混凝土类材料动态压缩强度在多维应力状态下的应变率效应

对混凝土类材料动态压缩应变率效应研究的发展及问题进行了概述,对比不同应力状态下混凝土类材料动态压缩应变率效应的表现特征,揭示了不同加载路径下实测动态强度提高系数的显著差异。研究表明,在高应变率下,基于初始一维应力加载路径的试件将因横向惯性效应导致的侧向围压而演化至多维应力状态,传统霍普金森杆技术无法获得高应变率下基于真实一维应力路径的动态强度提高系数,在强度模型中直接应用实测数据将过高估计材料的动态强度。鉴于应变率效应的加载路径依赖性,将仅包含应变率的强度提高系数模型扩展至同时计及应变率和应力状态的多维应力状态模型,并结合Drucker-Prager准则在强度模型中给予了实现。针对具有自由和约束边界试件开展的数值霍普金森杆实验表明,多维应力状态下的应变率效应模型可以考虑应变率效应随应力状态改变的特点,从而准确预测该类材料的动态压缩强度。研究结果可为正确应用霍普金森杆技术确定脆性材料的动态压缩强度提供参考。     

预应变对中子辐照高纯铝拉伸性能的影响

金属材料的中子辐照硬化和脆化一直都是核能安全领域十分关注的重要问题之一. 为了进一步认识预应变对中子辐照金属材料塑性形变和最终断裂特性的影响规律, 及其微观机理, 本文研究了10%拉伸预应变高纯铝的拉伸应力-应变曲线、失稳应力和失稳应变等随辐照剂量的变化规律. 结果表明, 辐照剂量越高, 预应变高纯铝内部孔洞的尺寸和数密度越高, 导致屈服强度和极限拉伸强度越高, 均匀延伸率和失稳应变越小, 表现出典型的辐照硬化和脆化效应, 但失稳应力与辐照剂量几乎无关. 相同辐照剂量条件下, 预应变引入的高密度位错能够显著降低辐照孔洞的尺寸和数密度, 加之辐照退火效应的综合影响, 导致预应变能够降低高纯铝屈服强度的增长率和失稳应变的下降率, 从而表现出一定的抑制辐照硬化和脆化的能力, 预应变还能够提高高纯铝的失稳应力, 但整体而言预应变并不能提高高纯铝的延性. 最后, 基于J-C本构模型的中子辐照退火态金属材料的脆化模型能够直接应用于预应变金属材料, 且模型预测结果与实验结果吻合较好.      

The strain-rate effect and the incremental plastic wave in copper

An experimental investigation was conducted to determine the degree of sensitivity of commerically pure copper to strain rate and to note the effect of this sensitivity on the velocity of propagation of shearing strain in copper. Thin-walled cylindrical specimens of copper were loaded in torsion to eliminate the effects of radial inertia. All specimens were annealed and then cold worked in torsion to obtain necessary specimen uniformity. Quasi-static tests were performed on short-length specimens to determine the shearing stress-strain curve of copper at a very low strain rate. The strain-rate sensitivity of copper at low strain rates, from 3×10^?4/sec to 5/sec, was tested by loading short specimens at a very slow continuous rate and then suddenly increasing the strain rate. A quasi-static test was also performed to determine the effect of creep on prestressed copper. Dynamic tests involving strain rates up to 500/sec were performed on long specimens with a torsional impact machine. Specimens were tested under stress-free and prestressed initial conditions. The prestressed specimen was loaded at a slow, continuous rate before impact to avoid the undesirable effects of creep which would have occurred with a static preload. Results from the quasi-static tests showed that copper is noticeably sensitive to strain rate in the low strain-rate regions, but that the sensitivity becomes almost constant as the strain rate is increased. Results from the dynamic tests showed that large strains propagated at speeds which agreed well with speeds predicted by the strain-rate-independent theory of plastic-wave propagation. The lower-level strains in the prestressed specimen, however, propagated at much higher speeds than are predicted by the strain-rate independent. Because radial-inertia effects were not present, this discrepancy in measured and predicted speeds for low-level strains must be due to the strain-rate sensitivity of copper.     

一种基于电磁霍普金森杆的材料动态包辛格效应测试装置及方法

金属材料在复杂载荷条件下的动态力学行为研究一直备受关注，但受限于实验设备，金属材料的动态包辛格效应响应一直都难以获得。为了探究金属材料的包辛格效应与应变率效应之间的关系，本文中提出一种基于电磁霍普金森杆(electromagnetic split Hopkinson bar，ESHB) 的非同步加载实验技术，为测试金属材料在高应变率加载下的包辛格效应提供了一种有效的实验方法。本文中，首先介绍了非同步加载装置的主要特点，即可以用两列由脉冲发生器产生的应力波对受载试样进行连续的一次动态拉-压循环加载，且加载过程保证了应力波的一致性。分析了应力波对试样加载过程中的波传播历程，确保了加载过程的连续性。随后介绍了动态加载过程，数据处理方法和波形分离手段，并对动态加载过程进行应力平衡性分析，论证了实验装置的可靠性。最后采用该方法测试了5%预应变下6061铝合金动态压缩-动态拉伸的包辛格效应，并与准静态下的实验结果进行对比。实验结果表明，该材料单轴压缩没有明显的应变率效应，但其包辛格效应具有应变率依赖性，高应变率下材料的包辛格应力影响因子由0.07增大至0.17，具有显著的提升，这对传统意义上铝合金材料应变率不敏感的结论提出了挑战。     

Two-dimensional analysis of the split hopkinson pressure bar system

The split Hopkinson pressure bar is widely used to measure the dynamic properties of solid materials. This paper presents the results of the first comprehensive two-dimensional numerical analysis of the technique, and quantitatively describes the effects of realistic friction and of variations in both the specimen geometry and the imposed strain-rate on the validity of the assumptions used in analyzing experimental data. A two-dimensional axisymmetric numerical analysis is used to compute all components of the stress, strain and strain-rate tensors at each mesh point within the specimen and the elastic bars. The calculated response of the pressure bars is used to reconstruct the stress-strain behavior of the specimen and this is compared to both the input stress-strain curve and the actual calculated stress-strain states in the specimen. Thus, the validity of the assumptions and the corrections used in the analysis of the data is determined.Inertia and friction between the specimen and the elastic bars affect the response of the specimen differently for different length-to-diameter ratios. Inertia effects produce stress waves propagating radially and axially in the specimen and may result in an oscillating reconstructed stress-strain curve. If the ends of the specimen are well lubricated and care is taken to minimize the effects of inertia, the reconstructed stress-strain curve agrees with the input. However, serious stress and strain nonuniformity exists when the ends are not lubricated and this results in a reconstructed stress-strain curve where, for any given strain, the stress magnitude is larger than the correct value. A comparison of the calculations with experiment shows excellent agreement for various interface conditions. Finally, the inertia correction of E.D.H. Davies and S.C. Hunter (1963) is found to be reasonable.     

A numerical study on the rate sensitivity of cellular metals

Metallic foams have non-linear deformation behavior, which make them attractive in many applications. Many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, but they contain conflicting, and sometimes confusing, conclusions on the strain-rate and inertia effect of cellular metals. In this paper, the dynamic crushing behavior of 2D Voronoi honeycomb is studied by finite element method. The influences of inertia, strain hardening and strain-rate hardening of metal matrix on the deformation mode and plateau stress of the honeycomb are investigated. Three deformation modes are found in different velocity ranges. According to the numerical results, it is found that the plateau stress increases significantly with the increase of impact velocity due to non-uniform deformation induced by inertia. The strain-hardening effect is slight in our numerical tests and the rate effect of the honeycomb is obviously weaker than that of the cell wall material.     

泡沫铝率相关性能的有限元模拟

构建了三维随机分布球形泡孔模型,模拟开、闭孔混合结构泡沫铝材料的微细观结构,并通过有限元方法计算了10~104 s-1应变率范围内、孔隙率35%~65%泡沫铝材料的率相关性以及应变率和相对密度变化对泡沫铝动态压缩力学性能的影响。研究表明:中、低应变率下,泡沫铝材料率相关性能主要取决于基体材料的应变率敏感性;高应变率下,泡沫铝材料率相关性能受基体材料的应变率敏感性以及微结构惯性联合作用,且相对密度较低泡沫铝材料的微结构惯性效应更显著。     

Constitutive modeling of the dynamic fracture of smooth tensile bars

A recently developed viscoplastic-damage type of constitutive theory for high strain-rate flow processes and ductile fracture is used to model the deformation and fracture of dynamically loaded smooth cylindrical tensile bars. The analysis assumes polycrystalline materials which usually contain microvoids with an average density of the order of 10⁶ per cm³ that are dispersed homogeneously throughout. It is shown that for dynamically imposed loading that produce nominal strain rates ranging between 5 × 10² − 5 × 10³ sec ⁻¹, the inhomogeneous fields of stress and deformation caused by wave propagation and wave reflection induce necking at different locations along the gauge section, depending upon the strain-rate imposed. This occurs without imposition of any geometrical or material irregularity to preposition the location of the necking. The imposed rate of strain is also shown to affect the magnitude of the strain at which necking initiates, as well as the strain required for fracture.     

Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism

The seemingly contradictory understandings of the initial crush stress of cellular materials under dynamic loadings exist in the literature, and a comprehensive analysis of this issue is carried out with using direct information of local stress and strain. Local stress/strain calculation methods are applied to determine the initial crush stresses and the strain rates at initial crush from a cell-based finite element model of irregular honeycomb under dynamic loadings. The initial crush stress under constant-velocity compression is identical to the quasi-static one, but less than the one under direct impact, i.e. the initial crush stresses under different dynamic loadings could be very different even though there is no strain-rate effect of matrix material. A power-law relation between the initial crush stress and the strain rate is explored to describe the strain-rate effect on the initial crush stress of irregular honeycomb when the local strain rate exceeds a critical value, below which there is no strain-rate effect of irregular honeycomb. Deformation mechanisms of the initial crush behavior under dynamic loadings are also explored. The deformation modes of the initial crush region in the front of plastic compaction wave are different under different dynamic loadings.     

The dynamic growth of a void in a plastic material and an application to fracture

The problem of the dynamic growth of a spherical void in applied stress and strain-rate fields is solved approximately using a variational method. The solution is applied to a model of fracture by void growth from brittle or incoherent inclusions. It is shown that the speed of fracture is limited by inertia near the crack tip. Some numerical results are obtained from data for high strength steels.     

损伤引起的反向应变率效应及其对本构关系和热粘塑性失稳的影响

对于材料在高应变率下的应变率无关和应变率负敏感现象,本文根据铸镁合金的宏观与微观相结合的试验结果,提出了一个基于损伤弱化的反向应变率效应机制,并建议了一个计及这一反向效应的热粘塑性本构方程。由此可以解释材料的表观应变率强化、表观应变率无关和表观应变率弱化三类基本情况。相应地,随损伤引起的反向应变率效应的增强,热粘塑性失稳也有三种基本情况:或在更高应变率或更大应变下发生绝热剪切,或由临界准则转化为临界应变准则,以及或在高应变率下不会发生绝热剪切。     

用于高强度材料的SHPB实验添加垫块法

提出了用于高强度材料的改进的SHPB实验方法添加垫块法,运用数值模拟方法,利用有限元程序LS-DYNA3D分析了添加垫块实验方法的合理性和可行性。根据一维应力波理论,给出了数据处理的修正方法。作为应用实例,采用改进的实验方法对高强度的Al2O3陶瓷材料的动态力学性能进行了研究,得到了比常规方法较高的应变率及应力应变范围的动态应力应变曲线,表明Al2O3陶瓷为应变率相关的非线性弹脆性材料。结果表明,添加垫块实验方法可有效地防止实验中压杆端面的变形,提高试件的应力应变及应变率水平。添加垫块实验方法为在SHPB装置上实现高强度材料的动态实验提供了一种方便实用的途径。     

Dynamic fracture of concrete – compact tension specimen

The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of the crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single crack due to the mode-I fracture. However, with the increase of loading rate crack branching is observed. Up to certain threshold (critical) loading rate the maximal crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the crack propagation becomes independent of the loading rate. The critical crack velocity at the onset of crack branching is found to be approximately 500 m/s.     

5083H111铝合金宽应变率拉伸动态本构模型

结合5083H111铝合金较宽应变率范围2×10-4 ~ 4×102s-1内的拉伸实验数据,揭示该铝合金的拉伸“V”型率效应特征,分析对数应变率敏感系数λ和切线模量Et的应变率和应变相关性,进而通过对Johnson-Cook模型的修正来建立合理描述5083H111铝合金较宽应变率范围内的动态拉伸本构模型。建立的动态本构模型中,流动应力包括应变率相关和应变相关两部分。该模型合理描述了5083H111铝合金的拉伸“V”型率效应特征,预测结果与实验结果较为一致。另外,结合破坏应变的对数应变率敏感系数β,得到了拉伸破坏应变预测方程,其预测结果也与实验结果基本一致。     

Dynamic limit analysis formulation for impact simulation of structural members

This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain hardening, strain-rate hardening and thermal softening. The time dependent term in the governing equation is integrated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-rate hardening and thermal softening as well as strain hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstrates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.     

45钢柱壳膨胀断裂的应变率效应

采用前照明高速分幅照相技术拍摄到在爆轰加载下45钢柱壳表面裂纹生成、扩展及产物泄漏过程的清晰图像,较准确地测量了膨胀断裂的时间与应变。 45钢柱壳在炸药爆轰加载下,断裂应变随应变率的增加而增加,当应变率达到一定值,断裂应变随应变率的增加而降低,出现了动态断裂中的塑性峰现象。     

Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

Summary A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape. Received 17 October 1997; accepted for publication 19 March 1998     

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10^?3 and 10³ s^?1 for ?150, ?100, ?50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump. The low strain-rate results show a well-defined elastic limit but no yield drop, a small yield plateau is found at room temperature. The subsequent strain hardening shows a maximum at 200°C, when serrated flow occurs and the ductility is reduced. The high strain-rate results show a considerable drop of stress at yield. The post-yield flow stress decreases steadily with increasing temperature, throughout the temperature range investigated. At room temperature and below, the strain-hardening rate becomes negative at large strains. The adiabatic temperature rise in the dynamic tests was computed on the assumption that the plastic work is entirely converted to heat. This enabled the isothermal dynamic stress-strain curves to be calculated, and showed that considerable thermal softening took place. The initial response to a strain-rate jump is approximately elastic, and has a magnitude which increases with decrease of testing temperature; it is little affected by the amount of prestrain. At 200 and 400° C, a yield drop occurs after the initial stress increment. The post-jump flow stress is always greater than that for the same strain in a constant-rate dynamic test, the strain-hardening rate becoming negative at large strains or low testing temperature. This observed effect of strain-rate history cannot be explained by the thermal softening accompanying dynamic deformation. These and other results concerning total ductility under various strain-rate and temperature conditions show that strain-rate history strongly affects the mechanical behavior of the mild steel tested and, hence, should be taken into account in the formulation of constitutive equations for that material.     

Techniques for measuring stress-strain relations at high strain rates

The qualitative dependence of the mechanical behavior of some materials on strain rate is now well known. But the quantitative relation between stress, strain and strain rate has been established for only a few materials and for only a limited range. This relation, the so-called constitutive equation, must be known before plasticity or plastic-wave-propagation theory can be used to predict the stress or strain distribution in parts subjected to impact stresses above the yield strength. In this paper, a brief review of some of the experimental techniques for measuring the stress, strain, strain-rate relationship is given, and some of the difficulties and shortcomings pointed out. Ordinary creep or tensile tests can be used at plastic-strain rates from 10^?8 to about 10^?1/sec. Special quasi-static tests, in which the stress- and strain-measuring devices as well as the specimen geometry and support have been optimized, are capable of giving accurate results to strain rates of about 10²/sec. At higher strain rates, it is shown that wave-propagation effects must be included in the design and analysis of the experiments. Special testing machines for measuring stress, strain and strain-rate relationships in compression, tension and shear at strain rates up to 10⁵/sec are described, and some of the results presented. With this type of testing machine, the analysis of the data requires certain assumptions whose validity depends upon proper design of the equipment. A critical evaluation of the accuracy of these types of tests is presented.     

Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.