JH-2 Model Research Articles

High strain-rate behavior of polycrystalline and granular ice: An experimental and numerical study

We study the stress–strain response of two different types of ice, viz. polycrystalline ice and granular ice, between −1° – 0 °C over a strain-rate range of 100s−1 to 300s−1 employing the split Hopkinson pressure bar (SHPB). Polycrystalline ice samples, prepared by freezing water in plastic moulds, exhibit a compressive strength ranging from 7 to 10 MPa within the considered strain-rate range. The strain at peak stress remains below 0.2%, indicating brittle behavior. The stress-strain curve of polycrystalline ice displays a prolonged tail, suggesting that the damaged ice specimen retains some strength. High-speed imaging during tests reveals the damage mechanism in ice is fragmentation and axial splitting. A user subroutine based on the Johnson–Holmquist II (JH-2) model is implemented in the commercial finite element (FE) software ABAQUS to predict ice's response at high strain-rates, which captures the softening present in the experimental stress–strain curve. Intact strength parameters and strain-rate sensitivity constants in the JH-2 model are determined from our experimental data and literature results, ensuring alignment with experimental peak stress. Fractured strength and damage evolution parameters are determined by matching post-peak responses from simulations to experiments. Temporal damage evolution from FE simulations aligns well with high-speed images from experiments, providing additional validation. Extending the study to granular ice, samples are prepared by crushing polycrystalline ice and refreezing it. The compressive strength of granular ice at a nominal strain-rate of 200±50s−1 is found to be 4±0.7 MPa. The granular ice, which is a mixture of polycrystalline ice and voids, is homogenized using rule-of-mixture to obtain the elastic properties. The FE simulation results utilizing the JH-2 parameters that we determine matches well with the experimental data, demonstrating that the JH-2 model is well suited to predict the high strain-rate behavior of both types of ice.

Predicting ballistic resistance based on the mechanical properties of armored ceramics

The relationship between the mechanical and ballistic properties of armored ceramics was studied using a numerical method that combines finite element simulation and machine learning. A dataset containing the physical properties, mechanical properties, and ballistic performance of ceramic was built through numerical simulation with the JH-2 model. The machine learning method was employed to establish a relationship between residual penetration depth and ceramic’ properties, including its density, elastic modulus, Poisson's ratio, Hugoniot elastic limit (HEL), dynamic compressive strength, quasi-static compressive strength, and bending strength. Through finite element simulation and machine learning, univariate analysis of the physico-mechanical properties of ceramics was achieved by predictive modeling. It was found that density, dynamic compressive strength, quasi-static compressive strength, and HEL had the most significant impact on the residual penetration depth, making them the key controlling parameters for the ballistic performance of ceramics. By combining the prediction results of the machine learning model with the influence patterns of the parameters, a predictive formula for the ceramic protection coefficient based on the key parameters was established.

Dynamic flexural strength of Aluminosilicate glass with a perspective of impulsive and quasi-impulsive responses: An experimental–numerical coupled evaluation

The flexural strength of glass is a critical design parameter for applications encountering impact loadings. However, the micro defects, specimen geometry, loading rate, and load transformation from a quasi-dynamic to quasi-impulsive state may influence the measurement accuracy. Due to the stochastic and amorphous nature of the material, an accurate determination of the flexural strength remains a challenge. In this two-fold study, a coupled experimental–numerical strategy was devised to evaluate the dynamic flexural strength. In the first phase, three-point bending experiments were conducted on a novel “Electromagnetic Split Hopkinson Pressure Bar (ESHPB)”. The incident stress signal and fracture time were recorded from experimental data, while the flexural strength was indirectly computed from a numerical algorithm. A quantitative comparison of the flexural strength with those in existing literature established the accuracy of the proposed methodology. Results of the study indicate that the specimen response became independent of the support conditions under impulsive loading. That being said, the specimen behaved like it had an infinite span length, and the measured flexural strength remained the same whether the specimen was supported or not. Besides, the specimen also maintained contact at the interfaces of the incident bar and fixture supports for the entire loading duration. In the second part of this study, the computed flexural strength was used to calibrate the existing JH-2 model. Numerical prediction of the damage propagation corroborated with that obtained from reprography images, though qualitatively. This work presents a precise and robust methodology to determine the dynamic flexural strength of brittle ceramics like Aluminosilicate glass over traditional experimental procedures to facilitate its adoption.

Dynamic mechanical response and constitutive model of (Ti37.31Zr22.75Be26.39Al4.55Cu9)94Co6 high-entropy bulk metallic glass

In this work, the mechanical response and fracture characteristics of (Ti37.31Zr22.75Be26.39Al4.55Cu9)94Co6 high-entropy bulk metallic glass (HE-BMG) were investigated in detail over a wide range of strain rates (10−4–105 s−1). The HE-BMG exhibited a negative strain rate sensitivity under uniaxial compression, with the strength showing more significant rate dependence under dynamic conditions. The shear band behavior translated from the dominance of multiple shear bands propagations under quasi-static compression to the rapid propagation of a single shear band to form cracks under dynamic compression. Under dynamic loading, the shearing velocity increased along an arc-shaped displacement path, and the local stress state on the shear fracture surface shifted from compressive-shear to tensile-shear, accompanied by changes in fracture morphologies. The spall strength of HE-BMG decreased as flyer impact speed increased, while the long-term dependence of spall strength on strain rate may be positive. With the increase of impact speed, the main microstructural features of the spalling surface translated from flat regions accompanied by dimples to cup-cone structures. Furthermore, the complete parameters of the Johnson–Holmquist II (JH-2) model for HE-BMG were obtained based on experimental data. Numerical simulations of planar impact, penetration, and hypervelocity impact are in good agreement with experimental results, demonstrating the validity of the JH-2 model parameters. The current work has important guiding value for the application of HE-BMG in space debris protection.

Erosion behaviour of B4C/TiB2/Mo ceramic nozzles

Abstract B4C/TiB2/Mo ceramic nozzles were obtained by uniaxial hot-pressing. The mechanical properties and erosion behaviour of B4C/TiB2/Mo ceramic nozzles were investigated. Volume erosion rate was used to rank the erosion behaviour of the B4C/TiB2/Mo ceramic nozzles. The relationship between mechanical properties and the volume erosion rate of the nozzles was discussed. X-ray diffraction analysis showed that in-situ reaction to form TiB2 happened during sintering. Scanning electron microscopy was employed to observe the fracture surfaces and eroded surfaces of B4C/TiB2/Mo ceramic nozzles. A model of erodent particles and nozzle during the erosion test was established using the JH2 model. The maximum von Mises stresses on the entry, middle and exit surfaces of the nozzle were calculated. The result showed that the hardness played a key role in influencing the erosion behaviour of B4C/TiB2/Mo ceramic nozzles. Erosion mechanisms of B4C/TiB2/Mo ceramic nozzles at the entry, middle and exit bore area were mainly brittle fracture, fracture & plowing and micro-plowing, respectively.

Study on the dynamic response characteristics of lining structures in large-section tunnel blasting using JH-2 model analysis

The lining structures of tunnels are typically constructed using sprayed or cast concrete materials, and their performance and quality during tunnel excavation and blasting are crucial for the stability and safety of tunnels. Therefore, the safe distance between the lining structure and blasting source should be determined to avoid concrete damage caused by blasting vibrations. In this study, taking the subway tunnel of Danshan Station in Qingdao as an example, the JH-2 model is introduced as the constitutive model of the tunnel blasting simulation, and the JH-2 model parameters of the local surrounding rock are obtained by experiments, and finally the numerical simulation and theoretical verification are carried out to study the safety distance of shotcrete under various safety judgment standards. The results indicate that the JH-2 model can effectively simulate the propagation of stress waves under different media conditions, and the closer the strength parameters and pressure constant of the lining structure are to those of the surrounding rock, the safer the concrete–rock bonding interface. During tunnel blasting construction using the ring blasting method, the peak particle velocity (PPV) of the lining structure increases with an increase in the arch angle. Based on the numerical simulation results, we recommend that concrete lining be constructed at a distance of at least 62 m from the blasting source to avoid damage caused by vibrations. The effect of concrete tensile failure caused by longitudinal stress is much smaller than the damage to the bonding interface caused by the PPV and can be neglected.

Damage characteristics and dynamic responses of high arch dams under rockfall impact loads

Rockfall is a typical natural disaster that is sudden, high in speed, unpredictable, and can easily adversely affect the structures. High arch dams are usually constructed in deep valleys, where rockfall is a typical destructive load. However, there is currently a lack of research on the effects of rockfall on the safe operation of high arch dams. Therefore, the Wudongde arch dam in China is selected in this paper for exploring damage characteristics and dynamic responses of high arch dams under rockfall impact loads. To improve the authenticity of numerical simulation, a coupled model is established based on the actual dam shape and terrain characteristics of the dam. The concrete damaged plasticity model is used for dam concrete and the rockfall is described by the JH-2 model to simulate mechanical properties of materials and reflect strain rate effects. The trajectories of falling rocks at the dam site are first investigated to analyze the locations where they may impact the dam. Based on the obtained results, two impact positions are considered possible in the analysis, namely, the dam crest and the gate slot, and then the nonlinear dynamic responses of the dam impacted by rockfall at different positions are compared. Finally, a sensitivity analysis is carried out to evaluate the influence of the rockfall properties on the damage characteristics of the dam. The results indicate that the trajectory and impact velocity of falling rocks are related to the falling height, rock size, and initial velocity. The rockfall impact on the dam crest has little influence on the safety of the dam for the robust mass dam concrete, while the track beam near the gate slot is vulnerable to rockfall impact. The damage degree to the structure is related to rockfall properties. Compared to larger-sized rockfalls, rockfalls with a diameter of 1 m cause minimal damage to the structure and have little impact on its safety. Higher impact velocity and stiffness of the rock lead to more severe damage, while the effect is relatively smaller compared to the rockfall size. The high stiffness also reduces the damage to the rock itself.

JH-2 constitutive model of sandstone for dynamic problems

This paper demonstrates the application of the Johnson–Holmquist II (JH-2) model with correlated and validated parameters to simulate the behavior of a sandstone. The JH-2 model is used to simulate various tests, including single-element tests, structural quasi-static uniaxial and triaxial compression tests, and the split Hopkinson pressure bar test. Additionally, the model is used to simulate drop-weight impact test using a ball bearing and two loading scenarios involving small-scale blasting and projectile impacts. Quantitative and qualitative comparisons demonstrate that the JH-2 model agrees well with both experimental and analytical results. Limitations of the model are also highlighted, particularly for quasi-static problems, as the model was originally developed for high-strain-rate simulations. Ultimately, this study demonstrates that the JH-2 rock constitutive model can obtain reasonable results for a material other than the material for which the model was originally correlated and validated. This paper provides valuable guidance for modeling and simulating sandstone and other rock materials subjected to dynamic loadings.

Meshfree modeling of brittle surface erosion by sharp-angled particle impact with Johnson–Holmquist-II(JH-2) model

A SPH model is established, combined with JH-2 model for solving brittle surface erosion problems, which is validated by impact experiments. Simulations are conducted by varying particle incident parameters. Results show that crack formation is affected by impact angle αi, initial orientation θi, and impact velocity Vi. While crack propagation direction is mainly dominated by θi. Surface fragmentation caused by lateral cracks can greatly increase brittle surface erosion, which is most likely to occur at θi= +30°. Without surface fragmentation, a critical orientation angle exists. Secondary impact is also a critical factor for surface erosion and determined by θi. Particles with smaller θi tend to roll on the surface, whereas larger θi particles are more likely to bounce off the surface.

Research on blasting cumulative dynamic damage of surrounding rock in step construction tunnel

In the process of cyclic blasting during tunnel excavation, the reserved surrounding rock sustains irreparable damage accumulation. For safe tunnel construction, it is imperative to understand the characteristics of blasting dynamic cumulative rock damage. Sonic wave test and numerical simulation methods were applied to the research. The JH-2 model was adopted as the damage model of surrounding rock. Based on the data transfer method between solvers in ABAQUS software, the cumulative damage was calculated. The damage characteristics were obtained by combining the sonic wave test results. According to the research findings, the entire reserved surrounding rock has periodic damage characteristics. Each periodic damage area has a funnel shape along the tunnel’s longitudinal direction, with a length of 160 cm, and 1.07 times the excavation footage. The latter excavation footage's blasting effect on the damaged area of the previous footage rock is 40 cm long, with three cumulative damage patterns. The three cumulative damage patterns more clearly reveal the surrounding rock's additional damage law, the degree of additional damage is greatest with the distance of 5–20 cm from the latter excavation footage. The research can provide appropriate theoretical guidance for the design of the step-blasting construction tunnel's blasting scheme and lining.

Comparison of selected blasting constitutive models for reproducing the dynamic fragmentation of rock

Understanding the behavior of rock under blast- and shock-induced loadings requires a high-fidelity constitutive model. The present paper provides a detailed comparison study of three selected material models that are available in the most popular hydrocodes: the Johnson-Holmquist II (JH-2) model, the Johnson-Holmquist Concrete (JHC) model and the Karagozian and Case concrete (KCC) model. Numerical simulations are carried out to evaluate their performance under different stress conditions and to verify their effectiveness in realistically reproducing dolomite behavior. The outcomes are compared qualitatively based on specimen failure and quantitatively based on measured characteristics. The pros and cons of each model are presented and analyzed. Based on the comparison study, the JH-2 model is selected to simulate a representative blast in a mining face. The cracking, fracturing and fragmentation are correctly captured by the JH-2 model, proving its efficiency in the simulation of drilling and blasting in a mining face.

Determination of the material model parameters for high pressure densification induced glass inferred through analytical comparison and its ballistic performance as used in composite laminates

The Drucker Prager material model, Ductile Damage and Mie-Gruneisen equation of state parameters for high-pressure densification induced glass were derived analytically in the current study by comparing them to the Johnson Holmquist-II (JH-2) model. These parameters were then utilized to simulate the ballistic impact behaviour of bullet-resistant glass in ABAQUS/Explicit and the results were compared to the simulation results using JH-2 model in ANSYS/Autodyn and the results were found in good agreement. Following that, their experimental equivalents were tested for validation prospective. The findings were then compared to conventional bullet-resistant glass. It was found that the new bullet-resistant glass fabricated from layers of high-pressure densification induced glass was superior in strength as compared to the conventional bullet-resistant glass.

Study on parameter acquisition and optimization methods of JH-2 constitutive model for ceramic

In this study, based on AD995 and sapphire, the method of obtaining and optimizing the key parameters of the Johnson-Holmquist constitutive model (JH-2 model) for typical brittle materials was established. The parameter acquisition method was optimized by analyzing the limitations of the traditional parameter acquisition method. The value ranges of the intact strength parameters were calculated using the results of the mechanical property tests of the materials; the well-fitted intact strength parameters (A, N, C and T) were obtained by combining with the parameter optimization procedure. The sensitivity of the dynamic compression test and the penetration process to the damage-related parameters (B, M, D1 and D2) was analyzed by numerical simulation methods. The damage-related parameters in the JH-2 model were obtained using a chaotic global optimization algorithm combined with numerical simulations of dynamic compression tests and penetration tests. The calculation accuracy of the traditional and optimized parameters were compared by numerical simulation results of penetration tests for different ceramic composite structures. The simulation results of the optimized parameters basically match with the experimental results, and the calculation accuracy is much higher than that of the traditional parameters, which verifies the effectiveness and superiority of the parameter optimization method.

Three-stage breakage model for laminated glass plate under low-velocity impact

Two failure modes of laminated glass under impact loading are summarized, after which a series of experiments are carried out and a three-stage breakage model for laminated glass plate is proposed. The three-stage breakage model consists of an elastic stage (stage Ⅰ), a stage of total breakage of the back glass layer (stage Ⅱ) and a stage of total breakage of both layers of glass (stage Ⅲ). Furthermore, a combined TCK-JH2 constitutive model is proposed for the numerical analysis conducted with Finite Element Method (FEM). In this constitutive model, the TCK model is employed when the material is under tensile condition whereas the JH2 model is employed when the material is under compressive condition. Moreover, a stiffness recovery behavior is defined. The criterion of tension and compression is studied as well.

A modified JH2 model with improved strength model, damage evolution, and equation of state for rock under impact and blasting loads

Rock fragmentation by blasting is widely applied in geotechnical engineering, requiring the development of the rock damage constitutive model. A modified Johnson-Holmquist Ceramic (M-JH2) model, which adds an initial yield strength surface, is proposed to characterize the rock damage process under blasting loads. In addition, a new damage scale factor was proposed to capture the strain hardening and gradual softening behaviors. Tensile and compressive damages are treated separately to describe the tensile-compressive asymmetry, and the volumetric plastic strain is introduced into the compressive damage. Moreover, the EOS of the original JH2 model is modified by including unloading and reloading paths. To calibrate the model, benchmark examples were established in the LS-DYNA with the M-JH2 models, such as single element tests, Split Hopkinson Pressure Bar test, rock blasting fracture, and crater blasting field test. The results show that the M-JH2 model agrees well with the classic experiments. The M-JH2 model improves the JH2 model in strain hardening, gradual softening, and the sensitivity difference of damage evolution between tension and compression in a Brazilian disc dynamic splitting test.

Smoothed Particle Hydrodynamics Modeling of Thermal Barrier Coating Removal Process Using Abrasive Water Jet Technique

Abstract In this work, a new smoothed particle hydrodynamics (SPH)-based model is developed to simulate the removal process of thermal barrier coatings (TBCs) using the abrasive water jet (AWJ) technique. The effects of water jet abrasive particle concentration, incident angle, and impacting time on the fracture behavior of the TBCs are investigated. The Johnson–Holmquist plasticity damage model (JH-2 model) is used for the TBC material, and abrasive particles are included in the water jet model. The results show that the simulated impact hole profiles are in good agreement with the experimental observation in the literature. Both the width and depth of the impact pit holes increase with impacting time. The deepest points in the pit hole shift gradually to the right when a 30-deg water jet incident angle is used because the water jet comes from the right side, which is more effective in removing the coatings on the right side. A higher concentration of abrasive particles increases both the width and depth, which is consistent with the experimental data. The depths of the impact pit holes increase with the water jet incident angle, while the width of the impact holes decreases with the increase in the water jet incident angle. The water jet incident angle dependence can be attributed to the vertical velocity components. The erosion rate increases with the incidence angle, which shows a good agreement with the analytical model. As the water jet incident angle increases, more vertical velocity component contributes to the kinetic energy which is responsible for the erosion process.

A dynamic bounding surface plasticity damage model for rocks subjected to high strain rates and confinements

A dynamic bounding surface plasticity damage model is developed for rocks with the consideration of high strain rates and confinements. This is achieved through adopting the strength surface of Holmquist-Johnson-Cook (HJC model)/ Johnson-Holmquist-ceramic (JH2 model) model as bounding surface, and employing the critical state concept for brittle-ductile transition. In addition, a simple continuum damage evolution law is taken for strength degradation and a simple vertical mapping rule is adopted to link current stress state with its corresponding strength state. A series of hardening rules that account for both plasticity and strain rate, and damage evolution law, etc., are proposed within the framework of consistent condition of dynamic model. A ‘S’ shape dynamic increase factor (DIF) function is adopted to consider the strain-rate effect of dynamic loadings, which aims to adjust the size of bounding surface with the consideration of radial enhancement. The proposed model is validated through modeling conventional triaxial compression tests under different confining pressures, dynamic triaxial tests, and Split Hopkinson Pressure Bar (SHPB) tests with various strain rates. Good agreement between modeling results and experimental data indicates that dynamic characteristics of rock, including rate and confinements dependency, are captured well by the proposed model. The proposed model is then implemented into a commercial software, GDEM, to simulate the stress wave propagation problem. Simulation results by the proposed model and two benchmark models are compared, which further validate the capability and applied potential of the proposed model.

Dynamic Properties of Mortar in High-strength Concrete

Mortar is the matrix in concrete; at the meso-scale, concrete is a composite consisting of mortar matrix, coarse aggregate particles, and the interfacial transition zones between them. In this investigation, the mortars of three high-strength concretes were subjected to uniaxial compression and splitting tension at different speeds, from static to dynamic, to examine the effects of strain rate on their stress-strain and failure behaviour. Notable strain rate sensitivity was observed in both the compressive and tensile behaviour of the mortars, with the tensile response displaying greater rate dependence. The rate dependence for both tensile and compressive responses, varies little with mortar strength; i.e. similar rate sensitivity was noted for the three mortars studied. The dynamic increase factor (DIF) was adopted to evaluate strain rate dependence. Both the tensile and compressive DIF display a two-stage variation with strain rate, i.e. an initial gradual increase up to a transition strain rate, followed by a rapid rise thereafter; the transition occurs at ∼1 s−1 for tension, and ∼30 s−1 for compression. By fitting experimental data, empirical formulae were proposed for both the tensile and compressive DIFs of mortar. Finite element (FE) simulations of the static and dynamic tension/compression tests were also performed, using the JH-2 model to describe mortar. Good correlation between the simulations and experiments provides substantiation that strain rate dependence of the tensile/compressive strengths measured in dynamic tests are actual material properties.

Procedure for determining the constants of JH-2 (Johnson – Holmquist) dynamic fracture model for brittle materials

A simplified method for evaluating the constants in the JH-2 (Johnson – Holmqvist) model of the dynamic fracture for brittle materials is presented. The classical procedure suggests the use of 21 independent parameters describe the material, and the problem of their determination entails a large number of calculations experiments which hamper the use of the JH-2 model. The proposed technique requires fewer complex calculations and experimental data to determine the parameters of the material thus making it more feasible in use. In this work, the technique is used to search for the parameters of aluminum oxide (Al2O3) with a density of 99.5%, which is the material of a ceramic barrier subjected to high-speed interaction with the impactor. We present the results of three tests for penetration of a corundum plate: two of them are used to determine the constants of the model, and the third is used to verify the obtained values. Note that, the results obtained using the presented approach match quite accurately the experimental data, which is demonstrated in the course verification of the procedure.

An improved material model for loading-path and strain-rate dependent strength of impacted soda-lime glass plate

The main purpose of this work is to develop a macro material constitutive model for inorganic glass response description under impact conditions. Firstly, the quasi-static and dynamic strength of soda-lime glass was obtained through uniaxial compression and combined compression-shear loading tests. The strain-rate and loading-path dependence of glass strength was observed from these experimental results. An improved model of impacted soda-lime glass plate was proposed based on the JH-2 model including the loading-path influence through an additional factor as a function of the Lode parameter. In commercial code Abaqus, the improved model is implemented through a user-defined material subroutine. Additionally, simulation of the static test, SHPB test, and impact test on glass specimens respectively is conducted to validate the model with updated material constants. The comparisons illustrate that the improved model of soda-lime glass provides better accuracy and efficiency predictions of glass responses at various loading conditions.