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%.     

Mechanical properties of low-carbon steels over a wide range of temperatures and strain rates applied to processes of thin sheet rolling

Results are given for mechanical tests on a number of low-carbon steels in uniaxial tension and compression in the strain rate range 10^–3–4·10³ sec^–1 and at temperatures of 293–573 K. An increase is confirmed for strength and ductility characteristics with an increase in strain rate. It is shown that the sensitivity of metals to strain rate depends on the specific temperature and rate conditions of loading. On the basis of experimental data obtained analytical dependences are suggested for the resistance of materials to deformation on the degree and rate of deformation, and also on temperature.Translated from Problemy Prochnosti, No. 8, pp. 76–84, August, 1990.     

Constitutive modeling of nitrogen-alloyed austenitic stainless steel at low and high strain rates and temperatures

In this paper, microstructures-based constitutive relations are introduced to simulate the thermo-mechanical response of two nitrogen-alloyed austenitic stainless steels; Nitronic-50 and Uranus-B66, under static and dynamic loadings. The simulation of the flow stress is developed based on a combined approach of two different principal mechanisms; the cutting of dislocation forests and the overcoming of Peierls–Nabarro barriers. The experimental observations for Nitronic-50 and Uranus-B66 conducted by Guo and Nemat-Nasser (2006) and Fréchard et al. (2008), respectively, over a wide range of temperatures and strain rates are also utilized in understanding the underlying deformation mechanisms. Results for the two stainless steels reveal that both the initial yielding and strain hardening are strongly dependent on the coupling effect of temperatures and strain rates. The methodology of obtaining the material parameters and their physical interpretation are presented thoroughly. The present model predicts results that compare very well with the experimental data for both stainless steels at initial temperature range of 77–1000 K and strain rates between 0.001 and 8000 s⁻¹. The effect of the physical quantities at the microstructures on the overall flow stress is also investigated. The evolution of dislocation density along with the initial dislocation density contribution plays a crucial role in determining the thermal stresses. It was observed that the thermal yield stress component is more affected by the presence of initial dislocations and decreases with the increase of the originated (initial) dislocation density.     

Compression of polypropylene across a wide range of strain rates

Three grades of polypropylene were tested in uniaxial compression at room temperature, across a wide range of strain rate: 10^?4?s^?1 to 10⁴?s^?1. One grade is a conventional polypropylene homopolymer. The two other grades are the polypropylene forming the matrix phase of a continuous glass fibre-reinforced thermoplastic composite prepreg, with and without blending with a carbon-black master batch. Tests at the highest strain rates were performed using a compression split Hopkinson pressure bar. The test specimens, for all the three rates, were imaged using appropriate digital cameras in order to observe the deformation process. In addition, the images obtained were analysed digitally to obtain true strain measurements for the medium rates category. All three grades of polypropylene showed pronounced strain-rate dependence of compressive yield stress, increasing by factors of up to 4 across the range of rates. At the lowest rates, there was close agreement between the yield stresses for all three materials, and also close agreement with the Eyring theory. Considering the highest strain rates, however, yield stresses increased more rapidly with log(strain-rate) than would be expected from a linear Eyring prediction and values for the three materials diverged. This was attributed to the contributions made in each material by both alpha and beta relaxation processes. Also prominent in the medium- and high-rate experimental results was pronounced post-yield strain softening, greatest at the highest strain-rates. This resulted from a combination of thermal softening from adiabatic heating, and structural rejuvenation as often seen in glassy polymers in quasi-static tests.     

Tensile mechanical behaviour of quenched and annealed isotactic polypropylene films over a wide range of strain rates

The tensile mechanical behaviour of quenched and annealed isotactic polypropylene (iPP) films has been analysed over a wide range of strain rates, i.e. from 10^–3 to 3×10⁺²s^–1. Evolution of mechanical properties of such films versus strain rate has been analysed through the microstructure. Thus, both the Young's modulus and the yield stress could be mainly controlled not only by the crystallinity ratio but also by the physical cross-linking degree of the amorphous phase induced by crystalline entities. For a given crystallinity ratio, the drawability of quenched and annealed iPP films is mainly controlled by the sum of the effects induced by both the physical cross-linking degree of the amorphous phase and the perfection degree of the crystalline phase. The increase in annealing temperature leads to the opposite evolution of these two microstructural parameters and then to opposite effects on the drawability of films. Changes in original microstructure of quenched films induced by drawing at various draw ratios and at various strain rates are also discussed.     

Constitutive descriptions for hot compressed 2124-T851 aluminum alloy over a wide range of temperature and strain rate

The compressive deformation behaviors of 2124-T851 aluminum alloy were investigated over a wide range of temperature and strain rate on Gleeble-1500 thermo-simulation machine. The results show that the true stress–true strain curves exhibit a peak stress at a very small strain, after which the flow stresses decrease until high strains, showing a dynamic flow softening. The measured flow stress was modified by friction correction, and the corrected flow stresses are lower than the measured ones, which nicely reflect negative effects of the interfacial friction on the flow stress. A revised model is proposed to describe the relationships of the flow stress, strain rate and temperature of 2124-T851 aluminum alloy at elevated temperatures. The stress–strain values of 2124-T851 aluminum alloy predicted by the proposed model well agree with experimental results, which confirmed that the revised deformation constitutive equation gives an accurate and precise estimate for the flow stress of 2124-T851 aluminum alloy.     

A practical constitutive equation covering a wide range of strain rates

A practical constitutive equation of a single form combining stress, strain, strain rate and temperature effect is proposed with which the various material behaviors can be described covering a wide range of strain rates, especially the high strain rates. It is illustrated that the proposed form of the equation is useful when compared to some experimental results obtained under a dynamical uniaxial stress and an incremental torsional impact.     

High temperature compressive properties over a wide range of strain rates in an AZ31 magnesium alloy

High temperature compressive properties in AZ31 magnesium alloy were examined over a wide strain rate range from 10^–3 to 10³ s^–1. It was suggested that the dominant deformation mechanism in the low strain rate range below 10^–1 s^–1 was dislocation creep controlled by pipe diffusion at low temperatures, and by lattice diffusion at high temperatures. On the other hand, analysis of the flow behavior and microstructural observations indicated that the deformation at high strain rates of 10³ s^–1 proceeds by conventional plastic flow of dislocation glide and twinning even at elevated temperatures.     

Dynamic viscosity of gases over a wide range of temperatures. I

The results are presented of a generalization of the experimental data on the viscosities of He, Ne, Ar, Kr, Xe, and N₂ at atmospheric pressure over the range of temperatures from the boiling point at atmospheric pressure to 2000 K using polynomial approximating relationships.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 6, pp. 982–987, June, 1989.     

Turbulent boundary-layer buoyant flow modeling over a wide Prandtl number range

Summary. This work is devoted to the free turbulent convection theory applied to a vertical plate under uniform heat flux density conditions by using the integral formalism approach. A fully developed model is derived for a large Prandtl number range over the real distinct boundary layer thicknesses. Comparisons are established with the few data in literature. Of practical interest are the deduced dynamical similarity law and Nusselt number correlations. The transition events are found to be Prandtl number dependent, and the results suggest the thermal transition to be reached in space before the dynamical one up to Pr = 100.     

Plastic behavior and constitutive relations of DH-36 steel over a wide spectrum of strain rates and temperatures under tension

To understand the plastic characteristics of DH-36 steel, uniaxial tensile tests have been performed on dog bone samples. The strain rate range is from 0.001 to 3000/s, and the initial specimen temperatures are 293–800 K. To obtain the isothermal flow stress at high strain rates, dynamic recovery technique in Hopkinson Tension Bar has been used, and the interrupt and reloading tests have been performed. The value of strain rate sensitivity has been calculated based on the isothermal stresses at different strain rates. Similar to results from compressive tests, the dynamic strain aging has been observed under tension. Microstructure analysis of the samples after interrupt tests has been carried out by scanning electron microscopy (SEM). The results show that: (1) the strain rate sensitivity value is ∼0.0115 in terms of the isothermal flow stress (uncoupled with temperature) at a given strain, corresponding to 0.0045 coupled with temperature; (2) the 3rd dynamic strain aging (DSA) occurs at some relatively constant strain rates within certain temperature region under tension; DSA shifts to higher temperature or even disappears with increasing strain rates. Finally, in depth analysis of the data based on dislocation mechanisms, it leads to a physically based model which has taken into account the 3rd DSA effects. Good agreement between the theoretical prediction and experimental results has been obtained.     

Material characterisation and constitutive modelling of a tungsten-sintered alloy for a wide range of strain rates

The behaviour of a tungsten-sintered alloy has been investigated using a combination of tension tests, modified Taylor-impact tests and planar-plate-impact (PPI) tests using the VISAR technique. A logarithmic yield stress–strain rate dependency as it is predicted by the original Johnson–Cook (JC) strength model covering a strain rate range of 10 orders of magnitude has been measured. With the PPI tests the Hugoniot elastic limit and the spall strength, as well as the U_s–u_p relation have been determined. Model parameters for the JC strength model and an equation of state have been determined from the experimental results. The validation of the material model has been performed by numerical simulations of the modified Taylor-impact tests where an enhanced model validation has been done by comparing the measured and calculated VISAR signals while this technique is normally used for PPI tests only.     

The compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates

The compression yield behaviour of PMMA has been investigated, here, over a wide range of experimental conditions which cannot be reached in tensile tests owing to the brittle nature of the material. The plot of the ratio of the compression yield stress to absolute temperature, as a function of the logarithm of the strain-rate, gives a set of parallel curves which can be accurately superimposed by shifting along a slanting straight line. A master curve is built from which the yield behaviour may be predicted for any state of stress, or value of temperature and strain-rate in the glassy range, using Bauwens' yield criterion.The validity of the procedure is checked for compression tests at low temperatures, for tensile tests in the range of experimental conditions where PMMA yields and for torsional tests under hydrostatic pressure (data of Wardet al). In every case, the fit is found to be quite accurate.A region of experimental conditions is determined where the compression yield behaviour may not be described by the Ree-Eyring treatment involving a hyperbolic sine function. In this region, the Bauwens approach, which consists of a modification of the Ree-Eyring theory, taking into account a distribution of relaxation times and linking the yield behaviour with the mechanical loss peak, is found to give an acceptable fit to the data.