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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↗

DOE OSTI2022

Decoupling indentation size and strain rate effects during nanoindentation: A case study in tungsten

Materials indented at small scales may simultaneously exhibit indentation size and strain rate effects which complicate the identification of the mechanisms that control deformation and strength. Here, in this work, we explore the possibility that indentation size and rate effects in some materials can be decoupled in a simple way. Nanoindentation tests with various load-time histories were carried out to measure the hardness of a tungsten single crystal over a wide range of indentation depths (~500–3600 nm) and indentation strain rates (~5 ×10 –5 –2 ×10 –1 s –1 ). Under these conditions, this material exhibits significant indentation size and rate effects, but the size effect is, to a good approximation, independent of strain rate. It is shown that this behavior can be understood by the Nix-Gao model for the indentation size effect modified to include the effects of a strain rate dependent friction stress. As a consequence, the size and rate dependencies of the hardness can be expressed as the sum of two independent terms: H($\dot{ε}$ i , h c )=H f ($\dot{ε}$ i ) + (H 0 – H f ) $\sqrt{1+ \frac{h^*}{h_c}}$, where H($\dot{ε}$ i , h c ) is the hardness at given indentation strain rate ($\dot{ε}$ i ) and contact depth (h c ), H f ($\dot{ε}$ i ) is the hardness contributed by the rate dependent friction stress, and (H 0 – H f ) and h* are size and rate independent constants that follow from the Nix-Gao analysis. This formula, together with an expression for the rate dependence of H f , was successfully applied to decouple the indentation size and rate effects observed in tungsten. In addition, the physics underlying the rate independence of indentation size effect is discussed, which provides guidance for application of the proposed approach to other materials.

42 ENGINEERING↗

DOE OSTI2024

Multiscale Richtmyer-Meshkov instability experiments to isolate the strain rate dependence of strength

Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when η 0 k , the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same η 0 k but different length scales, characterized by the wavelength λ varying by a factor of 4.9 from 65 to 130 to 320 µ m . Three such targets with different fixed η 0 k ′ s were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as λ decreased. The different η 0 k targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for 320 − 65 µ m wavelength perturbations, the effective strain rates increased from 8.7 × 10 6 to 3.3 × 10 7 s − 1 , a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

NASA NTRS2002

Computational Simulation of the High Strain Rate Tensile Response of Polymer Matrix Composites

A research program is underway to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Under these types of loading conditions, the material response can be highly strain rate dependent and nonlinear. State variable constitutive equations based on a viscoplasticity approach have been developed to model the deformation of the polymer matrix. The constitutive equations are then combined with a mechanics of materials based micromechanics model which utilizes fiber substructuring to predict the effective mechanical and thermal response of the composite. To verify the analytical model, tensile stress-strain curves are predicted for a representative composite over strain rates ranging from around 1 x 10(exp -5)/sec to approximately 400/sec. The analytical predictions compare favorably to experimentally obtained values both qualitatively and quantitatively. Effective elastic and thermal constants are predicted for another composite, and compared to finite element results.

Goldberg, Robert K.↗

DOE OSTI2022

Strain-rate dependent deformation mechanisms in single-layered Cu, Mo, and multilayer Cu/Mo thin films

Here, strain-rate sensitivity and rate-dependent hardness, over a range of 10 -2 to 10 2 s -1 , of sputter-deposited single-layered Cu, Mo, and 5 nm Cu/ 5 nm Mo, and 100 nm Cu/ 100 nm Mo multilayer films with a total film thickness of 5 μm were measured using nanoindentation. The plastic zone underneath the nanoindents was characterized via cross-sectional transmission electron microscopy (XTEM). The multilayer films exhibited enhanced hardness but slightly reduced strain-rate sensitivity with decreasing layer thickness from 100 nm to 5 nm. Only the 5 nm Cu/ 5 nm Mo multilayer film exhibited shear bands underneath the nanoindents, and the size of the shear bands increased with increasing strain rate. In contrast, the 100 nm Cu/ 100 nm Mo multilayer film exhibited material pile-up around the indents and significant nanotwinning within Cu grains. The effect of strain rate and layer thickness on the hardness and strain rate sensitivity of the multilayer thin films is interpreted using a modified confined layer slip (CLS) model. The reduced rate sensitivity at 5 nm as compared to 100 nm correlates with abundant growth nanotwins in the Cu grains in 100 nm and formation of shear bands in 5 nm multilayers. In single layer films, a substructure with a high density of dislocations was observed consistent with the plastic strain gradient in the indent plastic zone. No evidence of deformation twins was noted in any of the samples.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Self-consistent hardness measurements spanning eleven decades of strain rate on a single material surface

A comprehensive understanding of material strength across strain rates typically requires the combination of results from different methods, which often vary in loading conditions and/or sampled volumes, leading to discrepancies in material behavior. This study presents a microindentation approach to measure hardness covering eleven orders of magnitude in strain rate, from quasi-static to phonon drag-dominated rates, on a single material surface under uniform testing conditions. By engineering the geometry of impactors used in laser induced particle impact testing, we extend the breadth of accessible strain rates, including multiple distinct rates exceeding 10⁵ s⁻¹. This self-consistent approach provides clearer insights into high-rate deformation mechanisms. Our results demonstrate a gradual increase in hardness with strain rate from quasi-static up to ultra-high rates, where a sharp upturn in hardness is observed.

Engineering↗

DOE OSTI2020

Shear localization in metallic materials at high strain rates

Three factors govern adiabatic shear localization: strain hardening (or softening), strain-rate hardening, and thermal softening. It is typically associated with large shear strains (>1), high strain rates (10 3 –10 7 s –1 ), and high temperatures (40–100% of melting point), all of which happen within narrow regions with widths of about 1–200 μm. It is often an undesirable phenomenon, leading to failure, but there are situations where it is desirable, e. g., the generation of machining chips. Here, we review the development of both theoretical and experimental achievements, from the initiation of shear bands to their propagation with emphasis on three aspects: novel experimental techniques, novel materials, and nano/microstructural effects. The principal characteristics of adiabatic shear bands in metallic materials at the nano- and micro-scale are described. Bands that were formerly identified as transformed actually consist of nanocrystalline/ultrafine grains. These grains result from the breakup of the microstructure by a rotational recrystallization process. The evolution of the microstructure inside shear bands and their interactions for hcp, bcc, and fcc alloys, high-entropy alloys, nanocrystalline alloys, and metallic glasses are analyzed mechanistically. In conclusion, the gaps in the field and opportunities for future research are identified. Modern experimental characterization and computational techniques enable a more profound and predictive understanding of adiabatic shear localization and its avoidance in advanced materials.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Effect of processing parameters and build orientation on microstructure and performance of AISI stainless steel 304L made with selective laser melting under different strain rates

Selective laser melting (SLM) process brings diverse potentials on geometry flexibility; therefore, it is more and more widespread to be employed in fabrication metal alloys served for industries. Nonetheless, a material characterization study is desired to carry on for better understanding the correlation among process, structure, microstructure, and performance. In the current study, the SLM fabricated AISI stainless steel 304L was fabricated with different process parameters and built orientations (horizontal, inclined, and vertical. The tensile behavior was evaluated under different strain rates (0.0001 /s, 0.001 /s, 0.01 /s, and 0.1 /s) and compared to the commercial cold-rolled and annealed counterpart. Grain structures, tensile strength, elongation-to-failure, strain rate sensitivity, work hardening, and fractographic analysis were evaluated in terms of the effect of energy density, build orientation, and strain rate. The output indicates the tensile strength increases with increasing strain rates. On the contrary, the elongation-to-failure shows a decreasing trend with strain rates. Tensile properties of specimens built in the horizontal and inclined orientations are more sensitive to strain rates due to the smaller dimension of grain structures. Tensile anisotropy depends on the energy input, where a high energy density could yield a strong build orientation-dependent anisotropy. Hall-Petch relationship is validated to explain the mechanical anisotropy in different built orientations for SLM alloys. The strain hardening exponent and work hardening rate are demonstrated to be positively correlated, and they increase with smaller grain sizes. The fine dimple features indicate the ductile fracture mode regardless of strain rates. The size of the ductile dimples seems to depend on the strain rates and build orientations.

36 MATERIALS SCIENCE↗

NASA NTRS2004

Suppression of Low Strain Rate Nonpremixed Flames by an Agent

The extinction and structure of non-premixed methane/air flames were investigated in normal gravity and microgravity through the comparison of experiments and calculations using a counterflow configuration. From a fire safety perspective, low strain rate conditions are important for several reasons. In normal gravity, many fires start from small ignition sources where the convective flow and strain rates are weak. Fires in microgravity conditions, such as a manned spacecraft, may also occur in near quiescent conditions where strain rates are very low. When designing a fire suppression system, worst-case conditions should be considered. Most diffusion flames become more robust as the strain rate is decreased. The goal of this project is to investigate the extinction limits of non-premixed flames using various agents and to compare reduced gravity and normal gravity conditions. Experiments at the NASA Glenn Research Center's 2.2-second drop tower were conducted to attain extinction and temperature measurements in low-strain non-premixed flames. Extinction measurements using nitrogen added to the fuel stream were performed for global strain rates from 7/s to 50/s. The results confirmed the "turning point" behavior observed previously by Maruta et al. in a 10 s drop tower. The maximum nitrogen volume fraction in the fuel stream needed to assure extinction for all strain rates was measured to be 0.855+/-0.016, associated with the turning point determined to occur at a strain rate of 15/s. The critical nitrogen volume fraction in the fuel stream needed for extinction of 0-g flames was measured to be higher than that of 1-g flames.

Olson, Sandra L.↗

NASA NTRS1991

High strain rate properties of unidirectional composites, part 1

Experimental methods were developed for testing and characterization of composite materials at strain rates ranging from quasi-static to over 500 s(sup -1). Three materials were characterized, two graphite/epoxies and a graphite/S-glass/epoxy. Properties were obtained by testing thin rings 10.16 cm (4 in.) in diameter, 2.54 cm (1 in.) wide, and six to eight plies thick under internal pressure. Unidirectional 0 degree, 90 degree, and 10 degree off-axis rings were tested to obtain longitudinal, transverse, and in-plane shear properties. In the dynamic tests internal pressure was applied explosively through a liquid and the pressure was measured with a calibrated steel ring. Strains in the calibration and specimen rings were recorded with a digital processing oscilloscope. The data were processed and the equation of motion solved numerically by the mini-computer attached to the oscilloscope. Results were obtained and plotted in the form of dynamic stress-strain curves. Longitudinal properties which are governed by the fibers do not vary much with strain rate with only a moderate (up to 20 percent) increase in modulus. Transverse modulus and strength increase sharply with strain rate reaching values up to three times the static values. The in-plane shear modulus and shear strength increase noticeably with strain rate by up to approximately 65 percent. In all cases ultimate strains do not vary significantly with strain rates.

Daniel, I. M.↗

NASA NTRSDate not supplied

Utilizing Strain Rate Jump Testing to Predict Flow Formability of Al Alloys Sensitive to Portevin-Le Chatelier Instabilities

Predicting the flow formability of Al alloys is challenging due to the incremental deformation, complex loading path, and wide range of strain rates characteristic of the process. State-of-the-art research efforts have primarily focused on formability metrics derived from ambient temperature, constant strain rate uniaxial tensile testing. However, Al alloys in formable tempers tend to exhibit serrated Portevin-Le Chatelier (PLC) flow. The appearance of PLC instabilities implies a negative strain rate sensitivity, loss of tensile area reduction capacity, and decreased formability. Elevated temperature and interrupted strain rate tensile tests of relevant Al alloys were conducted to investigate the effects of rapid changes in strain rate (analogous to a forming increment by a passing roller) on common formability metrics. Emphasis was placed on the character/extent of PLC instabilities using digital image correlation strain measurements. The outcome of this work highlights the possibility of predicting flow formability using strain rate jump testing.

flow forming↗

NASA NTRS1988

Pressure-strain-rate events in homogeneous turbulent shear flow

A detailed study of the intercomponent energy transfer processes by the pressure-strain-rate in homogeneous turbulent shear flow is presented. Probability density functions (pdf's) and contour plots of the rapid and slow pressure-strain-rate show that the energy transfer processes are extremely peaky, with high-magnitude events dominating low-magnitude fluctuations, as reflected by very high flatness factors of the pressure-strain-rate. A concept of the energy transfer class was applied to investigate details of the direction as well as magnitude of the energy transfer processes. In incompressible flow, six disjoint energy transfer classes exist. Examination of contours in instantaneous fields, pdf's and weighted pdf's of the pressure-strain-rate indicates that in the low magnitude regions all six classes play an important role, but in the high magnitude regions four classes of transfer processes, dominate. The contribution to the average slow pressure-strain-rate from the high magnitude fluctuations is only 50 percent or less. The relative significance of high and low magnitude transfer events is discussed.

Brasseur, James G.↗

NASA NTRS2003

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Goldberg, Robert K.↗

NASA NTRS1961

Effect of Strain Rate on Mechanical Properties of Wrought Sintered Tungsten at Temperatures above 2500 F

Specimens of wrought sintered commercially pure tungsten were made from 1/8-inch swaged rods. All the specimens were recrystallized at 4050 F for 1 hour prior to testing at temperatures from 2500 to 4000 F at various strain rates from 0.002 to 20 inches per inch per minute. Results showed that, at a constant temperature, increasing the strain rate increased the ultimate tensile strength significantly. The effects of both strain rate and temperature on the ultimate tensile strength of tungsten may be correlated by the linear parameter method of Manson and Haferd and may be used to predict the ultimate tensile strength at higher temperatures, 4500 and 5000 F. As previously reported, ductility, as measured by reduction of area in a tensile test, decreases with increasing temperature above about 3000 F. Increasing the strain rate at temperatures above 3000 F increases the ductility. Fractures are generally transgranular at the higher strain rates and intergranular at the lower strain rates.

Sikora, Paul F.↗

NASA NTRS2004

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

Goldberg, Robert K.↗

NASA NTRS1991

High strain rate properties of angle-ply composite laminates, part 3

Angle-ply graphite/epoxy and graphite/S-glass/epoxy laminates were characterized in uniaxial tension at strain rates ranging from quasi-static to over 500 s(sup -1). Laminate ring specimens of +/-15(sub 2s), +/-22.5(sub 2s), +/-30(sub 2s), +/-45(sub 2s), +/-60(sub 2s), +/-67.5(sub 2s), and +/-75(sub 2s) degree layups were loaded under internal pressure. Results were presented in the form of stress-strain curves to failure. Properties determined included moduli, Poisson's ratios, strength, and ultimate strain. In all seven laminates for the two materials tested the modulus and strength increase with strain rate. The effect of strain rate varies with layup, being lowest for the fiber dominated +/-15(sub 2s) degree laminates and highest for the matrix dominated +/-75(sub 2s) degree laminates. The highest increments over the static values are 10 to 25 percent for the +/-15(sub 2s) degree layup and 200 to 275 percent for the +/-75(sub 2s) degree layup. Ultimate strains do not show any significant trends with strain rate. In almost all cases the ultimate strain values are within +/-20 percent of the mean value and in half of the cases the deviation from the mean are less than 10 percent.

Daniel, I. M.↗

DOE OSTI2026

Effects of oxygen on the tensile properties and fracture behavior of the Ta-10 W refractory alloy at quasi-static and impact strain rates

This study investigates effects of pre-charged oxygen at levels up to ∼1750 ppm on the tensile properties of the refractory alloy Ta-10 W. Tests were conducted at temperatures to 1100 °C and strain rates from quasi-static (∼10−3 s−1) to impact (∼103 s−1). At all temperatures, ductility decreased with increasing oxygen concentration and could be visually identified as a ductile-to-brittle transition (DBT). Additionally, for a given oxygen concentration, ductility was lower at impact strain rate than at quasi-static. The DBT was accompanied by a change from ductile transgranular to more brittle modes, intergranular and transgranular cleavage. The oxygen concentrations associated with the DBT depend on test temperature and strain rate. However, the transitions themselves are not sharp and cannot be defined as occurring at a specific oxygen concentration. At impact strain rates, ductility is relatively insensitive to test temperatures in the range 300–1100 °C with similar embrittling effects of oxygen; however, oxygen has a more severe embrittling effect at room temperature. This behavior is reversed at quasi-static strain rates where the embrittling effect of oxygen is more severe at elevated temperatures than at room temperature. It appears this difference is related to the kinetics of oxygen diffusion to grain boundaries and crack tips. Specimens that were not pre-charged with oxygen but tensile tested in various partial pressures of oxygen underwent dynamic embrittlement during the test, with the degree of embrittlement increasing as the partial pressure of oxygen in the environment increased. Consistent with such a mechanism, ductility increased with increasing strain rate for a given oxygen partial pressure, which would be the reverse if only intrinsic dislocation mobilities were controlling.

Miller, Roger [ORNL] (ORCID:0000000172155851)↗

DOE OSTI2024

On the effect of strain rate during the cyclic compressive loading of liquid crystal elastomers and their 3D printed lattices

Nematic liquid crystal elastomers (LCEs) are a unique class of network polymers with the potential for enhanced mechanical energy absorption and dissipation capacity over conventional network polymers because they exhibit both conventional viscoelastic behavior and soft-elastic behavior (nematic director changes under shear loading). This additional inelastic mechanism makes them appealing as candidate damping materials in a variety of applications from vibration to impact. The lattice structures made from the LCEs provide further mechanical energy absorption and dissipation capacity associated with packing out the porosity under compressive loading. Understanding the extent of mechanical energy absorption, which is the work per unit mass (or volume) absorbed during loading, versus dissipation, which is the work per unit mass (or volume) dissipated during a loading cycle, requires measurement of both loading and unloading response. Here, in this study, a bench-top linear actuator was employed to characterize the loading-unloading compressive response of polydomain and monodomain LCE polymers and polydomain LCE lattice structures with two different porosities (nominally, 62% and 85%) at both low and intermediate strain rates at room temperature. As a reference material, a bisphenol-A (BPA) polymer with a similar glass transition temperature (9 °C) as the nematic LCE (4 °C) was also characterized at the same conditions for comparing to the LCE polymers. Based on the loading-unloading stress-strain curves, the energy absorption and dissipation for each material at different strain rates (0.001, 0.1, 1, 10 and 90 s -1 ) were calculated with considerations of maximum stress and material mass/density. The strain-rate effect on the mechanical response and energy absorption and dissipation behaviors was determined. The energy dissipation ratio was also calculated from the resultant loading and unloading stress-strain curves. All five materials showed significant but different strain rate effects on energy dissipation ratio. The solid LCE and BPA materials showed greater energy dissipation capabilities at both low (0.001 s -1 ) and high (above 1 s -1 ) strain rates, but not at the strain rates in between. The polydomain LCE lattice structure showed superior energy dissipation performance compared with the solid polymers especially at high strain rates.

36 MATERIALS SCIENCE↗