An Experimental Method to Determine the Tensile Strength of Concrete at High Rates of Strain

In the present work, dynamic tensile strength of concrete is experimentally investigated by means of spalling tests. Based on extensive numerical simulations, the paper presents several advances to improve the processing of spalling tests. The striker is designed to get a more uniform tensile stress field in the specimen. Three methods proposed in the literature to deduce the dynamic strength of the specimen are discussed as well as the use of strain gauges and a laser extensometer. The experimental method is applied to process data of several tests performed on wet micro-concrete at strain rates varying from 30 to 150/s. A significant increase of the dynamic tensile strength with strain-rate is observed and compared with data of the literature. In addition, post-mortem studies of specimens are carried to improve the analysis of damage during spalling tests.     

Simulation of spallation in brittle solids

A new model of dynamic fracture for brittle materials based on Perzyna's[1] idea and Seaman's experimental results[2] is developed. Numerical simulations of metal uranium[3] spalling process in its impact tests are carried out with the model. Fair agreement between the computation and experimental data has been obtained.     

Elastic characterization of orthotropic plates of any shape via static testing

The paper presents an inverse procedure for identifying elastic properties of isotropic or orthotropic materials from the full-field measurement of the surface displacements of plates under flexural loading configurations. The procedure is based on a numerical–experimental optimisation process which minimizes an error function defined by subtracting the experimental data from the outputs of the numerical analysis. In each iteration the optimisation process updates the values of the elastic constants in a finite element model of the specimen used in the experimental tests. The unknown parameters are simultaneously identified by a single test and without damaging the structural integrity of the specimen. The possibility of using the methodology for characterizing any-shaped plates was investigated. The applicability and the robustness of the procedure were carried out on aluminum and unidirectional Graphite/PEEK laminate specimens. Phase-shifting speckle interferometry was employed to detect the out-of-plane displacement field of a portion of the observed surface of the specimen.     

石英玻璃圆环高速膨胀碎裂过程的离散元模拟

采用离散元算法模拟了石英玻璃圆环受到外加动态载荷时的力学行为. 首先基于flat-jointed粘结模型,通过标准的单轴拉压、三点弯曲等数值实验来标定了石英玻璃的微观参数. 在此模型基础上,数值模拟再现了石英玻璃圆环在不同应变率下的膨胀碎裂过程. 为定量分析数值模拟结果,需要准确确定圆环的碎裂发生时刻. 模拟发现:伴随着石英玻璃圆环的断裂,圆环外表面粒子径向膨胀速度的时程曲线会发生突然升高然后下降的跳动;详细分析表明,这种跳动源自周向的脆性断裂诱发的卸载波(周向拉伸应力急剧下降)以及伴随而来的泊松膨胀,这种径向速度跳动现象为实验中检测脆性断裂发生时刻提供了可能. 进一步的数值研究表明:(1)石英玻璃圆环的断裂应变随着应变率的提高而增大,与韧性金属材料的膨胀环实验结果一致;(2)石英玻璃圆环的碎片平均质量随着应变率的增大而减小;(3)数值计算获得的碎片平均尺寸与已有的理论和实验结果比较吻合. 利用液压膨胀环实验装置对石英玻璃圆环进行了验证性实验,回收得到的碎片形貌及碎片个数与数值模拟的结果基本一致.      

Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling

The paper presents a numerical analysis of the inelastic deformation process in porous rocks during different stages of its development and under non-equiaxial loading. Although numerous experimental studies have already investigated many aspects of plasticity in porous rocks, numerical modeling gives valuable insight into the dynamics of the process, since experimental methods cannot extract detailed information about the specimen structure during the test and have strong limitations on the number of tests. The numerical simulations have reproduced all different modes of deformation observed in experimental studies: dilatant and compactive shear, compaction without shear, uniform deformation, and deformation with localization. However, the main emphasis is on analysis of the compaction mode of plastic deformation and compaction localization, which is characteristic for many porous rocks and can be observed in other porous materials as well. The study is largely inspired by applications in petroleum industry, i.e. surface subsidence and reservoir compaction caused by extraction of hydrocarbons and decrease of reservoir pressure. Special attention is given to the conditions, evolution, and characteristic patterns of compaction localization, which is often manifested in the form of compaction bands. Results of the study include stress-strain curves, spatial configurations and characteristics of localized zones, analysis of bifurcation of stress paths inside and outside localized zones and analysis of the influence of porous rocks properties on compaction behavior. Among other results are examples of the interplay between compaction and shear modes of deformation.To model the evolution of plastic deformation in porous rocks, a new constitutive model is formulated and implemented, with the emphasis on selection of adequate functions defining evolution of yield surface with deformation. The set of control parameters of the model is kept as short as possible; the parameters are carefully selected to have simple and intuitive physical interpretation whenever possible. Results demonstrate that evolution of the yield surface with deformation has major influence on the resulting characteristics of deformation patterns, which is not sufficiently acknowledged in the literature.     

Experimental and numerical investigation of fracture in a cast aluminium alloy

This paper describes an experimental and numerical investigation on the fracture behaviour of a cast AlSi9MgMn aluminium alloy. In the experiments, a modified Arcan test set-up was used to study mixed-mode fracture. During testing, the tension load and the displacement of the actuator of the test machine were recorded, simultaneously as a high-resolution digital camera was used to record a speckle-patterned surface of the specimen. The recorded images were post-processed using an in-house digital image correlation (DIC) software to obtain information of the displacement and strain fields in the specimen during the test. In addition, some newly implemented features in the DIC software allowed us to detect and follow the crack propagation in the material. The numerical calculations were carried out with a user-defined material model implemented in an explicit finite element code. In the model, the material behaviour is described by the classical J₂ flow theory, while fracture was modelled by the Cockcroft–Latham criterion, assuming the fracture parameter to follow a modified weakest-link Weibull distribution. With the proposed probabilistic fracture modelling approach, the fracture parameter can be introduced as a random variable in the finite element simulations. Crack propagation was modelled by element erosion, and a non-local damage formulation was used to reduce mesh-size sensitivity. To reveal the effect of mesh density and meshing technique on the force–displacement curves and the crack propagation, several different meshes were used in the numerical simulations of the modified Arcan tests. The numerical results were finally compared to the experimental data and the agreement between the measured and predicted response was evaluated.     

损伤演化对韧性金属碎裂过程的影响

固体在冲击拉伸载荷作用下会断裂成多个碎片,基于线性内聚力断裂假设的Mott-Grady模型能较好地预测碎裂过程所产生的平均碎片尺度的下限。然而实际上,韧性金属的损伤演化是多元化的,为此通过数值模拟方法研究了不同损伤演化规律对韧性碎裂过程的影响。利用ABAQUS/Explicit动态有限元软件数值再现了韧性金属杆（45钢）在高应变率下拉伸碎裂的过程,分析了线性和非线性损伤演化对韧性碎裂过程的影响规律。结果表明:损伤演化规律对韧性金属的碎裂过程具有显著影响,非线性指标α越大,碎裂过程产生的碎片数越少;Grady-Kipp碎裂公式仍能在一定范围内预测韧性碎裂过程中产生的碎片尺寸;当非线性指标α远大于零时,在较低冲击拉伸载荷作用下,数值模拟结果和Grady-Kipp模型预测值偏差较大,随着应变率增大,数值模拟结果与Grady-Kipp模型预测值吻合较好。     

An Experimental Technique for Spalling of Concrete

The spalling strength of concrete is measured by examining the strain wave profiles in a polymer buffer bar behind the slender concrete bar specimen placed between a large diameter (Φ100 mm) Hopkinson bar and the buffer bar. The experimental results indicate that the spalling strength is related to not only the compressive strength of concrete but also the impact velocities (the loading rates). The rate effect of spalling strength mainly results from the different cracking paths in concrete under different impact velocities. However when the input compressive stress to specimen exceeds the threshold required to trigger the compressive damage, the spalling strength decreases due to the evolution and cumulation of compressive damage in concretes. The repeated impact loading experiments indicate that damage plays an important role in the spallation process of concrete. The high speed video of the spalling fracture process shows that multiple spalling fractures may occur in the scab and damage accumulation resulting from stress wave propagation in scab is the main reason for the producing of multiple spallations.     

The “Inverse Hall-Petch” effect on the impact response of single crystal copper

Based on the available experimental and computational capabilities, a phenomenological approach has been proposed to formulate a hypersurface in both spatial and temporal domains to predict combined specimen size and loading rate effects on the material properties [1-2]. A systematic investigation is being performed to understand the combined size, rate and thermal effects on the properties and deformation patterns of representative materials with different nanostructures and under various types of loading conditions [3- 16]. The recent study on the single crystal copper response to impact loading has revealed the size-dependence of the Hugoniot curve. In this paper, the "inverse Hall-Petch" behavior as observed in the impact response of single crystal copper, which has not been reported in the open literature, is investigated by performing molecular dynamics simulations of the response of copper nanobeam targets subjected to impacts by copper nanobeam flyers with different impact velocities. It appears from the preliminary results that the "inverse Hall-Petch" behavior in single crystal copper is mainly due to the formation and evolution of disordered atoms and the interaction between ordered and disordered atoms, as compared with the physics behind the "inverse Hall-Petch"behavior as observed in nanocrystalline materials.     

爆轰加载下金属锡层裂破碎数值模拟

对爆轰加载下低熔点金属锡的层裂破碎问题开展了数值模拟。在利用实验数据对所采用数值方法和材料模型开展对比验证的基础上,通过对样品内部物理量时间及空间分布演化对比分析,剖析了冲击加-卸载中样品内部应力波与材料相互作用过程。此外,通过对比分析不同厚度锡样品在爆轰加载下的动态行为特征,进一步认识了自由面反射稀疏波、边侧稀疏波和入射稀疏波共同作用下层裂破碎演化机制。结果表明,当样品较薄时,层裂破碎行为由反射稀疏波主导;随着样品厚度的增大,反射稀疏波主导区缩小,入射稀疏波和边侧稀疏波主导区逐渐增大。     

Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to ALON

Within this two part series we develop a new material model for ceramic protection materials to provide an interface between microstructural parameters and bulk continuum behavior to provide guidance for materials design activities. Part I of this series focuses on the model formulation that captures the strength variability and strain rate sensitivity of brittle materials and presents a statistical approach to assigning the local flaw distribution within a specimen. The material model incorporates a Mie–Grüneisen equation of state, micromechanics based damage growth, granular flow and dilatation of the highly damaged material, and pore compaction for the porosity introduced by granular flow. To provide initial qualitative validation and illustrate the usefulness of the model, we use the model to investigate Edge on Impact experiments (Strassburger, 2004) on Aluminum Oxynitride (AlON), and discuss the interactions of multiple mechanisms during such an impact event. Part II of this series is focused on additional qualitative validation and using the model to suggest material design directions for boron carbide.     

Modelling of compressive behaviour of concrete-like materials at high strain rate

Uniaxial compression tests are the most common tests for characterizing the strength of concrete-like materials. The dynamic compression strength of concrete-like material is typically obtained by Split Hopkinson Pressure Bar (SHPB) tests. The increase in material strength under dynamic loading is usually attributed to the strain rate effect and modelled with a dynamic increase factor (DIF). However, it was observed by some researchers that the radial inertial confinement caused apparent increase of dynamic strength of concrete-like specimen in SHPB tests. They attributed the material strength increase to this inertial effect, instead of the strain rate effect. In the present study, numerical analyses are performed to investigate the compressive behaviour of concrete-like material at high strain rates. A homogeneous macroscale model and a heterogeneous mesoscale model are developed in the study. In the macroscale model, the material is assumed to be homogeneous and isotropic. In the mesoscale model, the test sample is modelled as a three-phase composite consisting of aggregate, mortar matrix and interfacial transaction zone (ITZ) between the aggregate and the mortar matrix. The aggregate is assumed to be circular and the ITZ is modelled as a thin boundary around the aggregate. In the both models, the materials are assumed to be insensitive to the strain rate first. Therefore, the obtained strength enhancement is only due to the inertial confinement. Strain rate sensitive material properties are then used in the two models in the calculations. Numerical simulations of the concrete samples under compression at different strain rates are carried out. The relative contribution of the inertial effect and the strain rate effect on the compressive strength DIF is examined based on the numerical results. The failure process of concrete specimen is also studied.     

初始应力状态对材料层裂破坏特性影响研究

通过对球面飞片加载条件下的应力/应变状态分析表明采用施加径向应变方法可以近似模拟球面加载的受力过程. 采用过盈配合的热装配方法对平面样品施加了径向预应变,一维平面应变气炮实验结果显示初始预应力(变)明显降低了LY12铝层裂强度. 从空洞长大基本原理出发分析了各向异性受力条件下空洞长大的路径和所消耗能量不同于各向同性应力加载.通过数值模拟对含损伤的材料本构模型进行分析,得到了材料层裂强度与其外部宏观应力场密切相关,也间接的与构型相关的结论.      

材料超高温动态拉伸SHTB实验方法的有效性分析

针对高温拉伸分离式Hopkinson杆实验技术,通过数值模拟、实验验证以及几种典型材料的高温动态拉伸性能测试相结合的方法,对此实验技术中存在的几个关键问题进行了深入研究。结果表明:对于平板状钩挂式拉伸试样,通过标距段尺寸优化后,应力分布均匀,流动应力曲线与螺纹拉伸试样一致,且应力上升段后没有剧烈跳动;通过精确气动控制,在加载脉冲到来同时,可实现有效的试样快速同步组装和加载;当试样温度为1 200 ℃时,在冷加载杆与高温试样接触以及应力波加载试样的整个过程中,试样平均温度下降约1.3%,而加载杆端温升低于180 ℃。为了验证此实验技术,对3D打印TC4、镍基单晶高温合金DD6进行了最高温度约1 200 ℃时的高温动态拉伸力学性能实验测试。     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests

A heterogeneous material model based on macro-mechanical observations is proposed for simulation of fracture in steel projectiles during impact. A previous experimental study on the deformation and fracture of steel projectiles during Taylor bar impact tests resulted in a variety of failure modes. The accompanying material investigation showed that the materials used in the impact tests were heterogeneous on scales ranging from microstructure as investigated with SEM to variation in fracture strains from tensile tests. A normal distribution is employed to achieve a heterogeneous numerical model with respect to the fracture properties. The proposed material model is calibrated based on the tensile tests, and then used to independently simulate the Taylor bar impact tests. A preliminary investigation showed that the simulations are sensitive to assumptions regarding the anvil behaviour and friction properties. A flexible anvil and a yield-limited friction law are shown to be necessary to correctly reproduce the experimental behaviour. The proposed model is then shown to be capable of correctly reproducing all fracture modes but one, and also predict critical impact velocities for projectile fracture with reasonable accuracy. Fragmentation at velocities above the critical velocity is not well reproduced due to excessive element erosion. Measures to make the element erosion process more physical are proposed and discussed with their respective drawbacks. The use of a simple fracture criterion in combination with an element erosion technique accentuates the effect of distributing the fracture parameter.     

一种基于SHTB的Ⅱ型动态断裂实验技术

冲击剪切载荷作用下动态断裂韧性的测定是材料力学性能和断裂行为研究中重要组成部分.为了测定材料的Ⅱ型动态断裂韧性,许多学者采用不同的试样与实验方法进行了实验,但限于实验条件,裂纹断裂模式往往是I+Ⅱ复合型,而不是纯Ⅱ型,因而不能准确测得材料的Ⅱ型动态断裂韧性.鉴于此,本文基于分离式霍普金森拉杆(split Hopkinson tension bar,SHTB)实验技术,提出一种改进的紧凑拉伸剪切(modified compact tension shear,MCTS)试样,通过夹具对MCTS试样施加约束,从而保证试样按照纯Ⅱ型模式断裂.采用实验-数值方法对MCTS试样动态加载过程进行分析,将实验测得的波形输入有限元软件ANSYS-LSDYNA,得到了裂纹尖端应力强度因子-时间曲线,并与紧凑拉伸剪切(compact tension shear,CTS)试样进行了对比.同时采用数字图像相关法进行了实验,验证了有限元分析结果.结果表明,MCTS试样在整个加载过程中K_I K_Ⅱ,裂纹没有张开;而CTS试样在同样的加载过程中K_IK_Ⅱ,出现裂纹张开现象.这说明MCTS试样能够准确地测定材料的Ⅱ型动态断裂韧性,为材料动态力学测试提供了一种有效的实验技术.     

Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes

Advances in computing as well as measurement instrumentation have recently allowed for the investigation of a wider spectrum of physical phenomena in dynamic failure than previously possible. With increasing demand for specialized lightweight, high strength structures, failure of inhomogeneous solids has been receiving increased attention. Such inhomogeneous solids include structural composites such as bonded and sandwich structures, layered and composite materials as well as functionally graded solids. Many of such solids are composed of brittle constituents possessing substantial mismatch in wave speeds, and are bonded together with weak interfaces, which may serve as sites for catastrophic failure (Rosakis and Ravichandran (2000)).In the present study numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes is presented. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) softening generated by microdamage mechanisms; (iii) thermomechanical coupling (thermal plastic softening and thermal expansion); (iv) rate sensitivity.To describe suitably the time and temperature dependent effects observed experimentally during dynamic loading processes the kinetics of microdamage has been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elastic–plastic response can be obtained. The identification procedure is developed basing on the experimental observations. The finite difference method for regularized elasto-viscoplastic model is used. The edge-cracked bimaterial specimen is considered. In the initial configuration, the height of the specimen is equal to 30 cm, width is 12.5 cm and the length of the initial crack is equal to 2.5 cm. The length of the boundary over which impact is applied is equal to 5 cm, the rise time is fixed at 0.1 μs and the impact velocity is varied. The impact area is localized symmetrically or asymmetrically to the shorter axis of the specimen (symmetry axis of the cohesive band). Basing on the available data of recent experimental observation Rosakis et al. (1999) that have been carried out for relatively thin specimens both the plane stress and plane strain conditions are considered. The material of the specimen is AISI 4340 steel, while PMMA is the cohesive band, both modelled by thermo-elasto-viscoplastic constitutive equations with effects of isotropic hardening and softening generated by microdamage mechanisms and thermomechanical coupling. Fracture criterion based on the evolution of microdamage is assumed. Both, isothermal and adiabatic processes are considered.Particular attention is focused on the investigation of the interactions and reflections of stress waves and the influence of these waves on the propagation of macrocrack within the interface band. The propagation of the macroscopic crack within the material of the interface band for both symmetrical and asymmetrical impact cases has been investigated. It has been found that macrocrack-tip speeds vary from the shear wave speed to the dilatational wave speed of the material and is higher than the Rayleigh surface wave speed. This result is in accord with the experimental observations performed by Rosakis et al. (1999).