Showing papers on "Strain rate published in 1979"

Determination of the plastic behaviour of solid polymers at constant true strain rate

Abstract: The methods of conventional tensile testing as applied to solid polymers are compared and reviewed critically. Experiments were performed using these techniques, and it is shown that large variations in local strain rate occur while necking and cold-drawing take place. A new tensile testing method is described in which the samples are tested atconstant local true strain rate. This technique is based on the use of a diameter transducer, an exponential voltage generator and a closed-loop testing machine. Flow curves for poly(vinyl chloride) and high density polyethylene were determined at room temperature over the strain rate range of 10−1 to 10−4 sec−1. It is shown that the flow behaviour of these two polymers can be approximated by the constitutive relation:\(\sigma = K \cdot \exp [(\gamma _ \in /2) \in ^2 ] \cdot \dot \in ^m\), whereK andγ∈ are constants andm, the rate sensitivity, is in the range 0.02 to 0.06. It is concluded that the positive curvature of the log σ flow curve is responsible for the stabilization of flow localization associated with cold drawing, and that the rate sensitivity plays a much smaller role.

The temperature variation of hardness of olivine and its implication for polycrystalline yield stress

Abstract: The variation of hardness with temperature was measured for olivine on a number of crystal faces by the Vickers diamond pyramid technique (up to 800°C) and by a mutual indentation technique (for temperatures up to 1500°C). A comparative review of hardness data and compressive creep measurements obtained under large confining pressures confirms the hypothesis of Rice [1971] that single-crystal hardness measurements, corrected for elastic effects, can be correlated to the fully ductile yielding of a polycrystal by intragranular dislocation mechanisms, including dislocation climb and glide. The computed differential yield stresses, σ (in gigapascals), which empirically correspond to a strain rate of 10−5 s−1, were well represented by an equation of the form σ = 9.1(±0.3) - 0.23(±0.01)T2, where T is the absolute temperature (in degrees Kelvin), and the quoted variances are for 1 standard deviation. The olivine data therefore predict a high-stress polycrystalline flow law that may be expressed as = 1.3 × 1012exp - [(60×103)/T][1 - (σ/9.1)]2 where is the strain rate in s−1. A similar functional dependence of strain rate on stress is indicated for Al2O3 for temperatures below 900°C but is contraindicated for MgO and NaCl. Using a semiempirical method of dislocation rosette analysis, the critical resolved shear stress on the {110} [001] slip system was estimated (to 20%) over the temperature range 20°C to 780°C as 1.2 GPa and 0.3 GPa, respectively. These data are useful in providing an upper bound to the yield stress in a region of stress and temperature space not easily accessible by other experimental methods.

Critical fracture stress and fracture strain models for the prediction of lower and upper shelf toughness in nuclear pressure vessel steels

Abstract: Critical fracture stress and stress modified fracture strain models are utilized to describe the variation of lower and upper shelf fracture toughness with temperature and strain rate for two alloy steels used in the manufacture of nuclear pressure vessels, namely SA533B-1 (HSST Plate 02) and SA302B (Surveillance correlation heat). Both steels have been well characterized with regard to static and dynamic fracture toughness over a wide range of temperatures (−190 to 200°C), although validJIc measurements at upper shelf temperatures are still somewhat scarce. The present work utilizes simple models for the relevant fracture micromechanisms and local failure criteria to predict these variations in toughness from uniaxial tensile properties. Procedures are discussed for modelling the influence of neutron fluence on toughness in irradiated steel, and predictions are derived for the effect of increasing fluence on the variation of lower shelf fracture toughness with temperature in SA533B-1.

Interaction between recrystallization and precipitation during the high temperature deformation of HSLA steels

Abstract: A new mechanical method is described for following the progress of precipitation in niobium-modified steels. The technique is based on the determination of the strain to the peak stress in high temperature, constant strain rate compression tests. The peak strain is sensitive to holding or aging time prior to testing, thus permitting the kinetics ofstatic precipitation to be determined in either the re crystallized or the predeformed condition. A modification of this technique permits the determination of the kinetics ofdynamic pre-cipitation. The rates of static and dynamic precipitation measured in this way are generally ‘faster’ than the kinetics determined by other methods. The results indicate that the addition of niobium to austenite retards recrystallization in two distinct ways. There is a significant delay introduced by what appears to be a solute effect. In addition, under conditions where precipitation is more rapid thansolute- retarded recrystallization, the operation of the recrystallization process is prevented or retarded until precipitation is complete or nearly complete.

Dynamic recrystallization kinetics

Abstract: Dynamic recrystallization in two austenitic stainless steels has been monitored by (i) observations of the high-temperature stress/strain behaviour, and (ii) metallographic measurements on rapidly quenched, partially reacted specimens. Particular effort has been put into assessing the influence of pre-existing grain size on the kinetics of dynamic recrystallization at a specified temperature and strain rate. A theory due to Cahn, which is intended to describe the kinetics of transformations where nucleation is strictly confined to pre-existing grain boundaries, has been applied to the dynamic recrystallization problem. Some measure of agreement with observation is obtained but only on the proviso that proper attention is paid to repeated nucleation at the recrystallization front, and that a distinct variation of active grain boundary area during the reaction is recognized and considered.

Deformation of Polycrystals

Abstract: SUMMARY Deformation of polycrystals is treated as the average behavior of an agglomerate of individual crystallites and their interaction across the grain boundaries. After considering the effect of grain boundaries on yield, in a rather general way the similarities between stress strain curves of single crystals and polycrystals are discussed, including the implication for commonly used stress strain relationships. Since - as known from polyslip in single crystals - the polycrystal curve consists of two stages (II and III) which are differently affected by deformation temperature, these two stages are treated separately. The range of athermal hardening (stage II) is described quantitatively by incorporating the processes of dislocation storage near the grain boundary into the well established stage II theories of single crystals. It is concluded from this discussion, that the influence of grain size on yielding and on work hardening at low strains is phenomenologically well explored and rather well understood theoretically. The range of temperature dependent work hardening (stage III) is interpreted as being the stage where the dislocation structure evolves towards a well defined cell structure, which approaches a steady state pattern as strain proceeds. The influence of temperature and strain rate on steady state appears to be the same for single crystals (deformed in polyslip) and polycrystals in the normal range of grain sizes. Although the differences between different materials can be related to the values of certain material parameters, understanding of stage III suffers from our ignorance of the basic dislocation mechanisms which control cell formation. In the last part effects of very large strains are shortly considered. Texture development is taken as an example how information about details of the deformation of the grains can be deduced from a comparison of experimentally obtained and of theoretically derived pole figures. Eventually it is discussed that at very large strains new effects appear, which are beyond the scope of the common theoretical concepts of work hardening and plastic flow.

In situ deformation of b.c.c. crystals at low temperatures in a high-voltage electron microscope Dislocation mechanisms and strain-rate equation

Abstract: In situ deformation of thin foils of niobium, molybdenum and α-iron has been performed in a high-voltage electron microscope, at temperatures ranging from 70 to 400 K. The observations of dislocation mobility, interaction with obstacles and several multiplication mechanisms are discussed. The ratio of screw to non-screw dislocation velocities is strongly temperature dependent and it is shown that a transition occurs in a narrow temperature range, which is characteristic for a given metal. It has been found that the different behaviour of the three metals investigated is greatly influenced by the different cross-slip abilities of the screw dislocations. Simple equations are derived to describe the simultaneous interactions of screw dislocations with localized obstacles and lattice friction. Only a few and measurable parameters are used, and therefore a rate equation can be derived in order to allow a comparison with the results of conventional tests to be made. In particular, the transition temper...

Static recrystallization and restoration after hot deformation of Type 304 stainless steel

Abstract: Specimens of Type 304 stainless steel have been deformed in torsion at temperatures of 950–1150°C and annealed for different times before quenching or continuing the deformation. The kinetics of static recrystallization and the recrystallized grain size have been determined by quantitative metallography. Increasing strain and decreasing original grain size both reduce recrystallization time and recrystallized grain size. Increasing strain rate and decreasing temperature of deformation have a similar, but smaller effect. Annealing temperature also strongly influences recrystallization time (activation energy 425 kJ mol−1), but not recrystallized grain size. The effects of all the experimental variables are described in terms of simple parametric relationships. The kinetics of static restoration have been determined both from hardness tests on quenched specimens and from interrupted torsion tests. The extent of restoration is related in a non-linear manner to fraction recrystallized. This arises par...

Microstructural influences on superplasticity in Ti-6AI-4V

Abstract: The strong dependence of the superplastic behavior of metals and alloys on grain size has been demonstrated, and it is now well known that a fine grain size is normally a requirement for superplasticity. However, the microstructure of certain alloy systems such as Ti-6A1-4V cannot always be adequately characterized by a single parameter such as grain size. In two-phase α β alloys such as Ti-6A1-4V, other microstructural parameters such as volume fractions of the two phases, grain aspect ratio, grain size distribution and crystallographic texture may also influence superplasticity. For example, if “grain switching” is an important deformation mechanism in superplastic flow as suggested by Ashby and Verall, then factors such as grain aspect ratio and range of grain sizes would be expected to have an effect on superplastic behavior. In this study, these microstructural features were determined for several different heats of Ti-6Al-4V, and the corresponding superplastic properties were evaluated in terms of their fully characterized microstructure. The flow stress as a function of strain rate, strain rate sensitivity exponent (m) as a function of strain rate and total elongation on properties were found to be strongly influenced by microstructural parameters such as grain aspect ratios, grain size and grain size distribution.

Differential stress determined from deformation‐induced microstructures of the Moine Thrust Zone

Abstract: The dislocation structure, recrystallization, and elongation of quartz grains in tectonites from three localities along the Moine thrust fault have been analyzed by transmission electron and optical microscopy. The dislocation density, 5×108 cm−2, and the grain size after recrystallization, 15 μ, in the basal quartzite unit at the Stack of Glencoul are independent of distance from the fault, to the maximum sampling distance of ∼100 m. The differential stress level determined from the deformation-induced microstructures is on the order of 100 MPa. The magnitude of the differential stress at the fault decreases by a factor of 2 from Knockan Crag to Loch Eriboll, a distance of 50 km. At the Stack of Glencoul, grains in the basal quartzite are progressively elongated and recrystallized approaching the fault, corresponding to a progressive increase in strain. At 100 m from the fault, the aspect ratio of relict quartz grains is ∼1:1; at 0.01 m it is 85:1. A quantitative estimate of the strain, based on the aspect ratios of the relict quartz grains, as a function of distance from the fault has been used to calculate strain rate and temperature profiles. For a creep activation energy of 0.19 MJ mol−1 the temperature decreases away from the fault with a gradient of 7.5×10−3 °C cm−1. For a differential stress of 100 MPa, a steady state thrust sheet velocity of 11 cm yr−1 would be required to produce this gradient. At 100 m from the fault, 5% of the quartzite is recrystallized from 1-mm to 15-μm grains; at 0.01 m it is 100% recrystallized to 15-μm grains. This small grain size probably favored grain boundary deformation mechanisms over grain matrix mechanisms and thus helped to concentrate the strain at the fault. Systematic changes in the elongation and recrystallization of quartz grains in Lewisian Gneiss and Moine Schist are obscured by the constraints imposed by other mineral phases. The small size of the grains after recrystallization, highly serrated grain boundaries, and large densities of free dislocations suggest that very little static recovery followed the plastic deformation event.

A non-linear uniaxial integral constitutive equation incorporating rate effects, creep and relaxation

Abstract: A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.

Interrelationship between creep deformation and creep rupture in 2¼Cr-1Mo steel

Abstract: Creep deformation and rupture have been studied in 2¼Cr-IMo steel over the stress range 60-210 MN m⁻² at 565°C. Creep damage accumulates by the initiation and growth of extensive cavitation at the prior austenite grain boundaries. Cavity formation predominates during the initial transient and individual cavities appear to nucleate on grain boundary carbides. Quantitative analysis of the cavitation kinetics in relation to the creep deformation processes suggests that cavity growth is directly related to deformation occurring at the grain boundaries. It is inferred that the vacancy diffusion mechanism is inhibited and growth is limited by the local creep process occurring at the grain boundaries. At low stresses the latter is controlled by intra-granular recovery creep such that the overall rate of cavitation is proportional to the macroscopic strain rate. However, results obtained under biaxial shear conditions imply that the rate of cavitation is additionally dependent upon the normal boundary str...

Strain and strain-rate hardening effects in punch stretching of 5182-0 aluminum at elevated temperatures

Abstract: The influences of material properties on stretch forming are often studied by testing a wide variety of materials. However, differences in texture, fracture strain, and crystal structure are not taken into account. These material differences are eliminated in the present study by performing tests on a single material (5182-0 aluminum alloy) in which strain hardening, strain-rate hardening, and limit strain vary in a precise manner with temperature and strain-rate. This allows a comparison to be made between experimental results and analytical calculations to separate the contributions of these two types of hardening in distributing strain during elevated temperature forming. Furthermore, the influence of a change in limit strain to overall formability can be assessed since the hardening phenomenon is better understood. The strain distributions developed during forming over a spherical punch are calculated using the finite element method and material properties obtained from tensile tests at 25, 130, and 200°C at varying strain rates. These are compared to experimental strain distributions over the same temperature range. Measurements of limit strains are taken from forming limit diagrams. This research demonstrates that formability is improved at elevated temperatures through increases in both strain-rate hardening and limit strains.