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.
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.
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.
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.
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.
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.
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.
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.