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.     

Fracture energy of UHP-FRC under direct tensile loading applied at low strain rates

This research investigates the fracture energy of ultra-high performance fiber reinforced concretes (UHP-FRC) under direct tensile loading applied at relatively low strain rates. Nine UHP-FRC series incorporating three types of steel fibers (straight, end-hooked, and twisted fibers), each in three different fiber volume fractions, are tested under uniaxial tensile loading at four different strain rates, ranging from 0.0001 s⁻¹ to 0.1 s⁻¹. Particular attention is given to clearly distinguish between the dissipated energy during the strain hardening and softening portions of the loading regime. The test results show that: 1) the fracture energy is mainly influenced by a parameter, termed fiber factor, which is a function of the fiber volume fraction and slenderness, and 2) all three types of UHP-FRCs exhibit increases in fracture energy with increasing strain rates. The observed strain rate sensitivity of the fracture energy suggests it is likely associated with the strain sensitive micro-cracking that occurs during fiber pull-out.     

The variation of strain rate sensitivity exponent and strain hardening exponent in isothermal compression of Ti–6Al–4V alloy

The deformation behavior in isothermal compression of Ti–6Al–4V alloy is investigated in the deformation temperatures ranging from 1093 K to 1303 K, the strain rates ranging from 0.001 s⁻¹ to 10.0 s⁻¹ at an interval of an order magnitude and the height reductions ranging from 20% to 60% at an interval of 10%. Based on the experimental results in isothermal compression of Ti–6Al–4V alloy, the effect of processing parameters and grain size of primary α phase on the strain rate sensitivity exponent m and the strain hardening exponent n is in depth analyzed. The strain rate sensitivity exponent m at a strain of 0.7 and strain rate of 0.001 s⁻¹ firstly tends to increase with the increasing of deformation temperature, and maximum m value is obtained at deformation temperature close to the beta-transus temperature, while at higher deformation temperature it drops to the smaller values. Moreover, the strain rate sensitivity exponent m decreases with the increasing of strain rate at the deformation temperatures below 1253 K, but the m values become maximal at a strain rate of 0.01 s⁻¹ and the deformation temperature above 1253 K. The strain rate affects the variation of strain rate sensitivity exponent with strain. Those phenomena can be explained reasonably based on the microstructural evolution. On the other hand, the strain hardening exponent n depends strongly on the strain rate at the strains of 0.5 and 0.7. The strain affects significantly the strain hardening exponent n due to the variation of grain size of primary α phase with strain, and the competition between thermal softening and work hardening.     

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.     

Temperature dependent work hardening in Ti–6Al–4V alloy over large temperature and strain rate ranges: Experiments and constitutive modeling

The plastic deformation behaviors of Ti–6Al–4V alloy over wide ranges of strain rate (from 10⁻⁴ to 10⁴ s⁻¹) and temperature (from 20 to 900 °C) are investigated by the quasi-static and dynamic uniaxial compression tests. The microstructure evolution of Ti–6Al–4V alloy at different temperatures is discussed. Material generates higher ductility and formability when temperature is higher than 500 °C, which leads to the decrease of work hardening rate. The true stress–strain responses are modeled with the JC, modified JC, KHL and modified KHL models. In detail, a temperature dependent work hardening function is introduced into the original JC and KHL models. The parameters of the four models for Ti–6Al–4V alloy are calculated by GA optimization method. The average standard deviations between the experimental and calculated flow stresses range from 4% to 13%, which validates the accuracy of the models. In addition, comparison of flow stresses at dynamic (10,000 s⁻¹), the work hardening rates at dynamic (7500 s⁻¹), as well as the quasi-static jump experiments were proposed to further validate the models. The modified JC and modified KHL models could characterize the temperature dependent work hardening effect for Ti–6Al–4V alloy over large strain rate and temperature ranges.     

Numerical model to predict deformation of corrugated austenitic stainless steel sheet under cryogenic temperatures for design of liquefied natural gas insulation system

Austenitic stainless steel exhibits nonlinear hardening behavior at low temperature and under various strain rate conditions caused by the phenomenon of transformation-induced plasticity (TRIP). In this study, a uniaxial tensile test for 304L austenitic stainless steel was performed below ambient temperature (−163, −140, −120, −50, and 20 °C) and at strain rates (10⁻⁴, 10⁻³, and 10⁻² s⁻¹) to identify nonlinear mechanical characteristics. In addition, a viscoplastic damage model was proposed and implemented in a user-defined material subroutine to provide a theoretical explanation of the nonlinear hardening features. The verification was conducted not only by a material-based comparative study involving experimental investigations, but also by a structural application to the corrugated steel membrane of a Mark-III-type cargo containment system for liquefied natural gas. In addition, an accumulated damage contour was represented to predict the failure location by using a continuum damage mechanics approach.     

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.     

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.     

The mechanical properties of ionoplast interlayer material at high strain rates

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

Tensile deformation behavior of spray-deposited FVS0812 heat-resistant aluminum alloy sheet at elevated temperatures

The tensile deformation behavior of spray deposited FVS0812 heat-resistant aluminum alloy sheet was studied by uniaxial tension tests at temperatures ranging from 250 °C to 450 °C and strain rates from 0.001 to 0.1 s^− 1. The associated fracture surfaces were examined by scanning electron microscopy (SEM). The results show that the degree of work-hardening increases with decreasing temperature, and exhibits a small decrease with increasing strain rate; the strain rate sensitivity exponent increases with increasing temperature. The flow stress increases with increasing strain rate but decreases with increasing temperature. The total elongations to fracture increase not only with increasing temperature, but also with increasing strain rate, which is in marked contrast with the normal inverse dependence of elongation on the strain rate exhibited by conventional aluminum alloy sheets. The SEM fracture analysis indicates that the dependence of elongation on the strain rate may be due to the presence of a transition from plastic instability at lower strain rates to stable deformation at higher strain rates for fine-grained materials produced by spray deposition.     

Texture evolution and dynamic mechanical behavior of cast AZ magnesium alloys under high strain rate compressive loading

In this study, texture and compressive mechanical behavior of three cast magnesium alloys, including AZ31, AZ61 and AZ91, were examined over a range of strain rates between 1000 and 1400 s⁻¹ using Split Hopkinson Pressure Bar. Texture measurements showed that after shock loading, initial weak texture of the cast samples transformed to a relatively strong (00.2) basal texture that can be ascribed to deformation by twinning. Furthermore, increasing the aluminum content in the alloys resulted in increase in the volume fraction of β-Mg₁₇Al₁₂ and Al₄Mn phases, strength and strain hardening but ductility decreased at all strain rates. Besides, it was found for each alloy that the tensile strength and total ductility increased with strain rate. By increasing the strain rate, the maximum value of strain hardening rate occurred at higher strains. Also, it is suggested that a combination of twinning and second phase formation would affect the hardening behavior of the cast AZ magnesium alloys studied in this research.     

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 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.     

Analytical and experimental studies on mechanical behavior of composites under high strain rate compressive loading

An analytical method is presented for the prediction of compressive strength at high strain rate loading for composites. The method is based on variable rate power law. Using this analytical method, high strain rate compressive stress–strain behavior is presented up to strain rate of 5000 s⁻¹ starting with the experimentally determined compressive strength values at relatively lower strain rates. Experimental results were generated in the strain rate range of 472–1957 s⁻¹ for a typical woven fabric E-glass/epoxy laminated composite along all the three principal directions. The laminated composite was made using resin film infusion technique. The experimental studies were carried out using compressive split Hopkinson pressure bar apparatus. It was generally observed that the compressive strength is enhanced at high strain rate loading compared with that at quasi-static loading. Also, compressive strength increased with increasing strain rate in the range of parameters considered. Analytically predicted results are compared with the experimental results up to strain rate of 1957 s⁻¹.     

Effects of strain rate 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.     

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.     

Tensile flow behavior of ultra low carbon,low carbon and micro alloyed steel sheets for auto application under low to intermediate strain rate

This paper is concerned with tensile characteristics of auto grade low carbon, ultra low carbon and micro alloyed steel sheets under low to intermediate strain rates ranging from 0.0007 to 250 s⁻¹. Experimental investigation reveals two important aspects of these steels under intermediate strain rate deformation. Firstly, the yield stress increases with strain rate in all these steels. Of course yield stress increment is higher for low carbon and ultra low carbon steel sheets. Secondly, the strain hardening rate drastically decreases with strain rate for low carbon and ultra low carbon steel sheets, whereas it remains steady for micro alloyed steel sheets. Based on these observations, a constitutive model has been proposed which predicts the strain rate sensitive flow behavior of all these grades within the strain rate range of automotive crash event.     

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.     

High temperature flow behavior and constitutive model of alloy transition layer in composite steel tube prepared by centrifugal self-propagating high-temperature synthesis (SHS)

Centrifugal self-propagation high-temperature synthesis (SHS) is a newly developed composite preparation technique by which a ceramic-alloy-carbon steel multilayer composite tube can be prepared. The hot deformation behaviors of the alloy steel layer at 800 °C–1000 °C, strain rates of 0.01 s⁻¹, 0.1 s⁻¹, 1.0 s⁻¹ and 10 s⁻¹ were studied by Gleeble-1500 thermal simulator. Rheological curve characteristics were analyzed under different thermal compression processes and a phenomenological hyperbolic sinusoidal Arrhenius constitutive equation was established to characterize the rheological mechanics of the material. The results show that the alloy steel is sensitive to temperature and strain rate, and its value of true stress decreases with the increase of temperature and strain rate. Thermal deformation process is the interaction between work hardening and dynamic softening, which is accompanied by the increase and extinction of dislocations. Under the strain rate of 10 s⁻¹, the stress-strain curve has a significant decrease when the strain exceeds 0.5. According to the observation of microstructure, this phenomenon can be attributed to the micro-crack generated by the local instability flow in the denatured zone. With the strain rate decreases, the softening mechanism of the alloy changes from dynamic recovery to dynamic recrystallization. The calculation results of the Arrhenius constitutive equation (AARE = 6.54 %, R = 0.99452) indicate that the model can predict the flow stress of the alloy accurately.     

Strain hardening of as-extruded Mg-xZn (x = 1, 2, 3 and 4 wt%) alloys

The influence of Zn on the strain hardening of as-extruded Mg-x Zn(x = 1, 2, 3 and 4 wt%) magnesium alloys was investigated using uniaxial tensile tests at 10~(-3)s~(-1) at room temperature. The strain hardening rate,the strain hardening exponent and the hardening capacity were obtained from true plastic stress-strain curves. There were almost no second phases in the as-extruded Mg-Zn magnesium alloys. Average grain sizes of the four as-extruded alloys were about 17.8 μm. With increasing Zn content from 1 to 4 wt%, the strain hardening rate increased from 2850 MPa to 6810 MPa at(б-б_(0.2)) = 60 MPa, the strain hardening exponent n increased from 0.160 to 0.203, and the hardening capacity, Hc increased from 1.17 to 2.34.The difference in strain hardening response of these Mg-Zn alloys might be mainly caused by weaker basal texture and more solute atoms in the α-Mg matrix with higher Zn content.