材料性能对固体发动机结构完整性的影响

基于描述粘弹性材料特性的Burgers模型的本构关系以及基于该本构关系下的有限元方法 ,根据温度载荷和内压载荷的特点 ,分别建立了分析某固体发动机材料性能参数对结构完整性影响的有限元模型。应用MSC/NAS TRAN结构分析软件 ,详细分析了在温度和内压载荷作用下固体发动机材料性能参数对结构完整性的影响。在温度载荷的作用下 ,主要影响结构完整性的是推进剂的泊松比与热膨胀系数 ;在内压载荷作用下 ,主要影响结构完整性的是包覆层和推进剂的泊松比以及推进剂的初始模量。所得的结论可为固体发动机的生产设计提供参考     

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.     

Interface defeat studies of long-rod projectile impacting on ceramic targets

The interface defeat phenomenon always occurs when a long-rod projectile impacting on the ceramic target with certain velocity, i.e., the projectile is forced to flow radially on the surface of ceramic plates for a period of time without significant penetration. Interface defeat has a direct effect upon the ballistic performance of the armor piercing projectile, which is studied numerically and theoretically at present. Firstly, by modeling the projectiles and ceramic targets with the SPH (Smoothed Particle Hydrodynamics) particles and Lagrange finite elements, the systematic numerical simulations on interface defeat are performed with the commercial finite element program AUTODYN. Three different responses, i.e., complete interface defeat, dwell and direct penetration, are reproduced in different types of ceramic targets (bare, buffered, radially confined and oblique). Furthermore, by adopting the validated numerical algorithms, constitutive models and the corresponding material parameters, the influences of projectile (material, diameter, nose shape), constitutive models of ceramic (JH-1 and JH-2 models), buffer and cover plate (thickness, constraints, material), as well as the prestress acted on the target (radial and hydrostatic) on the interface defeat (transition velocity and dwell time) are systematically investigated. Finally, based on the energy conservation approach and taking the strain rate effect of ceramic material into account, a modified model for predicting the upper limit of transition velocity is proposed and validated. The present work and derived conclusions can provide helpful reference for the design and optimization of both the long-rod projectile and ceramic armor.     

Numerical simulation of the natural fragmentation of explosively loaded thick walled cylinders

The ability to predict the natural fragmentation of an explosively loaded metal casing would represent a significant achievement. Physically-based material models permit the use of small scale laboratory tests to characterise and validate their parameters. The model can then be directly employed to understand and design the system of interest and identify the experiments required for validation of the predictions across a wide area of the performance space. This is fundamentally different to the use of phenomenologically based material algorithms which require a much wider range of characterisation and validation tests to be able to predict a reduced area of the performance space. Eulerians numerical simulation methods are used to describe the fragmentation of thick walled EN24 steel cylinders filled with PBXN-109 explosive. The methodology to characterise the constitutive response of the material using the physically based Armstrong–Zerilli constitutive model and the Goldthorpe path dependent fracture model is described, and the results are presented. The ability of an Eulerian hydrocode to describe the fragmentation process and reproduce the experimentally observed fragment mass and velocity distributions is presented and discussed. Finally the suitability of the current experimental analysis methodology for simulation validation is addressed.     

航空轮胎用橡胶弹性体Mullins效应动态加载方法

航空轮胎用橡胶弹性体在服役过程中遭受严苛的动态循环工况。为了研究弹性体在此工况下的力学响应特征和损伤机理,提出基于应力波作用的Mullins效应动态加载实验方法。根据应力波传导与作用特征,采用Hopkinson压杆加载思路,设计和配置了各单元尺寸参数,进而搭建可用于橡胶弹性体材料动态循环加载的实验系统,并开展了航空轮胎用丁苯橡胶的动态循环加载试验。基于试验信号分析发现：加载系统实现了弹性体材料Mullins效应动态应变递增的试验加载。最后开展加载测试参数的影响因素分析,结果表明通过优化系统各单元可实现Mullins效应的动态加、卸载参数的控制。     

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.     

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.     

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.     

Experimental and numerical study of the blast wave decrease using sandwich panel by granular materials core

Among the intrinsic properties of some materials, e.g., foams, porous materials, and granular materials, are their ability to mitigate shock waves. This paper investigated shock wave mitigation by a sandwich panel with a granular core. Numerical simulations and experimental tests were performed using Autodyn hydro-code software and a shock tube, respectively. The smoothed particle hydrodynamics (SPH) method was used to model granular materials. Sawdust and pumice, whose properties were determined by several compression tests, were used as granular materials in the sandwich panel core. These granular materials possess many mechanisms, including compacting (e.g., sawdust) and crushing (e.g., pumice) that mitigate shock/blast wave. The results indicated the ineffectiveness of using a core with low thickness, yet it was demonstrated to be effective with high thickness. Low-thickness pumice yielded better results for wave mitigation. The use of these materials with a core with appropriate core reduces up to 88% of the shock wave. The results of the experiments and numerical simulations were compared, suggesting a good agreement between the two. This indicates the accuracy of simulation and the ability of the SPH method to modeling granular material under shock loading. The effects of grain size and the coefficient of friction between grains have also been investigated using simulation, implying that increasing the grain size and coefficient of friction between grains both reduce overpressure.     

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.     

Analysis of some critical aspects in hot machining of Ti-5553 superalloy: Experimental and FE analysis

In this study, a newly developed titanium superalloy, i.e., the Ti-5553 alloy has used for hot machining. This material replaced Ti-grade-5 alloy in the application of aerospace, automobile, and biomedical sector. However, similar to Ti-grade-5 alloy, the Ti-5553 alloy has a low thermal conductivity which makes it difficult-to-cut material categories hence, high tool wear, cutting force and bad surface finish. Hot machining of Ti-5553 has been studied at different machining condition (room and hot) using Deform-2D finite element analysis. The result from the simulation test was compared with the experimental value and reduction of cutting and thrust forces was observed. The experiment was carried out with the same input parameters as simulation, and good coherence between them observed. Additionally, cutting zone temperature, effective stress, etc. for both room and elevated the temperature are also discussed.     

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.     

Phenomenological modelling of flow behaviour of 20MnMoNi55 reactor pressure vessel steel at cryogenic temperature with different strain rates

In the present study a phenomenological constitutive model is developed to describe the flow behaviour of 20MnMoNi55 low carbon reactor pressure vessel (RPV) steel at sub-zero temperature under different strain rates. A set of uniaxial tensile tests is done with the variation of strain rates and temperature ranging from 10⁻⁴ s⁻¹ to 10⁻¹ s⁻¹ and -80 °C to −140 °C respectively. From the experimental data, family of flow curves at different temperatures and strain rates are generated and fitted exponentially. The strain rate and temperature dependence of the coefficients of the exponential flow curves are extracted from these curves and characterised through a general phenomenological constitutive coupled equation. The coefficients of this coupled equation are optimised using genetic algorithm. Finite element simulation of tensile tests at different strain rates and temperatures are done using this coupled equation in material model of Abaqus FEA software and validated with experimental results. The novelties of proposed model are: (a) it can predict precisely the flow behaviour of tensile tests (b) it is a simple form of equation where fitting parameters are both function of strain rate ratio and temperature ratio, (c) it has ability to characterize flow behaviour with decreasing subzero temperatures and increasing strain rates.     

点火载荷下翼柱型装药结构完整性数值分析

针对固体火箭发动机翼柱型装药在点火载荷下结构完整性问题,提出了一种考虑三维损伤黏弹性本构性的数值模拟方法.基于商业有限元软件的二次开发平台,编写用户子程序,展开有限元数值计算,获取翼柱型装药在固化降温、点火载荷下装药结构的应力、应变与位移场分布.结果表明,在温度载荷与点火载荷下,药柱内表面变形模式是不同的.然而,不管在...     

Optimal nonmyopic gambling strategy for the generalized Kelly criterion

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the optimal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997     

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.     

软硬交替多层膜法向压入过程的有限元分析

采用大变形弹塑性有限单元法,对高速钢基体上的软硬交替多层膜在法向压痕作用下的力学行为,进行了模拟和分析.为了研究膜层数和膜厚的影响,对从单层到16层的不同膜层体系进行了计算.通过对诸如膜层的变形、最大应力随膜层数的变化、界面剪应力分布、表面张应力分布等的分析,得出了这些参数的分布及其对膜层体系的摩擦学性能的影响.这些结果可为多层膜的结构优化设计提供定量的依据.     

加筋板架抗动能穿甲的等效防护厚度研究

为研究舰船舷侧结构抗穿甲性能,采用有限元分析了两种典型工况下板架的穿甲破坏模式、弹体的剩余速度和板架的变形吸能规律,提出了基于剪切冲塞模式的剩余速度理论计算模型,比较了不同等效计算方法得到的结果,并将理论计算结果分别与相关文献的实验结果和本文的有限元计算结果进行了比较,两者之间均吻合较好。结果表明,加强筋对板架的抗穿甲性能影响较大,而板架的实际等效厚度是决定其抗穿甲性能的主要因素;不同的等效计算方法与模型相对尺寸、弹体冲击速度以及命中位置有关,对于弹体直径相对较大且初始冲击速度较高时,不同的等效计算方法得到的结果基本一致。     

Dynamic inventory and pricing models for competing retailers

We address infinite‐horizon models for oligopolies with competing retailers under demand uncertainty. We characterize the equilibrium behavior which arises under simple wholesale pricing schemes. More specifically, we consider a periodic review, infinite‐horizon model for a two‐echelon system with a single supplier servicing a network of competing retailers. In every period, each retailer faces a random demand volume, the distribution of which depends on his own retail price as well as those charged by possibly all competing retailers. We also derive various comparative statics results regarding the impact several exogenous system parameters (e.g., cost or distributional parameters) have on the equilibrium decisions of the retailers as well as their expected profits. We show that certain monotonicity properties, engrained in folklore as well as in known inventory models for centralized systems, may break down in decentralized chains under retailer competition. Our results can be used to optimize the aggregate profits in the supply chain (i.e., those of the supplier and all retailers) by implementing a specific wholesale pricing scheme. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Optimal production growth for the machine loading problem

This paper investigates a production growth logistics system for the machine loading problem (generalized transportation model), with a linear cost structure and minimum levels on total machine hours (resources) and product types (demands). An algorithm is provided for tracing the production growth path of this system, viz. in determining the optimal machine loading schedule of machines for product types, when the volumes of (i) total machine hours, and (ii) the total amount of product types are increased either individually for each total or simultaneously for both. Extensions of this methodology, when (i) the costs of production are convex and piecewise linear, and (ii) when the costs are nonconvex due to quantity discounts, and (iii) when there are upper bounds for productions are also discussed. Finally, a “goal-programming” production growth model where the specified demands are treated as just goals and not as absolute quantities to be satisfied is also considered.