Modeling and testing strain rate-dependent compressive strength of carbon/epoxy composites

A technique for testing high modulus fiber-reinforced composites in compression at different strain rates is investigated. The rate-dependent compressive behavior of unidirectional AS4/3501-6 carbon/epoxy composite is characterized by using off-axis specimens. It is found that, in the compression test, a titanium coating applied at the contact ends of the off-axis specimen can greatly reduce contact frictions, allowing a fully developed extension–shear coupling so that a state of uniform stress in the specimen can be achieved. A rate-dependent nonlinear constitutive model and a dynamic compressive strength model (fiber microbuckling model) for the unidirectional AS4/3501-6 composite are established based on the low strain rate off-axis test data. Model predictions and experimental data including high strain rate data are in very good agreement indicating that the constitutive model and compressive strength model obtained with low strain rate data are valid for high strain rates as well. A technique is also developed to extract the longitudinal compressive strength of the composite from those of the off-axis specimens.     

Mechanical behaviour of carbon and glass hybrid fibre reinforced polyester composites

Mechanical behaviour of carbon fibre/glass mat/polyester resin hybrid composites of sandwich construction is studied through tension, flexure, impact and post-impact tension tests. Tensile and flexural strength, modulus and failure strain values are compared to the calculated values. Total impact fracture energy and residual (after impact) tensile strength values of hybrid composites are analysed with regard to corresponding values of carbon/polyester composites. Failure of tested coupons was analysed by visual inspection and observation by scanning electron microscopy.     

Dynamic compression of cellular cores: temperature and strain rate effects

Cross-linked polyvinyl chloride closed-cell foams were examined under quasi-static and high strain rate compression loading using a servo-hydraulic testing machine and a modified split Hopkinson pressure bar apparatus consisting of polycarbonate bars for strain rates up to 1900 s⁻¹. Three foam densities were examined viz. 75, 130, and 300 kg/m³. Each core density has been subjected to compressive loading at room and elevated temperatures. A reverse trend in failure modes was observed when moving from room to elevated temperatures at high strain loading, which was not found in quasi-static testing at elevated temperatures. Accordingly, post-impact tests were conducted to evaluate the residual strength of the foam cores subject to elevated temperatures and HSR. Results of the post-impact test revealed that the foam cores are still capable of taking some loading. The residual strength of cores was fairly constant regardless of temperature therefore recovery of volume does not signify an increase in residual strength of cores.     

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.     

Using split Hopkinson pressure bars to perform large strain compression tests on polyurea at low,intermediate and high strain rates

The strain rate sensitivity of polyurea is characterized using a modified split Hopkinson pressure bar (SHPB) system. The device is composed of a hydraulic piston along with nylon input and output bars. In combination with an advanced wave deconvolution method, the modified SHPB system provides an unlimited measurement time and thus can be used to perform experiments at low, intermediate and high strain rates. A series of compression tests of polyurea is performed using the modified SHPB system. In addition, conventional SHPB systems as well as a universal hydraulic testing machine are employed to confirm the validity of the modified SHBP technique at low and high strain rates. The analysis of the data at intermediate strain rates shows that the strain rate is not constant due to multiple wave reflections within the input and output bars. It is demonstrated that intermediate strain rate SHPB experiments require either very long bars (>20 m) or very short bars (<0.5 m) in order to achieve an approximately constant strain rate throughout the entire experiment.     

Tension behavior of unidirectional glass/epoxy composites under different strain rates

By considering wide applications of composite materials, having a proper knowledge of them under dynamic loading is necessary. In order to study the effects of strain rates on the behavior of the materials, special testing machines are needed. Most of the research in this field is focused on applying real loading and gripping boundary conditions on the testing specimens. In this study, behavior of unidirectional glass fiber reinforced polymeric composites under uni-axial loading is determined at quasi-static and intermediate strain rates of 0.001–100 s⁻¹. The tests were performed using a servo-hydraulic testing apparatus equipped with a strain rate increase mechanism. For performing the tests, a jig and a fixture are designed and manufactured. The performance of the test jig was evaluated and found to be adequate for testing of composites. Dynamic tests results are compared with the results of static tensile tests carried out on specimens with identical geometry. Experimental results show a significant increase of the tensile strength by increasing the strain rate. The tensile modulus and strain to failure are also observed to increase slightly by increasing the strain rate.     

Effects of strain rates on dynamic deformation behavior of Cu-20Ag alloy

Copper alloy is widely used in high-speed railway,aerospace and other fields due to its excellent electri-cal conductivity and mechanical properties.High speed deformation and dynamic loading under impact load is a complex service condition,which widely exists in the field of national defense,military and industrial application.Therefore,the dynamic deformation behavior of the Cu-20Ag alloy was inves-tigated by Split Hopkinson Pressure Bar (SHPB) with the strain rates of 1000-25000 s-1,high-speed hydraulic servo material testing machine with the strain rates of 1-500 s-1.The effect of strain rate on flow stress and adiabatic shear sensitivity was analyzed.The results show that the increase of strain rate will increase the flow stress and critical strain,that is to say,the increase of strain rate will reduce the adiabatic shear sensitivity of the Cu-20Ag alloy.The Cu-Ag interface has obvious orientation relationship with (111)Cu//(111)Ag;((1)11)Cu//((1)11)Ag;((2)00) Cu//((2)00)Ag and[0(1)1]Cu//[0(1)1]Ag with the increase of strain rate.The increase of strain rate promotes the precipitation of Ag and increases the number of interfaces in the microstructure,which hinders the movement of dislocations and improves the stress and yield strength of the Cu-20Ag alloy.The concentration and distribution density of dislocations and the precipitation of Ag were the main reasons improve the flow stress and yield strength of the Cu-20Ag alloy.     

Fatigue behaviour of continuous glass fibre reinforced composites

A study has been undertaken of fatigue in glass fibre reinforced composites. Two matrix resins were tested: a standard polyester and a polyurethane-vinyl-ester, which was designed to have a higher toughness. Three different types of glass fibre fabrics were used for reinforcement: a conventional woven roving and two stitch-bonded cloths. The glass cloths were combined into various lay-ups, in order to consider the effects of matrix, cloth and lay-up on the fatigue strength. Additionally, a study was undertaken to evaluate the micromechanisms that occurred during fatigue and how damage accumulated throughout the sample lifetime. This involved measuring stiffness changes during fatigue cycling, followed by microscopic study of the samples. It was found that similar damage micromechanisms occurred in each lay-up regardless of resin and cloth type, and these included matrix cracking, delamination and fibre breakage. However, differences were observed in the extent, location and rate of damage, and these were consistent with the variations seen in the fatigue strengths.     

The compressive behavior of isocyanate-crosslinked silica aerogel at high strain rates

Aerogels are low-density, highly nano-porous materials. Their engineering applications are limited due to their brittleness and hydrophilicity. Recently, a strong lightweight crosslinked silica aerogel has been developed by encapsulating the skeletal framework of amine-modified silica aerogels with polyureas derived by isocyanate. The mesoporous structure of the underlying silica framework is preserved through conformal polymer coating, and the thermal conductivity remains low. Characterization has been conducted on the thermal, physical properties and the mechanical properties under quasi-static loading conditions. In this paper, we present results on the dynamic compressive behavior of the crosslinked silica aerogel (CSA) using a split Hopkinson pressure bar (SHPB). A new tubing pulse shaper was employed to help reach the dynamic stress equilibrium and constant strain rate. The stress-strain relationship was determined at high strain rates within 114–4386 s⁻¹. The effects of strain rate, density, specimen thickness and water absorption on the dynamic behavior of the CSA were investigated through a series of dynamic experiments. The Young’s moduli (or 0.2% offset compressive yield strengths) at a strain rate ∼350 s⁻¹ were determined as 10.96/2.08, 159.5/6.75, 192.2/7.68, 304.6/11.46, 407.0/20.91 and 640.5/30.47 MPa for CSA with densities 0.205, 0.454, 0.492, 0.551, 0.628 and 0.731 g cm⁻³, respectively. The deformation and failure behaviors of a native silica aerogel with density (0.472 g cm⁻³), approximately the same as a typical CSA sample were observed with a high speed digital camera. Digital image correlation technique was used to determine the surface strains through a series of images acquired using high speed photography. The relative uniform axial deformation indicated that localized compaction did not occur at a compressive strain level of ∼17%, suggesting most likely failure mechanism at high strain rate to be different from that under quasi-static loading condition. The Poisson’s ratio was determined to be 0.162 in nonlinear regime under high strain rates. CSA samples failed generally by splitting, but were much more ductile than native silica aerogels.     

Mechanical properties of ceramic fiber-reinforced concrete under quasi-static and dynamic compression

The research herein is made on the quasi-static and dynamic mechanical properties of ceramic fiber reinforced concrete (CRFRC for short) through the adoption of a hydraulically-driven testing system as well as a 100-mm-diameter split Hopkinson pressure bar (SHPB) system. As test results have turned out, such quasi-static properties as compressive strength, splitting tensile strength and flexural strength of CRFRC increase with the rise in the volume fraction of fiber. Within the strain range of 20–120 s⁻¹, the effect of the axial strain acceleration on the dynamic strength of CRFRC could be ignored. Therefore, the dynamic increase ratio (DIF) derived from SHPB tests can truly reflect the dynamic enhancement of CRFRC. The dynamic strength, critical strain and specific energy absorption (SEA) of CRFRC are sensitive to the strain rate. The addition of ceramic fiber to plain concrete can significantly improve its properties—dynamic strength, critical strain and energy absorption. And also, an analysis is conducted of the mechanism for strengthening and toughening the concrete.     

Strain rate effects on the compressive property and the energy-absorbing capacity of aluminum alloy foams

The strain rate sensitivity of various relative densities, open-cell aluminum alloy foams fabricated by a powder metallurgical method is investigated under compression loading. Their response to strain rate has been tested over a wide range of strain rates, from 10⁻³ to 2600 s⁻¹ at room temperature. Within this range, the experimental results show that the yield strength and the energy absorbed increase with an increase of strain rate. However, the yield strength of higher relative density foams increases bilinearly with the logarithm of strain rate, and the yield strength of lower relative density foams shows only a linear increase. The compaction strain slightly decreases with an increase of strain rate. The higher relative density aluminum alloy foams are more sensitive to strain rate than the lower relative density foams.     

Compressive response of glass–fiber reinforced polymeric composites to increasing compressive strain rates

The utilization of composite materials instead of traditional materials in structural high-speed applications has induced the need for a proper knowledge of dynamic behavior as well as static behavior of them. The material and structural response vary significantly under dynamic loading as compared to static loading conditions. In order to investigate the dynamic responses of composite materials under dynamic loading at various strain rates, special testing machines are needed. Most of the researches in this field are focused on applying real loading and gripping boundary conditions on the testing specimens.The present study is carried out in order to characterize the compressive properties of unidirectional glass–fiber reinforced polymeric composites using a servo-hydraulic testing apparatus at varying strain rates, ranging from 0.001 to 100 s⁻¹. For performing practical tests, a jig and a fixture are designed and manufactured, which could insure the alignment of axial loads on the specimens. During of tests, the performance of the test jig is evaluated. It is found that the designed jig and the fixture perform very well during the test process. The results of the dynamic tests are compared with the results of the static tests carried out on specimens with identical geometry. Based on the experimental results obtained from the tests, empirical functions for the mechanical properties are proposed in terms of strain rates. The results of the study indicate that strain rate has a significant effect on the material response. It is found that the compressive strength and modulus both increased with increasing the strain rate. Also, the results show that the compressive strain to failure is generally insensitive to strain rate.     

Tensile behavior of carbon fiber bundles at different strain rates

Quasi-static and high strain rate tensile tests have been performed on T700 carbon fiber bundles and complete stress-strain curves at the strain rate range of 0.001 s^− 1 to 1300 s^− 1 were obtained. Results show that strain rate has negligible effect on both ultimate strength and failure strain, and T700 carbon fiber can be regarded as strain rate insensitive materials. On the basis of the fiber bundles model and the statistic theory of fiber strength, a damage constitutive model based on Weibull distribution function has been developed to describe tensile behavior of T700 fiber bundles. And the method to determine the statistic parameters of fibers by tensile tests of fiber bundles is established, too.     

Dynamic mixed-mode I/II delamination fracture and energy release rate of unidirectional graphite/epoxy composites

Mixed-mode open-notch flexure (MONF), anti-symmetric loaded end-notched flexure (MENF) and center-notched flexure (MCNF) specimens were used to investigate dynamic mixed I/II mode delamination fracture using a fracturing split Hopkinson pressure bar (F-SHPB). An expression for dynamic energy release rate G_d is formulated and evaluated. The experimental results show that dynamic delamination increases linearly with mode mixing. At low input energy E_i ? 4.0 J, the dynamic (G_d) and total (G_T) energy rates are independent of mixed-mode ratio. At higher impact energy of 4.0 ? E_i ? 9.3 J, G_d decreases slowly with mixed I/II mode ratio while G_T is observed to increase more rapidly. In general, G_d increases more rapidly with increasing delamination than with increasing energy absorbed. The results show that for the impact energy of 9.3 J before fragmentation of the plate, the effect of kinetic energy is not significant and should be neglected. For the same energy-absorption level, the delamination is greatest at low mixed-mode ratios corresponding to highest Mode II contribution. The results of energy release rates from MONF were compared with mixed-mode bending (MMB) formulation and show some agreement in Mode II but differences in prediction for Mode I. Hackle (Mode II) features on SEM photographs decrease as the impact energy is increased but increase as the Mode I/II ratio decreases. For the same loading conditions, more pure Mode II features are generated on the MCNF specimen fractured surfaces than the MENF and MONF specimens.     

Compressive behavior of closed-cell aluminum alloy foams at medium strain rates

Compressive behavior of closed-cell aluminum alloy foams at strain rates of 10⁻³-450 s⁻¹ has been studied experimentally. The fully stress-strain curves of specimens at medium strain rates were obtained using the High Rate Instron Test System, which can maintain a constant loading rate. The experimental results show that plateau stress and energy absorption capacity are remarkable dependent on strain rate, while the densification strain has a negligible dependence.     

A modified servo-hydraulic machine for testing at intermediate strain rates

Assessing the mechanical properties of materials at intermediate strain rates (1–200/s) is one of the major concerns in impact engineering. Servo-hydraulic machines are usually used at this range of strain rates. However, detrimental oscillations appear on the measured load for strain rates above 10/s. In this paper, we present a modified servo-hydraulic machine. The load is measured by a Hopkinson bar-like technique. Besides, the BCGO wave separation method is used to overcome the limited test duration problem. Moreover, the strain in the sample is measured using Digital Speckle Photographs (DSP) which is captured via high-speed video camera. This modified machine is an equivalent and alternative solution to the slow bar technique. It is applied to aluminium 2017 T4 alloy at strain rates of approximately 100/s. Compared to the piezoelectric force sensor, the Hopkinson bar-like method gives less-oscillating signals. The sample attaching device is also taken into account. It is considered as a rigid mass. This simple assumption is valid up to strain rates of some hundreds per second.     

High strain rate effects on direct tensile behavior of high performance fiber reinforced cementitious composites

Direct tensile behavior of high performance fiber reinforced cementitious composites (HPFRCCs) at high strain rates between 10 s⁻¹ and 30 s⁻¹ was investigated using strain energy frame impact machine (SEFIM) built by authors. Six series of HPFRCC combining three variables including two types of fiber, hooked (H) and twisted (T) steel fiber, two fiber volume contents, 1% and 1.5%, and two matrix strengths, 56 MPa and 81 MPa, were investigated. The influence of these three variables on the high strain rate effects on the direct tensile behavior of HPFRCCs was analyzed based on the test results. All series of HPFRCCs showed strongly sensitive tensile behavior at high strain rates, i.e., much higher post cracking strength, strain capacity, and energy absorption capacity at high strain rates than at static rate. However, the enhancement was different according to the types of fiber, fiber volume content and matrix strength: HPFRCCs with T-fibers produced higher impact resistance than those with H-fibers; and matrix strength was more influential, than fiber contents, for the high strain rate sensitivity. In addition, an attempt to predict the dynamic increase factor (DIF) of post cracking strength for HPFRCCs considering the influences of fiber type and matrix strength was made.     

E玻璃纤维增强环氧树脂基复合材料轴向拉伸力学性能的应变率效应

采用MTS-810材料试验机、Zwick-HTM5020高速拉伸试验机及分离式Hopkinson拉杆（SHTB）实验装置,并结合数字图像相关性（Digital image correlation,DIC）分析方法,对E玻璃纤维增强环氧树脂基复合材料棒材在10^-3~2 400 s^-1应变率范围内的轴向拉伸力学性能进行了较系统的实验研究,获得了不同应变率下材料的应力-应变曲线,揭示了应变率对材料的拉伸强度和断裂应变的影响规律。通过显微分析拉伸试样的断口形貌,揭示了试样的断裂机制及对应变率的依赖性。实验结果表明：E玻璃纤维增强环氧树脂基复合材料的力学性能具有强烈的应变率效应,归一化拉伸强度随着应变率对数线性增加,而归一化断裂应变则随着对数应变率线性减小;断口显微分析显示：E玻璃纤维增强环氧树脂基复合材料的轴向拉伸断裂模式依赖于应变率,低应变率加载下试样发生沿45°方向的剪切断裂,随着应变率增大,试样断裂模式逐渐过渡到沿轴向的拉伸断裂,特别是在高应变加载下,观察到大量的玻璃纤维丝被拉断,同时环氧树脂基体也发生严重的碎裂现象,这反映了基体材料与玻璃纤维之间相互约束作用在增强。     

Optimal design for the flexural behaviour of glass and carbon fibre reinforced polymer hybrid composites

A study on the flexural behaviour of hybrid composites reinforced by S-2 glass and T700S carbon fibres in an intra-ply configuration is presented in this paper. The three point bend test in accordance with ASTM D790-07 at various span-to-depth ratios was simulated using finite element analysis (FEA). For the purpose of validation, specimens of selected stacking configurations were manufactured following the hand lay-up process and tested in a three point bend configuration. The validated FEA model was used to study the effects of fibre volume fractions, hybrid ratio and span-to-depth ratio. It is shown that flexural modulus increases when the span-to-depth ratio increases from 16 to 32 but is approximately constant as the span-to-depth ratio further increases. A simple mathematical formula was developed for calculating the flexural modulus of hybrid composites, given the moduli of full carbon and full glass composites, and the hybrid ratio. Flexural strength increases with span-to-depth ratio. Utilisation of hybridisation can improve the flexural strength. A general rule is in order to improve flexural strength, the fibre volume fraction of glass/epoxy plies needs to be higher than that of carbon/epoxy plies. The overall maximum hybrid effect is achieved when the hybrid ratio is 0.125 ([0_G/0_7C]) when both V_fc and V_fg are 50%. The strength increases are 43.46% and 85.57% when compared with those of the full carbon and glass configurations respectively. The optimisation shows that the maximum hybrid effect is 56.1% when V_fc = 47.48% and V_fg = 63.29%.