Compression Split Hopkinson Pressure Bar Research Articles

Alumina nanoparticle filled epoxy resin: High strain rate compressive behavior

This study demonstrates high strain rate behavior of neat epoxy and epoxy resin reinforced with 2 wt% and 5 wt% alumina nanoparticles. The present study investigates effect of strain rate as well as effect of alumina nanoparticle dispersion on the compressive stress – compressive strain behavior of epoxy resin. Studies were carried out on compressive split Hopkinson pressure bar apparatus in the strain rate range of 700–3200 per sec. Significant enhancement of compressive strength of epoxy resin up to 147% was noted at high strain rate compared with that at quasi‐static loading. The corresponding increase for alumina nanoparticle filled epoxy resin was up to 142%. It was also observed that the compressive strength of epoxy resin increases up to 8.6% with the addition of alumina nanoparticles at a strain rate of 3000 per sec. Synthesis of alumina nanoparticle filled epoxy resin, high strain rate and quasi‐static testing and main findings of the study are presented in this article. POLYM. ENG. SCI., 54:2896–2901, 2014. © 2014 Society of Plastics Engineers

Construction of Johnson-Cook Model for Gr2 Titanium through Adiabatic Heating Calculation

This study derived the five parameters in Johnson-Cook equation of CP titanium Gr2. Quasi-static and dynamic compression tests were designed to measure mechanical properties at strain rates of 10-3s-1 and 6000s-1. In order to secure the validity of tested data, a novel fixture was proposed to reduce the displacement measurement error in MTS testing system and the signal processing procedure of compressive split Hopkinson pressure bar for the present study was demonstrated. With the tested data and calculated adiabatic heating temperature rise, parameters A, B, n, m, C have been derived based on mathematical deduction and solve. It was found that the constructed constitutive model fit the tested data well and was able to restore the yield strength value at high strain rate.

High temperature deformation behaviour of Haynes 188 alloy subjected to high strain rate loading

The high temperature deformation behaviour of Haynes 188 alloy is investigated by means of a compressive split-Hopkinson pressure bar system at temperatures ranging from 25 to 800°C and strain rates in the range of 1×103–5×103s−1. It is found that the stress–strain curves obtained under high temperature conditions exhibit a flow softening effect. The maximum activation energy has a value of 51kJ/mol and occurs at a temperature of 800°C under a true strain of 0.3 and a strain rate of 1×103s−1. The Zerilli–Armstrong fcc model is shown to provide an adequate description of the stress–strain response of the Haynes 188 alloy specimens under the considered strains, strain rates and temperatures. An adiabatic shear band is formed in the specimen tested at room temperature under a strain rate of 5×103s−1. The dislocation density increases with an increasing strain rate or a decreasing temperature and leads to a greater flow stress. A linear correlation is observed between the square root of the dislocation density and the true stress. The dislocation hardening relation has the form σ=σ0+α1Gbρ, where α1 has a value of 0.58 for the present Haynes 188 alloy specimens.

Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.

Dynamic mechanical properties and microstructure of Ti–6Al–7Nb biomedical alloy as function of strain rate

The deformation behaviour and microstructural evolution of Ti–6Al–7Nb biomedical alloy under high strain rate conditions are investigated using a compressive split Hopkinson pressure bar. Dynamic compression tests are performed at room temperature under strain rates ranging from 103 to 3×103 s−1. Experimental results show that the flow stress, workhardening coefficient and strain rate sensitivity of the Ti–6Al–7Nb alloy all increase with increasing strain rate. However, the activation volume decreases with increasing strain and strain rate. Moreover, it is shown that the high strain rate deformation behaviour of the Ti–6Al–7Nb alloy can be adequately described using the combined Johnson–Cook and Zerilli–Armstrong constitutive equation. The undeformed and deformed microstructures of the Ti–6Al–7Nb samples are found to consist of equiaxed primary α phase and transformed β phase. The size and volume fraction of the α phase increase with increasing strain rate. Moreover, the dislocation density also increases with increasing strain rate, thereby resulting in a significant strengthening effect.

Experimental method for dynamic residual strength characterisation of aircraft sandwich structures

This study investigates the effect of dynamic loading on the residual of sandwich structures used in aircraft interiors comprising glass fibre phenolic resin face sheets and Nomex® honeycomb core. A dynamic edgewise compression test method for residual strength testing of sandwich structures has been developed using a modified compressive Split Hopkinson Pressure Bar apparatus. Dynamic edgewise compression at strain rates of approximately 50 s−1 for undamaged specimens showed an average increase of 26% in compression strength compared with equivalent static edgewise compression tests. For low levels of indentation damage there was a 27% reduction in residual dynamic compressive strength compared with a 15% reduction in residual static compressive strength for equivalent prior damage. This new experimental method provides insights into the dynamic edgewise response of composite sandwich structures to aid in the design and development of future aeronautical structures.

An internal state variable material model for predicting the time, thermomechanical, and stress state dependence of amorphous glassy polymers under large deformation

This paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress state dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based internal state variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress state dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress states. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions.

Effect of compressive loading speed and stacking sequence on mechanical characteristics of satin weave E‐glass/epoxy composites

AbstractThis article experimentally investigated the in‐plane loading speed dependent mechanical properties and failure modes of satin weave E‐glass/epoxy composite laminates [45/−45/0/90]ns. Two types of E‐glass fabric/epoxy pre‐impregnated tapes were used to manufacture the composite laminates specimens. The low strain rate tests were conducted with an INSTRON™ testing machine, and the high strain rate tests done using a pulse shape modified compressive Split Hopkinson Pressure Bar apparatus. From the experimental result, it was concluded that under different strain rate loading, compressive strength, modulus, and strain at peak stress were rate sensitive. Optical and microscopic photos of the specimens were taken to determine operative failure modes. Within the studied strain rate regimes, the failure mode changed from splitting followed by fiber kink buckling to predominantly delamination and shear fracture as strain rate increases from quasi‐static to high strain rates. Compressive properties and failure modes were severely affected by strain rate, stacking sequence, and fabric material. POLYM. COMPOS. 2012. © 2012 Society of Plastics Engineers

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 5000s−1 starting with the experimentally determined compressive strength values at relatively lower strain rates. Experimental results were generated in the strain rate range of 472–1957s−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 1957s−1.

The effect of strain rate on the mechanical behavior of Teflon foam

The quasi-static (1 × 10−3, 1 × 10−2 and 1 × 10−1 s−1) and high strain rate (7200 and 9500 s−1) experimental and high strain rate numerical compression deformation of a Gore Polarchip™ CP7003 heat insulating Teflon foam was investigated. High strain rate tests were conducted with the insertion of quartz crystal piezoelectric transducers at the end of the transmitter bar of a compression Split Hopkinson Pressure Bar (SHPB) set-up in order to measure the force at the back face of the specimen. A fully developed numerical model of the SHPB test on Teflon was also implemented using LS-DYNA. The simulation stresses showed close correlations with the experimentally measured stresses on the bars. The developed model successfully simulated the high strain rate loading. The damage initiation and progression of experimental high strain rate tests were further recorded using a high speed camera and found to be very similar to those of the simulation high strain rate tests.

Calcined and natural frustules filled epoxy matrices: The effect of volume fraction on the tensile and compression behavior

The effects of calcined diatom (CD) and natural diatom (ND) frustules filling (0–12vol.%) on the quasi-static tensile and quasi-static and high strain rate compression behavior of an epoxy matrix were investigated experimentally. The high strain rate testing of frustules-filled and neat epoxy samples was performed in a compression Split Hopkinson Pressure Bar set-up. The frustules filling increased the stress values at a constant strain and decreased the tensile failure strains of the epoxy matrix. Compression tests results showed that frustules filling of epoxy increased both elastic modulus and yield strength values at quasi-static and high strain rates. While, a higher strengthening effect and strain rate sensitivity were found with ND frustules filling. Microscopic observations revealed two main compression deformation modes at quasi-static strain rates: the debonding of the frustules from the epoxy and/or crushing of the frustules. However, the failure of the filled composites at high strain rates was dominated by the fracture of epoxy matrix.

Effects of the Loading Direction on High Strain Rate Behavior of Woven Graphite/Epoxy Composites

Effects of the loading direction on high strain rate behavior of cylindrical woven graphite/epoxy composites are presented. Compressive split Hopkinson pressure bar (SHPB) was used for high strain rate experiments. Cylindrical specimens were loaded diametrically and transversely at the impact energies of 67 J, 163 J, and 263 J. Micro Laser Raman spectroscopy and scanning electron microscopy (SEM) were used for surface characterization. It is observed that diametrically loaded specimens show permanent plastic deformation with high ductility resulting in a catastrophic failure while transversely loaded specimens exhibit viscoplastic deformation with some recoverable damage. As a result of this, Raman peak shifted to higher values for the diametrically loaded fibers whereas almost no change was observed in the Raman shift of transversely loaded fibers.

Compression of polypropylene across a wide range of strain rates

Three grades of polypropylene were tested in uniaxial compression at room temperature, across a wide range of strain rate: 10−4 s−1 to 104 s−1. One grade is a conventional polypropylene homopolymer. The two other grades are the polypropylene forming the matrix phase of a continuous glass fibre-reinforced thermoplastic composite prepreg, with and without blending with a carbon-black master batch. Tests at the highest strain rates were performed using a compression split Hopkinson pressure bar. The test specimens, for all the three rates, were imaged using appropriate digital cameras in order to observe the deformation process. In addition, the images obtained were analysed digitally to obtain true strain measurements for the medium rates category. All three grades of polypropylene showed pronounced strain-rate dependence of compressive yield stress, increasing by factors of up to 4 across the range of rates. At the lowest rates, there was close agreement between the yield stresses for all three materials, and also close agreement with the Eyring theory. Considering the highest strain rates, however, yield stresses increased more rapidly with log(strain-rate) than would be expected from a linear Eyring prediction and values for the three materials diverged. This was attributed to the contributions made in each material by both alpha and beta relaxation processes. Also prominent in the medium- and high-rate experimental results was pronounced post-yield strain softening, greatest at the highest strain-rates. This resulted from a combination of thermal softening from adiabatic heating, and structural rejuvenation as often seen in glassy polymers in quasi-static tests.

High strain rate compressive behavior of epoxy LY 556: Radial constraint effect

Abstract A projectile impacting onto a target is a typical loading case. For the analysis of such cases, knowledge of high strain rate behavior of target materials is essential. Split Hopkinson pressure bar (SHPB) apparatus is generally used for evaluating the high strain rate behavior of materials. In conventional SHPB testing, the diameter of the incident and the transmitter bars is larger than the diameter of the specimen allowing for the radial expansion of the specimen due to Poisson's effect under compressive loading. However, in practical cases, the contact area of the projectile striking onto a structure is much smaller than the surface area of the structure. In such cases, radial expansion of the structure at the point of impact is constrained by the surrounding material. Materials may behave differently in the presence of radial constraint. The objective of the present study was to evaluate the effect of radial constraint on high strain rate properties of epoxy LY 556 using compressive SHPB apparatus. Two types of arrangements were used for providing radial constraint: (i) specimen with larger diameter than the diameter of the incident and the transmitter bars, (ii) specimen with diameter equal to the diameter of the incident and the transmitter bars with a metallic holder providing radial constraint. Epoxy LY 556 specimens were tested over a range of striker bar impact velocities. It was observed that the resistance of the specimen under compressive loading increases with radial constraint. Photographs of the fractured specimens and the schematic representation are also presented. The results of the earlier work have been found to be inline with the findings made in the present study.

Effect of molecular structures on dynamic compression properties of polyethylene

The properties of polymers are strongly affected by their molecular structures. Therefore, three different types of polyethylene; low density, low-linear density and high density polyethylene were used in this study to experimentally investigate the dependency and attractive effect of molecular structures towards compressive properties of polyethylene over a wide range of strain rate studied. For the mechanical tests, an experimental technique based on the compression split Hopkinson pressure bar was introduced to perform high strain rate testing whereas a conventional universal testing machine was used to perform static compression testing. Additionally, two constitutive equations were employed to validate the yield behaviour of all tested polyethylene specimens under different levels of strain rates. Results indicated that the molecular structure of polyethylene did affect its mechanical properties in terms of yield behaviour, stiffness, strength, rate sensitivity, activation volume and absorbed energy, respectively. Meanwhile, the levels of strain rates also played as secondary roles that influenced the mechanical properties of the polyethylene specimens. Of the three types of polyethylene specimens, high density polyethylene recorded an excellent performance in terms of yield behaviour, absorbed energy, stiffness, and strength properties than that of other polyethylene specimens. However, low linear polyethylene showed greater rate sensitivity than that of other polyethylene specimens under both static and dynamic regions. Interestingly, both constitutive models almost agreed with the experimental results.

Effects of the Contact Geometry on High Strain Rate Behavior of Woven Graphite/Epoxy Composites

Effects of the contact geometry on high strain rate failure behavior of woven graphite/epoxy composites are presented. Compressive split Hopkinson pressure bar was used for high strain rate experiments. Woven graphite/epoxy composites were loaded transversely using two different contact geometries at the impact energies of 67 J and 163 J. It is observed that smaller contact area gives higher damage, resulting in higher energy absorption, elastic modulus and strain rate and peak stress in the specimens.

Effect of Particle Sizes on Rate Sensitivity and Dynamic Mechanical Properties of Polypropylene/Silica (PP/Sio<sub>2</sub>) Nanocomposites

Filler-related characteristic such as particle size, shape and geometry are essential factors that need to be considered during the evaluation of the material’s performance especially in the area of particle filled composites. However, there is limited number of works are reported on this particular issue under high strain rate condition. Based on this concern, the paper presents an experimental results on the effect of particle sizes towards rate sensitivity and dynamic compressive properties of polypropylene/silica nanocomposites across strain rate from 10-2to 10-3s-1. The composite specimens were tested using universal testing machine for static loading and a compression split Hopkinson pressure bar apparatus for dynamic loading. Results show that, the stiffness and strength properties of polypropylene/silica nanocomposites were affected by the size of silica particles. However, the magnitudes of changed are somehow different between micro and nanosizes. On the other hand, particle size also plays a major contribution towards sensitivity of the polypropylene/silica nanocomposites where the smaller the reinforcement sizes, the less sensitive would be the composites. Overall, it is convenience to say that the particle size gives significant contribution towards rate sensitivity and dynamic mechanical properties of polypropylene/silica nanocomposites.

Effects of temperature and strain rate on deformation behaviour of Inconel 718 alloy

Cylindrical Inconel 718 specimens are compressed dynamically at temperatures ranging from −150 to 550 °C and strain rates in the range of 1000–5000s −1 using a compressive split Hopkinson pressure bar. It is found that the flow stress increases with increasing strain rate, but decreases with increasing temperature. The highest work hardening rate is observed in the specimen impacted at the lowest temperature (−150 °C) and the highest strain rate (5000s −1). However, the work hardening rate is weakened by the deformation-induced temperature rise under high strain and strain rate conditions. The strain rate sensitivity increases with increasing strain rate, but decreases with increasing temperature. The activation energy varies as a function of the strain rate and temperature, and has a maximum value of 40 kJ mol −1 under the considered test conditions. The greatest thermal softening effect occurs in the specimens deformed at the highest strain rate of 5000s −1 at temperatures of −150 °C and 25 °C, respectively. The microstructural observations confirm that the mechanical response of Inconel 718 is directly related to the effects of the strain rate and temperature on the evolution of the impacted microstructure.

Dynamic mechanical behaviour and dislocation substructure evolution of Inconel 718 over wide temperature range

A compressive split-Hopkinson pressure bar and transmission electron microscope (TEM) are used to investigate the mechanical behaviour and microstructural evolution of Inconel 718 at strain rates ranging from 1000 to 5000 s −1 and temperatures between −150 and 550 °C. The results show that the flow stress increases with an increasing strain rate or a reducing temperature. The strain rate effect is particularly pronounced at strain rates greater than 3000 s −1 and a deformation temperature of −150 °C. A significant thermal softening effect occurs at temperatures between −150 and 25 °C. The microstructural observations reveal that the strengthening effect in deformed Inconel 718 alloy is a result primarily of dislocation multiplication. The dislocation density increases with increasing strain rate, but decreases with increasing temperature. By contrast, the dislocation cell size decreases with increasing strain rate, but increases with increasing temperature. It is shown that the correlation between the flow stress, the dislocation density and the dislocation cell size is well described by the Bailey–Hirsch constitutive equations.

Measurement and prediction of compressive properties of polymers at high strain rate loading

Strain-rate effect is widely recognized as a crucial factor that influences the mechanical properties of material. Despite the acknowledge importance, the understanding of how such factor interact with the sensitivity of the polymers in terms of mechanical properties is still less reported. In this study, an experimental technique, based on the compression split Hopkinson pressure bar, was introduced to perform high strain rate testing, whereas, a conventional universal testing machine was used to perform static compression testing, to experimentally investigate the independent and interactive effects of strain rates towards mechanical properties of various polymers. Based on the experimental results, we parameterized two equation models, which were used to predict the yield behavior of tested polymer samplings. The experimental results indicate that, the yield stress, compression modulus, compressive strength, strain rate sensitivity and strain energy increased significantly with increasing strain rates for all tested polymers. Meanwhile, the yield strain and the thermal activation volume exhibit contrary trend to the increasing strain rates. Interestingly, the proposed constitutive models were almost agreed well with experimental results over a wide range of strain rate investigated. Of the three polymers, polypropylene shows the highest strain rate sensitivity at static and quasi-static region. On the other hand, at dynamic region, polycarbonate shows the highest strain rate sensitivity than that of polypropylene and polyethylene. Overall, both experimental and numerical models proved that the mechanical properties of polymer show significant sensitivity and dependency towards applied strain rates up to certain extent.