Experimental evaluation of the strength distribution of fibers under high strain rates by bimodal Weibull distribution

This paper proposes a bimodal Weibull distribution model for strain- rate- and temperature-dependent fiber strength. The relationships of the mechanical quantities between fiber and fiber bundles at different strain rates and temperatures under tensile impact are established. A method for determining mechanical parameters of fibers by tensile impact tests of fiber bundles is established. Experiments on E-glass bundles have been performed at six strain rates (90, 300, 800, 1100, 1300 and 1700 s⁻¹) at three different temperatures (−70, 14, 80°C). According to the statistical analysis and models, the mechanical parameters for the fiber and their relationships with strain rate and temperature are obtained from the tensile impact experimental results. The emulated stress/strain curves from the model are in good agreement with the test data. The theoretical model and test results show that the shape parameters, β^d₁ and β^d₂, are not only strain rate independent but also temperature independent. The scale parameters σ^d₀₁ and σ^d₀₂, which change with strain rate and temperature, are not constant.     

纤维束动态拉伸力学性能的实验研究

对Ｐｏｌｙｖｉｎｙ－ａｌｃｏｈｏｌ（ＰＶＡ），Ｅ－ｇｌａｓｓ和Ｋｅｖｌａｒ４９纤维束的应变率相关性和能量吸收能力进行了对比，冲击拉伸实验结果表明，除ＰＶＡ纤维束的初始弹性模量外，三种纤维束的力学性能均具有应变率相关性，其中ＰＶＡ和Ｅ－ｇｌａｓｓ的应变率敏感性较Ｋｅｖｌａｒ４９强烈；Ｋｅｖｌａｒ４９的能量吸收能力高于ＰＶＡ并且明显优于Ｅ－ｇｌａｓｓ。     

A statistical model and experimental study of the strain-rate dependence of the strength of fibres

In the present paper, statistical models of the strain-rate dependence of the strength of fibres and fibre bundles are established and their stress/strain equations are deduced. According to the models, an experimental method of determining mechanical parameters in the stress/strain equations by means of tensile impact loading of the fibre bundles is set up. In order to examine the validity of the models and the experimental method, tensile tests of the E-glass fibre bundles were performed at strain rates ranging from 10⁻⁴ to 10³ s⁻¹. The test results are in good agreement with the models. Hence, the models are reliable and the test method is feasible. The statistical models successfully explain the rate-dependent behaviour of the E-glass fibre.     

Characterization and constitutive modeling of aramid fibers at high strain rates

The quasi-static and rate-dependent mechanical properties of aramid yarns are presented together with a study on different methods of securing yarn specimens in tensile tests. While capstans were found to be suitable for quasi-static tests, they either were not strong enough or had too high inertia for dynamic tests in a Split Hopkinson Pressure Bar setup. Instead, specially designed clamps were used. A viscoelastic material model to describe the mechanical behavior of the yarns, including failure, is also presented. The material model was employed in the computational simulation of ballistic penetration of woven aramid fabrics. Comparison of the simulations and actual ballistic tests showed that predictions of the energy absorbed by the fabric were in good agreement with the experiments.     

黄麻纤维束力学性能的尺寸和应变率效应

为了探究黄麻纤维束的尺寸效应和应变率敏感性,利用C43电子式万能试验机和CEAST 9340落锤试验冲击系统分别在静动载条件下对黄麻纤维束进行测试,获得了杨氏模量、强度、峰值应变和韧性随标距和应变率的变化关系静载试验在1/600s-1应变率条件下进行,测试了6组不同标距(25、50、100、150、200和300mm)的试件;动载试验以应变率为变量,在4组不同的应变率(40、80、120和160s-1)条件下进行了测试,试件标距均为25mm。测试结果表明:随着试件标距增大,杨氏模量初始增大,当标距大于100mm时趋于稳定;强度、峰值应变和韧性均减小。随着应变率增大,杨氏模量和强度均增大;峰值应变初始减小后趋于稳定;韧性先减小后增大。鉴于植物纤维束材料较大的性能离散性,采用Weibull分布对试验数据进行拟合,获得了黄麻纤维束强度在不同试验条件(标距和应变率)下的分布规律。     

A statistical model and experimental study of the strain rate and temperature dependence of the strength of fibers

This paper proposes a statistical model for strain rate and temperature dependent fiber strength. The dependence of the parameters of the model on the mechanical quantities of fiber bundles under tensile impact at different temperatures is established. Test results have been performed on E-glass bundles, and these are discussed. They are in good correlation with the model. Hence, the model is reliable and the test method is feasible.     

304不锈钢箔材在不同应变速率下的拉伸性能研究

304不锈钢是一种常用的奥氏体不锈钢.在拉伸应变过程中,应变速率的变化会诱发马氏体转变量和转变速率,以及内部组织滑移线、位错、层错、形变孪晶密度的转变量和转变速率的不同,从而表现出不同的应变硬化行为.本文针对0.1 mm厚度304奥氏体不锈钢箔材,从断后伸长率,断面收缩率,屈服强度,抗拉强度及硬化指数5个方面,研究了室温条件下不同应变速率对其拉伸性能的影响.实验结果表明：马氏体转变理论同样适用于304奥氏体不锈钢箔材, 且0.1 mm厚度304不锈钢存在“越薄越脆,越小越强”的尺寸效应现象;同时,0.1 mm厚度304奥氏体不锈钢箔材拉伸力学性能随应变速率的变化主要表现在以下几方面：断后延伸率和断面收缩率均随着应变速率的增加而降低;低应变速率时,随着应变速率的增加屈服强度增大,而抗拉强度随应变速率的提高呈现减弱的相反规律;高应变速率下,304奥氏体不锈钢的强度主要由材料本身性能决定,应变速率的改变对强度的影响较小;准静态低应变速率下,硬化指数随应变速率增大而升高,较高应变速率下,硬化指数与应变速率变化无关.     

Tensile Behaviour and Strength Distribution of Polyvinyl-Alcohol Fibre at High Strain Rates

Mechanical properties of Polyvinyl-alcohol (PVA) fibre bundles were studied at three high strain rates (270/s, 600/s and 1500/s). It was found that, except for the elastic modulus, which remains unchanged, both the maximum stress and the failure strain show an apparent increase with strain rate. Two failure modes of PVA fibre under tensile impact were observed. A four-parameter Weibull function was adopted to describe the strength distribution of PVA fibre and the Weibull parameters were obtained by a fibre bundle testing method. Consistency between simulated and experimental results indicates that such a function and the method are valid and reliable.     

不同应变率下Kevlar49纤维束拉伸力学性能的实验研究

利用M TS810材料试验机及旋转盘式杆杆型冲击拉伸试验装置对Kevlar49纤维束进行了准静态拉伸及冲击拉伸实验研究, 首次在应变率为10-4/ s～ 103/s 范围内得到了Kevlar49纤维束完整的应力应变曲线。实验结果表明, Kevlar49纤维束的力学性能是与应变率相关的。在低应变率下Kevlar49纤维束对应变率不太敏感, 但比玻璃纤维束高; 在高应变率下Kevlar49纤维束对应变率敏感, 但不如玻璃纤维束强烈; 中应变率区是Kevlar49纤维束由应变率不太敏感到应变率敏感的过渡区。      

Statistical fracture of E-glass fibres using a bundle tensile test and acoustic emission monitoring

Mechanical strength studies have been carried out on fibre bundles used in composite manufacturing. The variability in mechanical properties of glass fibres has been studied using bundles of about 2000 filaments. The fibre strength distributions were analysed using the survival probability-applied strain (S–ε) curve, in relation with various experimental conditions. We also examine the effect of lubricant’s viscosity on the fracture behaviour of E-glass fibre bundles. Acoustic emission (AE) was monitored during the bundle tensile tests in order to verify that individual filament failures are statistically independent. On tensile tests with lubricated bundles of E-glass fibres, it is shown that each individual fibre break can be detected using AE. Hence, AE monitoring of a lubricated bundle of E-glass fibres provides a convenient and relatively quick method to obtain the Weibull parameters of strength distribution.     

The Experimental Study of the Strain-Rate Dependence of a Unidirectional Reinforced Gr/Al Metal Matrix Composite

Loading and loading-unloading tests of a unidirectional reinforced Gr/Al metal matrix composite have been carried out using a self-designed tensile impact apparatus, and quasi-static tensile tests have been performed on the Shimadzu-5000 testing apparatus. The stress/strain curves of composites have been obtained in strain rate range from 0. 0005 s^{– 1} to 1300 s^–1. The experimental results show that complete stress/strain curves of the material can be divided into two parts: the nonlinear elastic brittle deformation and residual deformation. The tests results also clearly indicate that the Gr/Al composite is a rate-sensitive material; namely the strength, failure strain and residual strength of composite all depend on strain rate. Statistical analysis and models were used to obtain the mechanical parameters for composites and their relationship with strain rate from experimental results. The simulated stress/strain curves from the model are in good agreement with the test data. The theoretical model and test results show that the shape parameter and the scale parameter ₀ are both independent of strain rate. The constituent, Gr fibers in Gr/Al composites, can be regarded as a rate-insensitive material, and the strain rate effect of Gr/Al composites is mainly caused by the Al alloy matrix.     

Understanding physical changes and strength loss of E-glass fibres following exposure to elevated temperatures

The strength loss of glass fibres (GFs) following exposure to elevated temperatures is a long-established phenomenon, yet the mechanism or mechanisms responsible for the strength decrease are not fully understood, aside from acknowledgement that surface flaws must become more severe by some means. As disposal of GF-based composite materials by landfill has become untenable in many regions, interest in composite recyclability has increased. Separation of GFs from thermosetting polymers generally requires the use of high temperatures, which produces very weak fibres with minimal commercial value. In this context, an understanding of the strength loss mechanisms is of importance in terms of efforts to mitigate fibre damage or to recover the strength of previously heated fibres. In addition to fibre strength loss, numerous other physical and chemical changes to heat treated or recycled GF have been described in the literature.

This review was chosen as a runner up of the 2016 Materials Literature Review Prize of the Institute of Materials, Minerals and Mining, run by the Editorial Board of MST. Sponsorship of the prize by TWI Ltd is gratefully acknowledged.     

Fracture strength testing of δ-alumina fibres with variable diameters and lengths

Tensile tests were performed on individual δ-alumina fibres (Saffil, RF grade). The results revealed a large scatter in strengths and a clear dependence of the fracture strength on the specimen volume. The tests were evaluated on the basis of the Weibull probability function, a special modification of the Weibull analysis being developed that successfully copes with the problem of testing fibres with various diameters and test lengths. For the sample studied the Weibull modulus, m, was found to be 2·2, with a scaling constant δ₀ = 6·0 MPa (units of volume mm³; i.e. V₀ = 1 mm³).     

标距和应变率对Kevlar49单束拉伸力学性能的影响

为探究Kevlar 49单束的尺寸效应及应变率敏感性, 首先, 利用MTS万能试验机对不同标距(25、50、100、150、200和300 mm)的Kevlar 49单束进行了准静态(应变率为1/600 s-1)拉伸测试; 然后, 利用Instron落锤冲击系统对标距为25 mm的试样进行了动态(应变率为40~160 s-1)拉伸测试; 最后, 利用Weibull模型进行统计分析, 量化了不同标距和应变率下Kevlar 49单束拉伸强度的随机变化程度。结果表明: Kevlar 49单束的拉伸力学性能与标距和应变率有相关性; 拉伸强度随标距的增加而减小, 但随应变率的增加而增大; 峰值应变和韧性均随标距和应变率的增加而减小; 提取的Weibull参数可用于数值模拟及工程应用。      

Effect of cooling rate on the high strain rate properties of boron steel

In this work, the effect of cooling rate on the high strain rate behavior of hardened boron steel was investigated. A furnace was used to austenize boron sheet metal blanks which were then quenched in various media. The four measured cooling rates during the solid state transformation were: 25 (compressed air quench), 45 (compressed air quench), 250 (oil quench) and 2200 °C/s (water quench). Micro-hardness measurements and optical microscopy verified the expected as-quenched microstructure for the various cooling rates. Miniature dog-bone specimens were machined from the quenched blanks and tested in tension at a quasi-static rate, 0.003 s⁻¹ (Instron) and a high rate, 960 s⁻¹ (split Hopkinson tensile bar). The resulting stress vs. strain curves showed that the UTS increased from 1270 MPa to 1430 MPa as strain rate increased for the specimens cooled at 25 °C/s, while the UTS increased from 1615 MPa to 1635 MPa for the specimens cooled at 2200 °C/s. The high rate tests showed increased ductility for the 25, 45 and 250 °C/s specimens, while the specimens cooled at 2200 °C/s showed a slight decrease. The Hollomon hardening curve was fit to the true stress vs. true strain curves and showed that the mechanical response of the high rate tests exhibited a greater rate of hardening prior to fracture than the quasi-static tests. The hardening rate also increased for the specimens quenched at higher cooling rates. Optical micrographs of the fractured specimens showed that the failure mechanism transformed from a ductile-shear mode at the lower cooling rates to a shear mode at the high cooling rates.     

Investigation of the strength of surface-treated carbon fibres embedded in resin, by means of model composite tests

The strength of single fibres of carbon embedded in epoxy resin has been estimated by continuous monitoring of fragmentation tests on single embedded fibres. These fibres had previously been treated to enhance their adhesion to the resin, and the effect of this treatment on the fibre strength is studied. The data generated have been analysed by using an adapted Weibull model which includes the influence of the ‘ineffective’ length at each fibre break. Weibull parameters determined from this analysis have been compared with those from tests carried out on fibres in free air. Similar Weibull moduli are obtained and, although absolute values of strength differ, similar trends are observed and a peak in strength is observed at an intermediate level of treatment in both sets of results.     

Statistics of single‐fibre tensile strength incorporating spatial distribution of microcracks

The random distribution of single‐fibre tensile strength has been commonly characterized by the two‐parameter Weibull statistics. However, the calibrated Weibull model from one set of strength data at a given gauge length cannot accurately predicts the strength variation of the fibre at different gauge lengths. Instead of presuming the two‐parameter Weibull distribution or any other specific statistical distribution for the single‐fibre strength to begin with, this work proposes an approach to incorporating the appropriate spatial flaw distribution within a fibre and synchronizing multiple sets of tensile strength data to evaluate the single‐fibre strength distribution. The approach is examined and validated by published single‐fibre strength data sets of glass, ceramic and synthetic and natural carbon fibres. It is shown that the single‐fibre strength statistics does not necessarily always follow the two‐parameter Weibull distribution.     

The static and high strain rate behaviour of a commingled E-glass/polypropylene woven fabric composite

In this paper the effect of strain rate on the tensile, shear and compression behaviour of a commingled E-glass/polypropylene woven fabric composite over a strain rate range of 10⁻³–10² s⁻¹ is reported. The quasi-static tests were conducted on an electro-mechanical universal test machine and a modified instrumented falling weight drop tower was used for high strain rate characterisation. The tensile and compression modulus and strength increased with increasing strain rate. However, the shear modulus and strength were seen to decrease with increasing strain rate. Strain rate constants for use in finite element analyses are derived from the data. The observed failure mechanisms deduced from a microscopic study of the fractured specimens are presented.     

Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: Part 3. Strength and strain at failure

In this report we present the results from the third part of a study on the influence of fibre length (0.1–50 mm) and concentration (3–60% w/w) on the properties of glass fibre-reinforced polypropylene laminates. These laminates were prepared in the laboratory using a wet deposition method and compared with samples prepared on a commercial melt impregnation GMT line. We found that laminate tensile strength increased linearly with fibre concentration up to 60% w/w. Laminate strength was also found to increase with increasing fibre length. At high values of fibre length (> 3–6 mm) the strength reached a plateau level which was directly dependent on fibre content. The matrix molecular weight appeared to have little direct influence on the level of laminate strength. However, the glass fibre sizing compatibility was found to have a strong effect on the tensile strength of both laboratory made wet deposited laminates and commercially prepared GMTs. The tensile strength of the GMT samples also showed a clear correlation with the measured fibre strength. A modified version of the Kelly-Tyson model gave calculated values of laminate strength which correlated well with the experimental data. We propose that the tensile strength of these laminates is governed by the properties of the fibres which have an orientation close to parallel with the loading direction.     

Experimental Characterisation of Aluminium 6082 at Varying Temperature and Strain Rate

Abstract: This article describes the experimental methodology used in overcoming the challenges of performing tests and recording results on specimens, which are suitable for such a wide range of test conditions. Uniaxial tensile tests were conducted on aluminium alloy 6082‐T352 at varying temperatures and strain rates to validate testing techniques and to determine the effect of these parameters upon this material. The applied strain rate varied over several orders of magnitude – using a screw‐driven tensometer for quasi‐static loading (6.9 × 10^?4 s^?1), a hydraulic piston rig for moderate strain rate (4.0 × 10¹ s^?1) and a tensile Hopkinson bar for high strain rate (1.5 × 10³ s^?1). Temperature was varied using a heat gun, and the air temperature was measured using a thermocouple in the hot air stream. Specimen temperature is determined by finite element modelling, and this correlates well with other work. Although it would have been possible to improve the design of individual tests for specific test conditions, an important objective was to conduct the entire series of tests in as consistent a manner as possible. The procedure for characterising the stress–strain behaviour for this material under these different loading conditions is also considered in some detail, as the real material behaviour deviates from simplified elasto‐plastic material models. Results presented for Al 6082 samples show a slight increase in yield stress with increasing strain rate, and a decrease in yield stress with increasing temperature.