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.     

Constitutive analysis to predict high temperature flow stress in 20CrMo continuous casting billet

The experimental true strain–true stress data from isothermal hot compression tests on a Gleeble-1500D thermal simulation machine, across a wide range of temperatures (1173–1373 K) and strain rates (1.5 × 10⁻³–1.5 × 10⁻² s⁻¹), were employed to study the deformation behavior and develop constitutive equations of 20CrMo alloy continuous casting billet steel. The objective was to obtain the relational expression for deformation activation energy and material constants as a function of true strain and the constitutive equation for high temperature deformation of 20CrMo based on the hyperbolic sine form model. A correlation coefficient of 0.988 and an average absolute relative error between the experimental and the calculated flow stress of 8.40% have been obtained. This indicates that the constitutive equations can be used to accurately predict the flow behavior of 20CrMo alloy steel continuous casting billet during high temperature deformation.     

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.     

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.     

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.     

A modified Zerilli–Armstrong constitutive model to predict hot deformation behavior of 20CrMo alloy steel

True stress and true strain values were obtained from isothermal hot compression tests conducted on a Gleeble thermal simulation machine, in a wide range of temperatures (1173–1373 K) and strain rates (1.5 × 10⁻³–1.5 × 10⁻² s⁻¹). The experimental data were used to develop a modified Zerilli–Armstrong constitutive model. The predicted flow stresses using the developed model were compared with experimental values. A correlation coefficient (R) of 0.989 and an average absolute relative error (AARE) of 7.71% between the measured and calculated flow stresses have been obtained. Comparing with a modified Johnson–Cook model developed in the authors’ previous study, the accuracy, the number of material constants involved and the computational time required of the model were evaluated.     

A comparative study on modified Johnson Cook,modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict the hot deformation behavior in 28CrMnMoV steel

The true stress-strain data from isothermal hot compression tests on Gleeble-3500 thermo mechanical simulator, in a wide range of temperatures (1173–1473 K) and strain rates (0.01–10 s⁻¹), were employed to establish the constitutive equations based on modified Johnson Cook, modified Zerilli–Armstrong, and strain-compensated Arrhenius-type models respectively to predict the high-temperature flow stress of 28CrMnMoV steel. Furthermore, a comparative study has been made on the capability of the three models to represent the elevated temperature flow behavior of this steel. Suitability of the three models were evaluated by comparing the accuracy of prediction of deformation behavior, correlation coefficient, average absolute relative error (AARE) and relative errors of prediction, the number of material constants, and the time needed to evaluate these constants. The results showed that the predicted values by the modified Johnson Cook and Zerilli–Armstrong models could agree well with the experimental values except under the strain rate of 0.01 s⁻¹. However, the strain-compensated Arrhenius-type model could track the deformation behavior more accurately throughout the entire temperature and strain rate range.     

Low-temperature superplasticity of Al2O3(p)/Ni–Co nanocomposites

Nanocomposites of Al₂O₃/Ni–Co prepared using Al₂O₃ of various particle sizes were fabricated by pulse current electrodeposition. Their superplastic tensile deformation was investigated at strain rates of 8.33 × 10⁻⁴ s⁻¹ and 1.67 × 10⁻³ s⁻¹ and temperatures of 723–823 K. The Al₂O₃ particle sizes and the deformation temperature had significant influence on the elongation of the deposited materials. The optimal superplastic condition and the maximum elongation were determined. A low temperature superplasticity with elongation of 632% was achieved at a strain rate of 1.67 × 10⁻³ s⁻¹ and 823 K. Scanning electron microscopy and transmission electron microscopy were used to examine the microstructures of the deposited and deformed samples. The grains grew to a micrometer dimensions and were elongated along the tensile direction after superplastic deformation. Superplasticity in electrodeposited nanocomposites is related to the presence of S at grain boundaries and to deformation twinning.     

Effect of strain rate on cushioning properties of molded pulp products

Molded pulp product is widely used in distribution chains as a cushioning packaging of industrial products due to its favorable cushioning capability. How to evaluate the cushioning capability of molded pulp product is the key issue many scholars are interesting in. The load carrying capacity and energy absorbing of the molded pulp products used in the cushion packaging of mobile phones both in the static compression and dynamic impact were investigated in this paper by applying the experiment and finite element analysis. The static compression was conducted with the compression speed of 12 mm/min corresponding to the nominal strain rate 3.8 × 10⁻³ s⁻¹, and the dynamic impact tests were conducted with three drop heights of 25, 50 and 80 cm corresponding respectively to the nominal strain rates 4.2 × 10¹, 6.0 × 10¹ and 7.5 × 10¹ s⁻¹. The high speed camera was used to record the dynamic impact process and deformation. The finite element model of molded pulp product was built, and the stress and displacement nephograms, the dynamic impact deformation process, the load–displacement curve and the energy absorption curve of the molded pulp product were archived. The comparison between the finite element analysis and the experiment was made. The load–displacement curve of the finite element analysis is in agreement with that of the experiment in the static compression, and the energy absorption curves of the finite element analysis with different nominal strain rates are in agreement with that of the experiment in the area of the point of optimum energy absorption. However, a growing gap between the finite element analysis and the experiment appears with the nominal strain rate increasing, which may be induced by the use of the static stress–strain curve of the material in the finite element analysis of dynamic impact. The molded pulp product experiences the process from structural deformation, local stress concentration, first local buckling, redistribution of stress, global buckling, to structural dilapidation and densification. Two obvious buckling processes occur because of its complicated structure and two layers in structure. However, some additional local buckling also occur before the global buckling of structure in the case of dynamic impact with higher nominal strain rate. The deformation processes of molded pulp product from the finite element analysis and the experiment recorded by high-speed camera are coincident. With the nominal strain rate increasing, the yield stress of molded pulp product increases obviously, and the shoulder point of the energy absorption curve moves upward to the right. The yield stress under the dynamic impact at a drop height of 80 cm increases 59.4% compared with that under the static compression, and the corresponding optimum energy absorption increases 85.4%. The effects of strain rate on the load carrying capacity and the energy absorption of molded pulp product are remarkable. The results can be applied to the design of molded pulp products.     

High strain-rate superplasticity of fine- and ultrafine-grained AA5083 aluminum alloy at intermediate temperatures

Superplastic behavior of fine and ultra fine-grained AA5083 Al alloy was examined using the shear punch test. To achieve fine- and ultra fine-grained microstructures, a relatively new severe plastic deformation (SPD) process, namely Double Equal Channel Lateral Extrusion (DECLE) was employed. The strain rate sensitivity indices (m) of samples were evaluated after 1, 2, 4, and 6 passes for shear strain rates in the range of 3 × 10^− 3 to 3 × 10^− 1 s^− 1 and temperatures in the range of 573 to 673 K. For microstructural observations, TEM images together with the corresponding SAED patterns were prepared and utilized. A considerable increase in the m-value was observed after the first pass of the operation for all testing temperatures. The best condition for achieving a good superplasticity for the alloy was found to be a single pass DECLE at 673 K in the strain rate range of 10^− 2 to 10^− 1 s^− 1. This process condition resulted in an m-value of 0.43, indicative of a high strain rate superplastic deformation behavior. Further passes of the SPD process did not show any sign of superplasticity until the last pass of the operation, during which the m-value slightly increased, compared with the previous pass.     

Hot shear deformation constitutive analysis and processing map of extruded Mg–12Li–1Zn bcc alloy

The hot shear deformation behavior of an extruded Mg–12Li–1Zn alloy was studied by shear punch test (SPT) in the temperature range 200–300 °C, and in the shear strain rate range 1.2 × 10⁻³–6.0 × 10⁻² s⁻¹. Based on the constitutive analysis of the SPT data, it was found that a sine hyperbolic function could properly describe the hot shear deformation behavior of the material. The activation energy of 108 kJ mol⁻¹ calculated from sine hyperbolic function together with the power-law stress exponents of 3.6–4.7 is indicative of lattice-diffusion-controlled dislocation climb mechanism as an operative deformation mechanism. As a new approach, the shear processing map was developed in order to determine the optimum processing condition, which was found to be 300 °C and 1.2 × 10⁻³ s⁻¹. Domains of the processing map are also interpreted on the basis of the associated microstructural observations. It was found that the post-deformation microstructure is sensitive to the Zener–Hollomon parameter, so that DRX was encouraged with decreasing Z-value.     

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.     

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.     

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.     

Dynamic tensile deformation and fracture of metal cylinders at high strain rates

An experimental study has been presented on the radial deformation of aluminium and copper cylinders of internal diameter 52 mm and wall thickness 1–7 mm, internally loaded with high explosives. High speed photography and flash radiography have been employed to record the distance–time (x–t) history of the cylinder wall, which has been found to expand under strain rates of 10⁴–10⁵ s⁻¹. The rupture of the cylinder is identified by the leakage of detonation gases, through the cracks in the cylinder wall. Rupture strains of 70–160% have been found for commercially pure aluminium. For a fixed wall thickness, the rupture strain increases with the strain rate. However, when the cylinder wall thickness is changed, a maximum is observed in a graph showing the strain and strain rate relationship. Aluminium appears to follow the Ivanov rupture criteria. From the experimental data the macroscopic viscosity coefficient for aluminium has been found to be 0.55–0.87×10³ Pa s. In the deformation of a copper cylinder the cracks initiate at strains of 30–60%, followed by rupture at very high strains up to 300%. The crack propagation velocity through the copper cylinder wall has been found to be 250–300 m/s. Recovered fragments show wall thinning by 50–60% and also exhibit shear fracture which dominates the radial fracture in high velocity deformation of the metal cylinder.     

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.     

Experimental study on tensile property of AZ31B magnesium alloy at different high strain rates and temperatures

As the lightest metal material, magnesium alloy is widely used in the automobile and aviation industries. Due to the crashing of the automobile is a process of complicated and highly nonlinear deformation. The material deformation behavior has changed significantly compared with quasi-static, so the deformation characteristic of magnesium alloy material under the high strain rate has great significance in the automobile industry. In this paper, the tensile deformation behavior of AZ31B magnesium alloy is studied over a large range of the strain rates, from 700 s⁻¹ to 3 × 10³ s⁻¹ and at different temperatures from 20 to 250 °C through a Split-Hopkinson Tensile Bar (SHTB) with heating equipment. Compared with the quasi-static tension, the tensile strength and fracture elongation under high strain rates is larger at room temperature, but when at the high strain rates, fracture elongation reduces with the increasing of the strain rate at room temperature, the adiabatic temperature rising can enhance the material plasticity. The morphology of fracture surfaces over wide range of strain rates and temperatures are observed by Scanning Electron Microscopy (SEM). The fracture appearance analysis indicates that the fracture pattern of AZ31B in the quasi-static tensile tests at room temperature is mainly quasi-cleavage pattern. However, the fracture morphology of AZ31B under high strain rates and high temperatures is mainly composed of the dimple pattern, which indicates ductile fracture pattern. The fracture mode is a transition from quasi-cleavage fracture to ductile fracture with the increasing of temperature, the reason for this phenomenon might be the softening effect under the high strain rates.     

Effects of Co content on tensile properties and deformation behaviors of Ni-based disk superalloys at different temperatures

Tensile properties of three Ni-based disk superalloys with 5 wt.%, 15 wt.% and 23 wt.% Co contents were investigated from room temperature (RT) to 725 °C with a constant strain rate of 3 × 10^− 4 s^− 1. It is found that addition of Co enhances the yield strength and the strain hardening capacity of the alloy in the studied temperature regime. It is due to the following two reasons: i.e. the interactions between a large volume fraction of fine secondary and tertiary γ′ precipitates with the dislocations in slip bands at lower temperatures and the formation of deformation microtwins at higher temperatures. However, the formation of deformation microtwins in the high Co-containing content alloy sharply decreases the ductility at higher temperatures.     

Hot deformation and processing map of an as-extruded Mg–Zn–Mn–Y alloy containing I and W phases

The hot deformation characteristics of an as-extruded ZM31 (Mg–Zn–Mn) magnesium alloy with an addition of 3.2 wt.% Y, namely ZM31 + 3.2Y, have been studied via isothermal compression testing in a temperature range of 300–400 °C and a strain rate range of 0.001–1 s^− 1. A constitutive model based on hyperbolic-sine equation along with processing maps was used to describe the dependence of flow stress on the strain, strain rate, and deformation temperature. The flow stress was observed to decrease with increasing deformation temperature and decreasing strain rate. The deformation activation energy of this alloy was obtained to be 241 kJ/mol. The processing maps at true strains of 0.1, 0.2, 0.3 and 0.4 were generated to determine the region of hot workability of the alloy, with the optimum hot working parameters being identified as deformation temperatures of 340–500 °C and strain rates of 0.001–0.03 s^− 1. EBSD examinations revealed that the dynamic recrystallization occurred more extensively and the volume fraction of dynamic recrystallization increased with increasing deformation temperature. The role of element Y and second-phase particles (I- and W-phases) during hot compressive deformation was discussed.