Soft-elasticity in monodomain liquid crystal elastomers (LCEs) is promising for impact-absorbing applications where strain energy is ideally absorbed at constant stress. Conventionally, compressive and impact studies on LCEs have not been performed given the notorious difficulty synthesizing sufficiently large monodomain devices. Here, we use direct-ink writing 3D printing to fabricate bulk (>cm3) monodomain LCE devices and study their compressive soft-elasticity over 8 decades of strain rate. At quasi-static rates, the monodomain soft-elastic LCE dissipated 45% of strain energy while comparator materials dissipated less than 20%. At strain rates up to 3000 s−1, our soft-elastic monodomain LCE consistently performed closest to an ideal-impact absorber. Drop testing reveals soft-elasticity as a likely mechanism for effectively reducing the severity of impacts – with soft elastic LCEs offering a Gadd Severity Index 40% lower than a comparable isotropic elastomer. Lastly, we demonstrate tailoring deformation and buckling behavior in monodomain LCEs via the printed director orientation.
Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The matters of interest here are the elastic-plastic response and ductile failure behavior of 6061-T651 aluminum alloy under the conditions described above. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of a modular $J_2$ plasticity model with isotropic hardening as well as a ductile failure model. Both included modules that accounted for temperature and strain rate dependence. The models were coupled with an adiabatic heating module to calculate the temperature rise due to the conversion of plastic work to heat. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10–4 and 103 1/s as well as four geometries of notched tension specimens and two tests on specimens with shear-dominated deformations. The test data collected allowed the calibration of both the plasticity and the ductile failure models. Most test specimens were extracted from a single piece of plate to maintain consistency. Notched tension tests came from a possibly different plate, but from the same lot. When using the model in structural finite element calculations, element formulations and sizes different from those used to model the test specimens in the calibration are likely to be used. A brief investigation demonstrated that the failure model can be particularly sensitive to the element selection and provided an initial guide to compensate in a specific example.
Numerical simulations of metallic structures undergoing rapid loading into the plastic range require material models that accurately represent the response. In general, the material response can be seen as having four interrelated parts: the baseline response under slow loading, the effect of strain rate, the conversion of plastic work into heat and the effect of temperature. In essence, the material behaves in a thermal-mechanical manner if the loading is fast enough so when heat is generated by plastic deformation it raises the temperature and therefore influences the mechanical response. In these cases, appropriate models that can capture the aspects listed above are necessary. The material of interest here is 304L stainless steel, and the objective of this work is to calibrate thermal-mechanical models: one for the constitutive behavior and another for failure. The work was accomplished by first designing and conducting a material test program to provide data for the calibration of the models. The test program included uniaxial tension tests conducted at room temperature, 150 and 300 C and at strain rates between 10–4 and 103 1/s. It also included notched tension and shear-dominated compression hat tests specifically designed to calibrate the failure model. All test specimens were extracted from a single piece of plate to maintain consistency. The constitutive model adopted was a modular $J_2$ plasticity model with isotropic hardening that included rate and temperature dependence. A criterion for failure initiation based on a critical value of equivalent plastic strain fitted the failure data appropriately and was adopted. Possible ranges of the values of the parameters of the models were determined partially on historical data from calibrations of the same alloy from other lots and are given here. The calibration of the parameters of the models were based on finite element simulations of the various material tests using relatively ne meshes and hexahedral elements. When using the model in structural finite element calculations, however, element formulations and sizes different from those in the calibration are likely to be used. A brief investigation demonstrated that the failure initiation predictions can be particularly sensitive to the element selection and provided an initial guide to compensate for the effect of element size in a specific example.
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 102 s−1. A Boltzmann description is used to present the effect of nominal strain rate on true failure strain.
Refractory metals are favorable materials in applications where high strength and ductility are needed at elevated temperatures. In some cases, operating temperatures may be near the melting point of the material. However, as temperature drops, refractory metals typically undergo a significant mechanical response change - ductile-to-brittle transition. These materials may be subjected to high strain rate loading at an ambient temperature state, such as an impact or crash. Knowledge of the high rate material properties are essential for design as well as simulation of impact events. The high rate stress-strain behavior of brittle metallic materials at ambient temperature is rarely studied because of experimental challenges, particularly when failure is involved. Failure typically occurs within the non-gage section of the material, which invalidates any collected stress-strain information. In this study, a method to determine a specimen geometry which will produce failures in the gage section is presented. Pure tungsten in thin-sheet form was used as a trial material to select a specimen geometry for high rate Kolsky tension bar experiments. A finite element simulation was conducted to derive a strain correction for more accurate results. The room temperature stress-strain behavior of pure tungsten at a strain rate of 24 s−1 is presented. The outcome of this experimental technique can be applied to other brittle materials for dynamic tensile characterization.
Soft ferromagnetic alloys are often utilized in electromagnetic applications due to their desirable magnetic properties. In support of these applications, the ferromagnetic alloys are also required to bear mechanical load under various loading and environmental conditions. In this study, a Fe–49Co–2V alloy was dynamically characterized in tension with a Kolsky tension bar and a Drop–Hopkinson bar at various strain rates and temperatures. Dynamic tensile stress–strain curves of the Fe–49Co–2V alloy were obtained at strain rates ranging from 40 to 230 s−1 and temperatures from − 100 to 100 °C. All dynamic tensile stress–strain curves exhibited an initial linear elastic response to an upper yield followed by Lüders band response and then a nearly linear work-hardening behavior. The yield strength of this material was found to be sensitive to both strain rate and temperature, whereas the hardening rate was independent of strain rate or temperature. The Fe–49Co–2V alloy exhibited a feature of brittle fracture in tension under dynamic loading with no necking being observed.
Fe-Co-2V is a soft ferromagnetic alloy used in electromagnetic applications due to excellent magnetic properties. However, the discontinuous yielding (Luders bands), grain-size-dependent properties (Hall-Petch behavior), and the degree of order/disorder in the Fe-Co-2V alloy makes it difficult to predict the mechanical performance, particularly in abnormal environments such as elevated strain rates and high/low temperatures. Thus, experimental characterization of the high strain rate properties of the Fe-Co-2V alloy is desired, which are used for material model development in numerical simulations. In this study, the high rate tensile response of Fe-Co-2V is investigated with a pulse-shaped Kolsky tension bar over a wide range of strain rates and temperatures. Effects of temperature and strain rate on yield stress, ultimate stress, and ductility are discussed.
Cylindrical dog-bone (or dumbbell) shaped samples have become a common design for dynamic tensile tests of ductile materials with a Kolsky tension bar. When a direct measurement of displacement between the bar ends is used to calculate the specimen strain, the actual strain in the specimen gage section is overestimated due to strain in the specimen shoulder and needs to be corrected. The currently available correction method works well for elastic-perfectly plastic materials but may not be applicable to materials that exhibit significant work-hardening behavior. In this study, we developed a new specimen strain correction method for materials possessing an elastic-plastic with linear work-hardening stress–strain response. A Kolsky tension bar test of a Fe-49Co-2V alloy (known by trade names Hiperco and Permendur) was used to demonstrate the new specimen strain correction method. This new correction method was also used to correct specimen strains in Kolsky tension bar experiments on two other materials: 4140 alloy, and 304L-VAR stainless steel, which had different work-hardening behavior.
Metallic alloys are extensively utilized in applications where extreme loading and environmental conditions occur and engineering reliability of components or structures made of such materials is a significant concern in applications. Adiabatic heating in these materials during high-rate deformation is of great interest to analysts, experimentalists, and modelers due to a reduction in strength that is produced. Capturing the thermosoftening caused by adiabatic heating is critical in material model development to precisely predict the dynamic response of materials and structures at high rates of loading. In addition to strain rate effect, the Johnson–Cook (JC) model includes a term to describe the effect of either environmental or adiabatic temperature rise. The standard expression of the JC model requires quantitative knowledge of temperature rise, but it can be challenging to obtain in situ temperature measurements, especially in dynamic experiments. The temperature rise can be calculated from plastic work with a predetermined Taylor-Quinney (TQ) coefficient. However, the TQ coefficient is difficult to determine since it may be strain and strain-rate dependent. In this study, we modified the JC model with a power-law strain rate effect and an explicit form of strain- and strain-rate-dependent thermosoftening due to adiabatic temperature rise to describe the strain-rate-dependent tensile stress–strain response, prior to the onset of necking, for 304L stainless steel, A572, and 4140 steels. The modified JC model was also used to describe the true stress–strain response during necking for A572 and 4140 steels at various strain rates. The results predicted with the modified JC model agreed with the tensile experimental data reasonably well.
Foam materials are extensively utilized in aerospace, military, and transportation applications to mitigate blast or shock impact. When foam materials are subjected to an external high-speed impact, shock, or blast loading, an elastic wave or shock wave will form and propagate through the thickness of the foam materials. In this study, silicone foam pads, which were confined laterally and pre-strained to different levels, were experimentally characterized and theoretically analyzed to understand their effects on wave propagation characteristics under impact loading. Depending on impact velocity, either an elastic strain wave or a shock wave would be generated in the silicone foam pad with different pre-strains. Above a certain impact velocity, a shock wave will be generated whereas, below this threshold impact velocity, an elastic strain wave will be generated. This threshold impact velocity depends on the pre-strain applied to the silicone foam pad. Equations are provided to estimate the wave propagation speed for either an elastic or a shock wave from the amount of pre-strain in the silicone foam pads and the impact velocity. These equations are expected to help improve silicone foam design and assembly processes for shock or blast mitigation applications.
Silicone foam is used as a shock mitigation material in a variety of systems to protect internal components from being damaged during external shock or impact loading. Characterizing the shock mitigation response of silicone foam under a variety of scenarios is a critical step in designing and/or evaluating new shock mitigation systems. In this study, a Kolsky bar with pre-compression capability was used with a passive radial confinement tube to subject the sample to various levels of pre-strain followed by impact loading. The effects of both pre-strain and impact velocity on impact energy dissipation behavior were investigated for silicone foam. The energy dissipation response of silicone foam is compared to a silicone rubber manufactured using the same processing methods to understand the energy dissipation characteristics of silicone foams transitioning to a silicone rubber. The final density of the foam or rubber plays a key role in both the total energy dissipation ratio in the time domain and the energy dissipation ratio as a function of frequency in the frequency domain.
Soft ferromagnetic alloys are often utilized in electromagnetic applications due to their desirable magnetic properties. In support of these applications, the ferromagnetic alloys are also desired to bear mechanical load at various environmental temperatures. In this study, a Permendur 2V alloy manufactured by Metalwerks Inc. (but referred to Hiperco 50A, a trademark of Carpenter Technologies Inc.) was dynamically characterized in tension with a Kolsky tension bar and a Dropkinson bar at various strain rates and temperatures. Dynamic tensile stress-strain curves of the Hiperco 50A alloy were obtained at the strain rates ranging from 40 to 230 s -1 and temperatures from -100 to 100degC. All tensile stress-strain curves exhibited an initial linear elastic response to an upper yield followed by a Eiders banding response and then a nearly linear work-hardening behavior. The yield strength of this material was found to be sensitive to both strain rate and temperature; whereas, the hardening rate was independent of strain rate or temperature. The Hiperco 50A alloy exhibited a feature of brittle fracture in tension under dynamic loading with no necking being observed. ACKNOWLEDGEMENTS The authors acknowledge Kyle Johnson, Jefferey Dab ling, Donald Susan, Jay Carroll, Adam Brink, Scott Grutzik, and Andrew Kustas for the valuable discussion of test plan and results. Thanks Donald Susan for specimen preparation for this project. The authors also thanks Randy Everett for his support to the operation of dynamic tests in this proj ect.
Polymeric foams have been extensively used in shock isolation applications because of their superior shock or impact energy absorption capability. However, as a type of soft condensed matter, the highly nonlinear, heterogeneous, and dissipative behavior of polymeric foams may result in an ineffective mitigation or isolation to shock/blast loading. To meet certain desired shock mitigation or isolation requirements, the polymeric foams need to be experimentally characterized to obtain their intrinsic material response. However, radial inertia during dynamic compression has become a severe issue and needs to be fully understood. In this study, we developed an analytical method to calculate the additional stress induced by radial inertia in a polymeric foam specimen. The radial inertia is generally caused by Poisson’s effect and associated with three different mechanisms – axial strain acceleration, large deformation, and Poisson’s ratio change. The effect of Poisson’s ratio change during deformation on radial inertia was specifically investigated for hyperelastic foam materials, and verified with experimental results obtained from Kolsky compression bar tests on a silicone foam.
Poisson’s ratio of soft, hyperelastic foam materials such as silicone foam is typically assumed to be both a constant and a small number near zero. However, when the silicone foam is subjected to large deformation into densification, the Poisson’s ratio may significantly change, which warrants careful and appropriate consideration in modeling and simulation of impact/shock mitigation scenarios. The evolution of the Poisson’s ratio of foam materials has not yet been characterized. In this study, radial and axial measurements of specimen strain are made simultaneously during quasi-static and dynamic compression test on a silicone foam. The Poisson’s ratio was found to exhibit a transition from compressible to nearly incompressible based on strain level and reached different values at quasi-static and dynamic rates.