Split Hopkinson Pressure Bar Apparatus Research Articles

Study on dynamic deformation-damage-ignition mechanism of GAP/RDX/TEGDN propellant

ABSTRACT Investigations on high-energy and low-vulnerability propellants can provide a better understanding for improving the operational effectiveness and survivability of strategic and tactical missiles. In the present study, the dynamic compressive mechanical properties and damage-ignition response mechanism of the GAP/RDX/TEGDN (GRT) propellant under high strain rates have been studied using a split Hopkinson pressure bar apparatus and a high-performance high-speed camera. The experimental results suggested that the mechanical properties of the GRT propellant, in terms of yield stress, initial compressive modulus, and ultimate stress, were greatly affected by the loaded strain rate. The true stress-strain curves exhibited an initial linear elasticity region followed by yielding a subsequent strain hardening and strain softening region stage. It has been found that the yield stress and ultimate stress increased with the strain rates. Moreover, at higher strain rates, the impulse increases significantly, leading to earlier and more intense ignition. The critical strain rate and the critical impulse of the GRT propellant are 5000 s−1 and 13.28 N · s, respectively. A judgment basis for GRT propellant ignition is established. Finally, according to the high-speed images and the posttest SEM images, it has been concluded that the dominant ignition mechanism of GRT propellant is flow at the macroscopic level and internal frictional heating at the mesoscopic level.

Role of confinement in coseismic pulverization: Testing the rock record of rupture directivity on the San Jacinto fault, Southern California

The San Jacinto fault juxtaposes Pleistocene Bautista Formation sediments against Cretaceous tonalite near Anza, California. While the tonalites show typical features of pulverized fault zone rocks on the NE side of the fault, the weakly consolidated Bautista Formation shows evidence of pulverization at a depth of 120 m, yet only background level deformation at 70 m, consistent with the expectation that a minimum confining pressure is required to initiate pulverization in poorly consolidated sediments. We test this hypothesis by simulating pulverization using a modified Split Hopkinson Pressure Bar apparatus, in which dry and wet sediments are subjected to up to three repeated dynamic triaxial compressive load cycles. We suggest unconsolidated sediments require a minimum confining pressure under axial compression to initiate pulverization and multiple seismic cycles to reach the observed fracture densities. Companion experiments conducted on Ottawa sand suggest sub-grain scale inelastic deformation in the bulk (i.e., not localized in deformation bands) occurs preferentially at high strain rates. Furthermore, the compressive origin of sediment pulverization, along with evidence of tensile fragmentation in cross-fault tonalite, supports a preferred northwest rupture direction along the southern section of the San Jacinto fault.

Fiber metal laminates for high strain rate applications with layerwise shock impedance tuning

Novel materials such as fiber-metal laminates (FMLs) have demonstrated significant potential in a variety of applications. They must contend with problems such fatigue, creep, high-speed projectile impact, and deformation at high strain rates while in use. When employed as structural materials in aircraft, especially when exposed to shock wave impact and high velocity impact, fiber-metal laminates’ high strain rate characteristics become crucial. Shock impedance matching is a revolutionary approach used for shock-tuning the separate layers. The novelty of the current work is in developing custom shielding laminates, with in-depth analysis on the response of the shock impedance tuning of individual layers on the laminate behaviour at high strain rates. In the current study, five stackups of FMLs comprising metallic (AA 6061-T6) and fiber-reinforced polymer (FRP) plies, were formulated, incorporating shock impedance matching. The fiber-polymer plies used in the FMLs include ultra-high molecular weight polyethylene (UHMWPE), p-aramid for supplementing the impact resistance. Transmission loss functions (TL) estimated from the impedance tube experiments were used to indicate the shock tuning of the various laminates. The laminates underwent testing using a Split Hopkinson Pressure Bar (SHPB) apparatus to determine their properties at high strain rates (350, textrm{s}^{-1} to 460, textrm{s}^{-1}). The variation in the Shock Energy (SE) absorbed by the laminates at various strain rates was analyzed as a function of the corresponding Transmission Loss employing regression. The dynamic stress-strain curves showed an increase in shock energy absorption at higher strain rates. The sequence SSP-IV and SSP-II showed the highest values of energy absorption as well as Transmission Loss.

Asynchronous time integration while achieving zero interface energy

This contribution deals with an asynchronous direct time integration of the finite-element model. The proposed method is applied to the phenomenon of wave propagation through an elastic linear continuum. The numerical model is partitioned into individual subdomains using the domain decomposition method by means of localized Lagrange multipliers. For each subdomain, different time discretizations are used. No restrictions for relation between subdomain’s time steps are imposed. The coupling of the subdomains is forced by an acceleration continuity condition. Additionally, we use the a posteriori technique to also provide the displacement and velocity continuity at the interfaces, and hence we obtain exact continuity of all three kinematic fields. The proposed method is experimentally validated using the modified SHPB (split Hopkinson pressure bar) setup.

Experimental study of the quasi-static and dynamic fracture toughness of notched and repaired concrete using semi-circular bend method

Concrete constructions commonly contain cracks or defects during forming and service, repair operations are necessary in many situations. However, limited investigations conducted on the dynamic fracture toughness (DFT) of repaired concrete structures. This paper investigates the cracking behavior of concrete structures through notched dynamic semi-circular bend (NSCB) tests performed using a split Hopkinson pressure bar (SHPB) apparatus with two measurement techniques, namely digital image correlation (DIC) and crack propagation gauge (CPG), to capture the flying half angular velocity and crack propagation speed of NSCB concrete specimens under various loads. The results demonstrate a linear increase in both DFT and crack propagation speed of concrete with the loading rate. Additionally, a threshold value exists beyond which the crack speed stabilizes, and the DFT is not evidently influenced by the notch depths. The cracks propagate along the aggregates and remain mostly intact under a relatively low loading rate. With an increased loading rate, the damage pattern of some otherwise deflected aggregates changes resulting in crack penetration and significantly reducing the fracture surface roughness. Repaired specimens exhibit greater energy dissipation at the same loading rate, thereby producing flying fragments with lower kinetic energy, which can prevent secondary damage to internal personnel and structures.

Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation, vehicular tunnels are often designed as two adjacent tunnels, which frequently experience dynamic stress waves from various orientations during blasting excavation. To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel, a split Hopkinson pressure bar (SHPB) apparatus was used to conduct a dynamic test on the twin-tunnel specimens. The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation. LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens. The findings indicate that, for a twin-tunnel exposed to a dynamic load from different orientations, the crack initiation position appears most often at the tunnel corner, tunnel spandrel, and tunnel floor. As the impact direction is created by a certain angle (30°, 45°, 60°, 120°, 135°, and 150°), the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel. As the impact loading angle (α) is 90°, the tunnel sustains minimal damage, and only tensile fractures form in the surrounding rocks. The orientation of the impact load could change the stress distribution in the twin-tunnel, and major fractures are more likely to form in areas where the tensile stress is concentrated.

Effect of graphene oxide on cement mortar under quasi-static and dynamic loading

Cement composites are the most widely used construction material in the world; however, research on their resistance to high strain loads is lacking. This study investigated the effect of graphene oxide (GO) on the static and dynamic mechanical properties and microstructure of cement mortar. Dynamic tests were performed using a split Hopkinson pressure bar apparatus at strain rates up to approximately 290 s−1. The mechanical behaviors of mortar specimens infused with 0.005 and 0.01 wt% GO (weight% of GO to cement) were compared against control specimens made with ordinary Portland cement. Enhancement in the strength of cement composites was evident in both compression and split-tension when GO was added in specific doses, particularly at higher strain rates. Correlation between the dynamic increase factor and the applied strain rate is found based on the compressive and split-tensile experimental data of tested mortar specimens. The findings of this study highlight the great potential of GO for improving the performance of cement composites under high strain rate loading.

Influence of Bamboo Fibers Weight Fraction on the Quasi-Static and Dynamic Compressive Responses of Epoxy Matrix Composites

ABSTRACT The influences of natural bamboo fibers (BFs) weight fraction on the microstructure, quasi-static and dynamic compressive responses of the epoxy resin matrix composites were investigated with the aid of scanning electron microscope, electronic universal testing machine and the modified Split Hopkinson pressure bar (SHPB) setup. The quasi-static compressive properties of the BFs/epoxy resin matrix composites suggested that the compressive strength were strongly improved with the addition of the natural BFs, which was attributed to the excellent strengthening effect. When the BFs content increased up to 15 wt.%, the compression ratio of the BFs/epoxy resin matrix composites showed 11% reduction than that of the unmodified epoxy resin. Moreover, the stress and strain were linear at the initial part but nonlinear when stress exceeds a certain value. SHPB impact tests results indicated that, compared with the pristine epoxy resin, the natural BFs reinforced epoxy matrix composite with 15 wt.% BFs exhibited the highest dynamic compressive strength, compression modulus and the best strengthening effect. Epoxy resin matrix composites also showed an obvious effect rate effective under impact load. Similar to that in the quasi-static compressive test, the addition of natural BFs has a positive effect in improving the compressive strength of the epoxy matrix.

Compressive Split Hopkinson Pressure Bar Apparatus: Part I - Design and Development

Optimum utilization of composite materials envisages its use under static as well as dynamic loading conditions. Hence, there is a need to assess the behavior of composite materials at high strain rates. Split Hopkinson Pressure Bar (SHPB) apparatus is widely used to assess high strain rate behavior of composites. Even though SHPB apparatus is widely used, its design methodology and development technique are not readily available. Design and devel- opment details of a compressive SHPB apparatus for characterizing mechanical properties of different materials at high strain rate loading are presented. Brief theoretical background necessary for the design of SHPB apparatus is presented based on one-dimensional wave propagation theory in elastic bars. Next, brief working principle of the apparatus and schematic arrangement are presented. Different components of the compressive SHPB appa- ratus are identified. Design, development and commissioning of the apparatus are discussed. Further, different instruments used and the calibration technique used are presented.

Compressive Split Hopkinson Pressure Bar Apparatus: Part II- Experimental Results

Investigations on high strain rate behavior of a typical unidirectional glass / epoxy composite under compressive loading are presented. Compressive Split Hopkinson Pressure Bar (SHPB) apparatus was used for the studies. Compressive properties were evaluated along longitudi- nal, transverse and thickness directions in the strain rate range of 548 - 2645 per sec. It is observed that the compressive strength is enhanced at high strain rate loading compared with those at quasi-static loading. Studies were also carried out on 10° and 45° off-axis specimens. In-plane shear strength was determined based on 10° off-axis compressive results. It is observed that the in-plane shear strength is increased at high strain rate loading compared with that at quasi-static loading. But it remains nearly constant with increasing strain rate at high strain rates.

Estimation of non-linear mechanical properties of rubber using Split Hopkinson pressure bar

The material non-linearity is a very important phenomenon in the behavior of the materials subjected to high strain rate loading. Rubber is a material which has high damping properties due to which it is more vulnerable in applications that involve absorption of vibration and shock; generally, these damping materials are subjected to high strain rate loading while absorbing the load. In the present work, various types of rubbers are subjected to very high-velocity impact due to which a very high strain rate loading is applied on the rubber specimens through the usage of Split Hopkinson Pressure Bar apparatus. The behavior of the rubber specimens at this high-velocity impact loading is studied through the variation of stress, strains, and strain rate with time. A comparison is drawn between various rubbers and the best rubber for the impact applied, is evolved and the same is presented in the work.

Dynamic Tensile Failure Characteristics and Energy Dissipation of Red Sandstone under Dry–Wet Cycles

Studying the dynamic properties of rocks in complex environments is of great significance to the sustainable development of deep-sea metal mineral resource extraction. To investigate the influence of dry–wet cycles on the dynamic tensile properties and energy dissipation of red sandstone, a series of dynamic Brazilian disc tests was carried out through the split Hopkinson pressure bar (SHPB) apparatus. The dynamic tensile behaviors and energy dissipation distribution of the red sandstone specimens after different dry–wet cycles (0, 10, 20, 30 and 40 cycles) were analyzed in this study. The degree of dynamic tensile fragmentation and energy dissipation of red sandstone is significantly affected by the loading rate. Specifically, when the number of dry–wet cycles remains constant, an increase in loading rate results in a significant reduction in the average fragment size, while the energy consumption density exhibits an approximately linear increase. At a fixed loading rate, the energy consumption density decreases approximately linearly with the increase in dry–wet cycles, and the higher the loading rate, the more sensitive the energy consumption density is to the dry–wet cycle. Under a fixed number of dry–wet cycles, the dynamic tensile strength has an exponential relation with the increase in energy consumption density.

Dynamic shear properties and microstructure evolution of commercially pure titanium with heterogeneous gradient microstructure

Heterogeneous gradient microstructure in commercially pure titanium (CP Ti) was fabricated through the explosion hardening (EH) technique followed by annealing treatment (AT). The heterogeneous gradient microstructure was characterized by a microhardness tester, optical microscope and transmission electron microscope. Subsequently, dynamic shear properties and microstructure evolution of the material were systematically studied by split Hopkinson pressure bar apparatus with hat-shaped shear specimens. Experimental results showed that various heterogeneous gradient microstructures were obtained by EH + AT at different annealing temperatures. Enhanced dynamic shear properties with special yield stress-fracture strain combinations were observed, exhibiting better mechanical properties than the other metallic materials. Such excellent mechanical properties originated from finer grain size, higher twin/dislocation density and gradient synergistic effect. During dynamic shear tests of gradient CP Ti, adiabatic shear bands (ASBs) were easy to nucleate, propagate and interact, especially on EH treated specimen surface due to the generation of high-density micro-defects. Formation of twins/dislocations during EH treatment promoted dynamic recovery during the ASBs nucleation stage, whereas AT delayed ASBs nucleation due to a decrease in micro-defects, which contributed to better ductility. During dynamic shear tests of gradient CP Ti, propagation of ASBs and cracks was delayed by the gradient microstructure. The adiabatic temperature rise of 2-EH treated CP Ti was calculated to be 108 °C when ASBs nucleated, which was so low that it was supposed to have no effect on ASBs nucleation.

The Strain Rate Effects of Coral Sand at Different Relative Densities and Moisture Contents.

A 37-mm-diameter split Hopkinson pressure bar (SHPB) apparatus was used for impact loading tests to determine the effects of the relative density and moisture content on the dynamic properties of coral sand. The stress-strain curves in the uniaxial strain compression state were obtained for different relative densities and moisture contents under strain rates between 460 s-1 and 900 s-1. The results indicated that with an increase in the relative density, the strain rate becomes more insensitive to the stiffness of the coral sand. This was attributed to the variable breakage-energy efficiency at different compactness levels. Water affected the initial stiffening response of the coral sand, and the softening was correlated with the strain rate. Strength softening due to water lubrication was more significant at higher strain rates due to the higher frictional dissipation. The volumetric compressive response of the coral sand was investigated by determining the yielding characteristics. The form of the constitutive model has to be changed to the exponential form, and different stress-strain responses should be considered. We discuss the effects of the relative density and water content on the dynamic mechanical properties of coral sand and clarify the correlation with the strain rate.

Experimental Investigation of the Dynamic Mechanical Properties of Polypropylene-Fiber-Reinforced Foamed Concrete at High Temperatures.

Polypropylene-fiber-reinforced foamed concrete (PPFRFC) is often used to reduce building structure weight and develop engineering material arresting systems (EMASs). This paper investigates the dynamic mechanical properties of PPFRFC with densities of 0.27 g/cm3, 0.38 g/cm3, and 0.46 g/cm3 at high temperatures and proposes a prediction model to characterize its behavior. To conduct the tests on the specimens over a wide range of strain rates (500~1300 s-1) and temperatures (25~600 °C), the conventional split-Hopkinson pressure bar (SHPB) apparatus was modified. The test results show that the temperature has a substantial effect on the strain rate sensitivity and density dependency of the PPFRFC. Additionally, the analysis of failure models demonstrates that with the melting of polypropylene fibers, the level of damage in PPFRFC under dynamic loading increases, resulting in the generation of a greater number of fragments.

Explicit asynchronous time scheme with local push-forward stepping for discontinuous elastic wave propagation: One-dimensional heterogeneous cases and Hopkinson bar experiment

This is a presentation of robust and accurate explicit time-stepping strategy for finite element modeling of elastic discontinuous wave propagation in strongly heterogeneous, multi-material and graded one-dimensional media. One of the major issues in FEM modeling is the existence of spurious numerical stress oscillations close to theoretical wave fronts due to temporal-spatial dispersion behavior of FE discretization. The numerical strategy presented for modeling of 1D discontinuous elastic waves is based on (a) pushforward-pullback local stepping — ensuring the elimination of dispersion due to different critical time step sizes of finite elements, (b) domain decomposition via localized Lagrange multipliers — to satisfy coupling kinematics and dynamic equations , (c) asynchronous time scheme — ensuring the correct information transfer of quantities for the case of integer ratios of time step size for all domain pairs. Dispersion behaviors, existence of spurious stress oscillations, and sensitivity of the dispersion to time step size are then suppressed. The proposed method is numerically tested with regard to the rectangular step pulse elastic propagation problem considering in-space varying Young’s modulus. To prove robustness and accuracy, a comparison with results from commercial software, an analytical solution, and experimental data from partial assembly of a split Hopkinson pressure bar (SHPB) setup is provided.

Energy-conserving interface dynamics with asynchronous direct time integration employing arbitrary time steps

The derivation and implementation of an asynchronous direct time integration scheme for domain-decomposed finite element models is presented. To maximize clarity in the description of the proposed asynchronous integration, the scheme is restricted to the linear-elastic stress wave propagation case. The proposed method allows the integration of individual subdomains with independent time steps. There is no requirement for an integer time steps ratio of the interacting domains while maintaining zero interface energy. The subdomains are connected by the condition of the continuity of the acceleration field at the interface. In addition, the a posteriori technique is applied to satisfy the continuity of the displacement and velocity fields. Another important contribution of this paper lies in the description of the implementation — we offer the reader a general description of the implementation of the case of any number of subdomains with any number of constraints between them, while the basics of the algorithm are explained on a single domain pair. The functionality of the asynchronous integrator is verified by solving selected problems and comparing with analytical solutions and experimental measurements obtained using a Split Hopkinson pressure bar setup.

Experimental investigation of the quasi-static and dynamic compressive behavior of polymer-based 3D-printed lattice structures

Because additive manufacturing (AM) allows the creation of complex structures that can be tailored or optimized based on mechanical and material specifications, it is increasingly used for various applications. Among others, it gives access to new designs of lightweight shields exhibiting good capabilities for absorbing dynamic loads and kinetic energy. In the present work, the quasi-static and dynamic compressive behavior of 3D polymeric lattice structures manufactured by the fused deposition modeling (FDM) process were evaluated. Two different materials were considered: ABS (Acrylonitrile Butadiene Styrene) and Tough-PLA (PolyLactic Acid). First, the tensile quasi-static mechanical properties of precursor filaments and 3D-printed dog-bone specimens were evaluated. Through these tests, it was observed that the printing process and orientation have a significant effect on the mechanical behavior of AM-produced samples. Then, quasi-static and dynamic compressive tests were conducted on AM-produced cylindrical specimens using two distinct printing topologies. The dynamic tests were performed with a split Hopkinson pressure bar (SHPB) apparatus. The results indicated that the compressive strength increases with the loading rate, indicating a strain rate sensitivity of the studied materials. Finally, three different 3D lattice structures were experimentally evaluated against crushing at two different deformation rates. It was noted that the geometrical design and relative densities of these structures have major effects on their energy absorption capability. However, no clear correlation seems to exist between energy absorption capabilities under quasi-static and dynamic loading conditions.

Experimental and numerical studies on pulse shaping techniques used in split Hopkinson pressure bar for testing concrete material

Split Hopkinson pressure bar (SHPB) is commonly used to characterise materials under high strain rates. However, conventional SHPB tests on brittle materials have encountered several experimental challenges for high strain rate loading. In relatively brittle materials like concrete, the deformation of the specimen is very small when subjected to impact loading; hence, it is very difficult to obtain the prerequisites of valid SHPB tests such as dynamic equilibrium and constant strain rate in the specimen. To overcome these issues, the current study presents the importance of the pulse shaper approach in SHPB application for the dynamic characterisation of concrete material. Selection of the appropriate dimension of pulse shaper assists in facilitating dynamic stress equilibrium and constant strain rate in the specimen. In the present study, copper pulse shapers are used for the evaluation of concrete under high strain rate loading using an SHPB set-up. Parameters such as the effect of dimensions (diameter and thickness) of pulse shapers on loading pulses, dynamic equilibrium, constant strain rate and material responses are studied. Experimental results reveal the prediction of suitable pulse shapers for 50–200/s strain rates. In addition, numerical simulation is also performed and results are validated with the experimental data.

Dynamic compressive behavior of concrete-filled steel tubes under single and multiple impacts

In this study, the dynamic compression behavior of concrete-filled steel tubes (CFSTs) under single and multiple impacts was investigated using the split Hopkinson pressure bar (SHPB) apparatus. Analyses of the failure patterns, dynamic stress-strain relationship and dynamic compressive strength of CFST members were conducted, and the results for CFSTs were compared with those for plain concrete samples. Moreover, the confinement mechanism of the CFST specimens during the axial impact was investigated, and the influences of strain rate, steel tube thickness, concrete strength and height-to-diameter ratio on the dynamic increase factor of the CFST (DIFCFST) were explored. The experimental results indicate that the CFST specimens had excellent impact resistance under single and multiple impacts, and the dynamic compressive behaviors of CFSTs exhibited significant strain-rate dependence. Larger loading gas pressure can strengthen the confinement from steel tube to concrete, leading to an increase in the dynamic compressive strength of the CFST. Dynamic compressive strength reduction generally occurred during multiple impacts, while the strength enhancement could be observed at lower impact level due to insufficient single impact energy. The DIFCFST decreased with increasing steel tube thickness and concrete strength, while the height-to-diameter ratio had less effect on the DIFCFST. Based on the experimental test data, an empirical formula was proposed for the DIFCFST considering the strain rate, the confinement factor and concrete strength to predict the dynamic compressive strength of CFST members under axial impact.