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.     

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.     

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.     

The influence of martensite,bainite and ferrite on the as-quenched constitutive response of simultaneously quenched and deformed boron steel – Experiments and model

This paper examines the relationship between as-formed microstructure and mechanical properties of a hot stamped boron steel used in automotive structural applications. Boron steel sheet metal blanks were austenized and quenched at cooling rates of 30 °C/s, 15 °C/s and 10 °C/s within a Gleeble thermal–mechanical simulator. For each cooling rate condition, the blanks were simultaneously deformed at temperatures of 600 °C and 800 °C. A strain of approximately 0.20 was imposed in the middle of the blanks, from which miniature tensile specimens were extracted. Depending on the cooling rate and deformation temperature imposed on the specimens, some of the as-quenched microstructures consisted of predominantly martensite and bainite, while others consisted of martensite, bainite and ferrite. Optical and SEM metallographraphic techniques were used to quantify the area fractions of the phases present and quasi-static (0.003 s⁻¹) uniaxial tests were conducted on the miniature tensile specimens. The results revealed that an area fraction of ferrite greater than 6% led to an increased uniform elongation and an increase in n-value without affecting the strength of the material for equivalent hardness levels. This finding resulted in improved energy absorption due to the presence of ferrite and showed that a material with a predominantly bainitic microstructure containing 16% ferrite (with 257 HV) resulted in a 28% increase in energy absorption when compared to a material condition that was fully bainitic with a hardness of 268 HV. Elevated strain rate tension tests were also conducted at 10 s⁻¹ and 80 s⁻¹ and the effect of strain rate on the ultimate tensile strength (σ_UTS) and yield strength (σ_Y) was shown to be moderate for all of the conditions. The true stress versus effective plastic strain (flow stress) curves generated from the tensile tests were used to develop the “Tailored Crash Model II” (TCM II) which is a strain rate sensitive constitutive model that is a function of effective plastic strain, true strain rate and area fraction of martensite, bainite and ferrite. The model was shown to accurately capture the hardening behaviour and strain rate sensitivity of the multiphase material conditions examined.     

Non-equilibrium split Hopkinson pressure bar procedure for non-parametric identification of complex modulus

A split Hopkinson pressure bar procedure was developed for non-parametric identification of complex modulus under conditions of non-equilibrium and axially non-uniform stress. Two simplified procedures were also established. The first requires low frequency and/or short specimen. The second, identical to a classical procedure based on equilibrium, requires that also the specimen-to-bar characteristic impedance ratio be low. Both overestimate the magnitude of the complex modulus, the second even at low frequencies. Tests were carried out with polymethyl methacrylate and aluminium bars and with polypropylene specimens having diameter 20 mm and lengths 10, 20, 50 and 100 mm. The complex moduli identified are in good to fair agreement with published results up to 10 kHz for all specimens with polymethyl methacrylate bars and for the 10–50 mm specimens with aluminium bars. The quality of the results is sensitive to truncation and to imperfect contact at the bar-specimen interfaces.     

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.     

Strain rate and gage length effects on tensile behavior of Kevlar 49 single yarn

In the present paper, Kevlar® 49 single yarns with different gage lengths were tested under both quasi-static loading at a strain rate of 4.2 × 10^?4 s^?1 using a MTS load frame and dynamic tensile loading over a strain rate range of 20–100 s^?1 using a servo-hydraulic high-rate testing system. The experimental results showed that the material mechanical properties are dependent on gage length and strain rate. Young’s modulus, tensile strength, maximum strain and toughness increase with increasing strain rate under dynamic loading; however the tensile strength decreases with increasing gage length under quasi-static loading. Weibull statistics were used to quantify the degree of variability in yarn strength at different gage lengths and strain rates. This data was then used to build an analytical model simulating the stress–strain response of single yarn under dynamic loading. The model predictions agree reasonably well with the experimental data.     

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.     

An inverse approach to determine the constitutive model parameters from axial crushing of thin-walled square tubes

Knowledge of the behaviour of structural components is essential for their design under crash consideration. Constitutive models describe their material behaviour in finite element (FE) codes. These constitutive models are in relation to the material parameters which have to be determined. The strain rates commonly observed in crash events are in the range of 0–500 s^-1. Classic experimental devices such as Hopkinson’s bars do not easily cover this range of strain rates. An inverse numerical approach based on the experimental quasi-static and dynamic axial crushing of thin-walled square tubes has therefore been developed to determine the constitutive model’s parameters. The inverse method is applied in this paper in two stages to determine the power type elastic–plastic constitutive model’s parameters and the Cowper–Symonds constitutive model’s parameters. The identified power law is compared with the results obtained by quasi-static tensile tests and shows that the identified parameters are intrinsic to the material behaviour. The Cowper– Symond’s parameters identified by this method are then used in FE simulation to predict the dynamic response of the same square tube subjected to bending loading. The results obtained show a good correlation between the experimental and numerical results.     

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.     

An assessment of mechanical behavior and fractography study of glass/epoxy composites at different temperatures and loading speeds

Effect of loading rate on fracture and mechanical behavior of autoclave cured glass fiber/epoxy prepreg composite has been studied at various loading (striking) rates (0.01-10³ mm/min). The maximum load carrying capacity and strain at yield continuously increases with increasing loading speed. The interlaminar shear strength (ILSS) value is high at low loading speed and becomes low at high loading speed with the transition of loading rate at approximately 300 mm/min. The formation of steps, welt interfacial failure and cleavage formation on matrix resin i.e. localized plastic deformation processes were dominating mechanisms for specimens tested at low loading rates, while brittle fracture of fiber, fiber pull-out and impregnation were dominating mechanisms for specimens tested at loading rates of 800 mm/min or higher.     

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.     

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.     

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

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

On dynamic deformation behavior of WE43 magnesium alloy sheet under shock loading conditions

In the present study, the texture evolution, microstructure and mechanical behavior of WE43 magnesium sheet at high strain rates are investigated. Samples cut along the rolling direction (RD), 45° from the RD, transverse direction (TD) and perpendicular to the RD-TD plane were tested at strain rates of 800, 1200 and 1400 s⁻¹ using Split Hopkinson Pressure Bar. It is observed that after shock loading, the initial weak texture converts to a weak (00.2) basal texture in all samples. Besides, it is found that the strength and ductility increase and twinning fraction decreases with increase in strain rate. Moreover, another effect of increase in strain rate is found to be the higher activation of pyramidal 〈c + a〉 slip systems. In addition, degree of stress and strain anisotropy is low particularly at higher strain rates, which is mainly related to the weak initial texture of the samples. A viscoplastic self-consistent model with a tangent approach is used to analyze the deformation mechanism during shock loading.     

Experimental study on high strain rate behavior of high strength 600–1000 MPa dual phase steels and 1200 MPa fully martensitic steels

As one of high grade advanced high strength steels (AHSSs), dual phase (DP) steel sheets and fully martensitic (MS) steel sheets have been successfully used in automotive crash-resistance components for its great benefit in reducing vehicle weight while improving car safety as well as their advantage in cost saving through cold forming instead of hot forming. The strain rate sensitivity of 600/800/1000 MPa DP and 1200 MPa MS were studied in this paper through a split Hopkinson tensile bar (SHTB) setup and compared with each other. The experiments showed that all dual phase (DP) AHSS ranging from 600 MPa to 1000 MPa are of positive strain rate sensitivity. While for the tested 1200 MPa MS, negative strain rate sensitivity has been found. Possible reason for the difference has been investigated through metallographical observation and their microstructures.     

Effects of radial inertia and end friction in specimen geometry in split Hopkinson pressure bar tests: A computational study

The split Hopkinson pressure bar (SHPB) technique has been used widely for the impact testing of materials in the strain-rate range from 10² to 10⁴ s⁻¹. However, some specific problems still remain mainly concerning the effects of radial inertia and end friction in a cylindrical specimen on the accurate determination of dynamic stress–strain curves of materials. In this study, the basic principle of the SHPB technique is revisited based on energy conservation and some modifications are made considering radial momentum conservation. It is pointed out that the radial inertia and end friction effects are coupled to each other in the SHPB specimen. Computational simulations using the commercial finite element (FE) code ABAQUS/Explicit ver. 6.8 are conducted to check the validity of the modifications for ductile pure aluminum specimens. Both rate-independent and rate-dependent models are adopted for the test material. Simulations are performed by varying two different control parameters: a friction coefficient between the specimen and the pressure bars and a slenderness ratio of the specimen (or thickness to diameter ratio).     

Hot tensile deformation behaviors and constitutive model of 42CrMo steel

The hot tensile deformation behaviors of 42CrMo steel are studied by uniaxial tensile tests with the temperature range of 850–1100 °C and strain rate range of 0.1–0.0001 s⁻¹. The effects of hot forming process parameters (strain rate and deformation temperature) on the elongation to fracture, strain rate sensitivity and fracture characteristics are analyzed. The constitutive equation is established to predict the peak stress under elevated temperatures. It is found that the flow stress firstly increases to a peak value and then decreases, showing a dynamic flow softening. This is mainly attributed to the dynamic recrystallization and material damage during the hot tensile deformation. The deformation temperature corresponding to the maximum elongation to fracture increases with the increase of strain rate within the studied strain rate range. Under the strain rate range of 0.1–0.001 s⁻¹, the localized necking causes the final fracture of specimens. While when the strain rate is 0.0001 s⁻¹, the gage segment of specimens maintains the uniform macroscopic deformation. The damage degree induced by cavities becomes more and more serious with the increase of the deformation temperature. Additionally, the peak stresses predicted by the proposed model well agree with the measured results.     

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.     

Plastic deformation in electrical conductors subjected to short-duration current pulses

In this paper, we consider the viscoplastic response of Al 6061-T6 and Cu-102 when subjected to a combination of mechanical load and high-intensity electric current. The specimens are subjected to mechanical loading under fixed-grip and dead-load conditions; in addition, the specimen is subjected to a nearly sinusoidal current pulse (frequency 4 kHz, duration ∼1 ms, and intensity ∼10⁹ A/m²). The resulting temperature increase causes the yield stress to drop and enables accumulation of plastic strain. A viscoplastic model is used to simulate the process; comparisons of the simulation results to time resolved measurements of strain and temperature are used to calibrate the viscoplastic model.