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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

On the Strain Rate Sensitivity Measured by Nanoindentation at High Strain Rates

The flow stress of a material can be strongly dependent on the rate of applied strain. Measuring the strain rate sensitivity can reveal key insights into the mechanisms that drive plastic deformation. Indentation techniques have been developed to measure the strain rate sensitivity at quasistatic strain rates, but accessing higher strain rate regimes has been saddled with experimental and technical challenges. With state-of-the-art indentation instrumentation now capable of recording load and displacement at data acquisition rates in excess of 1.25 MHz, we report how strain rate sensitivity testing methodologies, especially those aimed for higher indentation strain rates, may be validated using the well-studied time-dependent deformation behavior of tungsten. Here, the strain rate sensitivity for a (110) single crystal is shown to be consistent (m = 0.023 at 2 µm depth) across all tested strain rates and methods ranging from 10 -2 - 10 4 1/s.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Comparisons Between Array Derived Dynamic Strain Rate (ADDS) and Fiber‐Optic Distributed Acoustic Sensing (DAS) Strain Rate

Abstract Distributed acoustic sensing (DAS) strain rate and particle velocity can be compared through approximate scaling with medium velocity. We instead performed a direct comparison between array derived dynamic strain (ADDS) rate and DAS strain rate for six frequency bands. The PoroTomo project at Brady's Hot Springs, Nevada, deployed a 240‐geophone 3C array co‐located with fiber‐optic DAS system and 8.7 km of buried cable. We selected subsets of the geophone array to create four smaller arrays and computed ADDS. The horizontal components of the ADDS were rotated into the direction of the fiber‐optic cable and then compared with the observed DAS strain rates. From three example regional earthquakes of local magnitudes 2.9, 4.1, and 4.3, the ADDS are found to be coherent with DAS for frequencies ≤1 Hz. For frequencies >1‐Hz, this correlation decays quickly. Small differences between linear and areal dynamic strains at 1‐Hz suggest poor signal‐to‐noise or localized strain that is perturbed by shallow heterogeneities compare to the average strain propagating across the geophone array. The implication is that around 1‐Hz, straight fiber DAS is measuring axial strain along the fiber and can provide good approximations to translational particle motions. However, above 1‐Hz, DAS becomes more sensitive to shallow velocity gradients that can be beneficial for geophysical imaging yet becomes a limitation for traditional seismic analysis methods depending on absolute amplitude and phase from translational particle motions.

58 GEOSCIENCES↗
DOE OSTI2020

Nonmonotonic Strain Rate Dependence on the Strain Hardening of Polymer Nanocomposites

This Letter investigates the external deformation on modifying the polymer–nanoparticle (NP) and NP–NP interactions as well as their influences on the macroscopic properties of polymer nanocomposites (PNCs). Specifically, the applied uniaxial extension brings together the NPs along the transverse stretching direction and catalyzes the percolation transition from the initially well-dispersed NPs in the PNCs. The percolated NP network thus increases the strength of PNCs and leads to a strong surge in the elongation viscosity at very low strain rates, exhibiting the unexpected nonmonotonic strain rate dependence on the strain hardening. These results reveal explicitly the unconventional roles of the external deformation on modulating the relative strength of the polymer–NP and the NP–NP interactions, enabling advanced structures and properties control of PNCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Extending the range of constant strain rate nanoindentation testing

Constant strain rate nanoindentation hardness measurements at high sustained strain rates cannot be made in conventional nanoindentation testing systems using the commonly employed continuous stiffness measurement technique (CSM) because of the “plasticity error” recently reported by Merle et al. [Acta Mater.134, 167 (2017)]. To circumvent this problem, here we explore an alternative testing and analysis procedure based on quasi-static loading and an independent knowledge of the Young's modulus, which is easily obtained by standard nanoindentation testing. In theory, the method applies to any indentation strain rate, but in practice, an upper limit on the rate arises from hardware limitations in the testing system. The new methodology is developed and applied to measurements made with an iMicro nanoindenter (KLA, Inc.), in which strain rates up to 100 s -1 were successfully achieved. The origins of the hardware limitations are documented and discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Evolution of dislocation substructures in metals via high-strain-rate nanoindentation

Deformation at high strain rates often results in high stresses on many engineering materials, potentially leading to catastrophic failure without proper design. High-strain-rate mechanical testing is thus needed to improve the design of future structural materials for a wide range of applications. Although several high-strain-rate mechanical testing techniques have been developed to provide a fundamental understanding of material responses and microstructural evolution under high-strain-rate deformation conditions, these tests are often very time consuming and costly. In this work, we utilize a high-strain-rate nanoindentation testing technique and system in combination with transmission electron microscopy to reveal the deformation mechanisms and dislocation substructures that evolve in pure metals from low (10 –2 s –1 ) to very high indentation strain rates (10 4 s –1 ), using face-centered cubic aluminum and body-centered cubic molybdenum as model materials. The results help to establish the conditions under which micro- and macro-scale tests can be compared with validity and also provide a promising pathway that could lead to accelerated high-strain-rate testing at substantially reduced costs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Temporal dynamics of the alignment of the turbulent stress and strain rate

We report that the flux of energy between scales in turbulence can be cast as the result of the interaction between a turbulent stress and a rate of strain. Efficient energy transfer requires that these two tensors be oriented properly relative to each other, but previous work has shown that the instantaneous alignment between them is poor. Here, we consider the temporal dynamics of this alignment in a direct numerical simulation of isotropic turbulence. We show that the orientation of the stress lags behind that of the strain rate, both at a single location and along trajectories. However, the timescale of the reorientation of the stress in these cases does not follow the expected dynamical scaling with length scale. To capture the proper dynamical scaling, we reformulate the energy flux between scales using the right Cauchy-Green strain tensor and the second Piola-Kirchhoff stress tensor. Our results highlight the key role played by the deformation of fluid elements in the physics of the energy cascade, and suggest that their irreversible deformation is a Lagrangian manifestation of the cascade's broken time-reversal symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Mechanical characterization of 304L-VAR stainless steel in tension with a full coverage of low, intermediate, and high strain rates

A 304L-VAR stainless steel is mechanically characterized in tension over a full range of strain rates from low, intermediate, to high using a variety of apparatuses. While low- and high-strain-rate tests are conducted with a conventional Instron and a Kolsky tension bar, the tensile tests at intermediate strain rates are conducted with a fast MTS and a Drop-Hopkinson bar. The fast MTS used in this study is able to obtain reliable tensile response at the strain rates up to 150 s -1 , whereas the lower limit for the Drop-Hopkinson bar is 100 s -1 . Combining the fast MTS and the Drop-Hopkinson bar closes the gap within the intermediate strain rate regime. Using these four apparatuses, the tensile stress-strain curves of the 304L-VAR stainless steel are obtained at strain rates on each order of magnitude ranging from 0.0001 to 2580 s -1 . All tensile stress-strain curves exhibit linear elasticity followed by significant work hardening prior to necking. After necking occurrs, the specimen load decreases, and the deformation becomes highly localized until fracture. The tensile stress-strain response of the 304L-VAR stainless steel exhibits strain rate dependence. The flow stress increases with increasing strain rate and is described with a power law. The strain-rate sensitivity is also strain-dependent, possibly due to thermosoftening caused by adiabatic heating at high strain rates. The 304L-VAR stainless steel shows significant ductility. The true strains at the onset of necking and at failure are determined. The results show that the true strains at both onset of necking and failure decrease with increasing strain rate. The true failure strains are approximately 200% at low strain rates but are significantly lower (~100%) at high strain rates. The transition of true failure strain occurs within the intermediate strain rate range between 10 -2 and 10 2 s -1 . A Boltzmann description is used to present the effect of nominal strain rate on true failure strain.

304L-VAR stainless Steel↗
DOE OSTI2022

Crustal Strain Rates in the Western United States and Their Relationship with Earthquake Rates

Abstract We present a suite of strain rate models for the western United States based on geologic and geodetic data. The geologic data consist of Quaternary fault-slip rates and the geodetic data consists of a new compilation of Global Positioning System (GPS) velocities derived from continuous, semicontinuous, and campaign measurements. We remove postseismic deformation from the GPS time series in order for our geodetic strain rate model to best capture the interseismic strain accumulation rate. We present models based on either geologic or geodetic data, but also create a hybrid model. Although there are some differences between the models, the large-scale features are the same, with the noticeable exception for the Pacific Northwest where interseismic strain is naturally more distributed than the long-term strain release. We also present a map of earthquake rate densities based on mainshocks, and the result has similar spatial features similar to the strain rate models (at least in the southwestern United States). We perform a general correlation analysis between strain rate and seismicity rate (south of Cascadia) and find a change in linearity between seismicity and strain rates from slow to faster deforming areas with seismicity rates relatively lower for the latter. The extent of that change depends a bit on assumptions made on the declustering and completeness of the catalog, but the finding of a change in slope is robust across the different strain rate models. Linearity for all areas is only expected when Gutenberg–Richter parameters and parameters involved in the conversion from strain to moment rate are uniform across the study area. We discuss these qualifications, but find no single satisfactory explanation for our observation. Moreover, when considering a rather short time and space, theoretical considerations of sampling from a power-law distribution actually predict there to be a power law instead of a linear relationship, generally consistent with our observation.

Geochemistry & Geophysics↗
DOE OSTI2022

High strain-rate compression behavior of polymeric rod and plate Kelvin lattice structures

The compressive high strain-rate behavior of polymeric Kelvin lattice structures with rod-based or plate-based unit cells was investigated through experimental techniques and finite element simulations. Polymeric lattice structures with 5x5x5 unit cell geometries were manufactured on the millimeter scale using vat polymerization additive manufacturing and tested at low (0.001/s) and high (1000/s) strain-rates. High strain-rate experiments were performed and validated for a viscoelastic split-Hopkinson (Kolsky) pressure bar system (SHPB) coupled with high-speed imaging and digital image correlation (DIC). Experimental results at both low and high strain-rates show the formation of a localized deformation band which was more prevalent in low relative density specimens and low strain-rate experiments. Strain-rate effects of lattice specimens strongly correlate with effects of the base polymer material; both bulk polymer and lattice specimen demonstrated strain-rate hardening, strain-rate stiffening, and decreased fracture strain under dynamic loading. Results show mechanical failure properties and energy absorption depended strongly on the relative density of the lattice specimen and exhibited distinct scaling between relative density and geometry type (rod, plate) and loading rate. High relative density plate-lattices demonstrated inferior mechanical properties to rod-lattices; however, there exists a critical relative density for a given mechanical property (17%- 28%) below which plate-lattices outperform rod-lattices of similar mass. As a result, high strain-rate explicit finite element simulations were performed and showed good agreement with the mechanical failure trends and deformation modes observed in the experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2023

High strain rate nanoindentation testing: Recent advancements, challenges and opportunities

Recent advancements in electronics have renewed the interest in high strain rate nanoindentation testing, resulting in the development of new high strain rate nanoindentation test equipment and test methodologies. Here, in this work, the current state-of-the-art in high strain rate nanoindentation testing is critically reviewed, with focus on three key aspects - the testing equipment's dynamic mechanical and electronic response, test methodology, and post-processing of raw data to obtain hardness and strain rate. The challenges in instrument hardware design and post-test data analysis are discussed, along with optimal strain rate window for accurate high strain rate measurements. Specific focus will be on instrumented high strain rate testing using self-similar indenters at strain rates in excess of 100 s -1 , wherein load and depth of penetration into the sample are both measured or applied.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Ramp-release experiments for strength measurements: Strain-rate dependence

This paper presents an enhanced analysis method for investigating material properties at high strain rates, extending the capability of established experimental techniques to gain more information. The ramp-release method has been applied to many experiments reported at high (≈10 5 − 10 6 s −1 ) strain-rates. More recent data gathered at the National Ignition Facility (NIF) has enabled higher (≈10 8 s −1 ) strain-rates to be studied. Here, we present an initial application of ramp-release analysis to NIF ramp-compression data, illustrating both the opportunities and the practical challenges of extending these methods to laser-driven platforms. The higher strain-rates accessed at the NIF mean that there is more strain-rate enhancement to strength, and the experimental configuration means that this enhancement is more readily seen in the data. This is enabled by the capability of avoiding peak-compression attenuation through the sample thickness with a designed hold period made possible by the pulse-shaping capability of NIF. We propose that this combination of experimental conditions and an enhanced analysis method enables the strain-rate enhancement to strength to be studied, and potentially for this to inform physics models at smaller scales than the continuum.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: Application to alloy AZ31

We report the fundamental power-law relationship representing the flow rule in crystal visco-plasticity ensures uniqueness in the selection of slip systems accommodating imposed plastic strain-rates. The power-law relationship also introduces an artificially high strain-rate sensitivity in crystal plasticity simulations, unless a high value of the power-law exponent is used. However, the use of high values for the exponent is limited by numerical tractability. This paper presents a numerical method implemented in a crystal plasticity finite element (CPFE) model for embedding any value of the power-law exponent reflecting the true material strain-rate sensitivity. Importantly, the method does not increase computation time involved in the simulations. The enhanced CPFE model is used to interpret and predict a complex strain-rate sensitive response and microstructural evolution of AZ31 Mg alloy. Measured values of strain-rate sensitivity for slip and twinning modes are used in the simulations. Calculations show that the model successfully captures the phenomena pertaining to the effect of changing applied strain-rate on the mechanical response including flow stress and evolution of texture and twinning for a broad range of strain-rates ranging from 10 -3 s -1 to 10 3 s -1 and loading orientations in tension and compression. It is shown that such predictions are a consequence of not only relative amounts of slip and twinning activities driven by a set of accurately characterized hardening law parameters but also values of the strain-rate sensitivities inherent to individual deformation mechanisms. Besides, the model validates the measured strain-rate dependency of deformation mechanisms while accurately reproducing the mechanical data. Hence, the model can be used to verify and further refine or infer measured strain-rate sensitivity per deformation mechanism by reproducing experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Nanomechanical mapping and strain rate sensitivity of microcrystalline cellulose

Nanoindentation provides a convenient and high-throughput means for mapping mechanical properties and for measuring the strain rate sensitivity of a material. Here, nanoindentation was applied to the study of microcrystalline cellulose. Here, constant strain rate nanoindentation revealed a depth dependence of nanohardness and modulus, mostly attributed to material densification. Nanomechanical maps of storage modulus and hardness resolved the shape and size of voids present in larger particles. In smaller, denser particles, however, where storage modulus varied little spatially, there was still some spatial dependence of hardness, which can be explained by cellulose’s structural anisotropy. Additionally, hardness changed with the indentation strain rate in strain rate jump tests. The resulting strain rate sensitivity values were found to be in agreement with those obtained by other techniques in the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Strain-rate hardening enhances fatigue resistance of AlSi10Mg alloy at 350°C

The high cycle fatigue behavior of laser powder bed fusion processed AlSi10Mg has been investigated at 350 °C (T/T m ∼ 0.7). The alloy exhibited a fatigue strength of 30 MPa defined by runout after 10 7 cycles at a conventional loading frequency of 20 Hz, corresponding to a notable fatigue strength to ultimate tensile strength ratio of 0.73. The surprising fatigue resistance was attributed to the strain-rate hardening effect at high fatigue loading frequency relative to tensile loading rates at 350 °C. The strain-rate hardening effect was validated by performing ultrasonic fatigue tests (20 kHz loading frequency) with three orders of magnitude higher strain-rates than those at conventional loading frequency. The higher strain-rates in ultrasonic fatigue increased the magnitude of strain-rate hardening resulting in longer AlSi10Mg fatigue lives compared to fatigue at conventional frequency, thus confirming the strain-rate hardening effect. The fatigue crack initiation mechanism was strain-rate dependent. Post-mortem microstructural examination revealed intergranular cavitation inside clusters of fine equiaxed grains. The cavities interlinked with each other to initiate near-surface fatigue cracks at conventional frequency. Cavitation occurred to a lesser extent at the ultrasonic frequency. As a result, fatigue cracks initiated at pre-existing processing defects near the surface in ultrasonic fatigue samples. Finally, this investigation underscores the role of fine grain clusters in promoting high-temperature fatigue crack initiation and indicates a possible trade-off between printability via grain refinement and high-temperature fatigue resistance of additively manufactured alloys.

Additive manufacturing↗
DOE OSTI2025

Influence of strain-rate on the response of elastomeric architected materials

Architected materials have shown substantial promise in impact mitigation and protective applications, and there has accordingly been great interest in better characterizing their response at elevated strain rates due to impact. There remains ambiguity regarding the contribution of inertial and material responses to strain rate sensitivity, and, in particular, when these effects begin to gain dominance in the impact response of an architected material. The response of soft polymer architected materials as a function of strain rate, in particular, has been little investigated. We characterize the experimental impact response of four soft polymer architected lattice geometries across varying strain rates in the intermediate strain rate regime (∼10 3 s −1 ) using split-Hopkinson pressure bar loading and high speed video characterization of the resulting deformation fields. In conclusion, our results highlight the interplay of influence between constituent material, lattice geometry, length scale, and strain rate in determining the onset of significant inertia effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Strain rate effects on the mechanical behavior of porous titanium with different pore sizes

High strain-rate (up to 6600 s –1 ) and quasi-static compression tests are conducted on a powder-sintered porous titanium with different pore sizes (mean: 30 μm and 120 μm). In situ X-ray imaging is implemented to characterize the pores-scale deformation dynamics. The yield strength as a function of strain rate exhibits two stages of rate sensitivity, and the transition occurs at 1600 s –1 . X-ray images show that pore compaction and strain localizations occur preferentially at pores oriented perpendicular to the loading direction under quasi-static loading, but become more random under high strain-rate loading as a result of higher driving force and plastic deformation nucleation rate. Here, the more homogeneous nucleation of plastic deformation contributes to the increased rate sensitivity beyond 1600 s –1 . At the same strain rate, the yield strength of porous Ti as well as strain field homogeneity decreases significantly with increasing pore size. The small pore spacing in fine-pored Ti reduces the degree of stress concentrations around pores. Therefore, the higher stress concentrations in coarse-pored Ti lead to an earlier yield of matrix around pores and thus a lower bulk yield strength.

36 MATERIALS SCIENCE↗