Critical Stresses in Spalling and Dynamic Rupture of Metals

Results of dynamic rupture tests of a series of metals obtained using a composite Hopkinson bar and shock-wave loading of plane specimens are described. It is shown that the actual rupture strength at a strain rate of 5 · 10³ sec⁻¹ is very close to the spall strength at higher strain rates. Results of testing the same metals using a composite Hopkinson bar within a temperature range of 20–350°C are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 103–107, November–December, 2005.     

A Hybrid Experimental/Numerical Investigation of the Response of Multilayered MEMS Devices to Dynamic Loading

In order to probe the mechanical response of microelectromechanical systems (MEMS) subjected to dynamic loading, a modified split Hopkinson pressure bar was used to load MEMS devices at accelerations ranging from 10³–10⁵  g. Multilayer beams consisting of a PZT film sandwiched between two metal electrodes atop an elastic layer of silicon dioxide were studied because of their relevance to active MEMS devices. Experiments were conducted using the modified split Hopkinson pressure bar to quantify the effects of dynamic loading amplitude, duration, and temporal profile on the failure of the multilayered cantilever beams. Companion finite element simulations of these beams, informed by experimental measurements, were conducted to shed light into the deformation of the multilayered beams. Results of the numerical simulations were then coupled with independent experimental measurements of failure stress in order to predict the material layer at which failure initiation occurred, and the associated time to failure. High-speed imaging was also used to capture the first real-time images of MEMS structures responding to dynamic loading and successfully compare the recorded failure event with those predicted numerically.     

Testing Aluminum Alloy from Quasi-static to Dynamic Strain-rates with a Modified Split Hopkinson Bar Method

An aluminum alloy¹ was tested at quasi-static to dynamic strain-rates (from 10⁻¹ to 5 10³ s⁻¹), using a single measuring device, a modified Split Hopkinson Bar. A wave separation technique [Bussac et al., J Mech Phys Solids 50:321–350, 2002] based on the maximum likelihood method was applied to process the strain and velocity measurements recorded at various points on each bar. With this method, it is possible to compute the stress, strain, displacement and velocity at any point on the bar. Since the measurement time is unlimited, the maximum strain measured in a given specimen no longer decreases with the strain-rate, as occurs with the classical Split Hopkinson Bar method. ¹The authors wish to thank the automobile manufacturer who provided samples of the alloy used in this study. For reasons of commercial and industrial confidentiality, we were not informed about the composition of this alloy.     

Effect of Mass Density on the Compressive Behavior of Dry Sand Under Confinement at High Strain Rates

Dynamic compressive behavior of dry quartz sand (Quikrete #1961 sand quarried in Pensacola, FL) under confinement was characterized using a modified long split Hopkinson pressure bar (SHPB). Sand grains were confined inside a hollow cylinder of hardened steel and capped by cemented tungsten carbide cylindrical rods. This assembly was subjected to repeated shaking to consolidate sand to attain precise bulk mass densities. It is then sandwiched between incident and transmission bars on SHPB for dynamic compression measurements. Sand specimens of five initial mass densities, namely, 1.51, 1.57, 1.63, 1.69, and 1.75 g/cm³, were characterized at high strain rates near 600 s⁻¹, to determine the volumetric and deviatoric behaviors through measurements of both axial and transverse responses of a cylindrical sand sample under confinement. The stress–strain relationship was found to follow a power law relationship with the sand initial bulk density, with an exponent of 8.25, indicating a behavior highly sensitive to mass density. The energy absorption density and compressibility of sand were determined as a function of axial stress.     

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

A Long Split Hopkinson Pressure Bar (LSHPB) for Intermediate-rate Characterization of Soft Materials

In this study, we developed a long split Hopkinson pressure bar (LSHPB) for mechanically characterizing soft materials at intermediate strain rates. Using a proper pulse shaper, a loading pulse over 3 ms was produced for compression experiments on a PMDI foam material at the strain rates in the order of 10/s. The pulse shaping technique minimized the dispersion effects of stress wave when propagating through such a long bar system. Consistency of stress–strain curves obtained from the LSHPB and an MTS in the same strain rate range shows that a gap currently existing in intermediate strain-rate range is closed by the introduction of the LSHPB.     

Technique for Combined Dynamic Compression–Shear Testing of PBXs

We modify the split Hopkinson pressure bar and propose a compression–shear experimental method to investigate the dynamic behavior of polymer-bonded explosives (PBXs). The main apparatuses used include an incident bar with a wedge-shaped end and two transmission bars. We employ Y-cut quartzes with a rotation angle of 17.7° to measure the shear force and an optical system for shear strain measurement. A PBX with a density of 1.7 g/cm³ is investigated using the proposed method. Experimental results show that the specimen endures both compression and shear failure. Compression failure stress rises, and shear failure stress decreases as the strain rate increases. The sequences of shear and compression failure times are various at different strain rates. Based on the maximum shear failure criterion, we conclude that these phenomena are related to the experimental loading path.     

M-shaped Specimen for the High-strain Rate Tensile Testing Using a Split Hopkinson Pressure Bar Apparatus

An experimental technique is proposed to determine the tensile stress–strain curve of metals at high strain rates. An M-shaped specimen is designed which transforms a compressive loading at its boundaries into tensile loading of its gage section. The specimen can be used in a conventional split Hopkinson pressure bar apparatus, thereby circumventing experimental problems associated with the gripping of tensile specimens under dynamic loading. The M-specimen geometry provides plane strain conditions within its gage section. This feature retards necking and allows for very short gage sections. This new technique is validated both experimentally and numerically for true equivalent plastic strain rates of up to 4,250/s.     

Strain-Rate-Dependent Failure of a Toughened Matrix Composite

The strain-rate-dependent behavior of a toughened matrix composite (IM7/8552) was characterized under quasi-static and dynamic loading conditions. Unidirectional and off-axis composite specimens were tested at strain rates ranging from 10^?4 to 10³ s^?1 using a servo-hydraulic testing machine and split Hopkinson pressure bar apparatus. The nonlinear response and failure were analyzed and evaluated based on classical failure criteria and the Northwestern (NU) failure theory. The predictive NU theory was shown to be in excellent agreement with experimental results and to accurately predict the strain-rate-dependent failure of the composite system based on measured average lamina properties.     

Determination of Early Flow Stress for Ductile Specimens at High Strain Rates by Using a SHPB

In a dynamic experiment to obtain the high-rate stress–strain response of a ductile specimen, it takes a finite amount of time for the strain rate in the specimen to increase from zero to a desired level. The strain in the specimen accumulates during this strain-rate ramping time. If the desired strain rate is high, the specimen may yield before the desired rate is attained. In this case, the strain rates at yielding and early plastic flow are lower than the desired value, leading to inaccurate determination of the yield strength. Through experimentation and analysis, we examined the validity and accuracy of the flow stresses for ductile materials in a split Hopkinson pressure (SHPB) bar experiment. The upper strain-rate limit for determining the dynamic yield strength of ductile materials with a SHPB is identified.     

A Micromechanics Study of Lamellar TiAl

Microdeformation patterns of lamellar TiAl specimens with various grain sizes under uniaxial tension are mapped using the micro/nano experimental mechanics technique called SIEM (Speckle Interferometry w ith Electron Microscopy). The stress–strain relationships were obtained from deformations within decreasing areas ranging from mm² to μm². We found that the stress–strain relationship of the material depends on the size of strain measuring area in relation to the grain size. The stiffness at a grain boundary can be as large as 7–10 times more than that of the grain itself. From the data obtained so far, it seems that the traditional way of using PST (polysynthetically twinned) single crystal to predict polycrystalline behavior may not be appropriate.     

Dynamic compressive behavior of thick composite materials

The effect of strain rate on the compressive behavior of thick carbon/epoxy composite materials was investigated. Falling weight impact and split Hopkinson pressure bar systems were developed for dynamic characterization of composite materials in compression at strain rates up to 2000 s^–1. Strain rates below 10 s^–1 were generated using a servohydraulic testing machine. Strain rates between 10 s^–1 and 500 s^–1 were generated using the drop tower apparatus. Strain rates above 500 s^–1 were generated using the split Hopkinson pressure bar. Unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions, and cross-ply laminates were characterized. The 90-deg properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The 0-deg and cross-ply laminates show higher strength and ultimte strain values as the strain rate increases, whereas the modulus increnases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases, the dynamic stress-strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal direction and highest in the transverse direction.     

Experimental analysis of dynamic mechanical properties for artificially frozen clay by the split Hopkinson pressure bar

A device for impact compression experiments is the split Hopkinson pressure bar with a refrigerating attemperator. Data for incident and reflected waves are obtained by the measuring technique with strain gauges, and data for transmitted waves are obtained by the measuring technique with semiconductor gauges. Static compression tests of frozen clay are conducted at an identical temperature and different strain rates of 0.001 and 0.01 sec ⁻¹ . Dynamic stress-strain curves are obtained at strain rates of 360–1470 sec ⁻¹ . The low and high temperatures correspond to high and low strain rates, respectively. It is shown that both the temperature and strain rate affect the frozen soil deformation process. Different dynamic stress-strain curves obtained at the same temperature but different strain rates are found to converge. The test results indicate that frozen soil has both temperature-brittleness and impact-brittleness.     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Dynamic response and energy dissipation characteristics of balsa wood: experiment and analysis

Dynamic response of a cellular sandwich core material, balsa wood, is investigated over its entire density spectrum ranging from 55 to 380 kg/m³. Specimens were compression loaded along the grain direction at a nominal strain rate of 3 × 10³ s⁻¹ using a modified Kolsky (split Hopkinson) bar. The dynamic data are discussed and compared to those of quasi-static experiments reported in a previous study (Mech. Mater. 35 (2003) 523). Results show that while the initial failure stress is very sensitive to the rate of loading, plateau (crushing) stress remains unaffected by the strain rate. As in quasi-static loading, buckling and kink band formation were identified to be two major failure modes in dynamic loading as well. However, the degree of dynamic strength enhancement was observed to be different for these two distinct modes. Kinematics of deformation of the observed failure modes and associated micro-inertial effects are modeled to explain this different behavior. Specific energy dissipation capacity of balsa wood was computed and is found to be comparable with those of fiber-reinforced polymer composites.     

Torsional split Hopkinson bar tests at strain rates above 104s−1

The torsional split Hopkinson bar is used for testing materials at strain rates above 10⁴s⁻¹. This strain rate, which is an order of magnitude higher than is typical with this technique, is obtained by using very short specimens. Strain rates of 6.4×10⁴s⁻¹ have been achieved with specimens having a gage length of 0.1524 mm. Results from tests on 1100 aluminum show an increase in rate sensitivity as the strain rate increases.     

Hopkinson拉杆的入射波波形整形实验研究

目前,分离式Hopkinson杆实验技术已经被广泛用于测试材料在10~2~10~4s~(-1)应变率范围内的动态力学特性。为了抑制入射波的高频振荡,实现恒定应变率加载,本文利用分离式Hopkinson拉杆(SHTB)实验装置,研究了加载金属短杆(2A12T4铝合金)及整形垫片(纸板、PVC软塑料及带磁性胶皮)对入射波波形的影响。实验结果表明,整形垫片降低了入射应力脉冲的高频振荡,获得了比较平滑的入射应力脉冲,延长了上升时间。同时,利用所得的波形整形结果,对2A12T4铝合金进行了拉伸应力波脉冲加载的拉伸和断裂实验测试。     

Adiabatic shear localization in the dynamic punch test,part I: experimental investigation

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during a dynamic punch test is investigated. Specifically, the possibility and affects of adiabatic shear localization are examined. The three materials are chosen to encompass a wide range of physical properties. Punch tests are conducted at average shear strain rates from 10⁻³ to 10⁴ s⁻¹ on a servo-hydraulic compression machine, a mechanical press, and a Hopkinson bar apparatus. Experimental load displacement curves are obtained and fractographic and metallographic analysis is performed. Finite element simulations of punching operations are performed in the second part of this two part investigation to examine internal deformation not visible during experimental tests. More specifically, the role of adiabatic shear localization in burr formation is determined. Adiabatic shear localization occurs in the titanium alloy for the mechanical press and Hopkinson bar tests, while localization is not present for the 6061-T6 aluminum in any test. The 1018 steel begins to exhibit some transitional behavior toward shear localization in the Hopkinson bar experiments. It is seen that in the materials tested here, a combination of high strength and low strain hardening make a material more susceptible to adiabatic shear localization in punching operations.     

Effect of strain rate,moisture and temperature on the deformation behavior of polymer roll covers

Soft polymer roll covers, which are used in certain positions of paper manufacturing machines, have a vital role in the dynamics of two mating rotating rolls (i.e., nip dynamics). The polymer covers are often used in moist conditions where the loading rates are rather high and temperatures may vary from 45 to 60°C. In this paper, we study the dynamic mechanical behavior of two soft polyurethane composite roll covers under different conditions of temperature, moisture, and loading rate. For the tests in compression, both servohydraulic materials testing machines and the split Hopkinson pressure bar technique were used in the strain rate range of 0.001–1500 s⁻¹. The specimens, which were to be tested under moist conditions, were immersed in paper machine water (pH 4.5) until saturated moisture content was reached. The materials showed remarkable softening as well as decrease in the strain rate sensitivity in moist conditions.