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.     

Influence of stress triaxiality and strain rate on the failure behavior of a dual-phase DP780 steel

To better understand the in-service mechanical behavior of advanced high-strength steels, the influence of stress triaxiality and strain rate on the failure behavior of a dual-phase (DP) 780 steel sheet was investigated. Three flat, notched mini-tensile geometries with varying notch severities and initial stress triaxialities of 0.36, 0.45, and 0.74 were considered in the experiments. Miniature specimens were adopted to facilitate high strain rate testing in addition to quasi-static experiments. Tensile tests were conducted at strain rates of 0.001, 0.01, 0.1, 1, 10, and 100 s⁻¹ for all three notched geometries and compared to mini-tensile uniaxial samples. Additional tests at a strain rate of 1500 s⁻¹ were performed using a tensile split Hopkinson bar apparatus. The results showed that the stress–strain response of the DP780 steel exhibited mainly positive strain rate sensitivity for all geometries, with mild negative strain rate sensitivity up to 0.1 s⁻¹ for the uniaxial specimens. The strain at failure was observed to decrease with strain rate at low strain rates of 0.001–0.1 s⁻¹; however, it increased by 26% for an increase in strain rate from 0.1 to 1500 s⁻¹ for the uniaxial condition. Initial triaxiality was found to have a significant negative impact on true failure strain with a decrease of 32% at the highest triaxiality compared to the uniaxial condition at a strain rate of 0.001 s⁻¹. High resolution scanning electron microscopy images of the failure surfaces revealed a dimpled surface while optical micrographs revealed shearing through the thickness indicating failure occurred via ductile-shear. Finite element simulations of the tests were used to predict the effective plastic strain versus triaxiality history within the deforming specimens. These predictions were combined with the measured conditions at the onset of failure in order to construct limit strain versus triaxiality failure criteria.     

An experimental method for dynamic tensile testing of concrete by spalling

A new application of the spalling phenomenon in long specimens is reported in this paper. The new experimental technique is based on an experimental setup which consists of an air launcher of cylindrical projectiles with a Hopkinson bar as a measuring tool and a relatively long concrete specimen in contact with the bar. The incident compression wave transmitted by the Hopkinson bar into the specimen is reflected as a tensile wave causing spalling. Although such configurations have been reported in the past, the main advantage of the present approach lies in the application of the detailed analysis, based on the wave mechanics with dispersion, to extract the specimen behaviour. Such an approach leads to an exact estimation of the local failure stress in tension at high strain rates, even above 100 s⁻¹. This paper demonstrates, using two series of tests on concrete, that this experimental setup can cover one decimal order of strain rates, from ∼10 to ∼120 s⁻¹. The tests performed at high strain rates on wet and dry concrete have indicated that the tensile strength is substantially influenced by the loading rate or strain rate. The absolute value of the failure stress for wet and dry concrete is almost the same for a particular strain rate, which does not occur when subject to low strain rates in tension or compression. A brief discussion is offered on a high rate sensitivity of concrete strength in tension at high strain rates.     

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.     

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.     

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.     

Study on mechanical properties and constitutive model of 5052 aluminium alloy

The stress–strain relationship of 5052 aluminium alloy was investigated via quasi-static tensile tests and split Hopkinson pressure bar tests. The specimens were exposed to various temperatures (25–500°C) and strain rates (10^?4–0.7?×?10^4?s^?1). At strain rates ranging from 0.001 to 3000?s^?1, the material underwent significant work hardening. When the strain rate exceeded 5000?s^?1, the work hardening effect decreased and the flow stress was relatively constant. The Johnson–Cook constitutive model was modified to describe the deformation behaviour of the material subjected to high temperatures and strain rates. The accuracy of the modified model was verified through ballistic impact testing.     

Effects of strain rate on mechanical properties and failure mechanism of structural Al–Mg alloys

The effects of strain rate on the mechanical properties and failure mechanism of AA5754 and AA5182 sheets were investigated. Tensile tests were conducted at quasi-static (less than 10⁻¹ s⁻¹) and dynamic (600, 1100 and 1500 s⁻¹) strain rates at room and elevated temperature using an INSTRON machine and Tensile Split Hopkinson Bar (TSHB) apparatus, respectively. Shear band decoration, interrupted tensile tests, electron microscopy, and image analysis techniques were also utilized. The results obtained show that the studied alloys exhibit negative strain rate sensitivity at quasi-static rates, but mild positive sensitivity at dynamic rates. Different failure mechanisms were also observed. Strain localization and shear band formation was found to be a necessary pre-requisite for the development of damage and final failure under quasi-static conditions. In the dynamic strain rate regime however, less shear banding was observed. Void nucleation, growth and coalescence that is characteristic of dynamic tensile fracture appears to be the dominant mode for failure under dynamic conditions.     

High strain rate behavior of 4-step 3D braided composites under compressive failure

The out-of-plane and in-plane compressive failure behavior of 4-step 3D braided composite materials was investigated at quasi-static and high strain rates. The out-of-plane and in-plane direction compressive tests at high strain rates from 800/s to 3,500/s were tested with the split Hopkinson pressure bar (SHPB) technique. The quasi-static compressive tests were conducted on a MTS 810.23 tester and compared with those at high strain rates. The comparisons indicate that the failure stress, failure strain and compressive stiffness both for out-of-plane and in-plane loading directions are rate sensitive. For example, the failure stress, failure strain and stiffness are 55.19 MPa, 6.70% and 1.35 GPa respectively as opposed to 145.00 MPa, 1.21% and 13.50 GPa respectively for strain rate of 2,500 s⁻¹ under in-plane compression. The 3D braided composites have higher values of failure stress and strain for out-of-plane than for in-plane compression at the same strain rate; however, the in-plane compression stiffness is higher than that of out-of-plane compression at high strain rates. The compressive failure mode of 3D braided composites in the out-of-plane direction is mainly shear failure at various strain rates, while for the in-plane direction it is mainly cracking of matrix.     

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.     

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.     

On the use of the non direct tensile loading on a classical split Hopkinson bar apparatus dedicated to sheet metal specimen characterisation

The facilities used to determine behaviour laws under dynamic loading are classified into two categories: impulsive and impact loading. For the first category, the properties of the industrial materials and their evolution at moderate strain rates range is generally obtained using split Hopkinson bars devices. Shear, tensile or compression strain modes, observed on crashed frameworks, are then applied on specimens to establish classical plastic stress/strain relations. Tensile testing using a non direct loading configuration raise the problem of the set-up and the holding of sheet specimens on the split Hopkinson bars devices, which generally induces impedance mismatches and perturbs the elastic pulses during their run through the specimen assemblies. This paper presents an original tensile testing configuration required bonded sheet metal specimens on the external part of threaded sleeves. A test programme is carried out on two metallic alloys (XES low carbon steel and 2024 T3 aluminium) at plastic strain rates between 180 and 440 s⁻¹. All results are compared with others experimental raw databases and validate this first stage of tensile loading.     

Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part II: Numerical simulations

Split Hopkinson pressure bar (SHPB) tests have been used widely to measure the dynamic compressive strength of concrete-like materials at high strain-rates between 10¹ and 10³ s⁻¹. It has been shown in companion paper (Zhang M, Wu HJ, Li QM, Huang FL. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests Part I: Experiments. Int J Impact Eng 2009;36(12):1327–1334) that the axial strain acceleration is normally unavoidable in an SHPB test on brittle materials. Axial strain acceleration introduces radial confinement in the SHPB specimens and consequently enhances the compressive strength of concrete-like specimens. This paper employs numerical simulation to further demonstrate that the unexpected radial confinement in an SHPB test is responsible for the increase of the dynamic compressive strength of concrete-like materials at strain-rates from 10¹ to 10³ s⁻¹. It confirms the observations in Zhang et al. (Zhang M, Wu HJ, Li QM, Huang FL. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests Part I: Experiments. Int J Impact Eng 2009;36(12):1327–1334) that the dynamic increase factor (DIF) measured in SHPB tests can be reduced either by using tubular SHPB specimens or by reducing the diameter of the SHPB specimen. A kinetic friction model is proposed based on kinetic friction tests and is implemented in the numerical model. It shows that it is necessary to use a kinetic friction model, rather than a constant friction model, for more accurate numerical simulation of SHPB tests.     

Plastic flow behavior of Inconel 718 under dynamic shear loads

The plastic deformation behavior of nickel–iron alloy Inconel 718 in shear was measured at strain rates of 0.01 s⁻¹ and up to 3000 s⁻¹ with a quasistatic torsion machine and a split torsional Hopkinson bar, respectively. The measurements were analyzed to determine Johnson–Cook parameters and obtain material constitutive information needed for finite element simulations.     

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.     

The mechanical properties of ionoplast interlayer material at high strain rates

Ionoplast material has been recently introduced and extensively used as interlayer material for laminated glass to improve its post-glass breakage behavior. Due to its sound mechanical performance, the applications of laminated glass with ionoplast interlayer have been widely extended to the protection of glass structures against extreme loads such as shock and impact. The properties of this material at high strain rates are therefore needed for properly analysis and design of such structures. In this study, the mechanical properties of ionoplast material are studied experimentally through direct tensile tests over a wide strain rate range. The low-speed tests are performed using a conventional hydraulic machine at strain rates from 0.0056 s⁻¹ to 0.556 s⁻¹. The high strain-rate tests are carried out with a high-speed servo-hydraulic testing machine at strain rates from approximately 10 s⁻¹ to 2000 s⁻¹. It is found that the ionoplast material virtually exhibits elasto-plastic material properties in the strain rate range tested in this study. The testing results show that the material behavior is very strain-rate dependent. The yield strength increases with strain rate, but the material becomes more brittle with the increase in strain rate, with the ultimate strains over 400% under quasi-static loading, and decreasing to less than 200% at strain rate around 2000 s⁻¹. The testing results indicate that simply applying the static material properties in predicting the structure responses of laminated glass with ionoplast interlayer subjected to blast and impact loads will substantially overestimate the ductility of the material and lead to inaccurate predictions of structure response. The testing results obtained in the current study together with available testing data in the literature are summarized and used to formulate the dynamic stress–strain curves of ionoplast material at various strain rates, which can be used in analysis and design of structures with ionoplast material subjected to blast and impact loads.     

An experimental assessment of friction effects in the split Hopkinson pressure bar using the ring compression test

The potential error due to friction in compression split Hopkinson pressure bar (SHPB) tests is assessed and conditions for minimising this error are investigated. Theoretical friction factors are inferred from ring compression tests. Experimental results are reported for mild steel, copper and aluminium ring specimens tested quasi-statically (∼10⁻² s⁻¹), using a servo-hydraulic test machine, and at high strain rates (∼10³ s⁻¹) on a SHPB. Specimens were tested dry, or lubricated using a molybdenum disulphide grease. The influence of surface finish and strain rate on the friction effect is discussed. The inferred friction factors are in the range m=0.08–0.14 (equivalent to Coulomb friction coefficients between μ=0.05 and 0.08). These results imply that the friction error in routine compression SHPB tests of metals lies between 2% and 3%.     

Deformation behaviour of ultrafine grained Mg–7Gd–5Y–1.2Nd–0.5Zr alloy under high strain rates

The mechanical behaviour of Mg–7Gd–5Y–1.2Nd–0.5Zr (wt. %) alloy with ultrafine grains was measured by split Hopkinson pressure bar method under the strain rates of 1000, 1500, and 2000 s^?1 at room temperature. Dynamic tests were carried out along extrusion direction (ED), transverse direction (TD), and normal direction (ND). The results demonstrated that the flow stress increased with the increase of strain rate, showing a positive strain rate strengthening effect. There was no obvious anisotropy in dynamic compression along ED, TD, and ND, which was caused by rare earth elements and multi-pass deformation. This led to the adoption of plastic deformation mode dominated by non-basal slip and participated by tension twinning.     

The modified temperature term on Johnson Cook model for AZ31 magnesium alloy

The quasi‐state and dynamic mechanism of AZ31 magnesium alloy at a strain rates range of 0.001 s^‐1–2500 s^‐1 under a temperature range of 20 °C–250 °C were researched by compression tests using the electronic universal testing machine and split Hopkinson pressure bar system. The true stress‐strain curves at different strain rates and evaluated temperatures were obtained. The result shows that the thermal soften effect of AZ31 magnesium alloy is significant. By modifying the temperature term of the original Johnson Cook model of AZ31 magnesium alloy, a modified Johnson Cook model of AZ31 magnesium alloy has been proposed to reveal thermal soften effect on the deformation behavior of AZ31 magnesium alloy more precisely. With the modified Johnson Cook model and fracture model, the finite element method simulation of AZ31 magnesium alloy hat shaped specimen under impacting was conducted. The numerical simulation result is consistent with the experimental result, which indicates that the modified Johnson Cook model and fracture model are greatly valid to predict the deformation and fracture behavior of the AZ31 magnesium alloy hat shaped specimen under impacting.