Strain Rate Dependence Of Flow Stress Research Articles

Multiaxial Experiments and Constitutive Modeling of Superplasticity

In the first part of the paper, multiaxial experiments of 5083Al alloy are carried out at 833K at constant strain-rates to elucidate the characteristic features of superplastic deformation under general forming conditions. Monotonic tension, compression and torsion tests were performed by using solid circular cylindrical specimens together with thin-walled tubular specimens. The values of the equivalent strain-rate of von Mises type are specified as 2 × 10 -3 , 1 × 10 -3 , 5 × 10 -4 and 2 × 10 -4 s -1 . The significant strain-rate dependence of flow stress and the material softening due to cavity growth are observed under the tension tests. The results of the tension and compression tests show that the material hardens under tension while it softens under compression. The comparison between tension and torsion tests shows that the equivalent flow stress of von Mises type under torsion is much smaller than that of the tension at the same equivalent strain-rate of von Mises type. Based on these observations, a constitutive model of superplasticity is then formulated based on the finite deformation theory. The rate of deformation tensor is divided into the sum of the elastic and inelastic parts, and the former part is represented by the isotropic linear elastic law. The inelastic part is modeled based on the invariant theory by employing the steady-state creep law of hyperbolic sine type and by taking account of the effects of yielding, grain and cavity growth. The rate of drag stress is assumed to be the sum of the terms due to the grain and cavity growth. The evolution equation of the grain growth is formulated by taking account of static growth and strain-induced growth. The evolution equation of the cavity volume fraction is represented by the sum of the two terms due to cavity diffusion and viscoplastic deformation. Comparison of the results of the proposed model with those of the experiments shows that the proposed model gives satisfactory predictions.

Stress response by the strain-rate change in a binary stoichiometric Ni3Al single crystal

The strain-rate dependence of flow stress in single crystals of binary stoichiometric Ni Al has been studied in the temperature region of the yield3 stress anomaly. Below 400 K, the flow stress was found to be independent of strain rate, although it changed temporarily when the strain rate was changed. The strain-rate insensitivity can be explained by assuming that the flow stress is controlled by the multiplication and immobilization of mobile dislocations.

Stress response by the strain-rate change in binary, stoichiometric Ni3AI single crystal

ABSTRACTThe strain-rate dependence of flow stress in single crystals of binary, stoichiometric Ni3Al was studied in the temperature region of the yield stress anomaly. Below 400 K, the steady-state flow stress was found to be independent of strain rate, though it changed temporarily when the strain rate was changed. The strain-rate insensitivity can be explained by assuming that the flow stress is controlled by the multiplication/immobilization of mobile dislocations.

A study of work hardening in austenitic FeMnC and FeMnAlC alloys

Two austenitic FeMnAlC alloys with aluminium contents of 0 and 2.7 wt% were strained in tension between 193 and 823 K. Serrated stress-strain curves, inverse strain-rate dependence of flow stress, and high work hardening exhibited in particular temperature ranges for both alloys were characteristic of dynamic strain aging. The apparent activation energy for the onset of serration increased from 14.4 to 22.3 kcal/mol due to the addition of 2.7 wt% Al. It was found that the high work-hardening rate cannot be attributed to strain-induced deformation twinning when serrated stress-strain curves occurred. From the evidence of the present study and the known effect of aluminium on the diffusivity and activity of carbon in austenitic high-manganese steel, it is suggested that dynamic strain aging is the major cause of work hardening within the intermediate temperature range from 298 to 493 K for 0 wt% Al and 393 to 593 K for 2.7 wt% Al in the present austenitic FeMnAlC alloys.

超高温におけるＳＵＳ３０４鋼の非弾性特性と統一型構成式

To investigate the temperature and strain-rate dependence of flow stress and strain-hardening behaviour of austenitic stainless steel (SUS304), tension tests and creep tests were carried out in the temperature range between 750 and 1200°C under the strain-rate from 1.0×10-5 to 1.0×10-2 S-1.Some typical inelastic constitutive equations, such as the types of Perzyna and Bodner as well as the superposition model, relevant to describe the high temperature behaviour were used to simulate the test results. The material parameters of these equations were identified to simulate cyclic stress/strain hysteresis.The model of Perzyna was found to be most adequate for the simulation of material behaviour up to 1200°C.

Thermally Activated Deformation of KCl and KCl-KBr Single Crystals at Low Temperatures between 1.8 and 70 K

The critical-resolved shear stress and the strain-rate dependence of flow stress for KCl pure crystals and KCl-1, 4, 22 and 48 mol% KBr solid-solution crystals were measured over a temperature range between 1.8 K and 70 K. The activation analyses of the results showed that an Arrhenius rate equation for plastic deformation appeared to hold above 15 K for KCl and KCl-1 and 4 mol% KBr and above 25 K for KCl-22 and 48 mol% KBr, but not below these temperatures. Such discrepancy of the Arrhenius rate equation has been interpreted by the fluctuation of activation enthalpy due to random distribution of solute atoms. In the present interpretation the pre-exponential factor of the Arrhenius rate equation should have a strong temperature-dependence, especially in the low-temperature range, which agrees well with experimental results.

Nonisothermal Axisymmetric Forging

An approximate solution for nonisothermal upset forging is presented. A finite difference thermal analysis and an upper-bound deformation solution are used for this purpose. The thermal analysis is for a homogeneous state of strain, it ignores deformation heating, but accounts for all modes of heat flow during the transfer of the billet to the tooling and throughout the deformation. The upper-bound solution is based on admissible velocity field equations, the recorded temperature data from the thermal analysis, and constitutive equations for temperature, strain, and strain rate-dependence of flow stress. The size of the chilled zone is determined by minimization of total power for the deformation process. Theoretical predictions for load-displacement behavior and the size of the chilled zone are compared with the experimental results for 304 stainless and AISI 1042 steels.

Contact Pressure in Dynamic Compression of Clay Specimens and Its Application to Sheet Metal Forming

A new method for sheet metal forming which utilizes the strain-rate dependence of flow stress in the viscoplastic material and the friction-hill phenomenon is proposed. In order to assess its applicability, a dynamic compression test of clay specimens is carried out using a drop hammer apparatus, and the contact pressure on the specimen-platen interface is examined. It is concluded that the proposed method is applicable to sheet forming for relatively small articles. Based on experimental and theoretical considerations, a simple method for estimating the maximum pressure generated under any condition is presented. Some applications of' the process to sheet metal forming are shown.

The effects of liquid metal embrittlement on high temperature fatigue of 2.25 Cr-1 Mo steel in liquid lithium

The fatigue crack propagation characteristics of a 2.25 Cr-1 Mo steel were investigated in argon and lithium with either < 100 ppm or approximately 2000 ppm dissolved nitrogen. Data, which extend those presented previously, were obtained for temperatures of 673 to 873 K and loading frequencies of 0.05 to 20 Hz. At a constant imposed stress intensity factor, the growth rate in argon decreased with an increase in frequency for all test temperatures. In contrast, the growth rate was enhanced by the presence of lithium and shown to increase significantly with an increase in frequency at the lower test temperatures. The lithium enhanced growth rates resulted from strain rate induced liquid metal embrittlement (LME). The loading frequencytemperature conditions necessary for LME were predicted from a model based on the achievement of a critical strain rate dependent flow stress at the tip of a propagating fatigue crack. The results correlated with fractographic observations which showed a transition from deformation controlled fatigue crack growth at low frequencies to LME controlled cleavage formation at high frequencies.

Mechanism of work hardening in Hadfield manganese steel

When Hadfield manganese steel in the single-phase austenitic condition was strained in tension, in the temperature range - 25 to 300 °C, it exhibited jerky (serrated) flow, a negative (inverse) strain-rate dependence of flow stress and high work hardening, characteristic of dynamic strain aging. The strain rate-temperature regime of jerky flow was determined and the apparent activation energies for the appearance and disappearance of serrations were found to be 104 kJ/mol and 146 kJ/mol, respectively. The high work hardening cannot be a result of mechanical twinning because at -50 °C numerous twins were produced, but the work hardening was low and no twins were formed above 225 °C even though work hardening was high. The work hardening decreased above 300 °C because of the cessation of dynamic strain aging and increased again above 400 °C because of precipitation of carbides. An apparent activation energy of 138 kJ/mol was measured for static strain aging between 300 and 400 °C, corresponding closely to the activation energies for the disapperance of serrations and for the volume diffusion of carbon in Hadfield steel. Evidence from the present study, together with the known effect of manganese on the activity of carbon in austenite and previous internal friction studies of high-manganese steels, lead to the conclusion that dynamic strain aging, brought about by the reorientation of carbon members of C-Mn couples in the cores of dislocations, is the principal cause of rapid work hardening in Hadfield steel.

Temperature and strain-rate dependence of flow stress of tantalum in the superconducting and normal states

Flow stress changes with the transition between the superconducting and the normal states, and with the change of the strain-rate in both the states are measured as a function of temperature for high purity tantalum single crystals. The Δa−τ relation shows a significant difference between the superconducting and the normal states, while the Δa−T relation for a fixed strain-rate range does not, where Δa is the activation area, T the temperature, and τ the stress. This indicates that the softening with the superconducting transition is due to the modification of the activation enthalpy in the thermally activated motion of dislocations. The results are discussed in terms of the energy dissipation by electron scattering of the screw dislocation in overcoming the Peierls potential. Für hochreine Tantaleinkristalle werden die Fließspannungsänderungen beim Übergang zwischen dem supraleitenden und normalleitenden Zustand und bei der Änderung der Abgleitgeschwindigkeit in beiden Zuständen als Funktion der Temperatur gemessen. Die Δa-τ-Abhängigkeit zeigt eine bedeutende Differenz zwischen dem supraleitenden und normalleitenden Zustand, während die Δa-T-Abhängigkeit für einen festen Bereich der Abgleitgeschwindigkeit keine Differenz zeigt (Δa ist die Aktivierungsfläche, T die Temperatur und τ die Spannung). Das zeigt, daß der Erweichungseffekt beim supraleitenden Übergang einer Modifikation der Aktivierungsenthalpie in der thermisch aktivierten Versetzungsbewegung zugeschrieben werden muß. Diese Resultate werden auf Grund der Energieverluste der Schraubenversetzung durch Elektronenstreuung bei der Überwindung des Peierlspotentials diskutiert.

Dislocation dynamics in alpha titanium

The activation area and activation enthalpy are determined as a function of stress and temperature for alpha titanium. The results indicated that plastic flow below about 700°K occurs by a single thermally activated mechanism. Activation area determined by differential-stress creep tests falls in the range 80−8 b 2 and does not systematically depend on the impurity content. The total activation enthalpy derived from the temperature and strain-rate dependence of flow stress is 1.15 eV. The experimental data support a lattice hardening mechanism as controlling the low-temperature deformation in alpha titanium.

The effect of strain rate on the flow stress and dislocation behavior of a precipitation-hardened nickel-base alloy

The relationship between strain rate, flow stress and deformation mode for 〈001〉 single crystals of a precipitation-hardened nickel-base alloy has been investigated over the temperature range of 1400° to 1850° F and strain range 10 −1 to 6 × 10 3%/min. Planar, heterogeneous deformation, characterized by the glide of a/2 〈110〉 superlattice pairs, was found at the lower temperatures and higher strain rates. Under these conditions, the flow stress was independent of strain rate. Higher temperatures and lower strain rates, on the other hand, were conductive to homogeneous dislocation arrays and a strain-rate dependent flow stress. The 1550° and 1700° F flow stresses at high strain rates were almost twice those at low strain rates and were also greater than the flow stress at 1400° F. It is shown that this latter phenomenon is related to the effect of strain rate on the flow stress of the γ′ precipitate. Consideration is also given to the effect of the presence of a/2 〈112〉 dislocations on the 1400° F flow stress.

2%Ni鉄の変形応力の歪速度依存性

2%Ni鉄の変形応力の歪速度依存性