Effect of strain rate and deformation temperature on strain hardening and softening behavior of pure copper

The effects of the deformation temperature and the strain rate on the hot deformation behavior of pure copper were investigated based on compression tests. The expressions of strain hardening rate, dynamic recrystallization critical stress, saturated stress, dynamic recovery volume fraction and dynamic recrystallization volume fraction were determined. According to the processing map, the instability regions occur in regions of 400?450 °C, 0.001?0.05 s?1 and 450?750 °C, 0.05?1 s?1. The deformation mechanism in the stability region is dynamic recrystallization. The flow stress was predicted. The results also show that the true stress–true strain curves predicted by the extracted model are in good agreement with the experimental results.

Strain rate-dependent high temperature compressive deformation characteristics of ultrafine-grained pure aluminum produced by ECAP

To explore the effect of strain rate ε on the high temperature deformation characteristics of ultrafine-grained materials, the deformation and damage features as well as microstructures of ECAP-treated pure Al at different temperatures T and strain ratesε were systematically studied through compression tests and microscopic observations. The increase in ε eliminates strain softening at T≤473 K, and largely enhances the yield strength and flow stress at 473?573 K. The shear deformation dominates the plastic deformation of ECAP-treated Al. Many cracks along shear bands (SBs) are formed at T≥473 K and secondary SBs basically disappear at 1×10?3 s?1; however, at 1×10?2 s?1, cracks are only observed at temperature below 473 K, and secondary SBs become clearer at T≥473 K. The microstructures of ECAP-treated Al mainly consist of sub-grains (SGs). The increase in ε inhibits the SG growth, thus leading to the increases both in yield strength and flow stress at high temperatures.

Hot deformation behavior of microstructural constituents in a duplex stainless steel during high-temperature straining

The hot deformation characteristics of 1.4462 duplex stainless steel （DSS） were analyzed by considering strain partitioning between austenite and ferrite constituents. The individual behavior of ferrite and austenite in microstructure was studied in an iso-stress condition. Hot compression tests were performed at temperatures of 800-1100~C and strain rates of 0.001-1 s-1. The flow stress was modeled by a hyperbolic sine constitutive equation, the corresponding constants and apparent activation energies were determined for the studied alloys. The constitutive equation and law of mixture were used to measure the contribution factor of each phase at any given strain. It is found that the contribution factor of ferrite exponentially declines as the Zener-HoUomon parameter （Z） increases. On the contrary, the austenite contribution polynomially increases with the increase of Z. At low Z values below 2.6. x 1015 （lnZ---35.5）, a negative contribution factor is determined for austenite that is attributed to dynamic recrystallization. At high Z values, the contribution factor of austenite is about two orders of magnitude greater than that of ferrite, and therefore, austenite can accommodate more strain. Microstructural characterization via electron back-scattered diffraction （EBSD） confirms the mechanical results and shows that austenite recrystallization is possible only at high temperature and low strain rate.

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

High temperature deformation and recrystallization behavior of magnesium bicrystals with 90°<1010>and 90°<1120>tilt grain boundaries

The deformation mechanisms and dynamic recrystallization(DRX)behavior of specifically grown bicrystals with a symmetric 90°<1010>and 90°<1120>tilt grain boundary,respectively,were investigated under deformation in plane strain compression at 200℃and 400℃.The microstructures were analyzed by panoramic optical microscopy and large-area electron backscatter diffraction(EBSD)orientation mapping.The analysis employed a meticulous approach utilizing hundreds of individual,small EBSD maps with a small step size that were stitched together to provide comprehensive access to orientation and misorientation data on a macroscopic scale.Basal slip primarily governed the early stages of deformation at the two temperatures,and the resulting shear induced lattice rotation around the transverse direction(TD)of the sample.The existence of the grain boundary gave rise to dislocation pile-up in its vicinity,leading to much larger TD-lattice rotations within the boundary region compared to the bulk.With increasing temperature,the deformation was generally more uniform towards the bulk due to enhanced dislocation mobility and more uniform stress distribution.Dynamic recrystallization at 200℃was initiated in{1011}-compression twins at strains of 40%and higher.At 400℃,DRX consumed the entire grain boundary region and gradually replaced the deformed microstructure with progressing deformation.The recrystallized grains displayed characteristic orientations,such that their c-axes were perpendicular to the TD and additionally scattered between 0°and 60°from the loading axis.These recrystallized grains displayed mutual rotations of up to 30°around the c-axes of the initial grains,forming a discernible basal fiber texture component,prominently visible in the{1120}pole figure.It is noteworthy that the deformation and DRX behaviors of the two analyzed bicrystals exhibited marginal variations in response to strain and deformation temperature.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Deformation mechanism of fine grained Mg-7Gd-5Y-l.2Nd-0.5Zr alloy under high temperature and high strain rates

Fine grained Mg-7Gd-5Y-1.2Nd-0.5Zr alloy was investigated by dynamic compression tests using a Split Hopkinson Pressure Bar under the strain rates in the range 1000-2000 s^(-1) and the temperature range 293-573 K along the normal direction.The microstructure was measured by optical microscopy,electron back-scattering diffraction,transmission electron microscopy and X-ray diffractometry.The results showed that Mg-7Gd-5Y-1.2Nd-0.5Zr alloy had the positive strain rate strengthening effect and thermal softening effect at high temperature.The solid solution of Gd and Y atoms in Mg-7Gd-5Y-1.2Nd-0.5Zr alloy reduced the asymmetry of α-Mg crystals and changed the critical shear stress of various deformation mechanisms.The main deformation mechanisms were prismatic slip and pyramidal(a)slip,{102}tension twinning,and dynamic recrystallization caused by local deformation such as particle-stimulated nucleation.c 2020 Published by Elsevier B.V.on behalf of Chongqing University.

Modeling of strain hardening and dynamic recrystallization of ZK60 magnesium alloy during hot deformation

The flow stress behavior of ZK60 alloy at elevated temperature was investigated. The strain hardening and dynamic recrystallization of the alloy were modeled by Kocks-Meching model and Avrami equation, respectively. A new constitutive equation during hot deformation was constructed to predict the flow stress considering the dynamic recrystallization. The results show that the flow stress curves predicted by the proposed equation have high correlation coefficients with the experimental data, which confirms that the developed model is accurate and effective to establish the flow stress equation of ZK60 magnesium alloy during hot deformation. Microstructure observation shows that dynamic recovery occurs in the initial stage of hot deformation. However, the microstructure turns to recrvstallization structure as the strain increases.

Constitutive equations for high temperature flow stress prediction of 6063 Al alloy considering compensation of strain

In order to develop the appropriate constitutive equation which can precisely model high temperature flow stress of 6063 Al alloy, a series of isothermal hot compression tests were performed at temperatures from 573 to 773 K and strain rates from 0.5 to 50 s?1 on a Gleeble?1500 thermo-simulation machine. Zener–Hollomon parameter in an exponent-type equation was used to describe the combined effects of temperature and strain rate on hot deformation behaviour of 6063 Al alloy, whereas the influence of strain was incorporated in the developed constitutive equation by considering material constants (α,n,Q andA) to be 4th order polynomial functions of strain. The results show that the developed constitutive equation can accurately predict high temperature flow stress of 6063 Al alloy, which demonstrates that it can be suitable for simulating hot deformation processes such as extrusion and forging, and for properly designing the deformation parameters in engineering practice.

Construction and solution of strain model along thickness of aluminum alloy plate under plastic deformation

A thickness strain model of aluminium alloy plate under plastic deformation,based on thin plate assumption was proposed.It is found that when ratio of stress fractions is constant during in-plane loading,ratios of strain components under various loading conditions are linearly related and these points of ratios form a η-η line.Under these simple loadings,strains in thickness direction can be easily calculated by the η-η line equation without integral and differential work.When the plate is under more complicated loading conditions,the thickness can be computed by the proposed optimization and piecewise calculation model.Validation computations indicate that the relative error of the results of the presented model is less than 0.75% compared with the proven theories and FE simulation.Therefore,the developed model can be applied to engineering calculation,e.g.pre-stretching analysis of aerospace aluminium thick plate,with acceptable accuracy.

Research on elevated temperature deformation behavior of Ti-6Al-4V sheets

Hot deformation behaviors were studied by means of scanning electron microscopy （SEM） and uniaxial thermal tension. The effect of deformation temperature and strain rate on flow stress was evaluated, and deformation mechanism was analyzed. The results show that the stress-strain curves of Ti-6Al-4V （TC4） alloy sheet and TC4 alloy bar at elevated temperatures have different forms and rules. Flow stress of TC4 is controlled by both strain rate and deformation temperature. The flow stress decreases with the increase of high temperature. Deformation mechanisms exhibit dynamic recovery and recrystallization feature within high temperature region and grain boundary slip behaviors at low temperature.

Crustal strain rates of southeastern Tibetan Plateau derived from GPS measurements and implications to lithospheric deformation of the Shan-Thai terrane

The link between the crustal deformation and mantle kinematics in the Tibetan Plateau has been well known thanks to dense GPS measurements and the relatively detailed anisotropy structure of the lithospheric mantle.However, whether the crust deforms coherently with the upper mantle in the Shan-Thai terrane(also known as the Shan-Thai block) remains unclear.In this study, we investigate the deformation patterns through strain rate tensors in the southeastern Tibetan Plateau derived from the latest GPS measurements and find that in the Shan-Thai terrane the upper crust may be coupled with the lower crust and the upper mantle.The GPS-derived strain rate tensors are in agreement with the slipping patterns and rates of major strike-slip faults in the region.The most prominent shear zone, whose shear strain rates are larger than 100×10^(–9) a^(–1), is about 1000-km-long in the west, trending northward along Sagaing fault to the Eastern Himalayan Syntaxis in the north, with maximum rate of compressive strain up to –240×10^(–9) a^(–1).A secondary shear zone along the Anninghe-Xiaojiang Fault in the east shows segmented shear zones near several conjunctions.While the strain rate along RRF is relatively low due to the low slip rate and low seismicity there, in Lijiang and Tengchong several local shear zones are present under an extensional dominated stress regime that is related to normal faulting earthquakes and volcanism, respectively.Furthermore, by comparing GPS-derived strain rate tensors with earthquake focal mechanisms, we find that 75.8%(100 out of 132) of the earthquake T-axes are consistent with the GPS-derived strain rates.Moreover, we find that the Fast Velocity Direction(FVDs) at three depths beneath the Shan-Thai terrane are consistent with extensional strain rate with gradually increasing angular differences, which are likely resulting from the basal shear forces induced by asthenospheric flow associated with the oblique subduction of the India plate beneath the Shan-Thai terrane.Therefore, in this region the upper crust deformation may be coherent with that of the lower crust and the lithospheric mantle.

Effect of strain rate on the compressive deformation behaviors of lotus-type porous copper

Lotus-type porous copper was fabricated by unidirectional solidification, and compressive experiments were subsequently conducted in the strain rate range of 10-3-2400 s-1 with the compressive direction parallel to the pores. A GLEEBLE-1500 thermal-mechanical simulation system and a split Hopkinson pressure bar （SHPB） were used to investigate the effect of strain rate on the compressive deforma-tion behaviors of lotus-type porous copper. The influence mechanism of strain rate was also analyzed by the strain-controlling method and by high-speed photography. The results indicated that the stress-strain curves of lotus-typed porous copper consist of a linear elastic stage, a plateau stage, and a densification stage at various strain rates. At low strain rate （〈1.0 s^-1）, the strain rate had little influence on the stress-strain curves; but when the strain rate exceeded 1.0 s^-1, it was observed to strongly affect the plateau stage, showing obvious strain-rate-hardening characteristics. Strain rate also influenced the densification initial strain. The densification initial strain at high strain rate was less than that at low strain rate. No visible inhomogeneous deformation caused by shockwaves was observed in lotus-type porous copper during high-strain-rate deformation. However, at high strain rate, the bending deformation characteristics of the pore walls obviously differed from those at low strain rate, which was the main mechanism by which the plateau stress exhibited strain-rate sensitivity when the strain rate exceeded a certain value and exhibited less densification initial strain at high strain rate.

MICROSTRUCTURAL CHARACTERISTICS ASSOCIATED WITH HIGH- STRAIN-RATE PLASTIC DEFORMATION IN THE ELECTROFORMED COPPER LINER OF SHAPED CHARGES

The microstructures of electroformed copper liners of shaped charges that had undergone high-strain-rate deformation were observed by optical microscopy （OM） and scanning electron microscopy （SEM）. Meanwhile, the orientation distribution of the grains in the recovered jet was examined by electron backscattering Kikuchi pattern （EBSP） technique. EBSP analysis reveals that the fibrous texture observed in the as-electroformed copper liners disappeared after explosive detonation deformation. OM observation shows that the microstructure evolves system- atically from the jet center to its perimeter during cooling from high temperatures after explosive detonation deformation. This microstructural characteristic is similar to that of solidification, i.e. there exist equiaxed grains in the center of the jet and significant columnar grains around the equiaxed grains. The result reveals that there is melting-related phenomenon in the jet center. Corresponding microhardness variations from the jet center to its perimeter is also determined. All the phenomena can be explained by a strong gradient of temperature across the section of the jet during plastic deformation at high-strain-rate.

PREDICTION OF WELDING DEFORMATIONS BY FEM BASED ON INHERENT STRAINS

Welding deformations can be predicted by inherent strains that are assumed to be distributed in the welds and nearby area. This method is more convenient compared with the thermo elasto plastic finite element method because only elastic analysis is necessary. The problem is how to know the inherent strains in advance during deformation analysis. The relations between inherent strains and welding parameters based on some experimental curves and a 3 D FEM model were introduced. According to this study, the longitudinal and transverse inherent strains that are the most important factors on welding deformations can be determined. The effectiveness of the proposed methods is demonstrated through the deformation analysis of a large welded cylinder with multipass welds as an example.

The microstructure evolution and deformation mechanism in a casting AM80 magnesium alloy under ultra-high strain rate loading

Ultra-high strain rate impact tests were conducted by Split-Hopkinson pressure bar to investigate the microstructure evolution and impact deformation mechanism of a solution treated casting AM80 Mg alloy at 25, 150 and 250 ℃ with a strain rate of 5000 s^(-1). The microcrack and dynamic recrystallization(DRX) preferentially nucleate at grain boundary(GB) and twin boundary(TB), especially at the intersections between GBs and TBs, and then propagate along twin direction. In contrast, the adiabatic shear bands preferentially occur at high-density twined regions. At 25 ℃, the dominated deformation mechanisms are basal slip and twinning. As deformation temperature increases to 150and 250℃, the deformation gradually shifts to be dominated by a coordinated mechanism among non-basal slip, twinning and DRX. The flow stress behavior and deformation mechanism indicate that the degree of decrease in flow stress with temperature is associated with the change of deformation mode.

Effect of strain rate on hot deformation characteristics of GH690 superalloy

In order to clarify the effect of strain rate on hot deformation characteristics of GH690superalloy,the hot deformationbehavior of this superalloy was investigated by isothermal compression in the temperature range of1000?1200°C and strain raterange of0.001?10s?1on a Gleeble?3800thermo-mechanical simulator.The results reveal that the flow stress is sensitive to the strainrate,and the dynamic recrystallization(DRX)is the principal softening mechanism.The strain rate of0.1s?1is considered to be thecritical point during the hot deformation at1000°C.The DRX process is closely related to the strain rate due to the adiabatictemperature rise.The strain rate has an important influence on DDRX and CDRX during hot deformation.The nucleation of DRXcan be activated by twin boundaries,and there is a lower fraction ofΣ3n(n=1,2,3)boundaries at the intermediate strain rate of0.1s?1.

Flow stress equation in range of intermediate strain rates and high temperatures to predict roll force in four-pass continuous rod rolling

A flow stress equation was proposed to compute the roll force in the finishing stands of an actual rod mill where the strain rate and the temperature of the material range from 100 to 400 s-1 and from 900 to 1050 ℃,respectively.The underlying idea is to modify the Shida model and Misaka model,which provide flow stress equations（constitutive equations） frequently used to depict deformation behavior of high temperature material at different strain rates.The modified model was coupled with finite element method to compute the roll force during four-pass continuous rod rolling,where strain rates are in the range of 100-400 s-1 at high temperatures（900-1050 ℃）.The roll forces and the surface temperatures of the material at each stand were measured,and the measured data were compared with the computed values.Results reveal that the Misaka model is better than the Shida model for high temperatures and intermediate strain rates.The roll force error was-5.7 % when the Misaka model was used at 900 ℃.However,the error increased by-15.2% at 1050 ℃.When the modified Misaka model was used,the error was reduced to 1.8% on average.It can consequently be deduced that the modified Misaka model can be used to depict the deformation resistance behavior in intermediate ranges of strain rate and high temperature ranges in continuous rod rolling process.

A Model of Dynamic Recrystallization in Alloys during High Strain Plastic Deformation

Recrystallized grains, less than 200 nm in diameter were observed in heavily shear zones of a high strength low alloy steel and a Ni-based alloy, and Also grain refinement, less than 3 μm in diameter was made in high purity aluminum by ECAE at ambient temperature. The experimental results showed that high strain rate and large deformation could induce dynamic recrystallization.Based on dislocation dynamics and grain orientation change enhanced by plastic deformation,a model for the recrystallization process is developed. The model is used to explain the ultra fine grains which are formed at a temperature still much lower than that for the conventional recrystallization

Evaluating location specific strain rates, temperatures,and accumulated strains in friction welds through microstructure modeling

A microstructural simulation method is adopted to predict the location specific strain rates, temperatures, grain evolution, and accumulated strains in the Inconel 718 friction welds. Cellular automata based 2D microstructure model was developed for Inconel 718 alloy using theoretical aspects of dynamic recrystallization. Flow curves were simulated and compared with experimental results using hot deformation parameter obtained from literature work. Using validated model, simulations were performed for friction welds of Inconel 718 alloy generated at three rotational speed i.e., 1200, 1500, and1500 RPM. Results showed the increase in strain rates with increasing rotational speed. These simulated strain rates were found to match with the analytical results. Temperature difference of 150 K was noticed from center to edge of the weld. At all the rotational speeds, the temperature was identical implying steady state temperature(0.89 T_m) attainment.