Plastic Flow Of Metals Research Articles

A constitutive model for the deformation induced anisotropic plastic flow of metals

Abstract A mathematical framework is established for the equations governing inelastic deformation under multi-dimensional stress states and for the associated evolution equations of the internal state variables. The formulation is based on a generalization of the Prandtl-Reuss flow law. In the evolution equations for the inelastic state variables that control plastic flow, it is assumed that part of the rate of change is isotropic and the remaining part varies according to the sign and orientation of the current rate of deformation vector. This leads to a minimum of twelve components of the internal state tensor which represents resistance to inelastic deformation. In this manner, both initial and load history induced plastic anisotropy can be modeled. A specific set of equations for anisotropic plastic flow is developed consistent with the inelastic state variables.

Theoretical computer investigation of the high-speed shaping of free-flowing materials

1. An analysis of the process of high-speed shaping of free-flowing materials has been carried out on the basis of theoretical premises of continuum mechanics and plastic flow of metals. 2. Calculation formulas have been derived for the specific pressures, specific energy of shaping, and temperature rise in high-speed processes as functions of properties of free-flowing materials (σt.ψn, A, and Cv) and shaping conditions. 3. The formulas yield results which are in good agreement with experimental data, and can therefore be employed in design calculations of technical processes and installations.

Flow stress, subgrain size, and subgrain stability at elevated temperature

Well defined subgrain boundaries dominate the microstructural changes occurring during plastic flow of polycrystalline metals at elevated temperature. The quantitative influence of subgrain size on elevated-temperature plastic flow is considered. Based on the results of tests under constant-stress and constant-structure conditions, an equation is developed which predicts the creep rate as a function of subgrain size, stress, diffusion coefficient, and elastic modulus. In general, the subgrain size is a unique function of the current modulus-compensated flow stress, but if fine subgrains can be introduced and stabilized, large increases in creep strength may result. The applicability of the phenomenological relation developed to the behavior of dispersion-strengthened materials (where the second-phase particles may predetermine the effective subgrain size) is discussed. When subgrain effects are included, it is shown that the creep rate is less dependent on stacking fault energy than has been previously thought.

Is there an athermal region of plastic flow in metals at intermediate temperatures?

Abstract The question of the existence or otherwise of an athermal temperature region of plastic flow in metals is examined. It is suggested that the athermal region is absent in metals with large dislocation densities. Such an explanation is provoked by a fairly recent proposition that the unzipping of attractive junctions is a plausible rate-controlling mechanism at high temperatures.

Heat transport in drawing through curved dies

Inherent to the plastic flow of metals is heat energy generated by the irrecoverable work of deformation. While this thermomechanical phenomenon was documented by the end of the eighteenth century[/], it was not until the first quarter of this century that measurements were made of the heat generated as a percentage of expended plastic work[2]. W. S. Farren and G. I. Taylor established that, in the pulling of tensile specimens, that percentage was significant between 86% and 96% for alloys of steel, and aluminum. Industrially, the importance of this effect is in deformation processing, where elevated temperatures degrade material properties in the workpiece and lubricant [3,4,5]. Despite the need, few papers appear which show a method for studying heat transport in realistic metalworking processes. The present paper displays such a method in terms of an important process: axisymetrlc drawing of thick shell through curved dies.

Calculation of compressible turbulent boundary layers on straight-tapered swept wings

Huang, C. L., On Function for Anisotropic Proceedings of Symmetry, Similarity and GroupTheoretic Methods in Mechanics, University of Calgary, Canada, 1974. Huang, C. L. and Kirmser, P. G., A Criterion on for Orthotropic Fiber Science and Technology, 1975, to be published. Ely, R. E., Strength Results for Two Brittle Materials Under Biaxial Stresses, U. S. Army Missile Command—Redstone Arsenal Alabama, Technical Rept. RR-72-11,1972. Weng, T. L., Grade ATI Graphite, Proceedings of the Conference on Continuum Aspects of Graphite Design, Nov. 9-12, Gatlinburg, Tennessee, CONF-701105, NTIS, U.S. Dept. of Commerce, 1970. Hoffman, O., The Brittle of Orthotropic Journal of Composite Materials, Vol. 1, 1967, pp. 200-206. Hill, R., A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Procedings Royal Society (London), A, 193, 1948, pp. 281-297. Table 1 Calculations of Nash and Scruggs for the swept wing of Fig. 1 at A/oo =0.5. Gp =chordwise-average skin-friction coefficient

A penalty function approach to problems of plastic flow of metals with large surface deformations

An iterative solution permits determination of velocities in plastic flow using a finite element formulation. By updating co-ordinates very large deformation can be followed.

PILOT STUDY OF PREFORM DESIGN FOR SINTER FORGING

AbstractAn important difference between sinter forging and conventional forging is that of consolidation of the PM preform. It therefore follows that sinter forging would seem to be a hot-compaction process with some bulk metal plastic flow. The permitted amount of plastic flow is considerably less for a PM preform than for a preform produced from wrought material of equivalent composition, since PM preforms exhibit poor ductility and are therefore more prone to cracking. The purpose of this study is to produce some guidelines to assist in designing preforms for sinter forging and to attempt to minimize the ‘trial and error’ approach. This has been undertaken by the production and study of a component suitable for PM forging, which at present is produced by conventional forging.The lateral flow of metal was observed and investigations undertaken as to how density variations across the preform might assist the consolidation process. An iron powder containing 1% graphite and 1% zinc stearate was used in the...

Temperature-dependent slip line length in copper single crystals

Abstract An essential feature of any theory of strain hardening is a mechanism by which slip lines are blocked. In a recent paper on temperature-dependent plastic flow in strain-hardened metals (Alden 1972), it was suggested that expanding dislocation loops, and thus slip lines, are blocked by a co-operative process involving point-like obstacles (namely attractive forest dislocations), rather than by specific linear obstacles which surround the source, as in current theory (Seeker 1957, Hirsch and Mitchell 1967). A unique prediction of the new theory is that the slip line length should increase with decreasing temperature and increasing stress at constant structure; this occurs because increasing numbers of forest dislocations become penetrable at the higher stress. The purpose of these experiments was to test this prediction in copper single crystals. A series of crystals was identically restrained at 673°K, polished and incrementally strained to produce characteristic slip lines at several lower temper...

Dynamic Shear Stress—Analysis of Single Crystal Machining Studies

Experimental results obtained when single crystals of aluminum of known orientation are machined under identical cutting conditions are presented. Analysis of the data obtained shows that the dynamic shear stress remains constant for all orientations tested and is in good agreement with the calculated value for polycrystalline aluminum. The implications of these results to metal cutting theory and the metal physical foundations on which the concept of dynamic shear stress, as a true material property, rests are discussed. The possible role that the dynamic shear stress may play in determining the geometry of the metal cutting problem, a problem in partially constrained plastic flow of metals, is discussed.

The mechanism of “metarecovery” and its role in temperature dependent plastic flow

In this paper it is shown that some phenomena of temperature-dependent plastic flow, annealing, and microstructure in pure metals, previously thought to be diverse, can be understood as parts of a single theoretical framework. The important microstructural effects, frequently observed experimentally, but here discussed as the basis of a new theoretical equation of plastic strain, are the nonregularity of the obstacle dislocation structure and thermally-activated rearrangement to a lesser regularity (essentially, cell formation). In turn, these effects are shown to cause gradual yielding in annealed metals (“metarecovery”), isostructural changes in flow stress with change of temperature or strain rate, and transient creep.

On the importance of including recovery in phenomenological theories of plastic flow in metals

The phenomenological theory of plastic deformation recently proposed by Hart( 1) is criticized on the grounds that it does not include static recovery and therefore should not be applied at high temperature. In addition Hart's suggestion that a steady state deformation regime does not exist is questioned. It is pointed out that the evidence for no steady state cited by Hart was obtained for copper at room temperature where static recovery is not expected to occur. Also, it is suggested that his interpretation of delayed creep effects in terms of anelasticity is not consistent with direct structural observations. The results of constant stress interrupted creep tests, carried out on randomly oriented polycrystalline copper, cube textured copper and aluminum single crystals are reported. In these tests the sample is unloaded and annealed at the test temperature after it has reached steady state. Subsequently the sample is reloaded and the test is allowed to continue. Transients in strain rate which occur upon unloading and reloading indicate that recovery has occurred. The transient features of these tests cannot be explained as anelastic effects. These experimental results lead us to conclude that Hart's equation of state does not apply at temperatures where static recovery occurs.

Theory of plastic flow in strain-hardened metals

Abstract A major unsolved problem in the theory of plastic flow of strain-hardened metals is the falling reversible flow-stress ratio at high temperature. In this paper it is argued that both the irreversible and reversible changes in stress at high temperature are a consequence of dislocation climb. The reversible difference is a consequence of climb-controlled rearrangement while the irreversible difference is the result of the loss of dislocations through climb. As a result of rearrangement and of the non-regular obstacle structure, soft local regions exist in which plastic flow occurs preferentially. This preferential flow occurs to a large degree at high temperature so that thc flow stress is low. For the same structure at low temperature, local flow is not so pronounced and the stress is high. The theory is presented formally and the equations are derived with only moderate reference to dislocation models. In addition to the reversible change in stress, the equations suggest explanations for linear ...

Plastic Flow at the Chip-Tool Interface During Hot Machining

The plastic flow of metal adjacent to the chip-tool interface when machining heated workpieces is examined theoretically. It is shown that all metallic workpiece materials possess an optimum machining temperature which is dependent on the physical properties of the material. The temperature distribution in the plastic layer in the presence of an electric current normal to the interface is considered in relation to the general plastic flow of metals accompanied by Joule heating.

Acoustic Properties of Metals and Magnetostrictive Materials

The process of inducing plastic flow in metals under the combined action of static and large vibratory stresses using a high-powered horn driver is discussed. In particular, where the metal is ferromagnetic, one has the situation that many properties of the material, including magnetic properties, change under the combined stress action. This necessarily affects the end uses of the material as, for example, in magnetostrictive transducers. Experiments are described in which the properties of nickel are investigated, for example, and the plastic flow threshold curve under combined stress action is determined. It is found that vibratory stress is much more effective in producing flow than static stress. In addition, it is found that, subsequent to the occurrence of plastic flow, the mechanical Q of a sample is altered but partially recovers over a period of hours at room temperature, and the material is hardened against further flow. The separation of the total energy loss into macroeddy, elastic, and microeddy loss is discussed. The alteration of the magnetic properties of plastically flowed samples is quite marked at points near the flow maxima in the samples containing standing intense acoustic waves, and the change in internal friction provides a possible means for predicting impending fatigue in metals without destruction of the materials. [This work was supported by the Office of Naval Research.]

New developments in thermocompression bonding

A study of the plastic flow of metal which occurs during the formation of a thermocompression bond has led to the development of an improved form of thermocompression bond structure, the eyelet-bond, which enables aluminium wires to be bonded successfully to a number of substrate materials, including heavily oxidized aluminium and Kovar. The design of apparatus for making eyelet-bonds and methods of machining suitable bonding tools are discussed.

A Strengthening Effect of High Hydrostatic Pressure on Grain Boundary Walls of a Polycrystalline Zinc

DURING investigations of dislocation behaviour in a polycrystalline zinc a number of interesting facts were found. (All experiments were performed at room temperature and specimens 6 mm2 × 12 mm were machined from a commercially pure zinc cast of the composition shown in Table 1. Specimens were annealed at 350° C for 5 h and furnace-cooled to a grain size of American Society for Testing Materials micro-grain size No. 00 (except for one shown in Fig. 1 which was not annealed). The polishing and etching reagents for revealing grain boundaries and dislocations were similar to those used by J. J. Gilman1): (1) Twin formation and the movement of grain and twin boundaries besides crystallographic glide are responsible for a large plastic flow of this metal during uniaxial stressing, creep, relaxation and fatigue testings, as is shown in Fig. 1. (2) By the application of high hydrostatic pressure of the order of thousands of atmospheres, dislocations line up along grain boundaries. Twin formation is suppressed to a great extent and grain boundary movement is completely blocked. However, multiplication and movement of dislocations are still persistent and cause a plastic strain of the order of one ten-thousandth. Fig. 2 shows the build-up of dislocation walls along grain boundaries and dislocation line-ups in crystals with the application of hydrostatic pressure. (3) Once the aforementioned structure of dislocations is formed the zinc specimen is greatly strengthened: the result of uniaxial compression tests showed that the stiffness was increased by 20 per cent when a specimen was pressure-treated at 3,000 atm. for 1 h. When an initial compressive load of 70 kg was applied at a cross-head speed of 0.5 mm/min and the cross-head held still for several hours, the relaxation of load was observed to reduce to 2.3 kg for a pressure-treated specimen from 14.2 kg for a non-treated one.

An improved form of thermocompression bond

The mechanical reliability of both the ball and the chisel thermocompression bond, which are employed at the present time in many semiconductor devices, has been assessed by testing large numbers of sample bonds in a high speed centrifuge and in a microtensile testing machine. The rapid formation of detrimental compounds at a gold-aluminium interface prohibits the use of the gold wire-aluminium film ball bond in the fabrication of long life transistors and the all-aluminium chisel bond is considered to be relatively unreliable. A study of the plastic flow of metal which occurs during the formation of a thermocompression bond has led to the development of a new bond structure, the eyelet bond, which enables aluminium wires to be bonded successfully to a number of substrates, including heavily oxidized aluminium films and both clean and lightly oxidized Kovar surfaces with high and very reproducible bond strengths. Transistors in which the new structure has been used for bonding aluminium wires to the aluminium contact areas and to the plain Kovar posts have now been stored at a temperature of 300°c for 1000 hours. The initial characteristics have remained virtually unchanged and no deterioration in mechanical reliability has been observed.

The Effect of Hydrostatic Pressure on the Plastic Flow and Fracture of Metals

A description is given of an apparatus for carrying out tension tests under hydrostatic pressures of 60 ton/in2 or more. The results of an investigation of the effect of hydrostatic pressure on the tensile properties of a number of metals are given. It was found necessary to protect cast materials with a rubber sleeve. The fracture strain increased with hydrostatic pressure, but this increase was not linear but varied with the crystal structure of the metal. In zinc and Mazak a sudden transition from brittle to completely ductile behaviour occurred at a critical pressure; this was probably due to a flat stress/strain curve. It was found in tension tests under pressure that specimens could deform and neck in a characteristic tensile manner, even though all the stresses were compressive. Fracture also could occur when the axial stress was compressive. It was found that the present results on tension, and previous results in torsion on cast iron, conformed either to a criterion that fracture occurred when the largest tensile stress reached a critical value which decreased as the volumetric compressive stress increased, or to a maximum deviatoric stress criterion, the critical value increasing with volumetric stress.

An introduction to rail wear and rail lubrication problems

It is anticipated that the future trend in railroad's traffic is towards long, heavily loaded, bulk-materials carrying trains. Experience in the effects of this type of traffic on rail life has been studied closely on the Q.N.S. & L. Rly., over the past 8 years of its ore-haul operations. A survey is made of the types of wear which have been observed; plastic metal flow, cold working, surface and subsurface metal rupture and metal fatigue developments. Analysis of these development indicate that they arise from an intimate inter-relation of the magnitude of the wheel-loading to the load carrying capacity of the rail with respect to both rolling contact and structural support, the dynamic effects of a complex wheel to rail relationship which is aggravated by damaging impact loading, the metallurgy of the rail steel and the configuration of both the components and the assembly of the track structure. Certain remedial measures are suggested which include improved track and roadway structure, improved rail metallurgy, rail surface rehabilitation by grinding and inhibiting rail wear by improved lubrication. The latter is dealt with at some length, a current rail lubrication research program being described in detail. Of principal interest is the investigation of the behaviour of lubricants at sub-zero temperatures and the employment of special techniques such as radio-isotope tracing of the dispersal of rail lubricants along the track by rail traffic.