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. 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.
Long, Kevin N.; Chung, Christopher; Luo, Chaoqian; Yakacki, Christopher M.; Song, Bo; Yu, Kai
Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and enhanced energy dissipation with rate dependency. They are potentially transformative materials for applications in mechanical impact mitigation and vibration isolation. However, previous studies have primarily focused on the mechanics of LCEs under equilibrium and quasistatic loading conditions. Critical knowledge gaps exist in understanding their rate-dependent behaviors, which are a complex mixture of traditional network viscoelasticity and the soft elastic behaviors with changes in the mesogen orientation and order parameter. Together, these inelastic mechanisms lead to unusual rate-dependent energy absorption responses of LCEs. In this work, we developed a viscoelastic constitutive theory for monodomain nematic LCEs to investigate how multiple underlying sources of inelasticity manifest in the rate-dependent and dissipative behaviors of monodomain LCEs. The theoretical modeling framework combines the neo-classical network theory with evolution rules for the mesogen orientation and order parameter with conventional viscoelasticity. The model is calibrated with uniaxial tension and compression data spanning six decades of strain rates. The established 3D constitutive model enables general loading predictions taking the initial mesogen orientation and order parameter as inputs. Additionally, parametric studies were performed to further understand the rate dependence of monodomain LCEs in relation to their energy absorption characteristics. Based on the parametric studies, particularly loading scenarios are identified as conditions where LCEs outperform conventional elastomers regarding energy absorption.
A comprehensive study of the mechanical response of a 316 stainless steel is presented. The split-Hopkinson bar technique was used to evaluate the mechanical behavior at dynamic strain rates of 500 s−1, 1500 s−1, and 3000 s−1 and temperatures of 22 °C and 300 °C under tension and compression loading, while the Drop-Hopkinson bar was used to characterize the tension behavior at an intermediate strain rate of 200 s−1. The experimental results show that the tension and compression flow stress are reasonably symmetric, exhibit positive strain rate sensitivity, and are inversely dependent on temperature. The true failure strain was determined by measuring the minimum diameter of the post-test tension specimen. The 316 stainless steel exhibited a ductile response, and the true failure strain increased with increasing temperature and decreased with increasing strain rate.
Polymers are widely used as damping materials in vibration and impact applications. Liquid crystal elastomers (LCEs) are a unique class of polymers that may offer the potential for enhanced energy absorption capacity under impact conditions over conventional polymers due to their ability to align the nematic phase during loading. Being a relatively new material, the high rate compressive properties of LCEs have been minimally studied. Here, we investigated the high strain rate compression behavior of different solid LCEs, including cast polydomain and 3D-printed, preferentially oriented monodomain samples. Direct ink write (DIW) 3D printed samples allow unique sample designs, namely, a specific orientation of mesogens with respect to the loading direction. Loading the sample in different orientations can induce mesogen rotation during mechanical loading and subsequently different stress-strain responses under impact. We also used a reference polymer, bisphenol-A (BPA) cross-linked resin, to contrast LCE behavior with conventional elastomer behavior.
A comprehensive study of the mechanical response of a 316 stainless steel is presented. The split-Hopkinson bar technique was used to evaluate the mechanical behavior at dynamic strain rates of 500 s−1, 1500 s−1, and 3000 s−1 and temperatures of 22 °C and 300 °C under tension and compression loading, while the Drop-Hopkinson bar was used to characterize the tension behavior at an intermediate strain rate of 200 s−1. The experimental results show that the tension and compression flow stress are reasonably symmetric, exhibit positive strain rate sensitivity, and are inversely dependent on temperature. The true failure strain was determined by measuring the minimum diameter of the post-test tension specimen. The 316 stainless steel exhibited a ductile response, and the true failure strain increased with increasing temperature and decreased with increasing strain rate.
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.
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.
Impact loads can induce a series of undesirable physical phenomena including vibration, acoustical shock, perforation, fracture and fragmentation, etc. The energy associated with the impact loads can lead to severe structure damage and human injuries. A design approach which effectively reduces these negative impacts through shock/stress wave diversion is highly needed. In this paper, a computational model which predicts stress wave propagation by considering different beam geometries and configurations is developed. A novel concept of wave guide design which modifies the stress wave propagation path without disturbance is also presented. This design approach is not only useful for material property characterization particularly at intermediate or high strain rates, but also allows stress wave propagation in a desired direction as the shock/impact energy can be redistributed in controllable paths. The numerical results are experimentally verified through a Drop-Hopkinson bar apparatus at Sandia National Laboratories.
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.
The mechanical response of additively manufactured (AM) stainless steel 304L has been investigated across a broad range of loading conditions, covering 11 decades of strain rate, and compared with the behaviors of traditional ingot-derived (wrought) material. In general, the AM material exhibits a greater strength and reduced ductility compared with the baseline wrought form. These differences are consistently found from quasi-static and high strain rate tests. A detailed investigation of the microstructure, the defect structure, the phase, and the composition of both forms reveals differences that may contribute to the differing mechanical behaviors. Compared with the baseline wrought material, dense AM stainless steel 304L has a more complex grain structure with substantial sub-structure, a fine dispersion of ferrite, increased dislocation density, oxide dispersions and larger amounts of nitrogen. In-situ neutron diffraction studies conducted during quasi-static loading suggest that the increased strength of AM material is due to its initially greater dislocation density. The flow strength of both forms is correlated with dislocation density through a square root dependence akin to a Taylor-like relationship. Neutron diffraction measurements of lattice strains also correlate with a crystal plasticity finite element simulations of the tensile test. Other simulations predict a significant degree of elastic and plastic anisotropy due to crystallographic texture. Hopkinson tests at higher strain rates $\dot{ε}$ = 500 and 2500 s-1 ) also show a greater strength for AM stainless steel 304L; although, the differences compared with wrought are reduced at higher strain rates. Gas gun impact tests, including reverse ballistic, forward ballistic and spall tests, consistently reveal a larger dynamic strength in the AM material. The Hugoniot Elastic Limit (HEL) of AM SS 304L exceeds that of wrought material although considerable variability is observed with the AM material. Forward ballistic testing demonstrates spall strengths of AM material (3.27 -- 3.91 GPa) that exceed that of the wrought material (2.63 -- 2.88 GPa). The Hugoniot equation-of-state for AM samples matches archived data for this metal alloy.
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 100°C. 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.
Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratio of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. The Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.
Polymeric foams have been extensively used in shock isolation applications because of their superior shock or impact energy absorption capability. In order to meet the shock isolation requirements, the polymeric foams need to be experimentally characterized and numerically modeled in terms of material response under shock/impact loading and then evaluated with experimental, analytical, and/or numerical efforts. Measurement of the dynamic compressive stress-strain response of polymeric foams has become fundamental to the shock isolation performance. However, radial inertia has become a severe issue when characterizing soft materials. It is even much more complicated and difficult to address the radial inertia effect in soft polymeric foams. In this study, we developed an analytical method to calculate the additional stress induced by radial inertia in a polymeric foam specimen. The effect of changing profile of Poisson’s ratio during deformation on radial inertia was investigated. The analytical results were also compared 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.
A new apparatus – “Dropkinson Bar” – has been successfully developed for material property characterization at intermediate strain rates. This Dropkinson bar combines a drop table and a Hopkinson bar. The drop table was used to generate a relatively long and stable low-speed impact to the specimen, whereas the Hopkinson bar principle was applied to measure the load history with accounting for inertia effect in the system. Pulse shaping technique was also applied to the Dropkinson bar to facilitate uniform stress and strain as well as constant strain rate in the specimen. The Dropkinson bar was then used to characterize 304L stainless steel and 6061-T6 aluminum at a strain rate of ∼600 s−1. The experimental data obtained from the Dropkinson bar tests were compared with the data obtained from conventional Kolsky tensile bar tests of the same material at similar strain rates. Both sets of experimental results were consistent, showing the newly developed Dropkinson bar apparatus is reliable and repeatable.
Mining rock salt results in subsurface damage, which may affect the strength because of applied stress, anisotropy, and deformation rate. In this study, we used a Kolsky compression bar to measure the high strain rate response of bedded and domal salt at strain rates up to approximately 50 s−1 in parallel and perpendicular directions to bedding or foliation direction depending on rock salt type. Both types of salt exhibited a negative strain rate effect wherein a decrease in strength was observed with increasing strain rate compared to strength measured in the quasi-static regime. Both materials exhibited strength anisotropy. Fracturing and microfracturing were the dominant deformation mechanisms. High pore pressures and frictional heating due to the high loading rate may have contributed to reduction in strength.
Understanding the dynamic behavior of geomaterials is critical for refining modeling and simulation of applications that involve impacts or explosions. Obtaining material properties of geomaterials is challenging, particularly in tension, due to the brittle and low-strength nature of such materials. Dynamic split tension technique (also called dynamic Brazilian test) has been employed in recent decades to determine the dynamic tensile strength of geomaterials. This is primarily because the split tension method is relatively straightforward to implement in a Kolsky compression bar. Typically, investigators use the peak load reached by the specimen to calculate the tensile strength of the specimen material, which is valid when the specimen is compressed at quasi-static strain rate. However, the same assumption cannot be safely made at dynamic strain rates due to wave propagation effects. In this study, the dynamic split tension (or Brazilian) test technique is revisited. High-speed cameras and digital image correlation (DIC) were used to image the failure of the Brazilian-disk specimen to discover when the first crack occurred relative to the measured peak load during the experiment. Differences of first crack location and time on either side of the sample were compared. The strain rate when the first crack is initiated was also compared to the traditional estimation method of strain rate using the specimen stress history.
A new apparatus – “Dropkinson Bar” – has been successfully developed for material property characterization at intermediate strain rates. This Dropkinson bar combines a drop table and a Hopkinson bar. The drop table was used to generate a relatively long and stable low-speed impact to the specimen, whereas the Hopkinson bar principle was applied to measure the load history with accounting for inertia effect in the system. Pulse shaping technique was also applied to the Dropkinson bar to facilitate uniform stress and strain as well as constant strain rate in the specimen. The Dropkinson bar was then used to characterize 304L stainless steel and 6061-T6 aluminum at a strain rate of ∼600 s−1. The experimental data obtained from the Dropkinson bar tests were compared with the data obtained from conventional Kolsky tensile bar tests of the same material at similar strain rates. Both sets of experimental results were consistent, showing the newly developed Dropkinson bar apparatus is reliable and repeatable.
Understanding the dynamic behavior of geomaterials is critical for refining modeling and simulation of applications that involve impacts or explosions. Obtaining material properties of geomaterials is challenging, particularly in tension, due to the brittle and low-strength nature of such materials. Dynamic split tension technique (also called dynamic Brazilian test) has been employed in recent decades to determine the dynamic tensile strength of geomaterials. This is primarily because the split tension method is relatively straightforward to implement in a Kolsky compression bar. Typically, investigators use the peak load reached by the specimen to calculate the tensile strength of the specimen material, which is valid when the specimen is compressed at quasi-static strain rate. However, the same assumption cannot be safely made at dynamic strain rates due to wave propagation effects. In this study, the dynamic split tension (or Brazilian) test technique is revisited. High-speed cameras and digital image correlation (DIC) were used to image the failure of the Brazilian-disk specimen to discover when the first crack occurred relative to the measured peak load during the experiment. Differences of first crack location and time on either side of the sample were compared. The strain rate when the first crack is initiated was also compared to the traditional estimation method of strain rate using the specimen stress history.
