Viscous relations for the steady creep of polycrystalline ice

Various published data from constant-stress creep tests on ice, relating minimum strain-rate to applied stress at different temperatures, are presented and compared. A temperature dependent rate factor is constructed from the Mellor and Testa (1969a) uni-axial compression data at uni-axial stress 1.18 × 10⁶ N m^?2 over the temperature range 212.15 K–273.15 K. This factor is used to normalise the different sets of data at different temperatures to a common temperature for comparison, but normalised strain-rates at a fixed stress still vary by a factor of 3. Furthermore, it is shown that no alternative single rate factor will adequately correlate the data at two different temperatures.A least-squares method is used to express the strain-rate as an odd polynomial in the stress; distinct polynomials are found for different sets of data. Good matches are generally obtained over a uni-axial stress range 0–10⁶ N m^?2 by three terms: first, third and fifth powers of stress; but less satisfactory non-monotonic polynomials involving negative coefficients are obtained in most cases if the seventh power is also included. Expressing the stress as an odd polynomial in the strain-rate, however, is not satisfactory, which is a reflection of the shape of the response at higher strain-rates. Inverse sinh function expansions failed in general, but inverse tan function expansions give good agreement to some data.     

The dynamic tensile behavior of tough,ultrahigh-strength steels at strain-rates from 0.0002 s to 200 s

The present study examines the strain-rate sensitivity of four high-strength, high-toughness steels at strain-rates ranging from 0.0002 s⁻¹ to 200 s⁻¹: AerMet 100, modified 4340, modified HP9-4-20, and a recently developed Eglin AFB steel alloy, ES-1c. A newly developed dynamic servohydraulic method was employed to perform tensile tests over this entire range from quasi-static to near split-Hopkinson or Kolsky bar strain-rates. Each of these alloys exhibits only modest strain-rate sensitivity. Specifically, the semi-logarithmic strain-rate sensitivity factor β was found to be in the range of 14–20 MPa depending on the alloy. This corresponds to a ∼10% increase in the yield strength over the 6-orders of magnitude change in strain-rate. Interestingly, while three of the alloys showed a concomitant ∼3–10% drop in their ductility with increasing strain-rate, the ES-1c alloy actually exhibited a 25% increase in ductility with increasing strain-rate. Fractography suggests the possibility that at higher strain-rates ES-1c evolves towards a more ductile dimple fracture mode associated with microvoid coalescence.     

Effect of nitrogen on tensile flow behaviour of type 316 LN austenitic stainless steel

Abstract

The influence of nitrogen content on the tensile flow behaviour of type 316 LN austenitic stainless steel has been studied. Nitrogen content in the steel has been varied in the range 0·07 to 0·22 wt-%. Tensile tests were carried out over the temperature range of 300–1123 K at a nominal strain rate of 3×10^?3 s^?1. The tensile flow behaviour of the steels has been analysed based on the constitutive equation proposed by Voce. The Voce’s parameters of initial stress (σ_i) and saturation stress (σ_s) were found to increase linearly with increase in nitrogen content at all the test temperatures. Tensile properties of the steels were predicted from Voce constitutive equation parameters.     

Constitutive modeling and the effects of strain-rate and temperature on the formability of Ti–6Al–4V alloy sheet

The constitutive model considering the strain-rate and temperature effects was presented by fitting the true stress–strain curves of Ti–6Al–4V alloy over a wide range of strain-rates (0.0005–0.05 s⁻¹) and temperatures (923–1023 K). The Forming Limit Curve (FLC) of Ti–6Al–4V alloy at 973 K was measured by conducting the hemispherical dome test with specimens of different widths. The forming limit prediction model of Ti–6Al–4V alloy, which takes strain-rate and temperature sensitivity into account, was predicted based on Marciniak and Kuczynski (M–K) theory along with Von Mises yield criterion. The comparison shows that the limit strain decreases with temperature lowering but strain-rate increasing. The comparison between theoretical analysis and experiment of FLC verifies the accuracy and reliability of the proposed methodology, which considers the strain-rate and temperature effects, to predict limit strains in the positive minor strain region of Forming Limit Diagram (FLD).     

A numerical study of ductile void growth under dynamic loading conditions

A numerical study of void growth at differing global strain rates in the range 149 s^–1–2240 s^–1 and at start temperatures between 173 K and 573 K has been carried out for a material containing a three-dimensional periodic array of equally spaced, initially spherical voids. To take account of the effect of strain rate and temperature on the flow stress under dynamic adiabatic conditions, the well-established Zerilli-Armstrong constitutive relations for pure copper and iron have been employed. An instability criterion based on the maximum mean tensile stress has been used to identify the point at which unstable void growth occurs. For both materials, the strain at instability has been found to be dependent on stress triaxiality and start temperature but only weakly affected by strain-rate     

About the dynamic uniaxial tensile strength of concrete-like materials

Experimental methods for determining the tensile strength of concrete-like materials over a wide range of strain-rates from 10⁻⁴ to 10² s⁻¹ are examined in this paper. Experimental data based on these techniques show that the tensile strength increases apparently with strain-rate when the strain-rate is above a critical value of around 10⁰-10¹ s⁻¹. However, it is still not clear that whether the tensile strength enhancement of concrete-like materials with strain-rate is genuine (i.e. it can be attributed to only the strain-rate effect) or it involves “structural” effects such as inertia and stress triaxility effects. To clarify this argumentation, numerical analyses of direct dynamic tensile tests, dynamic splitting tests and spalling tests are performed by employing a hydrostatic-stress-dependent macroscopic model (K&C concrete model) without considering strain-rate effect. It is found that the predicted results from these three types of dynamic tensile tests do not show any strain-rate dependency, which indicates that the strain-rate enhancement of the tensile strength observed in dynamic tensile tests is a genuine material effect. A micro-mechanism model is developed to demonstrate that microcrack inertia is one of the mechanisms responsible for the increase of dynamic tensile strength with strain-rate observed in the dynamic tensile tests on concrete-like materials.     

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.     

Finite element analysis of small-scale hot compression testing

This paper models hot compression testing using a dilatometer in loading mode.These small-scale tests provide a high throughput at low cost,but are susceptible to inhomogeneity due to friction and temper-ature gradients.A novel method is presented for correcting the true stress-strain constitutive response over the full range of temperatures,strain-rates and strain.The nominal response from the tests is used to predict the offset in the stress-strain curves due to inhomogeneity,and this stress offset Δσ is applied piecewise to the data,correcting the constitutive response in one iteration.A key new feature is the smoothing and fitting of the flow stress data as a function of temperature and strain-rate,at multiple discrete strains.The corrected model then provides quantitative prediction of the spatial and tempo-ral variation in strain-rate and strain throughout the sample,needed to correlate the local deformation conditions with the microstructure and texture evolution.The study uses a detailed series of 144 hot compression tests of a Zr-Nb alloy.While this is an important wrought nuclear alloy in its own right,it also serves here as a test case for modelling the dilatometer for hot testing of high temperature alloys,particularly those with dual α-β phase microstructures(such as titanium alloys).     

Material modelling for dynamic strain ageing phenomenon of alloy 20MnMoNi55

Dynamic strain ageing (DSA) is observed in the tensile behaviour of 20MnMoNi55. The DSA phenomenon contributes extra hardening for a certain combination of straining rate and temperature. At temperature ranging from 200°C to 400°C and a straining rate of 10^?4–10^?2?s^?1, alloy 20MnMoNi55 exhibits DSA. In the present work, DSA stresses are calibrated as a function of strain, strain-rate and temperature. Modification of the Johnson–Cook material model by incorporating DSA has been attempted. The modified flow stress model is used in finite element computation to simulate the material behaviour for a wide range of temperature and strain-rates including the DSA regime. The simulated results are in good agreement with the experimental results.     

Hot deformation behavior and processing map of a Fe‐25Ni‐16Cr‐3Al alumina‐forming austenitic steel

The hot deformation behavior of a Fe‐25Ni‐16Cr‐3Al alumina‐forming austenitic steel was studied by hot compression using a Gleeble‐3500 thermal simulator. The compression tests were carried out in the temperatures range from 925 °C to 1175 °C and strain rates range from 0.01 s^‐1 to 10 s^‐1. It was concluded that the flow stress increased with decreasing deformation temperature and increasing strain rate. The constitutive equation was obtained and the activation energy was 420.98 kJ?mol^‐1 according to the testing data. According to the achieved processing map, the optimal processing domain is determined in the temperatures range of 1050 °C – 1075 °C and strain rates range of 0.03 s^‐1 ‐ 0.3 s^‐1. The evolution of microstructure characterization is consistent with the rules predicted by the processing map. During compression at the same temperature, the higher the strain rate is, the higher the hardness will be. The ultimate tensile strength of the steel is 779 MPa with a total elongation of 27.1 % at room temperature.     

Tensile properties and constitutive model of ultrathin pure titanium foils at elevated temperatures in microforming assisted by resistance heating method

Pure titanium (Ti) is often used for microparts in biomedical devices and implants. Microforming is a promising technology for the manufacture of microparts. Owing to the occurrence of size effects in microforming, the material flow is nonhomogeneous and the process parameters exhibit considerable scattering. Heat-assisted microforming is an effective process for solving these problems. To improve the heating rate, the resistance heating method has been introduced into the microforming process. To design an effective resistance-heating-assisted microforming process, the relationship between the electric current and the flow stress of the material should be determined.To achieve this, a tensile testing system incorporating the resistance heating method is developed in this study. The tensile properties of 0.05-mm-thick pure Ti foils are investigated by performing uniaxial tensile tests at elevated temperatures. The tensile tests are carried out at different angles (0°, 45°, and 90°) relative to the rolling direction, at various temperatures from room temperature (298 K) to 723 K, and under different strain rates from 10⁻⁴ to 10⁻¹ s⁻¹. To contribute to the design of the resistance-heating-assisted microforming process, the effect of the temperature and electrical current density on the material properties of ultrathin pure Ti foils is discussed. A constitutive model based on the Fields–Bachofen (FB) equation is derived to describe the flow stress of ultrathin pure Ti under different forming conditions. The effect of the electrical current density on the work hardening and strain rate sensitivity is included in the derived constitutive model. The good agreement between the calculated and experimental results confirms the feasibility of the proposed constitutive model for resistance-heating-assisted microforming.     

The compressive property and brittle-to-ductile transition of Ti3SiC2 ceramics

Compressive tests of polycrystalline Ti₃SiC₂ were performed from room temperature to 1423 K at strain rates of 1×10^–4 s^–1 and 2.5×10^–5 s^–1, respectively. The effect of strain rates on high-temperature compressive property was also investigated. Polycrystalline Ti₃SiC₂ exhibited positive temperature dependence of flow stress (flow stress anomaly) and showed a temperature peak at 1173 K. The brittle-to-ductile transition temperature (BDTT) for polycrystalline Ti₃SiC₂ was strain-rate sensitive, an approximately 100 K decrease in transition temperature was associated with four times of magnitude decrease in strain rate. In addition, the fracture morphology changed from predominately intergranular to mostly transgranular. The mechanism responsible for the brittle-to-ductile transition in Ti₃SiC₂ was involved in the onset of a thermally activated deformation process. Received: 6 July 1999 / Reviewed and accepted: 9 August 1999     

Thermo-mechanical behaviors of 3-D braided composite material subject to high strain rate compressions under different temperatures

This article reports the compressive behaviors of 3-D braided basalt fiber tows/epoxy composite materials under the temperature range of 23–210°C with the strain-rate range of 1300–2300 s^?1. A split Hopkinson pressure bar apparatus with a heating device was designed to conduct the out-of-plane compression tests. It was found that compression modulus, specific energy absorption, and peak stress decreased with the elevated temperatures, while failure strain gradually increased with the elevated temperatures. Compression modulus and peak stress were more sensitive to the temperature effect, whereas failure strain and specific energy absorption were more easily affected by the strain rate effect. The plasticity can be divided into two types: (a) the platform-shape plasticity; or (b) the slope-shape plasticity. The experimental condition of 150°C with 1827 s^–1 was a dividing threshold to differentiate the compression-failure mode and the shear-failure mode. The authentic microstructural finite element analysis results revealed that the distribution and accumulation of the inelastic heat led to the development of shear bands. Braided reinforcement had an important influence on the damage characteristics. When the temperature was below T_g, the material underwent a significant temperature rise during failure. But above T_g, the temperature rise was relatively steady.     

Deformation behavior and constitutive model for high temperature compression of a newly type of Ni3Al‐based superalloy

In order to investigate the hot deformation mechanism of a newly development Ni₃Al‐based superalloy, hot compression tests at temperatures between 1100 °C–1250 °C and the strain rates of 0.001 s^?1–1.0 s^?1 were conducted. The results show that the curves of true stress‐strain indicate the thermal deformation is a typical dynamic recrystallization process, which the peak stresses and steady‐state stresses increase with decreasing temperatures and increasing strain rates. The softening mechanism is mainly dynamic recrystallization. The experimental data of peak stresses and steady‐state stresses is employed to calculate the constants in the Arrhenius equation. The steady‐state stresses are considered more reasonable for solving the parameters in the Arrhenius equation. Based on the constitutive equation obtained, the calculated values of steady‐state stresses match well with the experimental values at the strain rates of 0.001 s^?1, 0.01 s^?1 and 0.1 s^?1, whereas there exists much deviation at 1.0 s^?1. For the sake of accuracy of predicted results at 1.0 s^?1 strain rate, a modified Zener‐Hollomon parameter Z’ is introduced. The results show that the modified constitutive equations established in this study could well predict the value of steady‐state stress in hot deformation of the newly development Ni₃Al‐based alloy.     

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.     

The relationship between creep and strength behavior of ice at failure

This work explores the correspondence between the results of creep and strength tests performed on isotropic polycrystalline ice. A unique experimental procedure, termed a two-mode test in the present work, allows the testing of a single specimen under conditions of constant deformation rate up to failure and constant load thereafter.Using this procedure, the prevailing values of stress, strain and strain rate can be compared at the failure point under the two test modes without the influence of specimen variation. The effect of the stress path prior to failure on the creep behavior after failure can also be investigated.Tests were performed at temperatures of ?5°C and ?10°C and initial strain rates ranged from 10^?6 to 2.2 × 10^?5 s^?1. Results indicate coincidence of the failure points from creep and strength tests in stress/strain-rate/strain space. Furthermore, it appears that within the range of variables tested, the creep behavior after the mode switch at failure is independent of the stress path experienced before failure.     

Modeling the constitutive relationship of powder metallurgy Al–W alloy at elevated temperature

The deformation behavior of Al–W alloy was researched with isothermal compression tests at various deformation temperatures and strain rates to evaluate the deformation activation energy and to develop the constitutive relationship equation, which is in pursuit of revealing the dependence of the flow stress on the strain, strain rate and deformation temperature. The compression tests were conducted in the temperature range between 420 and 570 °C and at strain rates between 0.001 and 5.0 s⁻¹. With the help of determination of related material constants (such as A, β and α) and activation energy Q (451.15 kJ mol⁻¹), the Arrhenius-type constitutive relationship equation of Al–W alloy is developed. It was found that the correlation coefficient R and the AARE is 0.997% and 4.08%, respectively. The results show that the Arrhenius-type model, which considers the combined influence of strain rate and deformation temperature, is able to provide the accurate prediction of high temperature flow stress for the researched alloy.     

The flow behavior and constitutive equation in isothermal compression of FGH4096-GH4133B dual alloy

The electron beam welding of superalloy FGH4096 and GH4133B was conducted, and the cylindrical compression specimens were machined from the central part of the electron beam weldments. Isothermal compression tests were carried out on electron beam weldments FGH4096-GH4133B alloy at the temperatures of 1020–11140 °C (the nominal γ′-transus temperature is about 1080 °C) and the strain rates of 0.001–1.0 s⁻¹ with the height reduction of 50%. True stress–true strain curves are sensitive to the deformation temperature and strain rate, and the flow stress decreases with the increasing deformation temperature and the decreasing strain rate. The true stress–true strain curves can indicate the intrinsic relationship between the flow stress and the thermal-dynamic behavior. The apparent activation energy of deformation at the strain of 0.6 was calculated to be 550 kJ/mol, and the apparent activation energy has a great effect on the microstructure. The constitutive equation that describes the flow stress as a function of strain rate and deformation temperature was proposed for modeling the hot deformation process of FGH4096-GH4133B electron beam weldments. The constitutive equation at the strain of 0.6 was established using the hyperbolic law. The relationship between the strain and the values of parameters was studied, and the cubic functions were built. The constitutive equation during the whole process can be obtained based on the parameters under different strains. Comparing the experimental flow stress and the calculated flow stress, the constitutive equation obtained in this paper can be very good to predict the flow stress under the deformation temperature range of 1020–1140 °C and the strain rate range of 1.0–0.001 s⁻¹.     

The tensile properties of a superplastic aluminium bronze

The high temperature tensile properties of a micrograin Cu-9.5% Al-4% Fe alloy, which is superplastic at 800° C, have been determined. Elongations at fracture of greater than 700% are achieved when the nominal strain-rate is in the range 3.9×10^–2 min^–1 to 7.9×10^–2 min^–1. The nature of plastic instability in superplastic materials is considered and it is shown that the amount of strain at the onset of plastic instability is inversely related to the applied strain-rate and is relatively independent of the strain-rate sensitivity exponent, m. The onset of plastic instability during a tensile test results in an increase of local strain-rate at the point of minimum cross-section and this, together with the existence of a triaxial stress state in the necked region, may produce errors in the m versus strain-rate plot if m is determined by the change-rate method. The initial strain-rate for maximum elongation is lower than the strain-rate for maximum m. This may be ascribed either to the influence of plastic instability or the formation of cavities at the higher strain-rates.     

Wechselverformung und Gefügeänderungen von Ck 15 und Ck 45

Microstructural Changes and Cyclic Deformation The crack initiation starts due to weakening and strengthening process during rotating bending. However a smaller plastic deformation amplitude is noticed at the same nominal stress compared to tension-compression stressed specimens. This results in a higher fatigue life. The different cyclic deformation behaviour was proofed by SEM (rotating bending specimens showed a lower slip line density compared to tension-compression specimens at the same nominal stress) and TEM investigations (the rotating bending specimens showed a smaller dislocation density at the same nominal stress). Furthermore it is showed, a correlation of cyclic stress strain data σ(ε_pls) between tension-compression and rotating bending specimens exists. This is also valid for the Manson-Coffin-relationship. the relation between lg ε_pls and lg N_B depends on the material (Ck 15, Ck 45) but not on the state of stress.