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A theoretical analysis of the stress state in specimen of the SHPB experiment was performed in consideration of lateral inertia effect. The nonuniformity of lateral stress in specimen and variety of deforming velocity in the loading process were taken into account in the analysis. A formula to correcting the lateral inertia effect was obtained. The force and deformation velocity of specimen-bar interfaces during the loading process got from a numerical simulation of SHPB were used to verify the theoretical analysis formula. It shows that the deviation of reconstructed curve from the inputted relationship can be brought down with the correction formula.

This paper studied the fractal characteristics of crack propagation in coal containing beddings under impact loading condition. Split Hopkinson pressure bar (SHPB) system was applied to determine the prepared notched semi-circular bending specimens. The high-speed camera was used to record the propagation characteristics of cracks. The image processing method and fractal dimension calculation software are combined to further analyze the effects of bedding and loading rate on the fractal characteristics of crack propagation in coal. The experimental results presented that the presence of bedding has a remarkable impact on the crack propagation. The crack velocity of coal samples with $45^{\circ }$ bedding angle is of the maximum, however, the crack velocity of samples with $0^{\circ }$ bedding angle is of the minimum. Bedding angles also have obvious influence on the fractal dimension of cracking path, the bedding angle of $45^{\circ }$ being the largest, and those of $22.5^{\circ }$ and $67.5^{\circ }$ having the intermediate values, while those of $0^{\circ }$ and $90^{\circ }$ being the smallest. Several points of instantaneous fractal crack velocity are close to the Rayleigh wave velocity ($C_r$). The crack velocities of coal specimens with bedding angles of $22.5^{\circ }$, $45^{\circ }$ and $67.5^{\circ }$ are prone to the high value.

The dynamic mechanical properties of Ti-6Al-4V alloy prepared by laser direct deposition (LDD) at different strain rates are of great significance for the application of LDD technology in the manufacture and repair of aero-engine parts. The quasi-static tensile test and dynamic compression test of Ti-6Al-4V alloy prepared by LDD (LDD-Ti-6Al-4V) were carried out under the quasi-static and high strain rate using INSTRON-5982 tensile test equipment and Split Hopkinson pressure bar (SHPB) equipment. The true stress–strain curve is obtained, which indicates that the LDD-Ti-6Al-4V has a strain rate strengthening effect. Moreover, the Johnson–Cook (J–C) constitutive model of LDD-Ti-6Al-4V was fitted based on experimental data, and the experimental process of SHPB was numerically simulated. The simulation results are basically the same as the experimental results, which proves the correctness of the J–C constitutive model of LDD-Ti-6Al-4V.

According to the scientific research needs of deep multi-field coupling true triaxial compression testing machines, it is necessary to find a suitable boundary material to be placed between the rock and the transmission bar to achieve the effects of wave elimination and energy absorption. This enables the conditions of the test requirements to be met under the interaction of true triaxial and strong disturbance. Therefore, the improved split Hopkinson pressure bar (SHPB) device was used to carry out a series of experiments on the wave elimination and energy absorption characteristics of different boundary materials, and to study the energy evolution characteristics and stress wave propagation laws of different materials under static–dynamic coupling loading. The results show that under single impact loading, owing to the difference in wave impedance between the material and the rock rod, the porous material will not only reflect the tensile wave that has a greater impact on the rock rod, but also its weakening effect on the reflection stress is weaker than that of the wave-absorbing metal plate. In terms of overall energy conversion, the energy absorption rate of the porous material PM-1 is superior, and the conversion rate of the reflection and transmission energies is also greatly reduced. Under the impact of cyclic loading, the reflection stress of the wave-absorbing metal plate increased slightly with an increase in the number of impacts. However, with the increase of impact times, the reflection peak stress of porous material PM-1 decreases at first and then increases, and the reflected wave changes from tensile wave to compression wave, which is not as good as that of wave dissipation metal plate in terms of repeatability and fatigue resistance.

Numerical simulations were conducted to validate computational and constitutive models for steel materials through dynamic material tests involving both tension and compression. These simulations involved the numerical modeling of the split Hopkinson pressure bar (SHPB) apparatus, with the appropriate loading applied directly in compression and indirectly in tension. To induce a tensile wave within the specimen, a shoulder, such as a coupler or collar, was interposed between the bars. The simulations were carried out using the LS-DYNA finite element code. In these numerical simulations of the SHPB tests, the MAT-15 Johnson–Cook material model was applied to represent mild steel. The resulting stress–strain relationships obtained under both compression and tension conditions were subsequently compared to corresponding experimental data. The primary objectives of these simulations were to determine the optimal placement of strain gauges on both the input and output bars of the tensile SHPB setup. Additionally, the simulations aimed to assess the influence of the gauge length-to-diameter ratio on the behavior of the mild steel specimen subjected to dynamic tension and compression. The results showed that the pulse produced due to the mechanical mismatch of the element at boundaries can be avoided using the length of the input bar smaller than the output bar. Further, the location of the strain gauge in the case of the output bar should be toward the output bar-shoulder interface, while in the case of the input bar, it should be considered at the center of the span of the bar.

Split Hopkinson pressure bar (SHPB) technique is the most important test method to characterize dynamic stress–strain relations of various materials at different strain rates, and this technique requires uniform deformation of specimen during the experiment. However, some studies in recent years have found obvious deformation localization within metal foam specimens in SHPB tests, which may significantly affect the reliability of the results. Usability of SHPB to characterize dynamic stress–strain relation of metal foam becomes doubtful. In this paper, based on experimental verification, we carried out numerical simulative SHPB tests to study the problem, in which the metal foam specimens were modeled to have 3D meso structures with properties of their matrix material. Numerical simulative SHPB tests of aluminum foam specimens with varying thickness at different strain rates were performed. Deformation distribution in each local region of the specimen was examined and a concept of “effective specimen” was presented. Appropriate specimen thickness and range of testing strain rate were suggested based on quantitative analysis. Finally, we recommended a method how to revise the nominal strain and strain rate measured by traditional SHPB method to acquire the reliable dynamic stress–strain relation.

The present work investigates the novel impact loading response of two-dimensional graphene oxide (GO) reinforced epoxy nanocomposites at high strain rate. The testing was performed up to 1000s${}^{-1}$ of high strain rate, where maximum damage occurs during the impact loading conditions. The Split Hopkinson Pressure Bar (SHPB) was used for the impact loading of the composite specimen. The nanofiller material GO was synthesized by chemical oxidation of graphite flakes used as the precurser. Synthesized GO was characterized using FTIR, UV-visible, XRD, Raman Spectroscopy and FE-SEM. Solution mixing method was used to fabricate the nanocomposite samples having uniform dispersion of GO as confirmed from the SEM images. Strain gauges mounted on the SHPB showed regular signal of transmitted wave during high strain rate testing on SHPB, confirming the regular dispersion of both the phases. Results of the transmission signal showed that the solution mixing method was effective in the synthesis of almost defect-free nanocomposite samples. The strength of the nanocomposite improved significantly using 0.5wt.% reinforcement of GO in the epoxy matrix at high strain rate loading. The epoxy GO nanocomposite showed a 41% improvement in maximum stress at 815s${}^{-1}$ strain rate loading.

As an ultra-soft material (elastic modulus in magnitude of kPa), polyvinyl alcohol (PVA) hydrogels have the potential to substitute articular cartilage, but the measurement of the dynamic stress–strain relations of ultra-soft materials is still challenging. In this paper, a double-striker electromagnetic driving split-Hopkinson pressure bar (SHPB) system was developed, in which all the bars were made of polycarbonate, and the polycarbonate striker was pushed by a metal striker driven electromagnetically to ensure the precise control of impact velocity. With the new SHPB system, well design of the size of hydrogel specimen and rational processing of the signal data, the stress–strain relations of hydrogels with varied PVA contents at different strain rates were measured successfully. Experimental results indicate that PVA hydrogels are a positive strain rate sensitive material with different strain-rate effects at low and high strain rates. Finally, based on the latest quasi-static constitution of the PVA hydrogel, a rate-dependent constitutive equation was recommended, which may well depict the mechanical behaviors of hydrogels with different fiber contents at varied strain rates. It also derives that the contributions of strain rate and fiber content on the mechanical behaviors of the hydrogel are relatively independent.

In this study, the effects of freeze–thaw cycles and cyclic impacts on frozen soil were systematically investigated. With an increase in the number of freeze–thaw cycles, the peak stress of frozen soil decreased until a stable state was achieved. Moreover, subjecting frozen soil to an increased number of cyclic impacts led to notable alterations in mechanical characteristics, including peak stress, critical strain and dynamic elasticity modulus. Both the freeze–thaw cycles and cyclic impacts were identified as primary damage mechanisms in understanding frozen soil degradation processes. Damage resulting from these impacts conformed to the Weibull distribution pattern. Damages induced by freeze–thaw cycles, individual impacts and cyclic impacts were integrated into the Zhu–Wang–Tang viscoelastic model (ZWT model). Relying on principles of elastic mechanics, the role of confining pressure on frozen soil was examined and subsequently integrated into an improved ZWT model. To evaluate the model’s effectiveness, its predictions were compared with experimental results.

Great progress has been made in the dynamic mechanical properties of concrete which is usually assumed to be homogenous. In fact, concrete is a typical heterogeneous material, and the meso-scale structure with aggregates has a significant effect on its macroscopic mechanical properties of concrete. In this paper, concrete is regarded as a two-phase composite material, that is, a combination of aggregate inclusion and mortar matrix. To create the finite element (FE) models, the Monte Carlo method is used to place the aggregates as random inclusions into the mortar matrix of the cylindrical specimens. To validate the numerical simulations of such an inclusion-matrix model at high strain rates, the comparisons with experimental results using the split Hopkinson pressure bar are made and good agreement is achieved in terms of dynamic increasing factor. By performing more extensive FE predictions, the influences of aggregate size and content on the macroscopic dynamic properties (i.e., peak dynamic strength) of concrete materials subjected to high strain rates are further investigated based on the back-propagation (BP) artificial neural network method. It is found that the particle size of aggregate has little effect on the dynamic mechanical properties of concrete but the peak dynamic strength of concrete increases obviously with the content increase of aggregate. After detailed comparisons with FE simulations, machine learning predictions based on the BP algorithm show good applicability for predicting dynamic mechanical strength of concrete with different aggregate sizes and contents. Instead of FE analysis with complicated meso-scale aggregate pre-processing, time-consuming simulation and laborious post-processing, machine learning predictions reproduce the stress–strain curves of concrete materials under high strain rates and thus the constitutive behavior can be efficiently predicted.

Several modifications on conventional SHPB experimentation were adopted to investigate effects of strain rate on mechanical behaviors of foam materials in this paper. Quasi-static and dynamic stress-strain curves of rigid fiber-polyurethane foams, aluminum foams and aluminum alloy foams were investigated. All experimental results indicated that strain rate effect on foam materials were obvious, although the matrixes, some of which were strain-rate sensitive and some were not, cell sizes and densities are all different.