Experimental study of strain-rate-dependent behavior of carbon/epoxy composite

The strain rate dependent behavior of IM7/977-2 carbon/epoxy matrix composite in tension is studied by testing the resin and various laminate configurations at different strain rates. Tensile tests have been conducted with a hydraulic machine at quasi-static strain rates of approximately 10⁻⁵ s⁻¹ and intermediate strain rates of about 1 s⁻¹. Tensile high strain rate tests have been conducted with the tensile split Hopkinson bar technique at strain rates of approximately 400–600 s⁻¹. Specimens with identical geometry are used in all the tests. The standard split Hopkinson bar technique is modified to measure strain directly on the specimen. The results show that strain rate has a significant effect on the material response.     

混凝土材料层裂强度的实验研究

利用f74大尺寸Hopkinson压杆和混凝土长杆试件研究了混凝土材料的层裂强度及其应变率效应。入射的压缩波通过压杆透入试件并反射成拉伸波而形成层裂。实验中采取在试件上多点贴应变片,讨论了应力波在混凝土试件中传播的波形弥散和幅值衰减,并在考虑了损伤演化影响的基础上确定了试件材料的层裂强度。对某种普通混凝土在不同应变率下的测试显示层裂强度受应变率影响明显。结果表明,本文提出了一种测定混凝土层裂强度的有效方法。     

Study on Dynamic Behavior and Tensile Strength of Concrete Using 1D Wave Propagation Characteristics

Concrete structures are usually fractured under dynamic loadings, so it is important to have a clear knowledge of their dynamic behavior and tensile strength. First, the principle of one-dimensional (1D) stress wave reflection and superposition at free surface is briefed, and the spalling test method based on the Hopkinson bar is presented. Then, the attenuation law of stress wave is explored and the dynamic tensile/compressive moduli of concrete are evaluated according to the wave propagation experiment. Lastly, the influences of strain rate on the spalling tensile strength and failure patterns of concrete are further analyzed. The testing results demonstrate that the attenuation of stress wave accords with an exponential law when propagating in the concrete bar. The difference between the dynamic elastic moduli of concrete in tension and in compression is minor. Spalling tensile strength is sensitive to strain rate, and there is an obvious linear correlation between dynamic increase factor (DIF) and strain rate in a log-log plot for strain rate above 1.0/s; a single fracture occurs at low strain rate, while multiple fractures are detected with increasing strain rate.     

Effects of strain rate and temperature on the tension behavior of polycarbonate

Tension stress–strain responses of polycarbonate are presented for strain rates of 1 × 10⁻³ s⁻¹–1700 s⁻¹ and temperatures ranging from −60 to 20 °C. The high rate tension tests are performed using a split Hopkinson tension bar apparatus. The influence of strain rate and temperature on the tension behavior of polycarbonate is investigated. Experimental results indicate that the tension behavior of polycarbonate exhibits nonlinear characteristics and rate-temperature sensitivity. The values of yield strength and strain at yield increase with the increase of strain rate and decrease with increasing temperature. A viscoelastic constitutive model consisting of a nonlinear spring and a nonlinear Maxwell element is proposed to characterize the rate and temperature dependent deformation behavior of polycarbonate prior to yielding.     

轴向钢筋增强混凝土一维应力层裂实验研究

基于φ74 mmSHPB实验平台进行了混凝土及轴向钢筋增强混凝土（UDRC）杆的一维应力层裂实验,采用超高速相机拍摄实验中杆表面的实时变形情况,使用数字图像相关法（DIC）分析杆表面的位移场及应变场演化过程,探讨混凝土及增强混凝土在应力波加载过程中发生拉伸断裂（层裂）的规律,并进一步结合有限元分析了钢筋在层裂过程中的作用。结果表明:UDRC杆中应力波的传播满足一维应力假设;钢筋对UDRC发生拉伸层裂的影响可以忽略,而在混凝土基体断裂后将使结构保持完整;断裂试件中的裂纹在拉压应力波交替作用下反复张开闭合,随着应力波在杆中的衰减而趋于稳定;UDRC与混凝土的层裂强度基本相同,且具有相似的应变率增强效应;在实验加载范围内,光圆钢筋和螺纹钢筋的结构增强效果没有区别。     

Effects of strain rate on transverse tension properties of a carbon/epoxy composite: studied by moiré photography

The dependence on strain rate of the mechanical properties of a high performance carbon fibre/epoxy composite loaded in transverse tension has been investigated. Dog-bone shaped specimens have been tested in quasi-static and dynamic loading conditions. The dynamic tests were performed in a split Hopkinson bar at strain rates between 100 and 800 s⁻¹. A moiré technique combined with high-speed photography, at framing rates of 0.25–1 MHz, was used for extraction of the local strain fields. The transverse mechanical properties were found to have weak or no dependence on strain rate. The average transverse modulus did not depend on strain rate, whereas the strain to and stress at failure were found to increase slightly with increased strain rate. For these dog-bone shaped specimens the strain evaluated by conventional Hopkinson bar technique was found to underestimate the true strain field measured by moiré technique. Finally, the moiré technique facilitated crack-propagation monitoring in real time. Crack speeds up to 2300 m s⁻¹ were measured at transverse crack propagation.     

Analytical and experimental studies on mechanical behavior of composites under high strain rate compressive loading

An analytical method is presented for the prediction of compressive strength at high strain rate loading for composites. The method is based on variable rate power law. Using this analytical method, high strain rate compressive stress–strain behavior is presented up to strain rate of 5000 s⁻¹ starting with the experimentally determined compressive strength values at relatively lower strain rates. Experimental results were generated in the strain rate range of 472–1957 s⁻¹ for a typical woven fabric E-glass/epoxy laminated composite along all the three principal directions. The laminated composite was made using resin film infusion technique. The experimental studies were carried out using compressive split Hopkinson pressure bar apparatus. It was generally observed that the compressive strength is enhanced at high strain rate loading compared with that at quasi-static loading. Also, compressive strength increased with increasing strain rate in the range of parameters considered. Analytically predicted results are compared with the experimental results up to strain rate of 1957 s⁻¹.     

超高韧性水泥基复合材料的层裂试验研究

层裂是材料遭受冲击、爆炸等高速荷载时的一种常见破坏方式。该文利用直径80 mm的霍普金森杆实验装置,研究了超高韧性水泥基复合材料UHTCC （Ultra High Toughness Cementitious Composites）中应力波的传播特性和材料的层裂强度。通过在试件表面粘贴5组应变片,获得了在0.2 MPa、0.3 MPa、0.4 MPa、0.5 MPa打击气压下,UHTCC中应力波的传播曲线。利用高速摄影机记录层裂试验,观测了UHTCC的层裂破坏过程。由试件表面应变片测得的应力波曲线,计算了材料中的应力波波速、动态弹性模量,分析了应力波在该材料中传播的衰减规律,并计算出不同打击气压下材料的层裂强度及应变率。试验结果显示: UHTCC的层裂过程相比混凝土具有更多的韧性特征; UHTCC中的应力波峰值在0 mm~500 mm范围内衰减迅速;在同等应变率下,UHTCC与静态抗拉强度相近的混凝土相比,层裂强度高出10 MPa左右,且UHTCC的层裂强度具有明显的应变率敏感性。     

Fracture energy of concrete at high loading rates in tension

The effect of high loading rates in tension on the failure energy and strength of concrete is reported in this paper. High loading rates exceeding 5000 GPa/s corresponding to strain rates higher than ∼120 s⁻¹ can be applied by use of Hopkinson bar set-up designed to produce spall. Tension tests were performed on cylindrical specimens made of micro-concrete. At high loading rates, or strain rates, the failure energy of micro-concrete, as well as the strength, was found to substantially increase.     

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.     

Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization

Understanding the behavior of concrete and mortar at very high strain rates is of critical importance in a range of applications. Under highly dynamic conditions, the strain-rate dependence of material response and high levels of hydrostatic pressure cause the material behavior to be significantly different from what is observed under quasistatic conditions. The behavior of concrete and mortar at strain rates of the order of 10⁴ s⁻¹ and pressures up to 1.5 GPa are studied experimentally. The mortar analyzed has the same composition and processing conditions as the matrix phase in the concrete, allowing the effect of concrete microstructure to be delineated. The focus is on the effects of loading rate, hydrostatic pressure and microstructural heterogeneity on the load-carrying capacities of the materials. This experimental investigation uses split Hopkinson pressure bar (SHPB) and plate impact to achieve a range of loading rate and hydrostatic pressure. The SHPB experiments involve strain rates between 250 and 1700 s⁻¹ without lateral confinement and the plate impact experiments subject the materials to deformation at strain rates of the order of 10⁴ s⁻¹ with confining pressures of 1–1.5 GPa. Experiments indicate that the load-carrying capacities of the concrete and mortar increase significantly with strain rate and hydrostatic pressure. The compressive flow stress of mortar at a strain rate of 1700 s⁻¹ is approximately four times its quasistatic strength. Under the conditions of plate impact involving impact velocities of approximately 330 ms⁻¹, the average flow stress is 1.7 GPa for the concrete and 1.3 GPa for the mortar. In contrast, the corresponding unconfined quasistatic compressive strengths are only 30 and 46 MPa, respectively. Due to the composite microstructure of concrete, deformation and stresses are nonuniform in the specimens. The effects of material inhomogeneity on the measurements during the impact experiments are analyzed using a four-beam VISAR laser interferometer system.     

High Strain Rate Compressive Tests on Wood

Abstract: The penetrating split Hopkinson pressure bar was used to study the response of dry maple wood under high strain rate impact load. Using longer bar and shorter specimens utilised the assumption of one‐dimensional stress waves travelling along the bars and specimen because the experiment fulfilled the ratio of diameter to length of bars condition in Kolsky bar experiments. The stress–strain relationships and behaviour of the fibre structure materials’ failure were investigated during the compressive dynamic tests at strain rates between 950¹ and 2000 s^?1. The mechanics of dynamic failure was studied and it was confirmed that deformation of specimen is a linear function of energy absorption by specimens.     

Ultra‐High‐Speed Full‐Field Deformation Measurements on Concrete Spalling Specimens and Stiffness Identification with the Virtual Fields Method

Abstract: For one decade, spalling techniques based on the use of a metallic Hopkinson bar in contact with a concrete sample have been widely employed to characterise the dynamic tensile strength of concrete at strain rates ranging from a few tens to hundreds of s^?1. However, the processing method based on the use of the velocity profile measured on the rear free surface of the sample (Novikov formula) remains quite basic. In particular, the identification of the whole softening behaviour of the concrete material is currently out of reach. In the present paper, a new processing technique is proposed based on the use of the virtual fields method (VFM). First, a digital ultra‐high‐speed camera is used to record the pictures of a grid bonded onto the specimen. Then, images of the grid recorded by the camera are processed to obtain full‐field axial displacement maps at the surface of the specimen. Finally, a specific virtual field has been defined in the VFM equation to use the acceleration map as an alternative ‘load cell’. This method applied to three spalling tests with different impact parameters allowed the identification of Young's modulus during the test. It was shown that this modulus is constant during the initial compressive part of the test and decreases in the tensile part when microdamage exists. It was also shown that in such a simple inertial test, it was possible to reconstruct average axial stress profiles using only the acceleration data. It was then possible to construct local stress–strain curves and derive a tensile strength value.     

钢纤维超高强混凝土动态力学性能

采用分离式霍普金森压杆装置对不同纤维体积率的钢纤维超高强混凝土进行不同应变率的冲击压缩试验,结果表明钢纤维超高强混凝土是应变率敏感材料,并测出其应变率敏感阀值,当应变率超过阀值后,钢纤维超高强混凝土的强度、韧度与弹性模量都随纤维体积率的增加而显著提高,在高应变率下,超高强混凝土基体成粉碎性破坏,而钢纤维超高强混凝土呈现出“裂而不散”的破坏形态。     

Strain rate effects on dynamic fracture and strength

An experimental procedure and accompanying theoretical analysis is presented to produce a well-characterized technique for quantifying dynamic fracture properties of quasi-brittle materials. An analytical and experimental investigation of mode I fracture of concrete was conducted under the dynamic loading of a split Hopkinson pressure bar. Fracture specimens in the form of notched-cavity splitting tension cylinders were subjected to stress wave loading that produced strain rates nearing 10/s. Fracture parameters were extracted by the application of the two-parameter fracture model, a nonlinear fracture model for quasi-brittle materials. Finite element analysis verified the experimental configuration and addressed inertial contributions within the dynamic environment. Ultra-high-speed digital photography was synchronized with the fracture process to provide additional validation and insight to the experimental technique. Results show that the effective fracture toughness and specimen strength both increase significantly with loading rate. The numeric and photographic results validate the experimental technique as a new tool in determining rate dependent material properties.     

Dynamic splitting tensile properties of concrete and cement mortar

To investigate the dynamic tensile behaviours of concrete and cement mortar, a 50‐mm split Hopkinson pressure bar was applied on Brazilian disc specimens for dynamic tensile experiments, in which strain rate varied from 10^?5 to 20 s^?1. The high‐speed camera testing technique was used to capture the dynamic fractured process of the specimens at relative high strain rate. The experimental results revealed that the dynamic tensile strength of concrete specimens has a stronger strain rate effect than that of cement mortar specimens. Then three typical failure patterns of the specimens were confirmed in dynamic experiments. In addition, one‐parameter semi‐empirical relation between dynamic tensile strength and strain rate was established. Finally, the limitation of dynamic splitting experiments on Brazilian disc specimens was discussed in detail at high strain rate, in which the crack initiates from the contact point between the incident bar and specimens rather than the centre of the specimens.     

Strain Rate Behavior of Closed-Cell Al-Si-Ti Foams: Experiment and Numerical Modeling

We present a combined experimental and numerical study on the strain rate effect of closed-cell Al-Si-Ti foams having different relative densities fabricated using the powder metallurgy foaming technique. The high strain rate tests were conducted with split Hopkinson pressure bar technique at 800 to 2500 s^?1. Two-dimensional mesoscale finite element models were created from tomographic images of the homologous foam. The rate sensitivity of the foam originates mainly from that of its parent material, increasing with increasing relative density. Stress elevation due to other effects, such as micro-inertia, shock wave, and gas pressure in individual cells, is negligible.     

High Strain Rate Compressive Tests on Woven Graphite Epoxy Composites

The behavior of composite materials may be different when they are subjected to high strain rate load. Penetrating split Hopkinson pressure bar (P-SHPB) is a method to impose high strain rate on specimen in the laboratory experiments. This research work studied the response of the thin circular shape specimens, made out of woven graphite epoxy composites, to high strain rate impact load. The stress-strain relationships and behavior of the specimens were investigated during the compressive dynamic tests for strain rates as high as 3200 s⁻¹. One dimensional analysis was deployed for analytical calculations since the experiments fulfilled the ratio of diameter to length of bars condition in impact load experiments. The mechanics of dynamic failure was studied and the results showed the factors which govern the failure mode in high strain deformation via absorbed energy by the specimen. In this paper, the relation of particle velocity with perforation depth was discussed for woven graphite epoxy specimens.     

Effect of strain rate on the tension–compression asymmetric responses of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si

An experimental investigation is performed to explore the tension–compression asymmetry of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si alloy over a wide range of strain rates. A split Hopkinson bar technique is used to obtain the dynamic stress–strain responses under uniaxial tension and compression loading conditions. Experimental results indicate that the alloy is a rate sensitive material. Both tension yield strength and compression yield strength increase with increasing strain rate. The mechanical responses of the alloy have the tension–compression asymmetry. The values of yield strength and subsequent flow stress in compression are much higher than that in tension. The yield strength is more sensitive to change with strain rate in tension than compression. The difference of the yield strength between tension and compression increases with the increase of strain rate. The tensile specimen is broken in a manner of ductile fracture presenting characteristic dimples, while the compressive specimen fails in a manner of localized shearing failure.     

Thermal Effects During Tensile Deformation of Ti‐6Al‐4V at Different Strain Rates

An in‐depth analysis of the effect of heat generated by plastic work on the observed tensile behaviour of Ti­6Al­4V at different strain rates is presented. Special emphasis is put on the transition from isothermal to adiabatic conditions and how this transition is affected by several process parameters such as material properties, environmental conditions and sample geometry. Experiments are performed in isothermal conditions at moderate temperatures, from ?10 to 70 °C, as well as at strain rates from quasi‐static speeds to more than 1000 s^?1 using a split Hopkinson tensile bar setup. This experimental data is used in conjunction with numerical simulations to determine the evolution of temperature during the experiments and the temperature and strain rate sensitivity of the material, as well as the Taylor–Quinney coefficient. Finally, a full model of the material behaviour is presented and used to define clear limits for adiabatic and isothermal conditions.