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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Hyperelastic foams have excellent impact energy absorption capability and can experience full recovery following impact loading. Consequently, hyperelastic foams are selected for different applications as shock isolators. Obtaining accurate intrinsic dynamic compressive properties of the hyperelastic foams has become a crucial step in shock isolation design and evaluation. Radial inertia is a key issue in dynamic characterization of soft materials. Radial inertia induced stress in the sample is generally caused by axial acceleration and large deformation applied to a soft specimen. In this study, Poisson's ratio of a typical hyperelastic foam-silicone foam-was experimentally characterized under high strain rate loading and was observed to drastically change across the densification process. A transition in the Poisson's ratio of the silicone foam specimen during dynamic compression generated radial inertia which consequently resulted in additional axial stress in the silicone foam sample. A new analytical method was developed to address the Poisson's ratio-induced radial inertia effects for hyperelastic foams during high rate compression.
In this study, a Johnson–Cook model was used as an example to analyze the relationship of compressive stress-strain response of engineering materials experimentally obtained at constant engineering and true strain rates. There was a minimal deviation between the stress-strain curves obtained at the same constant engineering and true strain rates. The stress-strain curves obtained at either constant engineering or true strain rates could be converted from one to the other, which both represented the intrinsic material response. There is no need to specify the testing requirement of constant engineering or true strain rates for material property characterization, provided that either constant engineering or constant true strain rate is attained during the experiment.
Kolsky tension bar experiments were improved for dynamic tensile stress-strain measurements with higher fidelity and minimal uncertainties. The difficulties associated with specimen gripping, relatively short gage section, and geometric discontinuity at the bar ends all compromise the accuracy of the traditional strain measurement method in a Kolsky tension bar experiment. In this study, an improved three-channel splitting-beam laser extensometer technique was developed to directly and independently track the displacement of the incident and transmission bar interfaces. By adopting a dual-channel configuration on the incident bar side, the resolution and measurement range of this laser extensometer were coordinated between the two channels to provide highly precise measurement at both small and large strains under high strain-rate loading condition. On the transmission bar side an amplified channel, similar to that used on the incident bar side, was adopted to measure the transmission bar displacement with high resolution. With this novel design, a maximum resolution of approximately 500 nm can be obtained for the bar displacement measurement, which corresponds to a strain of 0.0079% for a specimen with 6.35 mm gage length. To further improve the accuracy, a pair of lock nuts were used to tighten the tensile specimen to the bars in an effort not only to prevent the specimen from potential pre-torsional deformation and damage during installation, but also to provide better thread engagement between the specimen and the bar ends. As a demonstration of this technique, dynamic tensile stress-strain response of a 304L stainless steel was characterized with high resolution in both elastic and plastic deformations.
This review article is dedicated to the Dynamic Behavior of Materials Technical Division for celebrating the 75th anniversary of the Society for Experimental Mechanics (SEM). Understanding dynamic behavior of geomaterials is critical for analyzing and solving engineering problems of various applications related to underground explosions, seismic, airblast, and penetration events. Determining the dynamic tensile response of geomaterials has been a great challenge in experiments due to the nature of relatively low tensile strength and high brittleness. Various experimental approaches have been made in the past century, especially in the most recent half century, to understand the dynamic behavior of geomaterials in tension. In this review paper, we summarized the dynamic tensile experimental techniques for geomaterials that have been developed. The major dynamic tensile experimental techniques include dynamic direct tension, dynamic split tension, and spall tension. All three of the experimental techniques are based on Hopkinson or split Hopkinson (also known as Kolsky) bar techniques and principles. Uniqueness and limitations for each experimental technique are also discussed.
To understand interfacial interaction of a bi-material during an impact loading event, the dynamic friction coefficient is one of the key parameters that must be characterized and quantified. In this study, a new experimental method to determine the dynamic friction coefficient between two metals was developed by using a Kolsky tension bar and a custom-designed friction fixture. Polyvinylidene fluoride (PVDF) force sensors were used to measure the normal force applied to the friction tribo pairs and the friction force was measured with conventional Kolsky tension bar method. To evaluate the technique, the dynamic friction coefficient between 4340 steel and 7075-T6 aluminum was investigated at an impact speed of approximately 8 m/s. In addition, the dynamic friction coefficient of the tribo pairs with varied surface roughness was also investigated. The data suggest that higher surface roughness leads to higher friction coefficients at the same speed of 8 m/s.
Silicone foams and rubber are used in a variety of applications to protect internal components from external shock impact. Understanding how these materials mitigate impact energy is a crucial step in designing more effective shock isolation systems for components. In this study, a Kolsky bar with pre-compression and passive radial confinement capabilities was used to investigate the response of silicone foams and rubber subjected to impact loading at different speeds. Using the preload capability, silicone foam samples were subjected to increasing levels of pre-strain. Frequency-based analyses were carried out on results from silicone foams and rubber to study the effect of both pre-strain and material processing conditions on the mechanism of energy dissipation in the frequency domain. Additionally, effects of impact speed on energy dissipation through silicone foams and rubber were investigated.
Threaded joints are a common fastening method in applications where disassembly may be required. With a fair amount of investigation of static behavior of threaded joints, less emphasis has been placed on the behavior of threaded joints subjected to transient impact loads. Understanding how energy is transferred across threaded joints under impact loading conditions is critical for improved design and optimization for extreme mechanical environments. Many factors, such as pre - torque, pre - tension load, and impact speed can affect how energy is transferred or dissipated across threaded joins. In addition, high-fidelity numerical simulation of mechanical response of threaded components under blast or impact loading requires reliable experiments and subsequent analyses. In this study, the energy dissipation behavior through a threaded joint under impact loading conditions is investigated using a Kolsky tension bar. The aim is to study possible energy dissipation behavior in both time and frequency domains while the threaded joint remains intact. New analytical methods to understand both time-and frequency-domain behavior of threaded joints are presented. Energy dissipation characteristics through steel-to-steel and steel-to-aluminum threaded joints were then investigated with varying parameters such as pre-torque and impact velocity.
Understanding the interfacial behavior of two materials sliding relative to each other is import ant in computational modeling and simulating impact or shock response of components, subsystems, and even full-scale systems. Although often considered as a constant for different applications, the coefficient of friction may be dependent on a number of factors such as normal force, roughness, material type, temperature, and sliding velocity. In this study, a new method based on a Kolsky tension bar with a custom-made friction fixture was developed for measurement of the dynamic friction coefficient between two metallic materials at high sliding velocities. In this new method, polyvinylidene fluoride (PVDF) thin film force sensors were used to measure the normal force, while a strain gage on the transmission bar was used to measure the friction force. As such, the dynamic friction coefficient is calculated with the normal and friction forces. The impact velocity can be varied to investigate the dependency of friction coefficient on impact velocity. To evaluate the technique, friction coefficients between 4340 steel and 7075-T6 we re measured at three different sliding velocities of 4, 8 and 11 m/s. Effects of surface roughness, normal force, and impact speed were also explored . Decreased static and kinetic friction coefficient s were observed when the normal force was increased at constant sliding velocity. With increasing velocity, the friction coefficient remained fairly constant for the three velocities studied. Higher friction coefficients were measured when the specimen roughness was increased.
Elastomeric materials are used as shock isolation materials in a variety of environments to dampen vibrations and/or absorb energy from external impact to minimize energy transfer between two objects or bodies. Some applications require the shock isolation materials to behave as a low-pass mechanical filter to mitigate the shock/impact at high frequencies but transmit the energy at low frequencies with minimal attenuation. To fulfill this requirement, a shock isolation material needs to be carefully evaluated and selected with proper experimental design, procedures, and analyses. In this study, a Kolsky bar was modified with precompression (up to 15.5 kN) and confinement capabilities to evaluate low-pass shock isolation performance in terms of acceleration attenuation through a variety of elastomers. Also investigated were the effects of preload and specimen geometry on the low-pass shock isolation response.
Steel grades such as A572 and AISI 4140 are often used for applications where high rate or impact loading may occur. A572 is a hot-rolled carbon steel that is used where a high strength to weight ratio is desired. A grade such as AISI 4140 offers decent corrosion resistance due to higher chromium and molybdenum content and is commonly used in firearm parts, pressurized gas tubes, and structural tubing for roll cages. In these scenarios, the material may undergo high rate loading. Thus, material properties including failure and fracture response at relevant loading rates must be understood so that numerical simulations of impact events accurately capture the deformation and failure/fracture behavior of the involved materials. In this study, the high strain rate tensile response of A572 and 4140 steel are investigated. An increase in yield strength of approximately 28% was observed for 4140 steel when comparing 0.001 s-1 strain rate to 3000 s-1 experiments. A572 showed an increase in yield strength of approximately 52% when the strain rate increased from quasi-static to 2750 s-1. Effects on true stress and strain at failure for the two materials are also discussed.
Low carbon, high strength steel alloys such as Vascomax steels are used in a wide variety of extreme environments due to their high strength, high fracture toughness, and stability over a wide range of temperatures. In this study, Vascomax® C250 steel was dynamically characterized in compression using Kolsky compression bar techniques at two strain rates of 1000 and 3000 s-1. A pair of impedance-matched tungsten carbide platens were implemented to protect damage to the bar ends. The tungsten carbide platens were experimentally calibrated as system compliance which was then properly corrected for actual specimen strain measurements. In addition, elastic indentation of the high-strength compression sample into the platens was also evaluated and showed negligible effect on the specimen strain measurements. The Vascomax® C250 steel exhibited strain-rate effects on the compressive stress-strain curves. The dynamic yield strength was approximately 18% higher than quasi-static yield strength obtained from hardness tests. The dynamic true stress-strain curves of the Vascomax® C250 steel in compression were also computed and then compared with the previously obtained true tensile stress-strain curves at the same strain rates. The Vascomax® C250 steel exhibited a reasonable symmetry in dynamic compression and tensile stress-strain response. However, the fracture strains in dynamic compression were smaller than those in dynamic tension probably due to different fracture mechanisms in the different loading modes.
This memo concerns the transmission of mechanical signals through silicone foam pads in a compression Kolsky bar set-up. The results of numerical simulations for four levels of pad pre-compression and two striker velocities were compared directly to test measurements to assess the delity of the simulations. The nite element model simulated the Kolsky tests in their entirety and used the hyperelastic `hyperfoam' model for the silicone foam pads. Calibration of the hyperfoam model was deduced from quasi-static compression data. It was necessary, however, to augment the material model by adding sti ness proportional damping in order to generate results that resembled the experimental measurements. Based on the results presented here, it is important to account for the dynamic behavior of polymeric foams in numerical simulations that involve high loading rates.
Silicone foams have been used in a variety of applications from gaskets to cushioning pads over a wide range of environments. Particularly, silicone foams are used as a shock mitigation material for shock and vibration applications. Understanding the shock mitigation response, particularly in the frequency domain, is critical for optimal designs to protect internal devices and components more effectively and efficiently. The silicone foams may be subjected to pre-strains during the assembly process which may consequently influence the frequency response with respect to shock mitigation performance. A Kolsky compression bar was modified with pre-compression capabilities to characterize the shock mitigation response of silicone foam in the frequency domain to determine the effect of pre-strain. A silicone sample was also intentionally subjected to repeated pre-strain and dynamic loadings to explore the effect of repeated loading on the frequency response of shock mitigation.
Iridium alloys have been utilized as structural materials for certain high-temperature applications due to their superior strength and ductility at elevated temperatures. In some applications where the iridium alloys are subjected to high-temperature and high-speed impact simultaneously, the high-temperature high-strain-rate mechanical properties of the iridium alloys must be fully characterized to understand the mechanical response of the components in these severe applications. In this study, the room-temperature Kolsky tension bar was modified to characterize a DOP-26 iridium alloy in tension at elevated strain rates and temperatures. The modifications include (1) a unique cooling system to cool down the bars while the specimen was heated to high temperatures with an induction heater; (2) a small-force pre-tension system to compensate for the effect of thermal expansion in the high-temperature tensile specimen; (3) a laser system to directly measure the displacements at both ends of the tensile specimen independently; and (4) a pair of high-sensitivity semiconductor strain gages to measure the weak transmitted force. The dynamic high-temperature tensile stress-strain curves of the iridium alloy were experimentally obtained with the modified high-temperature Kolsky tension bar techniques at two different strain rates (~1000 and 3000 s-1) and temperatures (~750 and 1030 °C).
In this paper, a new type of highly stretchable strain sensor was developed to measure large strains. The sensor was based on the piezo-resistive response of carbon nanotube (CNT)/polydimethylsiloxane (PDMS) composite thin films. The piezo-resistive response of CNT composite gives accurate strain measurement with high frequency response, while the ultra-soft PDMS matrix provides high flexibility and ductility for large strain measurement. Experimental results show that the CNT/PDMS sensor measures large strains (up to 8 %) with an excellent linearity and a fast frequency response. The new miniature strain sensor also exhibits much higher sensitivities than the conventional foil strain gages, as its gauge factor is 500 times of that of the conventional foil strain gages.
Conventional Kolsky tension bar techniques were modified to characterize an iridium alloy in tension at elevated strain rates and temperatures. The specimen was heated to elevated temperatures with an induction coil heater before dynamic loading; whereas, a cooling system was applied to keep the bars at room temperature during heating. A preload system was developed to generate a small pretension load in the bar system during heating in order to compensate for the effect of thermal expansion generated in the high-temperature tensile specimen. A laser system was applied to directly measure the displacements at both ends of the tensile specimen in order to calculate the strain in the specimen. A pair of high-sensitivity semiconductor strain gages was used to measure the weak transmitted force due to the low flow stress in the thin specimen at elevated temperatures. The dynamic high-temperature tensile stress–strain curves of a DOP-26 iridium alloy were experimentally obtained at two different strain rates (~1000 and 3000 s−1) and temperatures (~750 and 1030 °C). The effects of strain rate and temperature on the tensile stress–strain response of the iridium alloy were determined. The iridium alloy exhibited high ductility in stress–strain response that strongly depended on strain-rate and temperature.
Iridium alloys have been utilized as structural materials for certain high-temperature applications, due to their superior strength and ductility at elevated temperatures. The mechanical properties, including failure response at high strain rates and elevated temperatures of the iridium alloys need to be characterized to better understand high-speed impacts at elevated temperatures. A DOP-26 iridium alloy has been dynamically characterized in compression at elevated temperatures with high-temperature Kolsky compression bar techniques. However, the dynamic high-temperature compression tests were not able to provide sufficient dynamic high-temperature failure information of the iridium alloy. In this study, we modified current room-temperature Kolsky tension bar techniques for obtaining dynamic tensile stress-strain curves of the DOP-26 iridium alloy at two different strain rates (~1000 and ~3000 s-1) and temperatures (~750°C and ~1030°C). The effects of strain rate and temperature on the tensile stress-strain response of the iridium alloy were determined. The DOP-26 iridium alloy exhibited high ductility in stress-strain response that strongly depended on both strain rate and temperature.
Kolsky compression bar experiments were conducted to characterize the shock mitigation response of a polymethylene diisocyanate (PMDI) based rigid polyurethane foam, abbreviated as PMDI foam in this study. The Kolsky bar experimental data was analyzed in the frequency domain with respect to impact energy dissipation and acceleration attenuation to perform a shock mitigation assessment on the foam material. The PMDI foam material exhibits excellent performance in both energy dissipation and accele-ration attenuation, particularly for the impact frequency content over 1.5 kHz. This frequency (1.5 kHz) was observed to be independent of specimen thickness and impact speed, which may re-present the characteristic shock mitigation frequency of the PMDI foam material under investigation. The shock mitigation characteristics of the PMDI foam material were insignificantly influenced by the specimen thickness. However, impact speed did have some effect.
A Hopkinson bar was employed to conduct transverse impact testing of twisted Kevlar KM2 fiber yarns at the same impact speed. The speed of Euler transverse wave generated by the impact was measured utilizing a high speed digital camera. The study included fiber yarns twisted by different amounts. The Euler transverse wave speed was observed to increase with increasing amount of twist of the fiber yarn, within the range of this investigation. The higher transverse wave speeds in the more twisted fiber yarns indicate better ballistic performance in soft body armors for personal protection.