Decoupling dislocation multiplication and velocity effects in metals at extreme strain rates

The dynamic behavior of metals is governed by collective dislocation motion and interactions that strongly depend on the applied strain rate. Metals exhibit weak strain rate sensitivity (SRS) below a certain threshold, followed by a distinct SRS upturn at higher loading rates. While this upturn is typically attributed to increased glide resistance at high dislocation velocity due to mechanisms such as phonon drag, the role of strain-rate-dependent dislocation multiplication and microstructural evolution under these extreme conditions remains elusive. Here, we decouple these two strengthening effects and show that, while dislocation velocity primarily governs the SRS upturn, the hardening due to microstructure evolution depends strongly on the initial dislocation density. Our investigation of hardness evolution across ten decades of strain rates in a quenched and tempered martensitic low-carbon steel (LCS) using laser-induced projectile impact tests (LIPIT) and nanoindentation reveals SRS upturn around 10^7 1/s. By performing in situ re-indentation of the formed craters, we probe the contribution of dislocations generated during initial deformation at different strain rates. We show that while dislocation multiplication plays a negligible role in fine-grained LCS with high dislocation density, a pronounced dislocation multiplication contributes to the hardness increase in pure iron with lower initial dislocation density. Our results show that, depending on the initial microstructure of metals, dislocation multiplication significantly governs high-strain-rate plasticity, in addition to dislocation velocity effects.

💡 Research Summary

This paper presents a comprehensive investigation into the fundamental mechanisms governing the plastic deformation of metals at extreme strain rates, with a focus on decoupling the often-conflated effects of dislocation velocity and dislocation multiplication. The study aims to elucidate the physical origins behind the well-documented upturn in strain rate sensitivity (SRS) observed in many metals beyond strain rates of approximately 10^7 /s.

The research employs two body-centered cubic (BCC) iron-based materials with starkly contrasting initial microstructures: a quenched and tempered martensitic low-carbon steel (LCS) featuring a fine lath structure with high intrinsic dislocation density, and commercially pure iron with large grains and low initial dislocation density. To span an unprecedented ten orders of magnitude in strain rate, the experimental methodology ingeniously combines two techniques: (1) quasi-static and dynamic nanoindentation (NI) for rates from ~10^-1 to 10^3 /s, and (2) laser-induced projectile impact testing (LIPIT) for ultra-high strain rates from 10^5 to over 10^7 /s. A critical innovation is the post-impact “re-indentation” of craters formed by LIPIT using quasi-static NI, which allows for the isolation and measurement of hardness contributions solely from defects generated during the high-rate deformation event.

To enable quantitative comparison between these disparate methods, the authors establish self-consistent definitions. Hardness is defined based on the total work done divided by the crater volume, and the nominal strain rate is defined using a work-averaged velocity derived from either the indentation history (NI) or finite element modeling (LIPIT). The Johnson-Cook plasticity model is calibrated via FEM to bridge the experimental data across the strain-rate spectrum.

The key findings are as follows. Both materials exhibit a distinct SRS upturn in hardness around 10^7 /s, confirming this as a general phenomenon. This upturn is primarily attributed to the increased drag on dislocations (e.g., phonon drag) as their velocities become relativistic, a conclusion supported by the consistent onset strain rate across materials.

However, the re-indentation experiments reveal a crucial divergence tied to initial microstructure. For the LCS with high initial dislocation density, the hardness measured inside the high-rate impact craters showed negligible dependence on the prior strain rate. This indicates that little additional dislocation multiplication or microstructural evolution occurred during high-speed deformation; the observed hardening was almost entirely due to the velocity-dependent resistance on the pre-existing and newly generated dislocations during the first impact.

In stark contrast, for pure iron with low initial dislocation density, re-indentation revealed a significant increase in hardness compared to its pristine state. This increase was more pronounced for craters formed at higher impact velocities. This provides direct evidence that in pure iron, substantial dislocation multiplication occurs during high-strain-rate deformation, and this multiplication contributes appreciably to the overall hardening, alongside the dislocation velocity effect.

In conclusion, the study successfully decouples the two strengthening mechanisms at extreme strain rates. It demonstrates that while the SRS upturn itself is universally governed by dislocation kinematics and drag forces, the additional contribution from strain-rate-dependent dislocation multiplication and structural evolution is not universal. Instead, it is strongly filtered by the material’s initial microstructure, particularly its initial dislocation density. This work establishes that the dynamic response of metals at extreme conditions is a complex interplay between intrinsic velocity limits and extrinsic, microstructure-dependent multiplication capabilities, offering a refined framework for predicting material behavior in high-impact and high-rate manufacturing applications.