Fracture energy of UHP-FRC under direct tensile loading applied at low strain rates

This research investigates the fracture energy of ultra-high performance fiber reinforced concretes (UHP-FRC) under direct tensile loading applied at relatively low strain rates. Nine UHP-FRC series incorporating three types of steel fibers (straight, end-hooked, and twisted fibers), each in three different fiber volume fractions, are tested under uniaxial tensile loading at four different strain rates, ranging from 0.0001 s⁻¹ to 0.1 s⁻¹. Particular attention is given to clearly distinguish between the dissipated energy during the strain hardening and softening portions of the loading regime. The test results show that: 1) the fracture energy is mainly influenced by a parameter, termed fiber factor, which is a function of the fiber volume fraction and slenderness, and 2) all three types of UHP-FRCs exhibit increases in fracture energy with increasing strain rates. The observed strain rate sensitivity of the fracture energy suggests it is likely associated with the strain sensitive micro-cracking that occurs during fiber pull-out.     

Properties of strain hardening ultra high performance fiber reinforced concrete (UHP-FRC) under direct tensile loading

Enhanced matrix packing density and tailored fiber-to-matrix interface bond properties have led to the recent development of ultra-high performance fiber reinforced concrete (UHP-FRC) with improved material tensile performance in terms of strength, ductility and energy absorption capacity. The objective of this research is to experimentally investigate and analyze the uniaxial tensile behavior of the new material. The paper reviews and categorizes a variety of tensile test setups used by other researchers and presents a revised tensile set up tailored to obtain reliable results with minimal preparation effort. The experimental investigation considers three types of steel fibers, each in three different volume fractions. Elastic, strain hardening and softening tensile parameters, such as first cracking stress and strain, elastic and strain hardening modulus, composite strength and energy dissipation capacity, of the UHP-FRCs are characterized, analyzed and linked to the crack pattern observed by microscopic analysis. Models are proposed for representing the tensile stress–strain response of the material.     

A tensile testing technique for fibre-reinforced composites at impact rates of strain

Journal of Materials Science - A brief review is given of techniques which have been employed in attempts to determine the mechanical properties of composite materials under tensile impact loading....     

Dynamic tensile deformation and fracture of metal cylinders at high strain rates

An experimental study has been presented on the radial deformation of aluminium and copper cylinders of internal diameter 52 mm and wall thickness 1–7 mm, internally loaded with high explosives. High speed photography and flash radiography have been employed to record the distance–time (x–t) history of the cylinder wall, which has been found to expand under strain rates of 10⁴–10⁵ s⁻¹. The rupture of the cylinder is identified by the leakage of detonation gases, through the cracks in the cylinder wall. Rupture strains of 70–160% have been found for commercially pure aluminium. For a fixed wall thickness, the rupture strain increases with the strain rate. However, when the cylinder wall thickness is changed, a maximum is observed in a graph showing the strain and strain rate relationship. Aluminium appears to follow the Ivanov rupture criteria. From the experimental data the macroscopic viscosity coefficient for aluminium has been found to be 0.55–0.87×10³ Pa s. In the deformation of a copper cylinder the cracks initiate at strains of 30–60%, followed by rupture at very high strains up to 300%. The crack propagation velocity through the copper cylinder wall has been found to be 250–300 m/s. Recovered fragments show wall thinning by 50–60% and also exhibit shear fracture which dominates the radial fracture in high velocity deformation of the metal cylinder.     

Experiments on concrete under uniaxial impact tensile loading

A problem of practical importance for designing of structural elements is discussed in this paper—the behaviour of concrete subjected to uniaxial impact tensile loading. The “Split Hopkinson Bar” technique was adopted for testing concrete in uniaxial tension at stress rates between 2 and 60 N/mm²/ms. A remarkable increase in tensile strength was observed due to high stress rate. The ratio of impact and static tensile strength varied between 1.33 and 2.34 for various concrete mixes. The influence of maximum aggregate size, water-cement ratio, cement content, cement type and quality, specimen humidity, static compressive strength and loading/casting direction upon the uniaxial impact tensile strength was studied. The high stress rate resulted in an increase of the modulus of elasticity of concrete in uniaxial tension. An explanation for the observed phenomena is suggested.     

Experiments on concrete under repeated uniaxial impact tensile loading

The fatigue behaviour of concrete was a new aspect in the experimental program focused on the behaviour of concrete subjected to uniaxial impact tensile loading. The results obtained in repeated impact tensile loading tests (at stress rates of 2–6 N/mm². ms) indicated that the impact fatigue was associated with progressive crack propagation resulting in accumulative damage of concrete. The upper stress limits varied between 1.7 and 0.6 times the static tensile splitting strength and specimen withstood 1 to 6,055 loading cycles respectively. The influence of water-cement ratio, cement content, specimen humidity, loading/casting direction and compressive strength upon the impact fatigue tensile strength of concrete was studied. The phenomena observed are discussed with the aid of fracture mechanics concepts.

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Résumé Un aspect nouveau dans la recherche du comportement du béton soumis en traction uniaxiale à des charges de choc est le comportement à la fatigue. Ce problème de fatigue a une grande importance pour des pieux de fondation. On a obtenu 89 résultats en faisant des essais répétitifs de choc en traction où la vitesse de mise en tension variait entre 2 et 6 N/mm². ms. Les limites des contraintes ont varié entre des valeurs égales à la résistance du choc en traction uniaxiale (1,7 f_b,r) et 0,6 fois la résistance statique à la traction par fendage. Les éprouvettes ont résisté à des variations de charge de 1 à 6 055. Les résultats montrent que la fatigue au choc allait de pair avec une augmentation progressive de la fissuration provoquée par la dégradation accumulative du béton. Il a été constaté que la résistance du béton à un effort de chocs repétés en traction augmente quand la valeur du facteur eau-ciment et la teneur en ciment augmentent. L'humidité des éprouvettes n'influence pas la résistance à la traction par chocs répétés. La résistance déterminée sur des éprouvettes chargées perpendiculairement à la direction du bétonnage était plus élevée que la résistance mesurée dans un essai où la direction de chargement et du bétonnage étaient parallèles. En général un béton de qualité inférieure a une meilleure résistance aux chocs répétés. On propose des explications des phénomènes observés par les théories de la mécanique de la rupture.

     

Tensile and work hardening properties of low carbon dual phase strip steels at high strain rates

Abstract

As a result of their unique combination of strength and ductility dual phase steels play an important role in reducing weight in automobile components and improving crashworthiness. The purpose of this paper is to quantify the crash performance of dual phase steels, as defined by the influence of low and high strain deformation rates (0·001 s^-1 and 100 s^-1 respectively), on the tensile and work hardening properties of a range of commercial dual phase products. The objective is to establish whether dual phase steels maintain their desirable mechanical property characteristics of low yield strength, high tensile strength and high work hardening rates during plastic deformation under the application of a high strain rate loading. The results confirmed that the yield/proof strength and tensile strength increased with increasing volume fraction of second phase constituents and increasing strain rate. In particular, a dual phase steel with a microstructure consisting of a significant volume fraction (>10–15%) of additional second phase material (bainite) is shown to display superior energy absorption properties. However, this is accompanied by poor ductility and work hardening characteristics.     

Dynamic compressive and splitting tensile properties of concrete containing recycled tyre rubber under high strain rates

In order to raise the efficiency of resource utilization, recycling waste rubber particles into concrete as aggregate has been widely accepted. When the size and content of the rubber particles are appropriate, rubberized concrete can achieve many excellent properties. This study investigated the impact of rubber replacement on dynamic compressive and splitting tensile properties of concrete. The split Hopkinson pressure bar tests of rubberized concrete containing 5%, 10%, 15% and 20% volume replacement for sand were completed. The failure modes, stress curves and dynamic strength values of rubberized concrete under high strain rates were recorded. The results reveal that the dynamic compressive and splitting tensile strength of rubberized concrete decrease with increasing rubber content. Meanwhile, peak strain increases with increasing rubber content. Dynamic increase factors (DIFs) of compressive and splitting tensile strength also were calculated, where rubberized concrete shows a stronger strain rate sensitivity. The analysis of specific energy absorption illustrates that rubberized concrete with 15% rubber replacement has the best impact toughness. In addition, ratios of dynamic compressive–tensile strength of rubberized concrete were calculated, which are between 3.82 and 5.39.     

Dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.     

中低应变率加载下弱胶结软岩动力学特性

我国西部侏罗系煤层上覆巨厚白垩系富水软岩,为了解此类软岩在冲击荷载作用下的力学本构关系及损伤演化规律,利用Hopkinson压杆装置对干燥、饱和红砂软岩进行中低应变率下的冲击试验,结果表明:红砂软岩峰值应力、峰值应变均表现出明显的应变率效应,其中峰值应力与应变率呈指数关系;相同应变率下,干燥红砂软岩的强度大于饱和状态,对冲击荷载表现出更强的抵抗能力,但饱和红砂软岩的宏观破坏强度大于干燥状态;低应变率加载下,干燥红砂软岩出现负损伤;结合微观机理分析,低应变率下,水对红砂软岩的弱化作用占据主导地位,随着应变率的增大,在惯性效应和水的Stefan效应共同作用下,饱和红砂软岩的动态强度得到强化;基于Z-W-T模型和应变等效原理,建立了服从Weibull分布的损伤本构方程,经验证能很好的反映红砂软岩的动态本构关系,具有一定的工程实际意义。     

Abnormal strain hardening in nanostructured titanium at high strain rates and large strains

Commercial purity nanostructured titanium prepared by equal channel angular pressing plus cold rolling (grain size ∼260 nm) exhibits a nonnegligible strain hardening behavior at large compressive strains (>15%) and quasistatic loading conditions. The degree of the strain hardening increases with increasing strain rates and becomes more pronounced at dynamic loading rates. This behavior is in contrast with what we have seen so far in other nanostructured materials, where flat stress-strain curves are often seen. It was concluded from transmission electron microscopy investigations that in addition to dislocation slips, deformation twinning may have played a significant role in plastic deformation of nanostructured Ti. The structural failure behavior is in-situ recorded by a CCD camera and reasoned according to the microscopic observations.     

中低应变率下闭孔泡沫铝动态力学性能研究

为探索闭孔泡沫铝的动态力学性能与吸能特性,基于万能材料试验机和高速液压伺服材料试验机在常温下分别对闭孔泡沫铝在准静态和中应变率下(0.001~100s^-1)的动态力学性能进行了测试,分析了不同应变率、不同相对密度和不同泡沫铝基体特性下闭孔泡沫铝的应力应变曲线特征和吸能特性变化。研究结果表明:中低应变率下的纯铝基体泡沫铝并不具备应变率效应,高脆性、相对密度较小的泡沫铝具备更好的吸能特性,塑性和脆性基体泡沫铝变形带分别呈现“V”形和“X”形,脆性基体泡沫铝同样不具备应变率效应。     

Compressive strength of ice at impact strain rates

The compressive strength of ice was measured at high strain rates of 10³ s⁻¹ order of magnitude. Since ice compressive strength is known to be strongly dependent on strain rate, properties corresponding to high strain rates are needed for engineering predictions of the behavior of ice under dynamic crushing scenarios. The split Hopkinson pressure bar (SHPB) apparatus was used to successfully measure compressive strength over a strain rate range of 400–2,600 s⁻¹. Strain rate variation was achieved by adjusting the specimen length and the velocity of the SHPB striker bar; increased velocity and reduced specimen length produced higher strain rates. Since the compressive strength was found to be nearly uniform over the measured strain rate range, an average value of 19.7 MPa is reported. However, when comparing the present results with data in the existing literature spanning several orders of magnitude in strain rate, a trend of continuously increasing strength for strain rates beyond 10¹ s⁻¹ can be observed.     

超高性能水泥基复合材料弯拉作用下虚拟应变硬化机制分析

根据 Tjiptobroto 的工作 , 假设初始裂纹为最终失效裂纹 , 引入非初始裂纹纤维基体间的部分剥离能耗散项和单位失效面上随机纤维有效根数 , 依据初始裂纹总耗散能与非初始裂纹耗散能的平衡准则 , 研究了水泥基复合材料的多裂纹扩展失效机制。根据超高性能水泥基复合材料特性 , 修正和简化了各能量耗散项 , 建立了基于能量平衡准则的超高性能水泥基复合材料多裂纹开裂失效机理的理论模型 , 用以预报该材料的裂纹扩展规律。数值预报了 Tjiptobroto 实验模型的多裂纹扩展数目和能量耗散项 , 并与其实验结果进行了对比 , 吻合较好。表明对具有高弹模钢纤维的超高性能水泥基复合材料引入部分剥离能项是必要的。本文中的理论模型也可作为超高性能水泥基复合材料初裂承载能力和极限承载能力预报的理论参考。      

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

A failure assessment diagram for strain hardening materials under cyclic and monotonic loading

Strain hardening is introduced in the failure assessment diagram by studying two simple collapse models. These models together with the new failure curves are used both to predict the maximum load of different types of specimens and to assess the stability of these specimens under controlled displacement. The models are also used to study crack growth under a cyclic load high enough to cause gross plastic deformation and thus invalidate Paris law.