Strain Rate History Research Articles

Strain rate effects and temperature history effects for three different tempers of 4340 var steel

Abstract A series of experiments is described in which specimens of AISI 4340 VAR steel are deformed in shear at temperatures ranging from −190°C.to 20°C. The tests were performed in a torsional Kolsky (split-Hopkinson) bar at quasistatic and dynamic strain rates. Before testing, all the specimens were normalized, austenitized and tempered to hardnesses of 55, 44 or 33, on the Rockwell C scale. In addition to constant temperature and constant strain rate tests, a number of experiments were performed to study strain rate and temperature history effects in these three tempers. For this purpose a prestrain was imposed at one temperature and strain rate, followed by continued straining at a new temperature or at a new strain rate. Results provide stress-strain curves in shear for the three tempers of this steel. Temperature effects appear greater between −190°C and −50°C than between −50°C and room temperature, particularly for the 200°C temper, while the strain rate sensitivity is about the same as found in mild steel. History effects are quite small for the 600°C and 425°C tempers, even at large strains. However, for the 200°C temper a prestrain at −50°C followed by a temperature change to −190°C requires a higher flow stress than does deformation imposed entirely at the lower temperature. Anomalous history effects of this nature have been seen before in steels, although this is the first evidence for their association with a particular temper.

Superplastic Al-Cu-Li-Mg-Zr alloys

Superplastic properties have been developed in Al-Cu-Li-Mg-Zr alloys. The alloys have low Zr levels (≤0.2 wt pct) and are experimental compositions that were originally designed as low-density, highmodulus, and high strength alloys for room temperature, aerospace structural applications. The alloys have been manufactured both by an ingot metallurgy (IM) route and a powder metallurgy (PM) route involving rapid solidification processing. After conventional manufacturing, the alloys are not superplastic but require further thermomechanical processing. The microstructural changes that occur during this processing are described. Superplastic properties have been evaluated as a function of temperature, strain rate, and processing history. Prior to thermomechanical processing, the alloys have elevated-temperature ductilities of 100 to 200 pct, strain rate sensitivities of about 0.25, and activation energies corresponding to lattice diffusion. After thermomechanical processing, the alloys have ductilities of 500 to 1000 pct, strain rate sensitivities of about 0.4, and activation energies corresponding to grain boundary diffusion. In addition, room temperature properties have been measured in the solution-treated and peak aged (T6) condition for all the alloys and comparison is made with other commercial, non-Li containing, superplastic alloys. Particular emphasis is placed on properties of interest in aerospace applications such as specific modulus, specific strength, and a buckling failure criterion.

An experimental study of simplified methods for the prediction of the deformation of structures subject to severe cyclic thermal loading

The paper describes a set of thermal shock experiments on copper plates between room temperature and 250°C. The experimentally observed creep rates are compared with the predictions of two alternative simplified methods of analysis. The first involves rapid and slow cycle solutions which are computed using finite elements for two constitutive equations derived from the same constant stress data. The second involves upper bounds derived from shakedown solutions. It is shown that conservative results can be computed provided an appropriate relationship between average strain rate and cyclic stress history is known. The experimental data shows a sharp transition from a rapid cycle to a slow cycle condition as the load is increased above the high temperature shakedown limit.

The influence of strain-rate history on the ambient tensile strength of AISI type 316 stainless steel

Abstract A major part of this work was to establish a new data base for AISI type 316H austenitic steel, related to its sensitivity to strain-rate history, and evaluate the observed mechanical response using one of the many modern approaches to constitutive modelling. The phenomenological description of the material was a series of interrupted tensile loading with strain-rate change from quasi-static to dynamic. These data clearly showed that the material strength, although strain-rate sensitive, is not affected by the strain-rate history, indicating that a mechanical equation of state could be applied. The Bodner-Partom constitutive theory is first calibrated by the monotonic stress-strain curves collected at steady constant strain rates, then used to predict the response under various types of interrupted strain-rate change tests.

Deformational history of LLDPE/LDPE blends on blown film equipment

AbstractA video camera tracer technique (T. A. Huang and G. A. Campbell, paper to be presented at ANTEC '85, Washington, D. C.) was used to obtain MD velocity profile and bubble shape above the air ring under industrial film blowing conditions. Subsequently, the velocity profile and bubble shape were utilized to calculate strain and strain rate histories for a fluid element before it solidified. The deformational history of a fluid element was compared between LDPE and LLDPE of similar melt index and density. Also, the study was extended to two groups of LLDPE/LDPE blends: blends rich in LLDPE and blends rich in LDPE. We used a 100‐mil die gap for extruding resins rich in LLDPE to avoid melt fracture. A 30‐mil die gap was used to process blends that were rich in LDPE. Under the same film blowing conditions and frost line height, LDPE exhibits higher peak strain rates than LLDPE and the peak strain rates for LDPE occur closer to the air ring. Moreover, the MD strain of LLDPE continues to increase above the frost line. Conversely, the MD strain profile of LDPE levels off quickly before the frost line. The observed differences in fluid element deformation between LLDPE and LDPE on the blown film line are attributed to the higher melt tension of LDPE. For LLDPE, a 10 wt % LDPE addition causes a significant increase in strain and strain rate at lower positions. Interestingly, a further addition up to 25 wt % LDPE causes little or no further change in deformational history. The increased strain rates associated with an increased strain results in a stabilized LLDPE bubble. For LDPE, only slight differences in strain and strain histories were observed with the addition of LLDPE up to 25%.

High strain rate properties of material: Design and development of a test equipment and methodology

Ballistic test equipment has been designed, constructed and commissioned for the firing of cylindrical projectiles at speeds up to 1000 m/s at small cylindrical/disc shaped test specimens placed upon a rigid anvil. Compressed air was used to propel the projectile whose speed before impact was measured using a laser-beam interruption device. An IMACON high speed camera was used to continuously record the deformation-time history of the specimen and these records were then used to obtain force, strain, stress and strain rate histories during the entire deformation process thus eliminating the need to obtain measured force-time history. The stress-strain curves over large strain were obtained from tests on specimens which where statically pre-strained to different levels. The effects of strain rate history and material inertia were found to be negligible, but the effect of friction was found to be significant and appropriate corrections were introduced.

Constitutive equations for hot-working of metals

Abstract Elevated temperature deformation processing - “hot-working,” is an important step during the manufacturing of most metal products. Central to any successful analysis of a hot-working process is the use of appropriate rate and temperature-dependent constitutive equations for large, interrupted inelastic deformations, which can faithfully account for strain-hardening, the restoration processes of recovery and recrystallization and strain rate and temperature history effects. In this paper we develop a set of phenomenological, internal variable type constitutive equations describing the elevated temperature deformation of metals. We use a scalar and a symmetric, traceless, second-order tensor as internal variables which, in an average sense, represent an isotropic and an anisotropic resistance to plastic flow offered by the internal state of the material. In this theory, we consider small elastic stretches but large plastic deformations (within the limits of texturing) of isotropic materials. Special cases (within the constitutive framework developed here) which should be suitable for analyzing hot-working processes are indicated.

Power-Formula Viscoplasticity, Its Modification and Some Applications

A power viscoplastic constitutive equation was first proposed by Bodner and Partom in 1972. This specific formula has its origin in the physical phenomenon of dislocation dynamics and due to the simplicity of its mathematical form, it is a useful constitutive equation in solving boundary value problems. In this paper a brief review of the basic relation is given, followed by discussion of some relatively less known features of this formula. The body of the paper deals with the modification of the equation to explore its potential in several directions. The first modification consists of making the “threshold stress” strain rate dependent. The second modification aims of modeling strain rate history dependency. Due to space the formulation of the boundary value problems of uniaxial testing and its implementation through finite element programs will not be reported here. Results demonstrating the effect of strain rate and strain-rate history are presented. They are in good qualitative agreement with available experimental data.

Dynamic Plasticity

Recent advances in the understanding of the dynamic plastic response of crystalline solids are discussed. At the level of individual dislocations progress is being made on measurements of dislocation mobility at high stress levels and on elastodynamics solutions for transient dislocation motions. More progress is required on the understanding of changes in mobile dislocation density during dynamic plastic deformation. Widespread use of the Kolsky (or split-Hopkinson) bar has resulted in a reasonably clear picture of the dependence of flow stress on plastic strain rate for polycrystalline metals deformed at strain rates up to 103s−1. Influences of strain-rate history, temperature, and pressure require further investigation. At strain rates of approximately 103s−1’ to 105s−1 there is increasing evidence of a marked increase in flow stress with increasing strain rate. Pressure-shear plate impact experiments appear to be attractive for studying plastic response in this high strain-rate regime. Differences, if any, between stress-path effects at quasi-static strain rates and at strain rates of 103s−1 and higher remain poorly understood. Larger-than-predicted precursor decay observed in plate impact experiments on single crystals remains unresolved and of continuing fundamental interest; however, the importance of precursor decay measurements in determining dynamic plastic response appears to be diminishing because surface effects and limitations on the resolution of wave-front profiles represent serious constraints on the inferences that can be drawn from precursor decay measurements. Modeling of dynamic plastic response of polycrystals in terms of the response of slip systems is in an early stage of development. Kinematics of finite deformation by crystalline slip and consistent averaging techniques for modeling polycrystalline response are understood reasonably well. Increased emphasis on the understanding of the dynamic plastic response of single crystals and on the influence of microstructure appear desirable for sustained progress. Physically based models of wide applicability are required.

Evaluating hardening laws at large tensile strains in sheet specimens

In the finite element modeling of sheet metal formability, the strains in the sheet are calculated from a hardening law which is normally derived from a tensile test. These laws are known to be accurate only up to the maximum uniform strain in tension. However, they are extrapolated during modeling to strains three to five times greater than the uniform strain. In assessing the applicability of these hardening laws at large strains, tensile specimens of 1008 AK steel and commercial purity titanium and zinc were gridded with a fine mesh and slowly pulled to failure. During the test, photographs were taken of the deforming grid in order to develop a complete strain and strain-rate history for each element across the minimum cross section. These data were combined with a hardening law for each material to calculate the total axial load on the specimen. Good agreement between the calculated and measured loads suggests that hardening laws for these materials can be extrapolated to large strains.

Strain rate history effects and observations of dislocation substructure in aluminum single crystals following dynamic deformation

Single crystals of aluminum are deformed in shear at a number of constant strain rates in the range 10 −5–1600 s −1 and to strains of about 20%. These constant-rate tests are supplemented by a series of jump tests in which a sharp increment in strain rate is imposed during the quasi-static straining. Thin foil samples of the strained specimens are examined by transmission electron microscopy (TEM). The constant-strain-rate tests show a linear increase in flow stress with the logarithm of strain rate up to 500 s −1, followed by a more rapid increase at higher strain rates. TeM observations after deformation at quasistatic strain rates reveal a cellular dislocation arrangement that develops into well-outlined subgrains as strain increases. Cells are also visible after dynamic deformation, but these cells are about one-quarter of the size of those produced by quasi-static deformation and their walls are not as well defined. Furthermore, results indicate that, as the cell size is reduced, both the flow stress and the strain rate sensitivity increase. The jump tests show a pronounced strain rate history effect and their results permit the calculation of an activation volume applicable to quasi-static straining. Results of this calculatin, which is based on macroscopic measurements and on the theory of thermally activated deformation of metals, are compared with an activation volume based on the dislocation densities measured after deformation.

Strain-rate history effects and microstructural aspects in lithium fluoride and aluminium single crystals after dynamic loading

Strain-rate history effects and microstructural aspects in lithium fluoride and aluminium single crystals after dynamic loading

Plastic wave propagation in materials with prestraining and strain rate history effects

Abstract The plastic wave propagation in materials with prescribed prestraining and strain rate history effects is investigated. The development is within the framework of the endochronic theory of viscoplasticity. The stress‐time, strain‐time profiles and wave velocity at different strain levels have been obtained theoretically and presented for comparison with experimental data on 1100–0 A1. Furthermore, the difference between the total strain rate and the plastic strain rate in the calculation have been thoroughly disscussed.

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10−3 and 103 s−1 for −150, −100, −50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump.

An examination of four viscoplastic constitutive theories in uniaxial monotonic loading

The predictions of four constitutive theories of viscoplasticity are examined and compared in uniaxial homogeneous deformations. Each theory is fitted to the same stress-strain data, and both analytical and numerical methods are employed to highlight similarities and differences between their predictions.Asymptotic limits are given which represent steady-state behavior of the solutions, and the limits are used to provide analytical methods for fitting test data. Different manifestations of strain-rate and stress-rate history effects predicted by the theories are compared, and the theories are shown to share a significant qualitative bias between responses to stress- and strain-controlled loading.

A GENERALIZED PHENOMENOLOGICAL RHEOLOGICAL MODEL FOR FISH FLESH

ABSTRACTThe mechanical properties of raw and cooked fish were qualitatively characterized by a generalized Maxwell model in which each of the Maxwell elements is modified by incorporation of a contact and two fracture elements. The activation and inactivation of elements have been used as a means of expressing transformation of the rheological characteristics, not only as a function of the strain and strain rate history but also as a function of temperature and time. Although no attempt has been made to quantify the number of elements and their characteristic constants, it is shown that the different modes of rheological behavior exhibited by fish flesh can consistently be described by this kind of model.

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Foliation development — The contribution, geometry and significance of progressive, bulk, inhomogeneous shortening

The geometric consequences of modelling deformation histories involving pure shear, simple shear, inhomogeneous simple shear and bulk inhomogeneous shortening are reviewed. It is shown that zones of rock affected by these deformation histories have similar discontinuities on most of their boundaries with unaffected rock. The “space problem” of progressive pure shear and bulk inhomogeneous shortening can only be resolved if the maximum finite elongation plunges down the dip of any associated foliation plane. However, many fold belts and a number of mylonite zones possess this property and consequently bulk shortening deformation histories must be considered in such cases. The strain field in these models does not account for the inherently heterogeneous nature of deformation on all scales and they generally cannot accommodate the anastomosing character of foliations as it reflects variation in strain. Hence a model is required that provides a solution to the boundary discontinuities associated with bulk shortening and which can accomodate the heterogeneous and anastomosing nature of strain in rocks.An unusual geometry called a “millipede microstructure” preserved in crenulated and crenulation cleavages and also in inclusion trails in plagioclase porphyroblasts is described in Bell and Rubenach (1980). This structure represents a specific deformation history which involved bulk inhomogeneous shortening. A number of constant-area (volume) models of the possible strain in this structure were developed that accommodate the effects of change and/or redistribution of volume, variation in strain and a heterogeneous distribution of inhomogeneity. They also provide a solution to the boundary discontinuities of progressive bulk inhomogeneous shortening.Some of the implications of these models are as follows: 1.(1) Mylonite zones can form by progressive, bulk, inhomogeneous shortening with or without a large non-coaxial component.2.(2) Foliations formed by progressive, bulk, inhomogeneous shortening must anastomose if the foliation is to remain planar on the average and that this reflects strain variation, both in degree and orientation.3.(3) Metamorphic differentiation associated with crenulation cleavage development may be controlled directly by strain, strain rate and local strain history variation and only indirectly by stress.4.(4) Foliations develop on the local scale parallel or nearly parallel to the XY plane of the strain ellipsoid whether they be slaty or crenulation cleavages, schistosity, gneissosity or mylonitic foliations. However on the bulk scale of a fold limb they will commonly lie at a low angle to the XY plane of the strain ellipse.5.(5) The microstructure of individual mineral species may provide criteria for distinguishing strain history, and individual minerals in favoured orientations for slip control subsequent development of heterogeneity.6.(6) Geometric criteria exist on various scales which allow differentiation between bulk shortening and shear strain histories.7.(7) Many arcuate fold belts can be readily explaned by non-plane strain during their development.

Strain rate history effects in LiF single crystals during dynamic loading in shear

A description is presented of experiments performed with LiF single crystals loaded at high strain rates in simple shear by means of a torsional Kolsky bar. Four specimens are used in each test; they are shaped as rectangular parallelepipeds and the tractions are applied in the [1 1 0] directions on the faces parallel to the ( 1 1 0) planes. The experiments provide a measure of flow stress as a function of strain at strain rates of 400 and 800 s −1; the results are compared with those of quasi-static tests performed at strain rates of 4.8 × 10 −5 and 1.6 × 10 −4 s −1 in the same apparatus. In addition, incremental strain rate experiments were performed. These consist in imposing first a quasi-static strain rate which is increased suddenly and with no intermediate unloading to a dynamic rate. The results showed that the flow stress of LiF is strongly sensitive to strain rate but that the effects of strain rate history, although present, are not pronounced. Microscopic observations using the etch pit technique showed that the dislocations are distributed uniformly after deformation at a constant quasi-static strain rate but that they congregate into wide bands as the result of incremental strain rate testing.

The Rate (Time)-Dependent Behavior of Ti-7Al-2Cb-1Ta Titanium Alloy at Room Temperature Under Quasi-Static Monotonic and Cyclic Loading

Uniaxial tests using a servocontrolled testing machine and strain measurement at the gage length were performed on a high-strength, low-ductility Titanium alloy. Tests involved monotonic and cyclic loadings with strain rates between 2 × 10−8 to 10−3 s−1, stress rates from 10−1 to 102 MPa s−1, repeated changes in strain rates, and short-term relaxation and creep tests. The inelastic behavior is strongly rate-dependent. Ratchetting is shown to increase as the stress rate decreases. No strain-rate history effect was found. A unique stress-strain curve is ultimately reached for a given strain rate irrespective of prior history as long as only positive stresses are imposed. In the plastic range the relaxation drop in a given time period depends only on the strain rate preceding the test and is independent of the actual stress and strain.