unusually wide range of conditions, with strain rates from 0.001 to 5000 per second and temperatures from 300 to 473 Kelvin. Under all these conditions, PEEK displayed classic elastic-plastic behavior, but with two competing trends: strain rate hardening, where the material grows stronger when deformed faster, and thermal softening, where it weakens as temperature rises. The researchers captured the elastic modulus with a sigmoidal function of normalized temperature, anchored around the glass transition, multiplied by a power-law term for strain rate effects. The plastic flow stress was described by combining a Johnson-Cook style strain hardening term with a three-segment strain rate sensitivity model and a linear thermal softening coefficient.

The details of that strain rate sensitivity are revealing. The normalized flow stress of PEEK rises gently at low strain rates, transitions through a smooth curved region between roughly 100 and 316 per second, and then climbs steeply at high rates, with the slope in the high-rate regime more than seven times that of the low-rate regime. This three-segment structure, connected with strict continuity at the turning points, reflects the polymer’s underlying relaxation physics, in which different molecular mechanisms dominate at different timescales. The model also incorporates a Mie-Grüneisen equation of state to handle volumetric compression and accounts for adiabatic heating, assuming that about 60 percent of plastic work converts to heat, a standard assumption for polymers in impact simulations.

With the material model in hand, the team built finite element simulations using a coupled Eulerian-Lagrangian approach, a technique well suited to problems involving extreme deformation where conventional mesh-based methods would tangle. The simulations reproduced the experimental observations closely, capturing crater shapes, rebound behavior, and energy losses. More importantly, the validated simulations became a data factory. By varying incident angles and impact velocities across many virtual experiments, the researchers generated a large dataset of ballistic responses that would have been prohibitively expensive and time-consuming to produce physically.

That dataset then trained a back-propagation neural network, the workhorse architecture of machine learning, to learn the mapping from impact conditions to outcomes. Once trained, the network predicted the full suite of ballistic response quantities: rebound angle, rebound velocity, and the geometric parameters of the crater, including its dimensions along three axes and its volume. The team distilled these predictions into phase diagrams, maps that delineate regimes of behavior as functions of incident angle and impact velocity, showing at a glance where the projectile rebounds steeply, where it skims and gouges, and how crater geometry shifts across the parameter space.

Critically, the researchers did not simply trust their neural network’s internal logic. They validated the machine learning predictions against an independent impact experiment, one not used in training, and found agreement. This closed loop, from physical experiment to physics-based simulation to machine learning and back to experimental verification, represents a template for how modern materials science increasingly operates. Rather than choosing between expensive experiments and idealized models, the workflow lets each element compensate for the weaknesses of the others: experiments anchor the simulations in reality, simulations supply the statistical volume that experiments cannot, and machine learning compresses both into fast, predictive tools.

The practical implications reach across several industries. For aerospace engineers, PEEK-based composites are attractive for their light weight and toughness, and understanding oblique impact behavior directly informs designs that must tolerate runway debris, hail, and bird strikes. The study’s reference list situates the work within a broader research program by the same groups, which has applied the same experiment-simulation-machine learning pipeline to polycarbonate, ultrahigh molecular weight polyethylene, magnesium alloys, Inconel 718, and high-entropy alloys. Together, these efforts are building a systematic, data-driven science of high-speed impact across material classes, replacing fragmented case-by-case testing with transferable methodology.

There is also a deeper scientific payoff. The constitutive model developed here encodes how PEEK’s molecular architecture, its semi-crystalline structure straddling a glass transition, manifests in macroscopic impact response. The pronounced strain rate sensitivity above the transition region suggests that molecular relaxation processes govern the polymer’s ability to absorb and dissipate impact energy, knowledge that could guide the design of next-generation thermoplastic armor, protective coatings, and impact-tolerant structures. As machine learning tools grow more sophisticated, the ability to generate validated phase diagrams of material behavior on demand may transform how engineers approach impact protection, turning what was once a domain of costly trial and error into a predictive, quantitative discipline. For a polymer that already bridges the operating room and the flight deck, that is a significant step forward.

Subject of Research: Oblique high-speed impact behavior and predictive modeling of polyether ether ketone (PEEK) plates

Article Title: Oblique impact of polyether-ether-ketone (PEEK) plates: ballistic experiments, FEM modeling and machine learning

Article References: Oblique impact of polyether-ether-ketone (PEEK) plates: ballistic experiments, FEM modeling and machine learning. (n.d.). https://doi.org/10.1007/s10853-026-13898-z

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13898-z

Keywords: PEEK, ballistic impact, oblique impact, finite element method, machine learning, neural network, constitutive model, polymers, strain rate hardening, thermal softening, crater geometry, aerospace materials