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.     

High Strain Rate Compressive Tests on Woven Graphite Epoxy Composites

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

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 Epon 826/DEA epoxy

Polymers are becoming increasingly used in aerospace structural applications, where they experience complex, non-static loads. Correspondingly, the mechanical properties at high strain rates are of increasing importance in these applications. This paper investigates the compressive properties of Epon 826 epoxy resin cured with diethynolamine (DEA) across strain rates from 10⁻³ to 10⁴ s⁻¹. Specimens were tested using an Instron mechanical testing machine for static loading, traditional split Hopkinson pressure bars (SHPBs) for high strain rates, and a miniaturized SHPB for ultra-high strain rates. Additionally, the material was tested using dynamic mechanical analysis to determine the effects of time and temperature equivalences on the strain rate behavior of the samples. The experimental data is used to fit the Mulliken-Boyce model, modified for one-dimension, which is able to capture the compressive mechanical properties over a range of strain rates.     

An investigation on the dynamic response of polymeric,metallic, and biomaterial foams

Mechanical characterization of foams at varying strain rates is indispensable for the selection of foam as core material for the proficient sandwich structure design at dynamic loading application. Both servo-hydraulically controlled Material Testing System (MTS) and Instron machines are generally considered for quasi-static testing at strain rates on the order of 10⁻³ s⁻¹. Split Hopkinson pressure bar (SHPB) with steel bars is typically utilized for characterizing metallic foams at high strain rates, however modified SHPB with polycarbonate or soft martial bars are used for characterizing polymeric and biomaterial foams at high strain rates on the order of 10³ s⁻¹ for impedance match between the foam specimens and bars. This paper reviews the effect of strain rate of loading, density, environmental temperature, and microstructure on compressive strength and energy absorption capacity of various closed-cell polymeric, metallic, and biomaterial foams. Compressive strength and energy absorption capacity increase with the increase in both strain rate of loading and density of foams, but decrease with the increase in surrounding temperature. Foams of same density can have different strength and can absorb unequal amount of energy at the same strain rate of loading due to the variation of microstructure.     

Compressive deformation behavior of ternary compound Cr<Subscript>2</Subscript>AlC

The compressive properties of ternary compound Cr₂AlC at different temperatures and strain rates were studied. When tested at a strain rate of 5.6 × 10⁻⁴ s⁻¹, the compressive strength decreases continuously from 997 ± 29 MPa at room temperature to 523 ± 7 MPa at 900 °C. The ductile-to-brittle transition temperature is measured to be in the range of 700 to 800 °C. When tested in the strain rate range of 5.6 × 10⁻⁵ to 5.6 × 10⁻³ s⁻¹, Cr₂AlC fails in a brittle mode at room temperature, whereas the deformation mode changes from a brittle to a ductile as the strain rate is lower than 5.6 × 10⁻⁴ s⁻¹ when compressed at 800 °C. The compressive strength increases slightly with increasing strain rate at room temperature and it is less dependent on strain rate when tested at 800 °C. The plastic deformation mechanism of Cr₂AlC was discussed in terms of dislocation-related activities, such as kink band formation, delamination, decohesion of grain boundary, and microcrack formation.     

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

Effects of the inertia-induced radial confinement on the dynamic increase factor (DIF) of a mortar specimen are investigated in split Hopkinson pressure bar (SHPB) tests. It is shown that axial strain acceleration is unavoidable in SHPB tests on brittle samples at high strain-rates although it can be reduced by the application of a wave shaper. By introducing proper measures of the strain-rate and axial strain acceleration, their correlations are established. In order to demonstrate the influence of inertia-induced confinement on the dynamic compressive strength of concrete-like materials, tubular mortar specimens are used to reduce the inertia-induced radial confinement in SHPB tests. It is shown that the DIF measured by SHPB tests on tubular specimens is lower than the DIF measured by SHPB tests on solid specimens. This paper offers experimental support for a previous publication [Li QM, Meng H. About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. Int J Solids Struct 2003; 40:343–360.], which claimed that inertia-induced radial confinement makes a large contribution to the dynamic compressive strength enhancement of concrete-like materials when the strain-rate is greater than a critical transition strain-rate between 10¹ and 10² s⁻¹. It is concluded that DIF formulae for concrete-like materials measured by split Hopkinson pressure bar tests need to be corrected if they are going to be used as the unconfined uniaxial compressive strength in the design and numerical modelling of structures made from concrete-like materials to resist impact and blast loads.     

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.     

Ductility and brittleness of bone

Human, bovine and equine bones show brittle to ductile transitions as a function of strain rate. The transition is not sharp, but occurs around a strain rate of 10⁻¹ s⁻¹. At lower rates, the strength increases proportional to the logarithm of the strain rate, at higher rates it decreases. Additionally, the work of fracture peaks around 10⁻¹ s⁻¹. Thermal activation analysis gives an activation volume of (1 nm)³, an activation enthalpy of 1 eV and an activation energy of about 0.5 eV. Plastic deformation occurs both within and between collagen fibrils. In the fibrils, the existence of screw dislocations parallel to the collagen molecules with a Burger’s vector of 1 nm length is postulated. Deformation occurs by thermally activated kink pair formation in these defects.     

Quasi-static and dynamic compressive behaviour of poly(methyl methacrylate) and polystyrene at temperatures from 293 K to 363 K

Flow stress, Young’s Modulus, energy and strain of fracture of poly(methyl methacrylate) (PMMA) and polystyrene (PS) were studied under compressive loading at strain rates of 10⁻⁴–10 s⁻¹ and temperatures from 293 K to temperatures ∼20 K below T _g. It was found that the energy of fracture shows an increase in the quasi-static strain rate (10⁻⁴–10⁻³ s⁻¹) region and becomes constant in the low strain rate (10⁻²–10 s⁻¹) region, while the strain of fracture shows a slow decrease with rate over the strain rate range tested. The activation energies and volumes of PMMA and PS at yield stress, 20% and 30% strain were evaluated using Eyring’s theory of viscous flow. ΔG was found to be constant for all strain rates and strains for both PMMA and PS. The activation volume for both materials increased as a function of strain.     

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.     

Compressive properties of Cu with different grain sizes: sub-micron to nanometer realm

High-quality ultra-fine grained (ufg) and nanocrystalline (nc) bulk Cu samples of proper sizes reliable for mechanical testing, with grain sizes (d) ranging from 720 down to 22 nm were prepared by means of room temperature ball-milling and consolidation processes. The specimens were subjected to compressive loading at the quasi-static strain rate of 10⁻⁴ s⁻¹ to large strains (ε = 50%). The specimens prepared from the 10-h-milled powder (d = 32 nm) were tested at a wide range of strain rates (10⁻⁴ to 1,860 s⁻¹), and the strain rate sensitivity (SRS) of the material was determined as a function of strain. The strength and work-hardening behavior were dramatically influenced by change in the grain size; the strength approached ∼900 MPa for the 30-h-milled Cu (d = 22 nm) at the strain level of ∼50%. The SRS increased several fold as the grain size was reduced to 32 nm. Further, the results obtained in this study were compared with those of other investigators on ufg and nc Cu, to gain insights into the effect of different processing routes on the investigated material properties.     

Mechanical properties of 304L stainless steel SMAW joints under dynamic impact loading

The impact properties of 304L Stainless Steel Shielded Metal Arc Welded (SMAW) joints are studied at strain rates between 10^{− 3} and 7.5× 10³ s^{− 1} using a compressive split-Hopkinson bar. The effects of strain rate on the flow response and fracture characteristics are fully evaluated. The results show that the tested weldments exhibit a pronounced strain rate sensitivity, and that changes in the strain rate result in a difference in the flow stress, fracture strain, and work hardening rate. Furthermore, it is noted that the strain rate sensitivity and activation volume vary with the magnitude of the strain rate, and are related to different work hardening stress levels. At all values of strain rate, the tested weldments fail as a result of adiabatic shearing, in which cracks initiate within the shear band and then propagate along this shear band until failure occurs. Observation of the fractured specimens reveals that the fracture surfaces of the fusion zone and base metal regions are characterized by the presence of elongated dimples. The variation in the observed dimple features with strain rate is consistent with the results of the impact stress-strain curves.     

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.     

An experimental investigation of rate-dependent deformation and failure of three titanium alloys

The response of three titanium alloys, Ti 6,4, Ti 550 and Ti 6,2,4,6, commonly used in aerospace applications, has been investigated at rates of strain between 10⁻⁴ and 10³ s⁻¹ in uniaxial tensile and compressive loading in ambient environment. This work identifies and discusses features of their behaviour that must be captured within material models developed for use in predictive modelling of response to in-service loading. That is, an increase in yield strength with increasing strain rate, a difference in yield strength between tensile and compressive loading regimes and, most importantly, the evolution of damage resulting in failure due to growth of voids in both tension and compression.     

Effect of strain rate on quasistatic tensile flow behaviour of solution annealed 304 austenitic stainless steel at room temperature

Room temperature tensile test results of solution annealed 304 stainless steel at strain rates ranging between 5 × 10⁻⁴ and 1 × 10⁻¹ s⁻¹ reveal that with increase in strain rate yield strength increases and tensile strength decreases, both maintaining power–law relationships with strain rate. The decrease in tensile strength with increasing strain rate is attributed to the lesser amount of deformation-induced martensite formation and greater role of thermal softening over work hardening at higher strain rates. Tensile deformation of the steel is found to occur in three stages. The deformation transition strains are found to depend on strain rate in such a manner that Stage-I deformation (planar slip) is favoured at lower strain rate. A continuously decreasing linear function of strain rate sensitivity with true strain has been observed. Reasonably good estimation for the stress exponent relating dislocation velocity and stress has been made. The linear plot of reciprocal of strain rate sensitivity with true strain suggests that after some critical amount of deformation the increased dislocation density in austenite due to the formation of some critical amount of deformation-induced martensite plays important role in carrying out the imposed strain rate.     

The strain rate and temperature dependence of microstructural evolution of Ti–15Mo–5Zr–3Al alloy

A compressive split-Hopkinson pressure bar apparatus and transmission electron microscopy (TEM) are used to investigate the deformation behaviour and microstructural evolution of Ti–15Mo–5Zr–3Al alloy deformed at strain rates ranging from 8 × 10² s⁻¹ to 8 × 10³ s⁻¹ and temperatures between 25 °C and 900 °C. In general, it is observed that the flow stress increases with increasing strain rate, but decreases with increasing temperature. The microstructural observations reveal that the strengthening effect evident in the deformed alloy is a result, primarily, of dislocations and the formation of α phase. The dislocation density increases with increasing strain rate, but decreases with increasing temperature. Additionally, the square root of the dislocation density varies linearly with the flow stress. The amount of α phase increases with increasing temperature below the β transus temperature. The maximum amount of α phase is formed at a temperature of 700 °C and results in the minimum fracture strain under the current loading conditions.     

Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive

Effects of temperature and strain rate on the cohesive relation for an engineering epoxy adhesive are studied experimentally. Two parameters of the cohesive laws are given special attention: the fracture energy and the peak stress. Temperature experiments are performed in peel mode using the double cantilever beam specimen. The temperature varies from −40 to + 80°C. The temperature experiments show monotonically decreasing peak stress with increasing temperature from about 50 MPa at −40°C to about 10 MPa at + 80°C. The fracture energy is shown to be relatively insensitive to the variation in temperature. Strain rate experiments are performed in peel mode using the double cantilever beam specimen and in shear mode, using the end notch flexure specimen. The strain rates vary; for peel loading from about 10⁻⁴ to 10 s⁻¹ and for shear loading from 10⁻³ to 1 s⁻¹. In the peel mode, the fracture energy increases slightly with increasing strain rate; in shear mode, the fracture energy decreases. The peak stresses in the peel and shear mode both increase with increasing strain rate. In peel mode, only minor effects of plasticity are expected while in shear mode, the adhesive experiences large dissipation through plasticity. Rate dependent plasticity, may explain the differences in influence of strain rate on fracture energy between the peel mode and the shear mode.     

Polymeric foam behavior under dynamic compressive loading

Polymeric foams are commonly used in many impact-absorbing applications and thermal-acoustic insulated devices. To improve their mechanical performances, these structures have to be modeled. Constitutive equations (for their macroscopic behavior) have to be identified and then determined by appropriate tests.Tests were carried out on polypropylene foams under high strain rate compression. In this work, the material behaviour has been determined as a function of two parameters, density and strain rate. Foams (at several densities) were tested on a uniaxial compression for initial strain rates equal to 0.34 s⁻¹ and on a new device installed on a flywheel for higher strain rates. This apparatus was designed in order to do stopped dynamic compression tests on foam. With this testing equipment, the dynamic compressive behaviour of the polymeric foam has been identified in the strain rate range [6.7.10⁻⁴s⁻¹, 100s⁻¹].Furthermore, the sample compression was filmed with a high speed camera monitored by the fly wheel software. To complete this work, picture-analysis techniques were used to obtain displacement and strain fields of the sample during its compression. Comparisons between these results and stress-strain responses of polypropylene foam allow a better understanding of its behaviour. The multiscale damage mechanism, by buckling of the foam structure, was emphasised from the image analysis.     

Effect of transient change in strain rate on plastic flow behaviour of low carbon steel

Plastic flow behaviour of low carbon steel has been studied at room temperature during tensile deformation by varying the initial strain rate of 3·3 × 10⁻⁴s⁻¹ to a final strain rate ranging from 1·33 × 10⁻³s⁻¹ to 2 × 10⁻³s⁻¹ at a fixed engineering strain of 12%. Haasen plot revealed that the mobile dislocation density remained almost invariant at the juncture where there was a sudden increase in stress with a change in strain rate and the plastic flow was solely dependent on the velocity of mobile dislocations. In that critical regime, the variation of stress with time was fitted with a Boltzmann type Sigmoid function. The increase in stress was found to increase with final strain rate and the time elapsed in attaining these stress values showed a decreasing trend. Both of these parameters saturated asymptotically at a higher final strain rate.