Constitutive equations to predict high temperature flow stress in a Ti-modified austenitic stainless steel

The experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1123–1523 K) and strain rates (10⁻³–10² s⁻¹), were employed to develop constitutive equations in a Ti-modified austenitic stainless steel. The effects of temperature and strain rate on deformation behaviors were represented by Zener-Holloman parameter in an exponent type equation. The influence of strain was incorporated in the constitutive analysis by considering the effect of strain on material constants. The constitutive equation (considering the compensation of strain) could precisely predict the flow stress only at 0.1 and 1 s⁻¹ strain rates. A modified constitutive equation (incorporating both the strain and strain rate compensation), on the other hand, could predict the flow stress throughout the entire temperatures and strain rates range except at 1123 K in 10 and 100 s⁻¹. The breakdown of the constitutive equation at these processing conditions is possibly due to adiabatic temperature rise during high strain rate deformation.     

Effects of strain on the workability of a high strength low alloy steel in hot compression

Based on the experimental results from the hot compression tests of 42CrMo steel, the efficiencies of power dissipation and instability parameter were evaluated. The effects of strain on the efficiency of power dissipation and instability parameter of 42CrMo steel have been discussed in detail. Processing maps were constructed by superimposition of the instability map over the power dissipation map. The dynamic recrystallization domains and instable zones were identified in the processing map. The effects of strain on microstructural evolutions were correlated with the processing maps. According to the 3D processing maps, the optimum domain of hot deformation is in the temperature range of 1050–1150 °C and strain rate range of 0.01–3 s⁻¹, with its peak efficiency of 32% at about 1140 °C and 0.23 s⁻¹, which are the optimum hot working parameters.     

Hot deformation characteristics of 2205 duplex stainless steel based on the behavior of constituent phases

High temperature behavior of 2205 duplex stainless steel was studied by considering behavior of each constituent phase. The specimens were subjected to hot compression tests at temperatures of 800–1100 °C and strain rates ranging from 0.001 to 1 s⁻¹ at intervals of an order of magnitude. The flow stress analysis showed that hot working empirical constants are different at low and high temperatures. The strain rate sensitivity m was determined and found to change from 0.12 to 0.21 for a temperature rise from 800 °C to 1100 °C. The apparent activation energy Q was calculated as 554 and 310 kJ/mol for low and high temperature, respectively. The validity of constitutive equation of hyperbolic sine function was studied and stress exponent, n, was assessed to be 4.2. Assuming the hyperbolic sine function for determination of strain rate and application of the rule of mixture, the interaction coefficients of δ-ferrite, P, and austenite, R, were estimated at different hot working regimes. It was found that the interaction coefficients are functions of Zener–Hollomon parameter Z and obey the formulas P = 1.4Z^−0.08 and R = 0.76Z^0.005. Therefore, it was concluded that at low Z values δ-ferrite almost accommodates strain and dynamic recovery is the prominent restoration process which may even inhibit dynamic recrystallization in austenite. Otherwise, at high Z, austenite controls the deformation mechanism of material and dynamic recrystallization leads in finer microstructure.     

Experimental analysis and constitutive modeling for the newly developed 2139-T8 alloy

Mechanical behavior of recently emerged 2139-T8 aluminum alloy, which is based on an Al–Cu–Mg–Ag system, has been characterized by uniaxial compression and tension experiments over a wide range of strain rates from 10⁻⁴ to 10⁴ s⁻¹ and for temperatures from −60 to 300 °C. Driven by experimental results, modifications to widely used Johnson–Cook constitutive model has been proposed, and model parameters have been determined. It has been shown that modified Johnson–Cook (MJC) model satisfactorily captures rate- and temperature-dependent variations in flow stress through enhanced coupling between temperature and strain hardening as well as temperature and strain-rate sensitivity. The modified model also provides flow stress prediction over the entire range of quasi-static and dynamic regimes by a single continuous function.     

Artificial neural network and constitutive equations to predict the hot deformation behavior of modified 2.25Cr–1Mo steel

Hot compression tests of modified 2.25Cr–1Mo steel were conducted on a Gleeble-3500 thermo-mechanical simulator at the temperatures ranging from 1173 to 1473 K with the strain rate of 0.01–10 s⁻¹ and the height reduction of 60%. Based on the experimental results, an artificial neural network (ANN) model and constitutive equations were developed to predict the hot deformation behavior of modified 2.25Cr–1Mo steel. A comparative evaluation of the constitutive equations and the ANN model was carried out. It was found that the relative errors based on the ANN model varied from −4.63% to 2.23% and those were in the range from −20.48% to 12.11% by using the constitutive equations, and the average root mean square errors were 0.62 MPa and 7.66 MPa corresponding to the ANN model and constitutive equations, respectively. These results showed that the well-trained ANN model was more accurate and efficient in predicting the hot deformation behavior of modified 2.25Cr–1Mo steel than the constitutive equations.     

Constitutive modeling for flow behavior of GCr15 steel under hot compression experiments

The thermal compressive deformation behavior of GCr15 (AISI-52100), one of the most commonly used bearing steels, was studied on the Gleeble-3500 thermo-simulation system at temperature range of 950–1150 °C and strain rate range of 0.1–10 s⁻¹. According to the experimental results, the stress level decreases with increasing deformation temperature and decreasing strain rate. The peak stresses on the true stress–strain curves suggest that the dynamic softening of GCr15 steel occurs during hot compression tests. To formulate the thermoplastic constitutive equation of GCr15 steel, Arrhenius equation and the Zener–Hollomon parameter in an exponent-type equation were utilized in this paper. In addition, a modified Zener–Hollomon parameter considering the compensation of strain rate during hot compression was employed to improve the prediction accuracy of the developed constitutive equation. Analysis results indicate that the flow stress values predicted by the proposed constitutive model agree well with the experimental values, which confirms the accuracy and reliability of the developed constitutive equation of GCr15 steel.     

Wear behavior of carbide coated Co–Cr–Mo implant alloy

The wear behavior of a new type of metal carbide surface coating on Co–Cr–Mo implant alloy was studied. The coating was created using a microwave plasma-assisted reaction. Codeposition of impurity diamond film, diamond particles, and soot was prevented by controlling process conditions. Wear tests were carried out using a sapphire ball-on-Co–Cr–Mo disc unidirectional sliding configuration with harsh conditions of high contact stress and slow sliding speed in both no-lubrication, and deionized water lubrication environments. In the case of uncoated Co–Cr–Mo discs, the effect of deionized water lubrication was remarkable and reduced the wear factor by one order of magnitude compared to the no-lubrication tests. The wear factor of carbide coated Co–Cr–Mo discs was slightly smaller than that of uncoated Co–Cr–Mo discs with deionized water lubrication (2.7×10^–6 mm³N^–1m^–1 vs. 4.2×10^–6mm³N^–;1m^–1). The addition of deionized water lubrication did not greatly affect the wear factor of carbide coated Co–Cr–Mo discs. The influence of surface geometry resulting from the brain coral-like surface morphology of carbide layers on wear behavior was analyzed considering stress concentrations and effective contact area.     

Hot workability of 00Cr13Ni5Mo2 supermartensitic stainless steel

The hot workability of 00Cr13Ni5Mo2 supermartensitic stainless steel was investigated by hot compression and hot tension tests conducted over the temperature range of 950–1200 °C and strain rates varying between 0.1 and 50 s^?1. The processing map technique was applied on the basis of dynamic materials model and Prasad instability criterion. Microstructure evolutions, Zener–Hollomon parameter as well as hot tensile ductility were examined. The results show that, as for the hot working of 00Cr13Ni5Mo2 supermartensitic stainless steel in the industrial production, the large strain deformation should be carried out in the temperature range 1140–1200 °C and strain rate range 0.1–50 s^?1, where the corresponding Zener–Hollomon parameters exhibit low values. Moreover, when deformed under high strain rate range (above 15 s^?1), the deformation temperature can be reduced reasonably.     

Investigation of hot ductility in Al-killed boron steels

The influence of boron to nitrogen ratio, strain rate and cooling rate on hot ductility of aluminium-killed, low carbon, boron microalloyed steel was investigated. Hot tensile testing was performed on steel samples reheated in argon to 1300 °C, cooled at rates of 0.3, 1.2 and 3.0 °C s⁻¹ to temperatures in the range 750–1050 °C, and then strained to failure at initial strain rates of 1 × 10⁻⁴ or 1 × 10⁻³ s⁻¹. It was found that the steel with a B:N ratio of 0.19 showed deep hot ductility troughs for all tested conditions; the steel with a B:N ratio of 0.47 showed a deep ductility trough for a high cooling rate of 3.0 °C s⁻¹ and the steel with a near-stoichiometric B:N ratio of 0.75 showed no ductility troughs for the tested conditions. The ductility troughs extended from 900 °C (near the Ae₃ temperature) to 1000 or 1050 °C in the single-phase austenite region. The proposed mechanism of hot ductility improvement with increase in B:N ratio in these steels is that the B removes N from solution, thus reducing the strain-induced precipitation of AlN. Additionally, BN co-precipitates with sulphides, preventing precipitation of fine MnS, CuS and FeS, and forming large, complex precipitates that have no effect on hot ductility.     

Flow behavior and microstructural evolution of Al–Cu–Mg–Ag alloy during hot compression deformation

The flow behavior of Al–Cu–Mg–Ag alloy and its microstructural evolution during hot compression deformation were studied by thermal simulation test. The flow stress increased with increasing the strain rate, and decreased with increasing the deforming temperature, which can be described by a constitutive equation in hyperbolic sine function with the hot deformation activation energy 196.27 kJ/mol, and can also be described by a Zener–Hollomon parameter. The dynamic recrystallization only occurred at low Z values, which must be below or equal to a constant of 5.31 × 10¹³ s⁻¹. With decreasing Z value, the elongated grains coarsed and the tendency of dynamic recrystallization enhanced. Correspondingly, the subgrain size increased and the dislocation density decreased. And the main soften mechanism of the alloy transformed from dynamic recovery to dynamic recrystallization.     

Application of neural networks to predict the elevated temperature flow behavior of a low alloy steel

In order to study the workability and establish the optimum hot forming processing parameters for 42CrMo steel, the compressive deformation behavior of 42CrMo steel was investigated at the temperatures from 850 °C to 1150 °C and strain rates from 0.01 s⁻¹ to 50 s⁻¹ on Gleeble-1500 thermo-simulation machine. Based on these experimental results, an artificial neural network (ANN) model is developed to predict the constitutive flow behaviors of 42CrMo steel during hot deformation. The inputs of the neural network are deformation temperature, log strain rate and strain whereas flow stress is the output. A three layer feed forward network with 12 neurons in a single hidden layer and back propagation (BP) learning algorithm has been employed. The effect of deformation temperature, strain rate and strain on the flow behavior of 42CrMo steel has been investigated by comparing the experimental and predicted results using the developed ANN model. A very good correlation between experimental and predicted result has been obtained, and the predicted results are consistent with what is expected from fundamental theory of hot compression deformation, which indicates that the excellent capability of the developed ANN model to predict the flow stress level, the strain hardening and flow softening stages is well evidenced.     

Hot deformation behavior and microstructure evolution of twin-roll-cast Mg–2.9Al–0.9Zn alloy: A study with processing map

The hot deformation behavior and microstructure evolution of twin-roll-cast of Mg–2.9Al–0.9Zn–0.4Mn (AZ31) alloy has been studied using the processing map. The tensile tests were conducted in the temperature range of 150–400 °C and the strain rate range of 0.0004–4 s⁻¹ to establish the processing map. The different efficiency domains and flow instability region corresponding to various microstructural characteristics have been identified as follows: (i) the continuous dynamic recrystallization (CDRX) domain in the range of 200–280 °C/≤0.004 s⁻¹ with fine grains which provides a potential for warm deformation such as deep drawing; (ii) the discontinuous dynamic recrystallization (DDRX) domain around 400 °C at high strain rate (0.4 s⁻¹ and above) with excellent elongation which can be utilized for forging, extrusion and rolling; (iii) the grain boundary sliding (GBS) domain at slow strain rate (below 0.004 s⁻¹) above 350 °C appears abundant of cavities, which result in fracture and reduce the ductility of the adopted material; and (iv) the flow instability region which locates at the upper left of the processing map shows the metallographic feature of flow localization.     

Experimental studies on the dynamic tensile behavior of Ti–6Al–2Sn–2Zr–3Mo–1Cr–2Nb–Si alloy with Widmanstatten microstructure at elevated temperatures

The tensile behavior of a newly developed Ti–6Al–2Sn–2Zr–3Mo–1Cr–2Nb–Si alloy, referred as TC21, is investigated at temperatures ranging from 298 to 1023 K and under constant strain rate loadings ranging from 0.001 to 1270 s⁻¹. The results show that temperature and strain rate have significant effects on the tensile behavior of the material. At low strain rates of 0.001 and 0.05 s⁻¹, a discontinuity is found in the yield stress–temperature curve. And the discontinuity temperature increases with increasing strain rate. The analysis of temperature and strain rate dependence of unstable strain indicates a high-velocity-ductility phenomenon at elevated temperatures. Scanning electron microscope (SEM) analysis shows that the material is broken in a mixture manner of ductile fracture and intergranular fracture under low strain rates at room temperature, while the fracture manner changes to totally ductile fracture under other testing conditions. The width and depth of ductile dimples increase with increasing temperature. No adiabatic shear band is found in the tensile deformation of the material.     

High temperature deformation behavior of a near alpha Ti600 titanium alloy

The high temperature deformation behavior of a near alpha Ti600 titanium alloy was investigated with isothermal compression tests at temperatures ranging from 800 to 1000 °C and strain rates ranging from 0.001 to 10.0 s⁻¹. The apparent activation energy of deformation was calculated to be 620.0 kJ mol⁻¹, and constitutive equation that described the flow stress as a function of the strain rate and deformation temperature was proposed for high temperature deformation of Ti600 titanium alloy in the α + β phase region. The processing map was calculated to evaluate the efficiency of the forging process in the temperatures and strain rates investigated and to recognize the instability regimes. High efficiency values of power dissipation over 55% obtained under the conditions of strain rate lower than 0.01 s⁻¹ and temperature about 920 °C was identified to represent superplastic deformation in this region. Plasticity instability was expected in the regime of strain rate higher than 1 s⁻¹ and the entire temperature range investigated.     

Microstructure and superplasticity of Mg–Al–Ca electromagnetic casting alloys after hot extrusion

Microstructure and superplastic properties of the plates extruded from the Ca containing Mg alloy (1 wt.% Ca–AZ31) billets fabricated by electromagnetic casting (EMC) without and with electromagnetic stirring (EMS) were examined. The linear intercept grain sizes of the extruded materials were 3.7 μm and 2.1 μm, respectively. The material extruded from the EMC + EMS billet exhibited good superplasticity at low temperatures as well as at high strain rates, including the tensile elongations of 370% at 1 × 10⁻³ s⁻¹, −523 K and 550% at 1 × 10⁻² s⁻¹, −673 K. These values largely exceeded those of the AZ31 alloys with the similar grain sizes. The superior superplasticity of the extruded EMC + EMS billet could be attributed to fine grains and high grain stability at elevated temperatures by the presence of finely dispersed particles of thermally stable (Al,Mg)₂Ca phase. The constitutive equations were developed for describing the high-temperature deformation behavior of the fine-grained 1 wt.% Ca–AZ31 alloys with different grain sizes in wide range of temperature and strain rate.     

Plastic deformation behavior in dual-phase Ni–31Al intermetallics at elevated temperature

Plastic deformation behavior of dual-phase Ni–31Al intermetallics at elevated temperature was examined. It was found that the alloy exhibited good plasticity under an initial strain rate of 1.25 × 10⁻⁴ s⁻¹ to 8 × 10⁻³ s⁻¹ in a temperature range of 950–1075 °C. A maximum elongation of 281.3% was obtained under an initial strain rate of 5 × 10⁻⁴ s⁻¹ at 1000 °C. The strain rate sensitivity, m value was correlated with temperature and initial strain rate, being in the range of 0.241–0.346. During plastic deformation, both the two phases Ni₃Al and NiAl in dual-phase Ni–31Al could co-deform without any void formation or debonding, the initial coarse microstructure became much finer after plastic deformation. Dislocation played an important role during the plastic deformation in dual-phase Ni–31Al alloy, the deformation mechanism in dual-phase Ni–31Al could be explained by continuous dynamic recovery and recrystallization.     

Investigation of fracture and determination of fracture toughness of modified 9Cr–1Mo steel weld metals using AE technique

Three-point bending test and acoustic emission technique are used to determine the fracture toughness and fracture process of three types of modified 9Cr–1Mo steel weld metals. Scanning electron microscopy is used to accomplish fractography analysis of fracture specimens. Microstructure of weld metals is investigated using optical microscopy and transmission electron microscopy. The fracture process and factors which affect fracture of the 9Cr–1Mo steel weld metals in post-weld heat treated condition are studied. Experimental results show that the modified 9Cr–1Mo steel weld metals fracture by a quasi-cleavage mechanism at ambient temperature. The microstructure of the weld metals is composed of mainly tempered martensite with M₂₃C₆ precipitates. In weld metals, microcracks nucleate from non-metallic inclusions. Fractures develop very quickly when cracks started to propagate. Comparatively, in weld metals with low strength, microcracks initiate at a low stress, but propagation of cracks is limited by plastic deformation. In weld metals with high strength, microcracks nucleate at high stresses, but cracks propagate very quickly and lead to almost immediate fracture of the specimens. As a result, weld metals with the low strength have a higher fracture toughness, while weld metals with higher strengths has a lower fracture toughness.     

A modified Zerilli–Armstrong model for alloy IC10 over a wide range of temperatures and strain rates

IC10 is a newly developed Ni₃Al-based superalloy. To investigate its flow behaviors, tensile experiments were conducted over a wide range of temperatures (293–1073 K) and strain rates (10⁻⁵–10⁻² s⁻¹) on Material Test System. Experiments show that: (1) flow behaviors are not sensitive to strain rates at room temperature; (2) flow behaviors varies slightly with the temperature at the same strain rate. Z–A model, one of the most widely used models, is employed in describing the flow behaviors of IC10. Normally, the parameters in Z–A model are regarded as constants at various conditions and whole deforming process, which do not agree with the actual process and will decrease its predicted accuracies. In order to improve the predicted accuracies, Z–A model is modified by adding the functions to consider the effects of temperature, strain rate and deforming process on certain parameter. The modified model is used to predict flow behaviors of IC10 at different experiment conditions. Compared with the predicted data of original Z–A model and the experimental data, it is found that the predicted accuracy of the modified Z–A model is improved obviously. The max average relative error decreased from 6.37% to 3.86%.     

Constitutive relationship and hot deformation behavior of Armco-type pure iron for a wide range of temperature

The hot deformation behavior and constitutive relationship of Armco-type pure iron were investigated using isothermal compression tests with a wide range of temperature and strain rate ranging from 923 to 1523 K, and 0.1 to 10 s⁻¹, respectively. When deformed with a single phase, the flow stress of Armco-type pure iron increases accompanied by the increase of strain rate and the decrease of deformation temperature. Instability phenomenon of Armco-type pure iron appears when deformed with dual phase. γ-Fe undergoes completed discontinuous dynamic recrystallization (dDRX) at all hot deformation conditions. α-Fe undergoes uncompleted dDRX process at high temperature and low strain rate, however, dynamic recovery (DRV) process is the main restoration process for α-Fe at low temperature and high strain rate. The modified Arrhenius-type constitutive equation considering strain compensation is used to describe the flow stress of γ-Fe and α-Fe. From correlation coefficient (R), root mean square error (RMSE) and average absolute relative error (AARE), the predictability of the constitutive equation for the two phases of Armco-type pure iron was evaluated.