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.     

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.     

Impact and fracture response of sintered 316L stainless steel subjected to high strain rate loading

This paper describes the use of a material testing system (MTS) and a compressive split-Hopkinson bar to investigate the impact behaviour of sintered 316L stainless steel at strain rates ranging from 10^− 3 s^− 1 to 7.5 × 10³ s^− 1. It is found that the flow stress–strain response of the sintered 316L stainless steel depends strongly on the applied strain rate. The rate of work hardening and the strain rate sensitivity change significantly as the strain rate increases. The flow behaviour of the sintered 316L stainless steel can be accurately predicted using a constitutive law based on Gurson's yield criterion and the flow rule of Khan, Huang and Liang (KHL). Microstructural observations reveal that the degree of localized grain deformation increases at higher strain rates. However, the pore density and the grain size vary as a reversible function of the strain rate. Impacts at strain rates higher than 5.6 × 10³ s^− 1 are found to induce adiabatic shear bands in the specimens. These specimens subsequently fail as a result of crack propagation along the dominant band. The fracture surfaces of the failed specimens are characterized by dimple-like structures, which are indicative of ductile failure. The depth and the density of these dimples are found to decrease with increasing strain rate. This observation indicates a reduction in the fracture resistance and is consistent with the observed macroscopic flow stress–strain response.     

Strain rate dependent plastic mutation in a bulk metallic glass under compression

This paper reported a strain rate dependent plasticity in a Zr-based bulk metallic glass (BMG) under axial compression over a strain rate range (1.6 × 10⁻⁵–1.6 × 10⁻¹ s⁻¹). The fracture strain decreased with increasing strain rate up to 1.6 × 10⁻³ s⁻¹. A “brittle-to-malleable” mutation occurred at strain rate of 1.6 × 10⁻² s⁻¹, subsequently, the macro plasticity vanished at 1.6 × 10⁻¹ s⁻¹. It is proposed that the result is strongly related to the combined action of the applied strain rate, the compression speed, and the propagating speed of the shear band. When the three factors coordinated in the optimal condition, multiple mature shear bands were initiated simultaneously to accommodate the applied strain, which propagated through the specimen and distributed homogeneously in space, dominating the overall plastic deformation by consuming the entire specimen effectively.     

Experimental study on the dynamic tensile behavior of a poly-crystal pure titanium at elevated temperatures

A new technique for measuring dynamic tensile behavior of metallic materials at elevated temperatures was developed. This technique employs a rapid contact heating method to obtain a stable and nearly homogenous high temperature field in the testing gage of the specimen. As an application of this new technique, a commercially pure titanium (CP-Ti) was tested in the strain rate range of 300 s⁻¹–1400 s⁻¹ and in a temperature range of 298 K–973 K. Quasi-static experiments (10⁻³ s⁻¹, 10⁻² s⁻¹) were also performed in the same temperature range for comparison. The testing results indicated that both temperature and strain rate have pronounced influence on the mechanical behavior of CP-Ti.     

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.     

The dynamic mechanical response of SiC particulate reinforced 2024 aluminum matrix composites

The compression properties of the aluminum alloy 2024 metal matrix composites reinforced with 50 vol.% SiC particles were investigated using Instron testing machine and split Hopkinson pressure bar (SHPB) in this paper. The compression stress–strain curves were obtained at the strain rates ranging from 1 × 10^− 3 to 2.5 × 10³/s. The fracture surfaces were characterized by scanning electron microscopy. The results showed that SiCp/2024 Al composites exhibited high strain-rate sensitivity. The strength of composites tended to increase–decrease with increasing of strain rates. The effect of the strain rate on elongation was also discussed.     

Combined effect of strain-rate and mode-ratio on the fracture of lead-free solder joints

The critical strain energy release rate for the solder joint fracture was measured as a function of the strain rate and the mode ratio of loading. These data are useful in predicting the fracture of solder joints loaded under arbitrary combinations of tension and shear during the impact conditions typical of falling portable electronic devices. In this study, strain rates from quasi-static (close to 0 s^− 1) to 61 s^− 1 were investigated at phase angles from 0 to 60°, typical of the range found in microelectronic devices. Copper–solder–copper double cantilever beam (DCB) model specimens were prepared using SAC305 solder at cooling rates and times above liquidus typical of actual ball grid arrays (BGAs). A drop tester was designed and built to achieve different strain rates at various mode ratios. The critical initiation strain energy release rate, J_ci, increased about 70% from quasi-static to intermediate strain rates, before decreasing by more than 67% from intermediate strain rates to 42 s^− 1.     

Modeling quasi-static and high strain rate deformation and failure behavior of a (±45) symmetric E-glass/polyester composite under compressive loading

Quasi-static (1 × 10⁻³–1 × 10⁻² s⁻¹) and high strain rate (∼1000 s⁻¹) compressive mechanical response and fracture/failure of a (±45) symmetric E-glass/polyester composite along three perpendicular directions were determined experimentally and numerically. A numerical model in LS-DYNA 971 using material model MAT_162 was developed to investigate the compression deformation and fracture of the composite at quasi-static and high strain rates. The compressive stress–strain behaviors of the composite along three directions were found strain rate sensitive. The modulus and maximum stress of the composite increased with increasing strain rate, while the strain rate sensitivity in in-plane direction was higher than that in through-thickness direction. The damage progression determined by high speed camera in the specimens well agreed with that of numerical model. The numerical model successfully predicted the damage initiation and progression as well as the failure modes of the composite.     

Mechanical behavior and deformation micromechanisms of polypropylene nonwoven fabrics as a function of temperature and strain rate

The mechanical behavior and the deformation and failure micromechanisms of a thermally-bonded polypropylene nonwoven fabric were studied as a function of temperature and strain rate. Mechanical tests were carried out from 248 K (below the glass transition temperature) up to 383 K at strain rates in the range ≈10⁻³ s⁻¹ to 10⁻¹ s⁻¹. In addition, individual fibers extracted from the nonwoven fabric were tested under the same conditions. Micromechanisms of deformation and failure at the fiber level were ascertained by means of mechanical tests within the scanning electron microscope while the strain distribution at the macroscopic level upon loading was determined by means of digital image correlation. It was found that the nonwoven behavior was mainly controlled by the properties of the fibers and of the interfiber bonds. Fiber properties determined the nonlinear behavior before the peak load while the interfiber bonds controlled the localization of damage after the peak load. The influence of these properties on the strength, ductility and energy absorbed during deformation is discussed from the experimental observations.     

Experimental study on influence of section thickness on mechanical behavior of die-cast AM60 magnesium alloy

Influence of section thickness on mechanical behavior of die-cast AM60 magnesium alloy has been experimentally studied. Tension, compression and shear tests with this material were performed on a universal test machine at strain rates from 5 × 10⁻⁴ s⁻¹ to 5 × 10⁻² s⁻¹. Specimens were cut from plates with five as-cast section thicknesses of 6.5 mm, 5.2 mm, 3.9 mm, 2.6 mm and 1.3 mm. According to the test results, flow stress becomes less sensitive to section thickness with larger section thickness, and the influence of strain rate on flow stress is also decreasing with larger section thickness. At different stress states, the tested material follows the von-Mises yield criterion. And stress state is found to be the main factor influencing the fracture behavior.     

Characterization of hot compression behavior of a new HIPed nickel-based P/M superalloy using processing maps

Isothermal forging was a critical step process to fabricate the high-performance nickel-based superalloy. The temperature and strain rate served the most critical role in determining its microstructure and mechanical properties. In this article, we employed the hot compression to simulate the isothermal forging process upon the temperature ranging from 1000 °C to 1100 °C in combination with a strain rate of 0.001–1.0 s^− 1 for a new P/M nickel-based alloy. The activation energy was determined as 903.58 kJ/mol and the processing maps at a strain range of 0.4–0.7 were developed. The instability domains were more inclined to occur at strain rates higher than 0.1 s^− 1 and manifested in the form of adiabatic shear bands. The map further demonstrated that the regions with peak efficiency of 55% were located at 1080 °C/0.0015 s^− 1 and 1095 °C/0.014 s^− 1, respectively. Obvious dynamic recrystallization could be detected at the strain rate 0.01 s^− 1 leading to a significant flow stress drop and the grain growth was remarkably triggered under 1100 °C. The findings can shed light on the forging processing optimization of the new nickel-based superalloy.     

A characterization for the flow behavior of 42CrMo steel

In order to evaluate the flow stress and the dynamic softening characteristics of casting 42CrMo steel, isothermal upsetting experiments with height reduction 60% were performed at the temperatures of 1123 K, 1198 K, 1273 K and 1348 K, and the strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1 s⁻¹ and 10 s⁻¹ on thermal physics simulator Gleeble 1500. The flow behavior of the applied stress as a function of strain, strain rate and temperature exhibits a more pronounced effect of temperature than strain rate, and a typical characteristic of dynamic recrystallization softening. To characterize the flow behavior more factually and accurately, the traditional Fields–Backofen equation was amended, and an innovative mathematical model containing a softening item s, n-value and m-value variable functions was brought forth. The stress–strain curves calculated by the derived flow stress equation are fit with the experimental results well not only at the hardening stage but also at softening stage.     

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.     

The hot deformation behavior and processing map of Ti–47.5Al–Cr–V alloy

The high temperature flow behavior of as-extruded Ti–47.5Al–Cr–V alloy has been investigated at the temperature between 1100 °C and 1250 °C and the strain rate range from 0.001 s^− 1 to 1 s^− 1 by hot compression tests. The results showed that the flow stress of this alloy had a positive dependence on strain rate and a negative dependence on deformation temperature. The activation energy Q was calculated to be 409 kJ/mol and the constitutive model of this material was established. By combining the power dissipation map with instability map, the processing map was established to optimize the deformation parameters. The optimum deformation parameter was at 1150 °C–1200 °C and 0.001 s^− 1–0.03 s^− 1 for this alloy. The microstructure of specimens deformed at different conditions was analyzed and connected with the processing map. The material underwent instability deformation at the strain rate of 1 s^− 1, which was predicted by the instability map. The surface fracture was observed to be the identification of the instability.     

Damage evolution in Ti6Al4V–Al3Ti metal-intermetallic laminate composites

The crack propagation and damage evolution in metal (Ti6Al4V)-intermetallic (Al₃Ti) laminate composites were investigated. The composites (volume fractions of Ti6Al4V: 14%, 20% and 35%) were tested under different loading directions (perpendicular and parallel directions to laminate plane), to different strains (1%, 2%, 3%) and at different strain rates (0.0001 and 800–2000 s⁻¹). Crack densities and distributions were measured. The crack density increases with increasing strain, but decreases (at a constant strain) with increasing volume fraction of Ti6Al4V. Differences in crack propagation and damage evolution in MIL composites under quasi-static (10⁻⁴ s⁻¹) and dynamic (800–2000 s⁻¹) deformation were observed. The fracture stress does not exhibit significant strain-rate sensitivity; this is indicative of the dominance of microcracking processes in determining strength. Generally, the crack density after dynamic deformation is higher than that after quasi-static deformation. This is attributed to the decreased time for crack interaction in high-strain rate deformation. The effect of crack density, as quantified by a damage parameter, on elastic modulus and stress–strain relation were calculated and compared with experimental results.     

Influence of processing parameters on hot workability and microstructural evolution in a carbon–manganese–silicon steel

In this work, the influence of processing variables such as strain, strain rate, temperature and cooling medium, on workability, microstructural evolution and mechanical properties of a carbon–manganese–silicon (C–Mn–Si) steel have been studied. Hot deformation of the C–Mn–Si steel has been carried out using compression testing over a domain 1223–1473 K and 0.001–10 s^− 1 where the steel is in austenitic phase field. The effect of cooling medium on the microstructural evolution has been studied by carrying out post-deformation cooling of the specimens in air and water media. Influence of the cooling medium on properties of the steel has been evaluated by comparing the hardness and Charpy impact test results. Based on the flow behavior analysis and microstructural examinations the optimum domain for the hot deformation of C–Mn–Si steel is found to be in the ranges of 1273–1350 K and 3–10 s^− 1. Flow instability in C–Mn–Si steel is manifested in the form of deformation bands in the microstructure. The signature of instability is not influenced by the phase transformation. The hardness of the material is dependent on the temperature of deformation and influenced by cooling medium. However, it does not show any correlation with deformation strain rate.     

Effect of short nylon-6 fibres on natural rubber-toughened polystyrene

Composites based on polystyrene and natural rubber at a ratio of 85/15 were prepared by melt mixing with nylon-6 fibres using an internal mixer. The loading of short nylon-6 fibre, untreated and resorcinol formaldehyde latex (RFL)-treated, was varied from 0 to 3 wt.%. Tensile and flexural test samples were punched out from sheets and tested to study the variation of mechanical and dynamic mechanical properties. The tensile behaviour of the composite has been determined at three different strain rates (4.1 × 10⁻⁴ s⁻¹, 2 × 10⁻³ s⁻¹ and 2 × 10⁻² s⁻¹). Both the tensile strength and Young’s modulus of the composite increased with strain rate. The tensile strength, tensile modulus, flexural strength and flexural modulus increased with the increase in fibre content up to 1 wt.%, above which there was a significant deterioration in the properties. The RFL-treated fibre composites showed improved mechanical properties compared to the untreated one. Dynamic mechanical analysis (DMA) showed that the storage modulus of the composite with RFL-treated fibre was better compared to the untreated one. The fibre–matrix morphology of the tensile fractured specimens was studied by scanning electron microscopy (SEM). The results suggested that the RFL treatment of nylon fibre promoted adhesion to the natural rubber phase of the blend, thereby improving the mechanical properties of the composite.     

Effects of initial grain size on hot deformation behavior of commercial pure aluminum

The effects of initial grain size of commercial pure aluminum on hot deformation behavior were investigated using hot compression tests. The hot compression tests were carried out on the pure aluminum samples with the initial grain sizes of 50, 150 and 450 μm using various strains, strain rates and different deformation temperatures. It was found that the hot deformation behavior of used material was sensitive to deformation conditions and initial microstructure. Results indicate that the initial grain size has significant effect on the flow stress. Flow stress decreases when the grain size decreases from 450 to 50 μm and when strain rate is lower than 0.05 s⁻¹. This procedure is reversed at strain rate of 0.5 s⁻¹. Furthermore, effects of other parameters like the strain rates and deformation temperatures on the flow stresses and hardening rates were investigated. It was also found that the inhomogeneity of microstructure distribution at different positions of the deformed specimens depended on the amount of deformation concentration at particular points and other processing parameters such as initial grain sizes, strain rates and deformation temperatures. In addition the geometric dynamic recrystallization (GDRX) was observed in the specimens highly strained (0.7) at elevated temperature (500 °C) using polarized light microscope and sensitive tint (PLM + ST).     

Dedicated linear – Voce model and its application in investigating temperature and strain rate effects on sheet formability of aluminum alloys

This paper proposes a method to investigate the effects of temperature and strain rate on the forming limit curves (FLCs) by combining a modified Voce constitutive model (Lin-Voce model) with the numerical simulation of Marciniak test. The tensile tests are firstly carried out at different forming temperatures (20, 230 and 290 °C) and strain rates (2.5, 120 and 150 s⁻¹) for AA5086 sheet. A modified Voce constitutive model (named Lin-Voce model) is proposed to describe the deformation behavior of AA5086 and its material parameters are identified by inverse analysis technique. Then, the proposed constitutive model is verified by comparing numerical and experimental results obtained by tensile tests and Marciniak test, respectively. Finally, the numerical simulation of Marciniak test is carried out at different temperatures (100, 200 and 300 °C) and strain rates (2.5, 120 and 150 s⁻¹), and the effects of temperature and strain rate on the FLCs of AA5086 are investigated and discussed.