Research on the influences of confining pressure and strain rate on NEPE propellant: Experimental assessment and constitutive model

In order to study the influences of confining pressure and strain rate on the mechanical properties of the Nitrate Ester Plasticized Polyether (NEPE) propellant, uniaxial tensile tests were conducted using the self-made confining pressure system and material testing machine. The stress-strain responses of the NEPE propellant under different confining pressure conditions and strain rates were obtained and analyzed. The results show that confining pressure and strain rate have a remarkably influence on the mechanical responses of the NEPE propellant. As confining pressure increases (from 0 to 5.4 MPa), the maximum tensile stress and ultimate strain increase gradually. With the coupled effects of confining pressure and strain rate, the value of the maximum tensile stress and ultimate strain at 5.4 MPa and 0.0667 s⁻¹ is 2.03 times and 2.19 times of their values under 0 MPa and 0.00333 s⁻¹, respectively. Afterwards, the influence mechanism of confining pressure on the NEPE propellant was analyzed. Finally, based on the viscoelastic theory and continuous damage theory, a nonlinear constitutive model considering confining pressure and strain rate was developed. The damage was considered to be rate-dependent and pressure-dependent. The constitutive model was validated by comparing experimental data with predictions of the constitutive model. The whole maximum stress errors of the model predictions are lower than 4% and the corresponding strain errors are lower than 7%. The results show that confining pressure can suppress the damage initiation and evolution of the NEPE propellant and the nonlinear constitutive model can describe the mechanical responses of the NEPE propellant under various confining pressure conditions and strain rates. This research can lay a theoretical foundation for analyzing the structural integrity of propellant grain accurately under working pressure loading.     

Dynamic necking of a near α titanium alloy at high strain rates:Experiments and modelling

The tensile behaviour of near α Ti3Al2.5 V alloy, conceived for applications in aerospace and automotive engineering, is characterized from quasi-static to high strain rates. The material is found to present noticeable strain rate sensitivity. The dynamic true strain rate in the necking cross-section reaches values up to ten times higher than the nominal strain rate. It is also observed that beyond necking the dynamic true stress-strain curves present limited rate dependence. The experimental results at different strain rates are used to determine a suitable constitutive model for finite element simulations of the dynamic tensile tests. The model predicts the experimentally macroscopic force-time response, true stress-strain response and effective strain rate evolution with good agreement.     

Neural network modeling to evaluate the dynamic flow stress of high strength armor steels under high strain rate compression

An artificial neural network (ANN) constitutive model is developed for high strength armor steel tempered at 500 °C, 600 °C and 650 °C based on high strain rate data generated from split Hopkinson pressure bar (SHPB) experiments. A new neural network configuration consisting of both training and validation is effectively employed to predict flow stress. Tempering temperature, strain rate and strain are considered as inputs, whereas flow stress is taken as output of the neural network. A comparative study on Johnson–Cook (J–C) model and neural network model is performed. It was observed that the developed neural network model could predict flow stress under various strain rates and tempering temperatures. The experimental stress–strain data obtained from high strain rate compression tests using SHPB, over a range of tempering temperatures (500–650 °C), strains (0.05–0.2) and strain rates (1000–5500/s) are employed to formulate J–C model to predict the high strain rate deformation behavior of high strength armor steels. The J-C model and the back-propagation ANN model were developed to predict the high strain rate deformation behavior of high strength armor steel and their predictability is evaluated in terms of correlation coefficient (R) and average absolute relative error (AARE). R and AARE for the J–C model are found to be 0.7461 and 27.624%, respectively, while R and AARE for the ANN model are 0.9995 and 2.58%, respectively. It was observed that the predictions by ANN model are in consistence with the experimental data for all tempering temperatures.     

Prediction of flow stress of 7017 aluminium alloy under high strain rate compression at elevated temperatures

An artificial neural network(ANN) constitutive model and JohnsoneC ook(Je C) model were developed for 7017 aluminium alloy based on high strain rate data generated from split Hopkinson pressure bar(SHPB) experiments at various temperatures. A neural network configuration consists of both training and validation, which is effectively employed to predict flow stress. Temperature, strain rate and strain are considered as inputs, whereas flow stress is taken as output of the neural network. A comparative study on Johnsone Cook(Je C) model and neural network model was performed. It was observed that the developed neural network model could predict flow stress under various strain rates and temperatures. The experimental stressestrain data obtained from high strain rate compression tests using SHPB over a range of temperatures(25 e300 C), strains(0.05e0.3) and strain rates(1500e4500 s 1) were employed to formulate JeC model to predict the flow stress behaviour of 7017 aluminium alloy under high strain rate loading. The JeC model and the back-propagation ANN model were developed to predict the flow stress of 7017 aluminium alloy under high strain rates, and their predictability was evaluated in terms of correlation coefficient(R) and average absolute relative error(AARE). R and AARE for the J-C model are found to be 0.8461 and 10.624%, respectively, while R and AARE for the ANN model are 0.9995 and 2.58%, respectively. The predictions of ANN model are observed to be in consistent with the experimental data for all strain rates and temperatures.     

Cross-linking density and aging constitutive model of HTPB coating under prestrain thermal accelerated aging

In order to study the cross-linking density and aging constitutive relationship of HTPB coating during storage, the thermal accelerated aging tests at 0%, 3%, 6% and 9% prestrains were carried out. The cross-linking density of HTPB coating at different aging stages were tested using low-field ¹H NMR and the variation of cross-linking density was analyzed. The aging model of cross-linking density considering the chemical aging and the physical stretching factors was established. The uniaxial tensile tests were carried out on HTPB coating at different aging stages and the cross-linking density was introduced into Ogden hyperelastic constitutive model as a characterization parameter of correction coefficient. Combined with uniaxial tensile test results, a prestrain aging constitutive model of HTPB coating was established. The results show that the cross-linking density of HTPB coating increases rapidly at first and then slowly with the increase of thermal accelerated aging time without prestrain. Under prestrain conditions, the cross-linking density of HTPB coating decreases at the early stage, and increases rapidly at first and then slowly at the middle and late stages of thermal accelerated aging. The correlation coefficients of aging model of cross-linking density and aging constitutive model with test results are R > 0.9500 and R > 0.9900 respectively, which can be used to accurately describe the cross-linking density and aging constitutive relationship of HTPB coating under prestrain accelerated thermal aging conditions.     

Estimation of the kinetic parameters for thermal decomposition of HNIW and its adiabatic time-to-explosion by Kooij formula

A differential/integral method to estimate the kinetic parameters (apparent activation energy E_a and pre-exponential factor A) for thermal decomposition reaction of energetic materials based on Kooij formula are applied to study the nonisothermal decomposition reaction kinetics of hexanitrohexaazaisowurtzitane (HNIW) by analyzing nonisothermal DSC curve data. The apparent activation energy (E_a) obtained by the integral isoconversional non-isothermal method based on Kooij formula is used to check the constancy and validity of apparent activation energy by the differential/integral method based on Kooij formula. The most probable mechanism function of thermal decomposition reaction of HNIW is determined by a logical choice method. The equations for calculating the critical temperatures of thermal explosion (T_b) and adiabatic time-to-explosion (t_TIad) based on Kooij formula are used to calculate the values of T_b and t_TIad to evaluate the thermal safety and heat-resistant ability of HNIW. All the original data needed for analyzing the kinetic parameters are from nonisothermal DSC curves. The results show that the kinetic model function in differential form and the values of E_a and A of decomposition reaction of HNIW are 3(1 − α)[−ln(1 − α)]^2/3, 152.73 kJ mol⁻¹ and 10^11.97 s⁻¹, respectively, and the values of self-accelerating decomposition temperature (T_SADT), T_b and t_TIad are 486.55 K, 493.11 K and 52.01 s, respectively.     

Development of multi-physics numerical simulation model to investigate thermo-mechanical fatigue crack propagation in an autofrettaged gun barrel

In this research, a detailed multi-physics study has been carried out by numerically simulating a solid fractured gun barrel for 20 thermo-mechanical cycles. The numerical model is based on thermal effects, mechanical stress fields and fatigue crack mechanics. Elastic-plastic material data of modified AISI 4340 at temperatures ranging from 25 to 1200 °C and at strain rates of 4, 16, 32 and 48 s⁻¹ was acquired from high-temperature compression tests. This was used as material property data in the simulation model. The boundary conditions applied are kept similar to the working gun barrel during continuous firing. A methodology has been provided to define thermo-mechanically active surface-to-surface type interface between the crack faces for a better approximation of stresses at the crack tip. Comparison of results from non-autofrettaged and autofrettaged simulation models provide useful information about the evolution of strains and stresses in the barrel at different points under combined thermo-mechanical loading cycles in both cases. The effect of thermal fatigue under already induced compressive yield due to autofrettage and the progressive degradation of the accumulated stresses due to thermo-mechanical cyclic loads on the internal surface of the gun barrel (mimicking the continuous firing scenario) has been analyzed. Comparison between energy release rate at tips of varying crack lengths due to cyclic thermo-mechanical loading in the non-autofrettaged and autofrettaged gun has been carried out.     

Dynamic globularization prediction during cogging process of large size TC11 titanium alloy billet with lamellar structure

The flow behavior and dynamic globularization of TC11 titanium alloy during subtransus deformation are investigated through hot compression tests. A constitutive model is established based on physical-based hardening model and phenomenological softening model. And based on the recrystallization mechanisms of globularization, the Avrami type kinetics model is established for prediction of globularization fraction and globularized grain size under large strain subtransus deformation of TC11 alloy. As the preliminary application of the previous results, the cogging process of large size TC11 alloy billet is simulated. Based on subroutine development of the DEFORM software, the coupled simulation of one fire cogging process is developed. It shows that the predicted results are in good agreement with the experimental results in forging load and microstructure characteristic, which validates the reliability of the developed FEM subroutine models.     

The mechanical performance and a rate-dependent constitutive model for Al3Ti compound

The Al₃Ti compound has potential application in the high temperature structure materials due to its low density, high strength and stiffness. The mechanical behaviors of the material under different loading rates were studied using compression tests. The results indicate that Al₃Ti is a typical brittle material and its compressive strength is dependent on the strain rate. Therefore, a series of rate-dependent constitutive equations are needed to describe its mechanical behaviors accurately. However, it is still short of professional research on the material model for Al₃Ti. In this study, the material model was developed on the basis of JH-2 constitutive equations using the experimental data. The model was then applied in simulating the impact process of Ti/Al₃Ti metal-intermetallic laminate composites so as to validate the established model. Good agreement between simulation and experiment results shows the constitutive model predict the material responses under high rate and large deformation accurately. This work provides more support for the theoretical and numerical research on the intermetallic.     

Low velocity impact studies of E-glass/epoxy composite laminates at different thicknesses and temperatures

Low velocity impact experiments were carried out on E-glass/epoxy composite laminates having varying thicknesses at sub zero and elevated temperatures using hemi spherical steel impactor of 16 mm diameter with impact energies in the rage of 50–150 J. The performance of the laminates was assessed in terms of energy absorption, maximum displacement, peak force and failure behaviour. Results indicated that the effect of temperature on energy absorption of the laminate is negligible although the laminates are embrittling at sub zero temperatures. However it has influence on failure behaviour and displacement. Peak force has increased linearly with increase in laminate thickness from 5 to 10 mm. However it got reduced by 25% when temperature was increased from −20 °C to 100 °C. Based on experimental results, laminate perforation energies were predicted using curve fitting equations. Statistical analysis was carried out using Taguchi method to identify the global effects of various parameters on laminate performance and confirmed that the laminate thickness has significant influence as compared to temperature, for the studied range.     

Experiment and simulation of launching process of a small-diameter steel cartridge case

In order to explore the rules of the deformation force during the launching of a small-diameter steel cartridge, the semi-closed bomb test method is used to test the greatest strains on chamber outer wall under the different chamber pressures. The pressure curves of cartridge chamber are measured in experiment, and the tensile test data of cartridge are loaded into the numerical calculation to compare with the experimental data. The conclusion was obtained that the calculated results match better with the experimental results by considering strain rate bilinear kinematic hardening material constitutive model. The forces on the various parts of the cartridge during launching and their deformation rules are achieved, in which the equivalent plastic strain decreases and the cylinder ring withstands the maximum equivalent stress when the cartridge case clings to the bore from the mouth to the bottom.     

围压下固体推进剂的破坏机理分析

贴壁浇筑的固体发动机推进剂药柱在点火状态下处于三向围压状态,而环向承受拉应变,亟待对围压下推进剂的破坏机理展开研究。基于自研的围压加载试验系统,通过开展推进剂在不同围压、温度和应变率下的单轴拉伸试验来研究围压、温度和应变率的耦合作用对推进剂力学行为的影响。针对围压下推进剂的力学响应特征,通过细观力学仿真进一步研究围压下推进剂的破坏形式,同时借助电镜扫描试验分析推进剂试样断面的形貌特征,通过试验和仿真相结合的手段分析了围压下推进剂的破坏机理。研究结果表明,围压下推进剂的损伤界面显著减少,且随着围压载荷的逐渐增加,推进剂的损伤形式从以颗粒脱湿为主转变为以颗粒破碎为主。     

关于有限变形非弹性有限单元法的研究进展

对有限变形非弹性有限单元法研究发展中的一些普遍关注的研究课题,进行了回顾和展望。这些课题包括:不同参考构形下的有限元列式、客观性应力率的合理定义、有限变形非弹性本构方程的精确描述、率本构方程的增量客观数值积分、塑性流动的不可压缩性与自锁现象、以及交界面接触与摩擦的处理。     

A bayesian optimisation methodology for the inverse derivation of viscoplasticity model constants in high strain-rate simulations

We present an inverse methodology for deriving viscoplasticity constitutive model parameters for use in explicit finite element simulations of dynamic processes using functional experiments, i.e., those which provide value beyond that of constitutive model development. The developed methodology utilises Bayesian optimisation to minimise the error between experimental measurements and numerical simulations performed in LS-DYNA. We demonstrate the optimisation methodology using high hardness armour steels across three types of experiments that induce a wide range of loading conditions: ballistic penetration, rod-on-anvil, and near-field blast deformation. By utilising such a broad range of conditions for the optimisation, the resulting constitutive model parameters are generalised, i.e., applicable across the range of loading conditions encompassed the by those experiments (e.g., stress states, plastic strain magnitudes, strain rates, etc.). Model constants identified using this methodology are demonstrated to provide a generalisable model with superior predictive accuracy than those derived from conventional mechanical characterisation experiments or optimised from a single experimental condition.     

点火瞬态过程对复合固体推进剂力学响应特性的影响

根据一个有效的非线性粘弹模型,导出复合固体推进剂微分形式本构方程和应变速率关系式。分析表明点火瞬态过程中压强与推进剂应变、升压速率与推进剂应变速率之间呈线性关系,线性系数均为推进剂初始模量。     

在分离式Hopkinson拉杆实验中确定临界实验条件的经验方法

在分离式Hopkinson拉杆实验中,常常需要获得试样在经历一个拉力脉冲拉断情况下的最低应变率,而在分离式Hopkinson拉杆装置中确定对应最低应变率的发射压力需要进行多次尝试性实验。为了更好地解决这一问题,提出一种简单的经验方法,可以通过一次拉断的实验结果计算出一个拉力脉冲拉断试样需要的最小发射压力及相应的应变率,进一步可以预测不同发射压力下的应变率。对4种铝合金试样进行拉伸实验,结果表明,利用提出的经验方法得到的应变率结果与实验结果吻合较好,可以有效地对发射压力和实验应变率进行预估。     

The non-isothermal gravimetric method for study the thermal decomposition kinetic of HNBB and HNS explosives

The hexanitrostilben (HNS) is a thermally stable explosive that can be prepared from hexanitrobibenzyl (HNBB). Therefore, the investigation of thermal stability of HNBB can be important in the yield of preparation of HNS. The decomposition kinetic of HNBB and HNS are studied by non-isothermal gravimetric method. The TG/DTG curves in non-isothermal method are obtained in range of 25°C–400 °C at heating rates of 3 °C/min, 5 °C/min, 8 °C/min, 10 °C/min and 12 °C/min. The data of weight-temperature are used for calculation of activation energy (E_a) of thermal decomposition reactions by methods of Ozawa, Kissinger, Ozawa-Flynn-Wall (OFW) and Kissinger-Akahira-Sunose (KAS) as model-free methods and Strink's equation as model-fitting method. The compensation effect is used for prediction of mechanism and determination of pre-exponential factor (lnA) of the decomposition reaction. A reduction 60 kj/mol for the average of activation energy of thermal decomposition reaction of HNBB is obtained versus HNS. This result shows the lower thermal stability of HNBB in comparison to HNS. The Avrami equation (A_3/2) with function f(α) = 3/2(1-α)[-ln(1-α)]^1/3 indicates the predicted mechanism for thermal decomposition reaction both explosives.     

Numerical investigation of the failure mechanism of cubic concrete specimens in SHPB tests

Cylindrical specimens are commonly used in Split Hopkinson pressure bar (SHPB) tests to study the uniaxial dynamic properties of concrete-like materials.In recent years,true tri-axial SHPB equipment has also been developed or is under development to investigate the material dynamic properties under tri-axial impact loads.For such tests,cubic specimens are needed.It is well understood that static material strength obtained from cylinder and cube specimens are different.Conversion factors are obtained and adopted in some guidelines to convert the material strength obtained from the two types of specimens.Previous uniaxial impact tests have also demonstrated that the failure mode and the strain rate effect of cubic specimens are very different from that of cylindrical ones.However,the mechanical background of these findings is unclear.As an extension of the previous laboratory study,this study performs numerical SHPB tests of cubic and cylindrical concrete specimens subjected to uniaxial impact load with the validated numerical model.The stress states of cubic specimens in relation to its failure mode under different strain rates is analyzed and compared with cylindrical specimens.The detailed analyses of the numerical simulation results show that the lateral inertial confinement of the cylindrical specimen is higher than that of the cubic specimen under the same strain rates.For cubic specimen,the corners are more severely damaged because of the lower lateral confinement and the occurrence of the tensile radial stress which is not observed in cylindrical specimens.These results explain why the dynamic material strengths obtained from the two types of specimens are different and are strain rate dependent.Based on the simulation results,an empirical formula of conversion factor as a function of strain rate is proposed,which supplements the traditional conversion factor for quasi-static material strength.It can be used for transforming the dynamic compressive strength from cylinders to cubes obtained from impact tests at different strain rates.     

Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue

If the number of customers in a queueing system as a function of time has a proper limiting steady‐state distribution, then that steady‐state distribution can be estimated from system data by fitting a general stationary birth‐and‐death (BD) process model to the data and solving for its steady‐state distribution using the familiar local‐balance steady‐state equation for BD processes, even if the actual process is not a BD process. We show that this indirect way to estimate the steady‐state distribution can be effective for periodic queues, because the fitted birth and death rates often have special structure allowing them to be estimated efficiently by fitting parametric functions with only a few parameters, for example, 2. We focus on the multiserver M_t/GI/s queue with a nonhomogeneous Poisson arrival process having a periodic time‐varying rate function. We establish properties of its steady‐state distribution and fitted BD rates. We also show that the fitted BD rates can be a useful diagnostic tool to see if an M_t/GI/s model is appropriate for a complex queueing system. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 664–685, 2015     

金属冲击温度的测量研究

文中介绍了冲击温度的多波长光谱辐射测量方法。利用光学高温计测量了４５号钢在２３０ＧＰａ左右的冲击压力下的冲击温度值,对所测得的结果进行了比较和分析。