Material Strength Doesn’t Follow the Rules
On the microscale, metallic materials are made of homogeneous crystalline regions—grains—separated by disordered boundaries. In general, materials with smaller grains are stronger because they have more grain boundaries, which impede deformation. But researchers have now demonstrated a radical departure from this rule: With rapid deformation, such as that from an explosive impact, finer grained metals are softer, not harder [1]. This new insight, the researchers hope, could be useful for engineers developing impact-resistant alloys for armor, aerospace structures, or hypersonic vehicles.
The yield strength of a material is the stress (force) at which it begins to deform permanently rather than springing back. At the atomic scale in crystalline materials, this deformation occurs when sections of the crystal slide past one another, facilitated by the motion of structural defects called dislocations. But at grain boundaries, dislocations are halted and can pile up, which translates into resistance to deformation and increased yield strength. Materials with smaller grains have more grain boundaries than those with larger grains, so smaller grains are associated with higher strength.
Engineers in the 1950s established the so-called Hall-Petch relationship, which states that the yield strength of a metal is inversely proportional to the square root of its grain size. This “smaller is stronger” paradigm is a foundation of metallurgy, guiding the production of everything from strong ultrafine-grained steels to nanocrystalline coatings.
However, according to materials scientist Mostafa Hassani of Cornell University, several recent studies have suggested that this relationship could break down for metals experiencing rapid deformations. That’s because fast deformation changes the key mechanism by which dislocations move. For slow deformations, dislocations move via a process called thermally activated dislocation gliding, in which thermal energy allows dislocations to push past many obstacles. At high deformation rates, dislocations move much faster and can travel ballistically—meaning that they move longer distances without encountering obstacles. But in this regime they experience friction from interactions with lattice vibrations (phonons), a phenomenon called phonon drag. Hassani and colleagues wanted to investigate in detail how this regime might affect the relationship between grain size and material strength.
When studying rapid deformations, engineers quantify the deformation speed through the so-called strain rate, which reflects the fractional change in a sample’s size occurring per second (s–1). To achieve strain rates as high as 109 s–1, Hassani and colleagues used a technique called laser-induced projectile impact testing.
In their experiment, a powerful laser pulse hits a 210-µm-thick piece of glass, the opposite surface of which is coated with a composite chromium-polymer film and silica microspheres tens of micrometers in diameter. The film material, turned to plasma by the laser energy, propels the microspheres at supersonic speeds toward a polished copper target. The researchers used high-speed photography to capture the impact and rebound velocities and confocal microscopy to measure the volumes of the resulting craters. The three targets they used had average grain sizes of 1, 6, and 100 µm. For strain rates from 1 to 100 s–1, the team used a standard technique called nanoindentation, where a microscopic diamond-tipped probe presses into a material with a controllable speed.
The researchers found that at strain rates up to 100 s–1, the expected Hall-Petch trend held: Smaller grains led to smaller craters, indicating higher hardness, which is closely related to yield strength. However, for ultrahigh strain rates in the range 108 to 109 s–1, this trend inverted. Smaller grains led to larger craters, implying a softer material under these extreme conditions.
To explain this inversion, Hassani and colleagues took the standard theory for thermally activated dislocation gliding and extrapolated it to their experiments’ high strain rates. They found that the predicted hardness for each sample was lower than the measured value, and they attributed the additional hardness to phonon drag. According to the data, this phonon-drag-associated hardness decreases with decreasing grain size. The researchers found that it drops from 4.2 gigapascals in 100-µm copper to 1.4 gigapascals in 1-µm copper. Part of their explanation for this reduction in phonon drag is that smaller grains inhibit ballistic motion of dislocations, which reduces dislocation–phonon interactions.
Materials scientist Christopher Schuh of Northwestern University in Illinois says that this work is in-line with other recent studies showing that some basic principles get turned on their heads under extreme conditions. “It will be exciting to see how materials design must be changed for high-rate applications in light of such phenomena,” he says.
–Mark Buchanan
Mark Buchanan is a freelance science writer who splits his time between Abergavenny, UK, and Notre Dame de Courson, France.
References
- L. Wu et al., “Smaller grains are not stronger: Microcrystalline metals at ultrahigh strain rates,” Phys. Rev. Lett. 136, 016104 (2026).