数值模拟中混凝土类材料应变率效应曲线的惯性效应修正

数值模拟是研究混凝土类材料在动载下响应的有效方法,准确输入材料真实的应变率效应曲线对预测结构在动载下的响应有重要作用。收集了1990年以来针对混凝土类材料的动态抗压实验数据,并将惯性效应对材料动态强度的影响进行剥离,得到真实的材料应变率效应引起的抗压动态强度放大因子（DIF_ε）与应变率对数的关系曲线。分析数据发现:实验得到的抗压动态强度放大因子（DIF_s）和惯性效应引起的抗压动态强度放大因子（DIF_i）都随试件尺寸的增大而增大;随着材料准静态强度增大,混凝土类材料DIF_i随应变率增长的增长幅度减小。对比拟合曲线与其他曲线可知,在高应变率下,新的应变率效应拟合曲线比已有半经验公式能更好地反映实验数据的DIF_ε;模拟时分别输入新的应变率效应曲线和CEB推荐公式,将输出结果与DIF_s对比,验证了新的应变率效应曲线的优越性。     

基于细观模拟的混凝土动态压缩强度尺寸效应研究

在混凝土静态破坏尺寸效应方面开展的研究已经较为完善,而在动态破坏尺寸效应方面的研究还远没有形成一个统一的认知。混凝土尺寸效应根源于内部组成的非均质性,从细观角度出发,考虑材料非均质及细观组分的应变率效应,将混凝土看作由骨料、砂浆及界面过渡区组成的三相复合材料,建立了混凝土动态破坏行为研究的细观数值分析方法,对不同应变率（1×10-5 s-1~2×102 s-1）及不同尺寸方形混凝土试件单轴压缩破坏行为进行模拟与分析。数值结果表明:混凝土动态与静态加载下压缩强度尺寸效应规律存在明显差异,在动态压缩强度尺寸效应规律中,存在一个临界应变率（约为1 s-1）,即:低于临界应变率时,应变率增大时,压缩强度随试件尺寸增大而减小,且尺寸效应逐渐被削弱;达到临界应变率时,混凝土动态压缩强度与尺寸无关,尺寸效应被完全抑制;高于临界应变率时,应变率增大时,压缩强度随试件尺寸增大而增大,尺寸效应逐渐增强。最后对混凝土动态强度尺寸效应的产生机理进行了分析与讨论。     

碾压混凝土HJC动态本构模型修正及数值验证

研究高应变率冲击爆炸荷载作用下水工碾压混凝土大坝结构的动力响应,离不开对筑坝材料动态力学特性和本构关系的深入认识。参考实际水工混凝土大坝筑坝材料的配合比和施工方式,制备碾压混凝土试样,分别开展了静态压缩试验和分离式霍普金森压杆(SHPB)试验,以探求碾压混凝土的动态力学特性。基于静、动态力学试验结果,对目前多用于描述混凝土类材料高应变率下力学行为的HJC模型的强度面、应变率增强效应和破坏准则进行了修正,并利用有限元计算手段,建立SHPB试验的数值模型,以验证修正HJC模型的有效性。结果表明:碾压混凝土在高应变率冲击荷载下的动态力学特性表现出明显的应变率效应,动态压缩强度随应变率增加而提高,且与试样尺寸有关。基于试验数据的改进HJC模型有效预测了碾压混凝土在高应变率冲击荷载作用下的动态力学行为,数值计算得到的重构应力——应变曲线基本与SHPB试验结果吻合,采用最大主应变失效准则模拟得到了与SHPB试验加载过程中接近的试样损伤破坏模式,研究成果可用于碾压混凝土结构的抗冲击爆炸设计中。     

超高韧性水泥基复合材料动态压缩力学性能的数值模拟研究

该文基于HJC本构模型,采用分离式霍普金森杆（SHPB）压杆系统,对掺有聚乙烯醇（PVA）纤维的超高韧性水泥基复合材料（PVA-UHTCC）的动态压缩力学性能进行了数值模拟研究。首先,通过系统分析确定了21项HJC本构参数,并验证了模拟的正确性。基于此,通过分析5组应变率下材料的动态压缩应力-应变曲线讨论了峰值应力动态增强因子DIF的应变率效应,并通过LS-DYNA软件探讨了破坏过程、破坏形态与应变率的关系。模拟结果表明:随着应变率的增加,PVA-UHTCC材料的动态压缩应力-应变曲线呈现由应变硬化主导向着损伤软化主导的转变趋势;此外,PVA-UHTCC峰值应力动态增强因子DIF具有明显的应变率效应,其值随着应变率增加而增加,且在不同应变率区间呈现不同敏感性;通过量化DIF这种分区敏感性,提出了适用于PVA-UHTCC材料的DIF与应变率对数lgε分段函数式;同时,通过对比钢纤维增强水泥基材料（SFRCC）和普通混凝土材料,发现PVA-UHTCC材料的DIF应变率敏感性较低。最后,通过LS-DYNA软件模拟试件裂缝扩展和压碎破坏过程,更好地理解了PVA-UHTCC材料动态压缩破坏行为。     

基于细观模拟的轻骨料混凝土动态压缩破坏及尺寸效应分析

轻骨料混凝土由于其轻质及保温隔热性能好等优点,越来越多被应用于实际工程结构。采用细观数值模拟方法,将轻骨料混凝土看作由骨料颗粒、砂浆基质及两者间界面过渡区组成的三相复合材料,采用塑性损伤本构关系模型,考虑应变率效应的影响,建立了对应的细观随机骨料模型,研究了轻骨料混凝土在动态压缩作用下的破坏行为及尺寸效应规律。发现:随着应变率的增加,惯性效应逐渐成为主导效应,动态压缩强度的尺寸效应逐渐被削弱,达到临界应变率时,尺寸效应被完全抑制。此外,结合率效应影响机制与规律,揭示了轻骨料混凝土动态压缩强度的尺寸效应机理,建立了"静动态统一"的尺寸效应半经验-半理论公式。     

冲击载荷下环氧树脂动态压缩力学响应实验研究

为了从细观角度研究碳/环氧复合材料的动态力学性能,利用分离式霍普金森压杆实验装置对其组分材料TDE86#环氧树脂体系进行动态冲击压缩实验,获得不同应变率加载条件下环氧树脂的应力一应变曲线,基于应力-应变曲线分析了应变率对环氧树脂动态压缩力学性能的影响.研究结果表明:环氧树脂具有明显的应变强化效应,随着应变率的增加,环氧树脂的强度基本没有变化,最大应力时的应变逐渐减小,动态模量和压缩刚度有很大程度的提高.     

聚脲材料动态压缩力学行为的数值模拟研究

以聚脲材料动态压缩力学特性为研究对象,提出了考虑动态弹性模量、动态强度因子和动态切线模量的简化三直线弹塑性本构模型;基于ANSYS/LS-DYNA有限元分析软件,建立了低、中、高不同应变率下聚脲材料压缩有限元模型,并与实验结果进行对比分析。结果表明：动态弹性模量增大因子、动态强度因子和动态切线模量因子随应变率增加而有规律的增大,均和应变率的对数呈双线性关系。在中低应变率下,三者的线性关系斜率都比较平缓;在高应变率下,三者的线性关系斜率都比较陡,且弹性模量动态增大因子的斜率比动态强度因子的更大,而第二阶段动态切线模量因子的斜率与动态强度因子的基本一致,但第三阶段动态切线模量因子的斜率是动态强度因子的2.3倍左右,说明高应变率下聚脲材料的后期应力强化效应更加显著。聚脲材料的简化三直线弹塑性本构模型可以在ANSYS/LS-DYNA有限元软件中较好地实现。该文建立的有限元模型能较为准确地模拟聚脲材料压缩实验,进一步验证了简化弹塑性本构模型在不同应变率压缩加载下的有效性。该研究可以为聚脲涂覆加固防护结构有限元模型提供材料模型参数依据。     

混凝土类材料SHPB实验若干问题探讨

分离式霍普金森压杆(SHPB)实验是研究混凝土类材料动态力学性能的主要方法。该文简要回顾了当前混凝土类材料SHPB实验中存在的若干问题(如端面摩擦、骨料大小、惯性效应、温度效应等)的研究进展;通过对混凝土SHPB实验的精细化数值模拟,进一步分析了惯性效应产生机理,提出了材料的塑性流动引起的横向加速度是产生围压的关键原因,围压波在试件中心的反射和边缘的卸载形成试件中围压从中心向四周逐渐减小的抛物线型分布;利用该文所提的SHPB实验惯性效应产生机理,较好地解释了SHPB实验的尺寸和主动围压的影响规律;基于自主研制的可进行围压和温度共同加载的SHPB实验装置TSCPT-SHPB,对在5MPa~25MPa围压作用下以及在40℃~80℃温度下盐岩动态力学性能进行实验研究,结果表明,高围压下应变率效应不如低围压下显著,温度越高,强度越低;基于考虑粗骨料大小、形状及空间随机分布的三维混凝土细观模型,对混凝土各细观组分对动态效应影响进行了研究,结果表明:各组分材料静态强度越高,混凝土动态强度也越高;在相同骨料粒径条件下,骨料体积率越高,混凝土动态强度也越高;而相同骨料体积含量条件下,骨料尺寸越大,混凝土动态强度越低。     

冲击载荷下圆环压缩变形特性研究

基于Johnson-Cook材料模型,应用数值模拟的方法,研究了圆环件在冲击载荷作用下的压缩变形规律。得到了冲击载荷下的摩擦系数-变形特性曲线,由此研究了不同载荷幅值(加载速度)、不同应变率敏感系数下的圆环内径变化规律以及对临界摩擦系数的影响。结果表明:摩擦系数-变形特性曲线和准静态结果基本趋势一致但有较大的差异,其中惯性效应起主要作用,应变率效应则起着次要作用。另外,此过程存在着临界摩擦系数,而应变率效应和惯性效应对圆环的临界摩擦系数影响不大,因此,临界摩擦系数可以作为试件的内在属性,应用于圆环的冲击锻压工程。     

高强高模聚乙烯纤维力学性能的应变率和温度效应

利用MTS810材料试验机、旋转盘式杆-杆型冲击拉伸装置和温度控制箱,在温度20℃~110℃、应变率为0.001/s~700/s范围内,对高强高模聚乙烯纤维束进行了准静态和高应变率冲击拉伸实验,得到了不同温度、不同应变率时纤维束的应力-应变曲线。结果表明:高强高模聚乙烯纤维束的初始弹性模量具有应变率和温度相关的特性,随应变率提高而增加,随温度提高而下降;在常温下,破坏应力从准静态到动态,具有明显的应变率相关性,随应变率提高而增加,但在20℃~110℃范围内、高应变率下,对应变率变化不敏感;失稳应变也具有应变率和温度相关的特性,随应变率提高而减小,随温度提高而增大。在高应变率下,断裂应变能密度主要由初始弹性模量和失稳应变共同决定,受温度效应和应变率效应的综合影响。     

Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I: Experiments

Effects of the inertia-induced radial confinement on the dynamic increase factor (DIF) of a mortar specimen are investigated in split Hopkinson pressure bar (SHPB) tests. It is shown that axial strain acceleration is unavoidable in SHPB tests on brittle samples at high strain-rates although it can be reduced by the application of a wave shaper. By introducing proper measures of the strain-rate and axial strain acceleration, their correlations are established. In order to demonstrate the influence of inertia-induced confinement on the dynamic compressive strength of concrete-like materials, tubular mortar specimens are used to reduce the inertia-induced radial confinement in SHPB tests. It is shown that the DIF measured by SHPB tests on tubular specimens is lower than the DIF measured by SHPB tests on solid specimens. This paper offers experimental support for a previous publication [Li QM, Meng H. About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. Int J Solids Struct 2003; 40:343–360.], which claimed that inertia-induced radial confinement makes a large contribution to the dynamic compressive strength enhancement of concrete-like materials when the strain-rate is greater than a critical transition strain-rate between 10¹ and 10² s⁻¹. It is concluded that DIF formulae for concrete-like materials measured by split Hopkinson pressure bar tests need to be corrected if they are going to be used as the unconfined uniaxial compressive strength in the design and numerical modelling of structures made from concrete-like materials to resist impact and blast loads.     

Mechanical response of a soft rubber compound compressed at various strain rates

Rate-dependent material constitutive behavior models are needed in numerical simulations of shock-mitigation structures. In this research, compressive stress–strain response of a soft rubber compound is obtained experimentally at quasi-static, intermediate and high strain rates under uniaxial-stress and uniaxial-strain loading states. Kolsky bars with modifications for characterizing soft materials and a long Kolsky bar are used to conduct the dynamic experiments, while an MTS load frame is used for conducting experiments at quasi-static rates. Compression experiments are conducted at each decade in the strain-rate scale without any gap typically seen in the intermediate range. The experimental results show significant strain-rate effects on the mechanical behavior of this soft material, which are summarized via a rate-dependent constitutive model.     

About the dynamic uniaxial tensile strength of concrete-like materials

Experimental methods for determining the tensile strength of concrete-like materials over a wide range of strain-rates from 10⁻⁴ to 10² s⁻¹ are examined in this paper. Experimental data based on these techniques show that the tensile strength increases apparently with strain-rate when the strain-rate is above a critical value of around 10⁰-10¹ s⁻¹. However, it is still not clear that whether the tensile strength enhancement of concrete-like materials with strain-rate is genuine (i.e. it can be attributed to only the strain-rate effect) or it involves “structural” effects such as inertia and stress triaxility effects. To clarify this argumentation, numerical analyses of direct dynamic tensile tests, dynamic splitting tests and spalling tests are performed by employing a hydrostatic-stress-dependent macroscopic model (K&C concrete model) without considering strain-rate effect. It is found that the predicted results from these three types of dynamic tensile tests do not show any strain-rate dependency, which indicates that the strain-rate enhancement of the tensile strength observed in dynamic tensile tests is a genuine material effect. A micro-mechanism model is developed to demonstrate that microcrack inertia is one of the mechanisms responsible for the increase of dynamic tensile strength with strain-rate observed in the dynamic tensile tests on concrete-like materials.     

Axial crushing of thin-walled high-strength steel sections

Quasi-static and dynamic axial crushing tests were performed on thin-walled square tubes and spot-welded top-hat sections made of high-strength steel grade DP800. The dynamic tests were conducted at velocities up to 15 m/s with an impacting mass of 600 kg in order to assess the crush behaviour, the deformation force and the energy absorption. Typical collapse modes developed in the sections and the associated energy absorbing characteristics were examined and compared with previous studies on high-strength steel. A significant difference was observed between the quasi-static and the dynamic crushing tests in terms of the deformation force and impact energy absorption. As this difference is attributed to strain-rate and inertia effects, material tensile tests at elevated strain rates have been carried out. A comparison is made with analytical methods and the response was under-predicted. In addition, numerical simulations of the axial crushing of the thin-walled sections were performed and comparisons with the experimental results were satisfactory. The validated numerical model was used to study the energy absorption capacity of thin-walled sections with variations in the yield strength, sheet thickness, flange width and spot-weld spacing. Structural effectiveness differences have been captured through simulations between spot-welded top-hat sections made of mild steel and high-strength steel.     

Inertia-sensitive impact energy-absorbing structures part II: Effect of strain rate

By employing the elastic-plastic structural model introduced in part I [1], which contains four compressible bars and four elastic-plastic “hinges” of finite length, the entire dynamic deformation history of Type II structures is traced. In contrast to part I, strain-rate effects are incorporated into the analysis throughout the entire response of the structure. The Cowper-Symonds relation is adopted and the yield stress varies with the current strain-rate during the dynamic response of the model. The numerical examples presented show that the strain-rate effect plays an equally important role to that of inertia on the dynamic behaviour of this kind of energy-absorbing structure if the material of the structure is rate-sensitive, e.g. made of mild steel. Compared with the corresponding quantities in the quasi-static case, the combined effects of strain-rate and inertia make the peak load much higher and the final displacement much smaller. It is also found that because the increase of the yield stress due to strain-rate sensitivity expands the range of elastic deformation, the elastic strain energy stored in the structure made of rate-dependent material is notably larger than that in the structure made of rate-independent material. This implies that when strain-rate effects are taken into account in the analysis, elasticity must play a more significant role and should not be neglected.     

Static and dynamic properties of high-density metal honeycombs

Metal honeycombs are commonly used to absorb energy in applications involving impact because of their high-energy capacity to weight ratio. The energy capacity of a material will be affected by any strain-rate effect in the material; thus knowledge of this property is necessary for design purposes. The materials studied in this work were a thick-walled aluminum and stainless-steel honeycomb. A method of testing the specimens in a state approximating uniaxial strain was developed for the large compressive deformations required with honeycombs, and used for both static and dynamic tests. For the dynamic tests, a gas gun was used to propel projectiles into fixed specimens of the test materials, and measurements of the force at the fixed ends of the specimens were used to determine the energy absorption properties of the materials. Initial strain rates to about 2000/s were obtained. Both materials showed a strain-rate effect.     

A note on the inertia and strain-rate effects in the tam and calladine model

The dynamic behaviour of a simple plate structure subjected to an axial impact is studied using an elastic-plastic model which takes into account inertia effects and the influence of material strain-rate sensitivity. The entire time-dependent deformation process, including elastic unloading and plastic reloading is obtained. The predictions for the absorbed energy are in reasonable agreement with the corresponding experimental results reported by Tam and Calladine and the detailed behaviour provides some further insight into the dynamic plastic buckling of structural elements.     

基于细观单元等效化方法的混凝土动态破坏行为分析

混凝土材料具有明显的应变率效应,对其力学性质增强机理的认识还不统一。在细观随机骨料模型基础上,采用特征单元尺度划分试件网格,推导了考虑材料拉/压强度应变率效应的细观单元等效本构关系,建立了非均质混凝土材料的细观单元等效化数值模型。基于二维模型对Dilger等混凝土动态压缩试验进行了数值模拟,获得的数值结果与试验数据及随机骨料模型结果吻合良好,证明了细观单元等效化方法的准确性;进而对三维混凝土试件动态单轴拉伸和压缩破坏模式及宏观力学性质的加载速率效应进行了研究。数值结果表明:随着加载速率的增加,混凝土裂纹(损伤)数量增大,混凝土破坏将耗散更多的能量,是混凝土动态强度提高的主要原因。