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.     

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.     

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.     

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.     

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.     

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.     

Hot deformation and processing maps of X-750 nickel-based superalloy

The deformation behavior of X-750 superalloy was investigated using the hot compression test in the temperature range of 850–1050 °C, and strain rate of 0.1–50 s⁻¹. The experimental results show that the flow stress of superalloy is significantly sensitive to the strain, the strain rate and the deformation temperature. Using dynamic materials model the processing maps of X-750 superalloy at strain of 0.1, 0.3 and 0.5 were established respectively. Microstructure observations reveal that the grain size as well as the volume fraction of the recrystallized grains increased at higher deformation temperature or lower strain rate. At strain of 0.5, the flow instability domain mainly located at lower temperature which is associated with shear band formation and flow localization. The optimum parameters for hot working of the alloy are deformation temperature of 1000–1050 °C and strain rate of 0.1–1 s⁻¹ according to the processing map and microstructure at true strain of 0.5.     

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.     

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.     

Quantitative Analysis of Work Hardening and Dynamic Softening Behavior of low carbon alloy Steel Based on the Flow Stress

In this study, the constitutive equation and DRX(Dynamic recrystallization) model of Nuclear Pressure Vessel Material 20MnNiMo steel were established to study the work hardening and dynamic softening behavior based on the flow behavior, which was investigated by hot compression experiment at temperature of 950 °C, 1050 °C, 1150 °C and 1250 °C with strain rate of 0.01 s⁻¹, 0.1 s⁻¹ and 10 s⁻¹ on a thermo-mechanical simulator THE RMECMASTOR-Z. The critical conditions for the occurence of dynamic recrystallization were determined based on the strain hardening rate curves of 20MnNiMo steel. Then the model of volume fraction of DRX was established to analyze the DRX behavior based on flow curves. At last, the strain rate sensitivity and activation volume V^* of 20MnNiMo steel were calculated to discuss the mechanisms of work hardening and dynamic softening during the hot forming process. The results show that the volume fraction of DRX is lower with the higher value of Z (Zener–Hollomon parameter), which indicated that the DRX fraction curves can accurately predicte the DRX behavior of 20MnNiMo steel. The storage and annihilation of dislocation at off-equilibrium saturation situation is the main reason that the strain has significant effects on SRS(Strain rate sensitivity) at the low strain rate of 0.01 s⁻¹ and 0.1 s⁻¹. While, the effects of temperature on the SRS are caused by the uniformity of microstructure distribution. And the cross-slip caused by dislocation piled up which beyond the grain boundaries or obstacles is related to the low activation volume under the high Z deformation conditions. Otherwise, the coarsening of DRX grains is the main reason for the high activation volume at low Z under the same strain conditions.     

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.     

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.     

Investigation of cold rolling variables on the formation of strain-induced martensite in 201L stainless steel

In this work, effects of cold rolling variables including strain, strain rate, strain path, initial austenite grain size and rolling temperature on the formation of strain-induced martensite in AISI 201L stainless steel are investigated. Cold rolling was carried out at −40, −10, and 25 °C with strain rates of 0.1–1.2 s⁻¹ and thickness reductions of 0–95%. The results showed that saturation strain of martensite formation during cold rolling at room temperature with the strain rate of 0.5 s⁻¹ was about 0.5. Increasing the strain, strain rate, and initial austenite grain size, decreasing rolling temperature, and the use of cross rolling resulted in an increase in the volume fraction of strain-induced martensite and a decrease in the saturation strain value. It was found that effect of decreasing rolling temperature and cross rolling was more effective on the formation of strain-induced martensite compared to other parameters, leading to a reduction of saturation strain from 0.5 to 0.28.     

Hot deformation behavior and workability characteristics of bimodal size SiCp/AZ91 magnesium matrix composite with processing map

The hot deformation behavior of (0.2 um 1.5 vol.% + 10 um8.5 vol.%) bimodal size SiCp/AZ91 magnesium matrix composite fabricated by stir casting was investigated at the temperature of 270–420 °C and strain rate of 0.001–1 S⁻¹. The flow stress at the strain of 0.5 was used for kinetic analysis. Results indicate that dislocation climb is likely to be the main deformation mechanism responsible for the present composite. By evaluating the efficiencies of power dissipation and instability parameters, the processing maps are developed to optimize the hot working processing. Two domains of dynamic recrystallization are found in the processing map. One exists at the temperature of 270–370 °C and strain rate of 0.001–0.01 s⁻¹ with maximum dissipation efficiency of 38%; the other exists at 420 °C and 0.01 s⁻¹ with peak dissipation efficiency of 24%. The instability region of flow behavior can also be recognized at the temperature of 270–320 °C and the strain rate of 0.1–1 s⁻¹. The characteristic microstructures predicted from the processing map agree well with the result of microstructure observations.     

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.     

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.     

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.     

Effect of processing parameters on the hot deformation behavior of as-cast TC21 titanium alloy

Isothermal compression tests of as-cast Ti–6A1–2Zr–2Sn–3Mo–1Cr–2Nb (TC21) titanium alloy are conducted in the deformation temperature ranging from 1000 to 1150 °C with an interval of 50 °C, strain rate ranging from 0.01 to 10.0 s⁻¹ and height reductions of 30%, 45%, 60% and 75% on a computer controlled Gleeble 3500 simulator. The true stress–strain curves under different deformation conditions are obtained. Based on the experimental data, the effects of deformation parameters on the hot deformation behavior of as-cast TC21 alloy were studied. The deformation mechanisms of the alloy in the whole regimes are predicted by the power dissipation efficiency and instability parameter and further investigated through the microstructure observation. It is found that at the height reductions of 30%, 45% and 60%, the softening of stress–strain curves at high strain rate (>1.0 s⁻¹) is mainly associated with flow localization, which is caused by local temperature rise, whereas at low strain rate, the softening is associated with dynamic recrystallization (DRX). However, the instability showed in flow localization occurs at low strain rate of 0.01 s⁻¹ when the height reduction reaches 75%. In addition, the effects of strain rate, deformation temperature and height reduction on microstructure evolution are discussed in detail, respectively.     

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.