Showing papers on "Strain rate published in 1989"

An analysis of the low temperature, low and high strain-rate deformation of Ti-6Al-4V

Abstract: The deformation behavior of Ti−6Al−4V at temperatures between 76 and 495 K, strain rates between 0.001 and 3000 s−1, and compressive strains to 0.3 has been investigated. Measurements of yield stress as a function of test temperature, strain rate, and prestrain history are analyzed according to the model proposed by Kocks and Mecking. The mechanical threshold stress (flow stress at 0 K) is used as an internal state variable, and the contributions to the mechanical threshold stress from the various strengthening mechanisms present in this alloy are analyzed. Transmission electron microscopy (TEM) is used to correlate deformation substructure evolution with the constitutive behavior. The deformation substructure of Ti-6-4 is observed to consist of planar slip in the α grains at quasistatic strain rates. At high strain rates, deformation twinning is observed in addition to planar slip. Increasing the temperature to 495 K is seen to alter the deformation mode to more random slip; the effect of this on the proposed deformation model is discussed.

A constitutive model for strain rates from 10−4 to 106 s−1

Abstract: We have developed an addition to the Steinberg–Guinan high strain‐rate constitutive model that extends its validity to strain rates as low as 10−4 s−1. With this new model, we have successfully reproduced a number of rate‐dependent, shock‐induced phenomena in tantalum, such as precursor on reshock, precursor decay, and shock smearing. We have also successfully calculated a plate‐impact experiment at a loading stress of 230 GPa as well as extensive data for yield strength versus strain rate at room temperature and yield strength versus temperature at a strain rate of 10−4 s−1.

Viscous–elastic–plastic modelling of one-dimensional time-dependent behaviour of clays

Abstract: Increased attention has recently been directed towards the influence of time and strain-rate effects on the behaviour of clays in one-dimensional (1-D) laboratory consolidation. The improved unders...

Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model

Abstract: F ull solutions to mixed rate boundary value problems over polycrystalline domains are performed via the finite element method. In order to make these finite element calculations feasible, an idealized two-dimensional crystal structure is studied. These boundary value problems rigorously satisfy the averaging theorems of Hill (Proc. R. Soc.A326, 131, 1972) so that well defined Taylor model analogue problems may be identified and solved. Comparisons between the finite element solutions and their corresponding Taylor model analogues yield a quantitative assessment of the Taylor model's validity with respect to its predictions of texture development and global stress-strain response. The finite element calculations also provide physical insight into the mechanisms contributing to the development of nonuniform and localized deformations in polycrystals.

Martensite formation, strain rate sensitivity, and deformation behavior of type 304 stainless steel sheet

Abstract: The strain and strain rate dependence of the deformation behavior of Type 304 stainless steel sheet was evaluated by constant temperature tensile testing in the temperature range of −80 °C to 160 °C. The strain rate sensitivity, strain hardening rate, and ductility reflected the compctition of two strengthening mechanisms: strain-induced transformation of austenite to martensite and dislocation substructure formation. At low temperatures, the strain rate sensitivity and strain hardening rate correlated with the strain-induced transformation rate. A maximum in total ductility occurred between 0 °C and 25 °C, and the contributions of strain rate sensitivity and strain hardening to independent maxima with temperature of the uniform and post-uniform strains are discussed.

The Brittle-Ductile Transition in Silicon. I. Experiments

Abstract: The experiments described in this paper investigate the fundamental processes involved in the brittle–ductile transition (BDT) in silicon, and form the basis of a new theoretical model (see following paper). The fracture (or bending) stresses of four-point bend specimens of silicon containing semicircular surface cracks, introduced by surface indentation, were determined over a range of temperatures and strain rates. A sharp transition, characterized by a rapid increase in fracture stress with temperature, occurs at a temperature ( T c ) that depends on the strain rate and the doping of the material used; these data are used to derive activation energies, which are found to be equal to those for dislocation glide. At temperatures above the sharp transition region, the specimens deform by macroscopic plastic yielding. Etch pitting experiments show that below T c no significant dislocation activity occurs; the sharp brittle–ductile transition is associated with a sudden growth of well-defined dislocation arrays from certain points on the precursor flaw, before fracture occurs. These only appear in a dynamic test at T ≽ T c ; at T = T c , they form only when the applied stress intensity factor K is of the same order as that for brittle failure ( K Ic ) at T T c . These experiments suggest that at T ≈ T c , a 9nucleation9 event precedes the generation of avalanches of dislocations when K ≈ K Ic . Static tests show that dislocations can be made to move from crack tips of K value as low as ca . 0.3 K Ic . Above the transition region general plasticity occurs, with slip being concentrated particularly around and spreading from the precursor flow. A 9warm-prestressing9 effect is observed, whereby the low-temperature fracture stress is increased by prestressing above T c .

Dynamic Shear Band Development in Plane Strain

Abstract: : Plane strain compression of a rectangular block is used as a model problem to investigate the dynamics of shear band development from an internal inhomogeneity. The material is characterized as a von Mises elastic-viscoplastic solid, with a hardness function that exhibits a local maximum. Regardless of whether the material is hardening or softening, plastic strain development involves the evolution of finger-like contours emanating from the inhomogeneity at 45 degrees to the compression axis. Once a given strain contour crosses the specimen, it fans out about its initial direction of propagation. For a softening solid, this fanning out ceases for some strain level greater than the strain at the hardness maximum and further straining takes place in an ever narrowing band. Many of the qualitative features of shear band development under dynamic loading conditions are the same as under quasi-static loading conditions, but a significant retardation of shear band development due to inertial effects is found.

Analysis and assessment of electromagnetic ring expansion as a high‐strain‐rate test

Abstract: The rapid expansion of electromagnetically launched thin metal rings is analyzed in detail, with particular emphasis on the determination of the expansion speed, currents, and specimen temperature as a function of launch voltage. Electrodynamic calculations for copper, tin, and lead rings are presented and compared with typical experimental results. Currents derived from Rogowski‐probe records and expansion speeds measured with a velocity interferometer (VISAR) are found to be in excellent agreement with these calculations. Currents are large, of the order of tens of kiloamperes, and heating of the specimen can be significant. It is found that, for good conductors such as copper, the maximum useful strain rate will be limited by the Joule heating of the specimen. For materials with resistivities and strengths substantially larger than those of copper, direct expansion of a specimen ring is difficult. Use of a composite ring, in which a high‐conductivity driver is used to launch a low‐conductivity specimen...

A study of the rapid deformation behaviour of a range of polymers

Abstract: Polymers are increasingly being used in applications where they are rapidly deformed. However, compared with metals, relatively few studies of their mechanical properties at high rates of strain have been published. This paper describes an investigation of the rapid deformation behaviour in compression of a number of widely used polymeric materials. The necessity of properly characterizing polymers is discussed, as the variation of commercial grades bearing the same name is considerable, and furthermore these materials are much more susceptible to change during storage than say metals. The importance of thermal properties to rapid, and hence adiabatic, deformation is pointed out, and tables of such properties are presented. Extensive use was made of high-speed photography (interframe time 7 $\mu $s) to study qualitatively the behaviour of solid discs of polymers at strain rates of 2.5 $\times $ 10$^{3}$ s$^{-1}$. The framing speed was sufficiently fast to capture fracture initiation and subsequent failure of all the polymers studied, including polycarbonate (PC), which fails in an almost explosive manner. The darkening of heat-sensitive film in contact with deforming discs was also investigated. Quantitatively, this technique was used to check the applicability of Avitzur's analysis (Avitzur (Israel J. Technol. 2, 295-304 (1964)) of a deforming annulus to polymers. Agreement was found to be good and hence friction could be measured during deformation at high rates of strain for the first time. Studies were also carried out to determine the best lubricant for rapid compressive testing. Petroleum jelly was found to reduce the friction closest to zero. An optically identical system was set up in an Instron mechanical testing machine both to perform friction studies and to explore deviation from incompressible behaviour. Agreement with Avitzur's analysis was found to be poorer, and no lubricant was found to reduce friction below about 3-4%. PC, with a very high value of frictional stress, showed evidence of a change in volume. Allowances were made for the elastic indentation of the anvils. Higher strain rates were achieved by using an instrumented drop-weight machine and a direct impact Kolsky bar, both developed in this laboratory. Care was taken to eliminate sources of error, including friction and calibration errors. The strain rate sensitivity of the polymers ranged from 5-15 MPa per decade of strain rate. However, most showed some softening as the strain rate was raised from 10$^{3}$ to 10$^{4}$ s$^{-1}$, the exceptions being polybutylene teraphthalate (PBT) and polyvinylidene difluoride (PVDF).

Viscoplastic modeling of texture development in quartzite

Abstract: Polycrystal plasticity theory has been successfully used to simulate development of preferred orientation in rocks. In particular, G. Lister and coworkers have done a comprehensive study, applying the Taylor theory to quartzite. In these calculations it was assumed that deformation is homogeneous; that is, all grains deform at the same rate, that critical resolved shear stresses (CRSS) of slip systems remain constant, and that deformation is rigid-plastic; that is, dislocations move only when the CRSS has been reached and then with indeterminate velocity. We have been investigating the influence of work hardening and of strain rate dependence on texture development. In particular, modification of the viscoplastic Taylor theory suggests that textures are greatly dependent on the rate sensitivity of flow stress when this stress exponent is small, such as in quartz where it is near 3. The influence of work hardening is less critical in the case of quartz. Results from Taylor simulations are also compared with those from a self-consistent theory. The latter sacrifices local strain continuity for better stress equilibrium. In the self-consistent scheme, grains which are favorably oriented for slip are allowed to deform at a faster rate. Texture patterns obtained with the two theories are moderately different. In self-consistent deformation a C axis maximum in the intermediate strain direction (Y) is generated which is absent in Taylor deformation but is a common feature of many natural quartz fabrics. Grains associated with this maximum are most strongly deformed. Deformation modeling with more realistic boundary conditions adds complexities but appears to be necessary in the case of anisotropic and rate sensitive rocks.

A system to reproduce and quantify the biomechanical environment of the cell

Abstract: An in vitro system that permits application of a uniform biomechanical stimulus to a population of cells with great precision has been developed. The device is designed to subject living cells to reproducible and quantifiable biaxial strains from 0 to 10% at rates from quasi-static to 1 s-1 and frequencies from 0 to 5 Hz. Equations for determining the strain in the substrate upon which the cells are grown, based on easily measured parameters, are derived and validated experimentally. The mechanical properties of the substrate are determined, and it is demonstrated that cells can easily be cultured in the apparatus. By use of the system, cloned bovine pulmonary artery endothelial cell clones are subjected to 5% biaxial strains applied at a peak strain rate of 0.5 s-1 and a frequency of 1 Hz for 7 h with cell viability greater than 84% and cell detachment less than 8%. We demonstrate that cells must be attached to the substrate for them to be stretched and that cell strain and substrate strain are not equal. With the use of fluorescently labeled beads as cell surface markers to measure the actual strain produced in the cells as a result of the deformation of the substrate, cell elongation was found to be approximately 60% of the strain in the substrate. This constant appeared to be affected by both in vitro cell age and morphology.

On linear versus nonlinear flow rules in strain localization analysis

Abstract: This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear “comparison material” is critically reviewed and compared to the criterion resulting from “actual” nonlinear plastic flow laws.

Magnesium-lithium alloys in metal matrix composites — A preliminary report

Abstract: Procedures are described for the fabrication of fibrous composites based on magnesiumlithium alloys as a matrix Such composites have been produced containing planar random and aligned (continuous and discontinuous) fibres of carbon, alumina and silicon carbide For all of these, except silicon carbide whiskers, significant fibre degradation occurred, during fabrication or subsequent heat treatments, either by chemical reaction or by grain boundary penetration of lithium Further consequences of the high atomic mobility exhibited by the matrix are manifest in the mechanical behaviour of the composites Although considerable property enhancement is possible by fibre reinforcement, a significant diffusional contribution to the stress relaxation mechanisms results in a dependence of work hardening rate and failure strain on temperature and strain rate, even around room temperature and at relatively high strain rates It is concluded that, although the system presents many practical difficulties, it is worthy of further study

Prismatic slip in beryllium

Abstract: An in situ study of prismatic glide in beryllium is made to provide a simple model for understanding the anomalous increase in elastic limit as a function of temperature. This effect is also observed in several ordered alloys such as superalloys. In this paper, Part I, the mechanism controlling the deformation is studied at the stress peak temperature (300 K). It consists of alternate cross-slip events between the basal and the prismatic plane, leading to a ‘locking-unlocking’ mechanism which is studied in detail. This new mechanism appears to be a variant of the Peierls mechanism, where screw dislocations exhibit a metastable spreading in the prismatic plane, in addition to the classical stable spreading in the basal plane. Quantitative in situ measurements give local values of several parameters (such as stress, probabilities of locking and unlocking and strain rate), and the velocity of dislocations and the local strain rate are theoretically expressed. The exact origin of the stress anomaly i...

Large-strain torsional deformation in aluminum at elevated temperatures

Abstract: A substantial amount of work has been produced recently in the area of large-strain deformation of aluminum at elevated temperatures using torsion tests. These studies have generated much interest because the equivalent uniaxial strain to failure of the aluminum can exceed 100, depending on the purity, strain rate and temperature. The research in this area has been performed principally by four groups and reported largely in less-circulated journals, proceedings and reports. The following review of the subject was written by three representatives from these groups. Emphasis was on establishing areas of substantial agreement as well as delineating aspects where further work will be helpful. The review is divided into two principal sections: macroscopic phenomenology and microstructural observations. The first includes discussions of ductility, stress-strain relationships and constitutive equations. The second includes discussions of grain elongation and thinning and grain boundary serration, subgrain sizes and morphologies, dislocation density, and subgrain boundary misorientation angles, as well as texture analysis. These investigations provide insight into the large-strain mechanical and microstructural phenomenology of materials in which elevated temperature softening proceeds by dynamic recovery.

Controlled Degradation of Polypropylene: A Comprehensive Experimental and Theoretical Investigation

Abstract: Experimental and modeling studies of the free-radical-induced degradation of polypropylene (PP) in the melt phase have been carried out. Experiments have been performed in a single-screw plasticating extruder using a peroxide as the free-radical source. Concentration of the peroxide was in the range 0.01–0.6 wt%. Results in the form of melt flow index (MFI) values, viscosity curves, and molecular weight distribution (MWD) of the produced resins are presented here. Based on these results, a constitutive equation describing the shear viscosity of the melt as a function of shear rate, temperature, and molecular weight has been derived. The extensional viscosity of these resins has been determined as a function of strain rate using Cogswell's analysis of converging flows. A previously developed kinetic model (plug flow) has been used to simulate the changes of the average molecular weights of the MWD, and a sensitivity analysis of this model has been carried out.

Dynamics of a class of vortex rings

Abstract: The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows.