Showing papers on "Strain rate published in 1992"

Ductility and strain-induced transformation in a high-strength transformation-induced plasticity-aided dual-phase steel

Abstract: The influence of forming temperature and strain rate on the ductility and strain-induced transformation behavior of retained austenite in a ferritic 0.4C-1.5Si-1.5Mn (wt pct) dual-phase steel containing fine retained austenite islands of about 15 vol pct has been investigated. Ex- cellent combinations of total elongations (TELs), about 48 pct, and tensile strength (TS), about 1000 MPa, were obtained at temperatures between 100 °C and 200 °C and at a strain rate of 2.8 X 10-4/s. Under these optimum forming conditions, the flow curves were characterized by intensive serrations and increased strain-hardening rate over a large strain range. The retained austenite islands were mechanically the most stable at temperatures between 100 °C and 200 °C, and the retained austenite stability appeared to be mainly controlled by strain-induced martensite and bainite transformations (SIMT and SIBT, respectively), with deformation twinning occur- ring in the retained austenite. The enhanced TEL and forming temperature dependence of TEL were primarily connected with both the strain-induced transformation behavior and retained aus- tenite stability.

On the strain and strain-rate dependence of the fraction of plastic work converted to heat: An experimental study using high speed infrared detectors and the Kolsky bar

Abstract: The conversion of plastic work to heat at high strain rates gives rise to a significant temperature increase which contributes to thermal softening in the constitutive response of many materials. This investigation systematically examines the rate of conversion of plastic work to heat in metals using a Kolsky (split Hopkinson) pressure bar and a high-speed infrared detector array. Several experiments are performed, and the work rate to heat rate conversion fraction, the relative rate at which plastic work is converted to heat, is reported for 4340 steel, 2024 aluminum and Ti-6A1-4V titanium alloys undergoing high strain and high strain rate deformation. The functional dependence of this quantity upon strain and strain rate is also reported for these metals. This quantity represents the strength of the coupling term between temperature and mechanical fields in thermomechanical problems involving plastic flow. The experimental measurement of this constitutive function is important since it is an integral part of the formulation of coupled thermomechanical field equations, and it plays an important role in failure mode selection — such as the formation of adiabatic shear bands — in metals deforming at high strain rates.

Exact solution of a restricted Euler equation for the velocity gradient tensor

Abstract: The velocity gradient tensor satisfies a nonlinear evolution equation of the form (dAij/dt)+AikAkj− (1/3)(AmnAnm)δij=Hij, where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of the velocity gradient. The homogeneous case (Hij=0) considered previously by Vielliefosse [J. Phys. (Paris) 43, 837 (1982); Physica A 125, 150 (1984)] is revisited here and examined in the context of an exact solution. First the equations are simplified to a linear, second‐order system (d2Aij/dt2)+(2/3)Q(t)Aij=0, where Q(t) is expressed in terms of Jacobian elliptic functions. The exact solution in analytical form is then presented providing a detailed description of the relationship between initial conditions and the evolution of the velocity gradient tensor and associated strain and rotation tensors. The fact that the solution satisfies both a linear second‐order system and a nonlinear first‐order system places certain restrictions on the solution path and leads to an asymptotic velocity gradient field with a geometry that is largely but not wholly independent of initial conditions and an asymptotic vorticity which is proportional to the asymptotic rate of strain. A number of the geometrical features of fine‐scale motions observed in direct numerical simulations of homogeneous and inhomogeneous turbulence are reproduced by the solution of the Hij=0 case.

Yielding of metal powder bonded by isolated contacts

Abstract: A macroscopic constitutive law is developed for the plastic yielding of a random aggregate of perfectly plastic spherical metal particles. The particles are bonded perfectly by isolated contacts and deformation occurs by plastic yielding of material at and near these contacts. The configuration is treated as isotropic and homogeneous as far as particle size and properties are concerned. The results are considered valid for aggregates with densities ranging from about 60% to around 90% of the theoretical fully dense level. The yield surface is obtained from the plastic dissipation at necks between particles given an imposed macroscopically uniform strain rate. The contact yield surface resulting from this analysis is sensitive to pressure as well as to deviatoric stress. The plastic strain rate direction is outwardly normal to the yield surface. Densification takes place when pressure is present, but a notable feature is a vertex on the yield surface at the points of pure positive and negative pressure. Consequently, plastic flow in the presence of pure pressure is nonunique, and deviatoric components may be superposed on densification.

The effect of dislocation drag on the stress-strain behavior of F.C.C. metals

Abstract: The introduction of viscous drag into a simple thermally activated dislocation model for the low temperature plastic deformation of f.c.c. metals leads to some surprising predictions about their stress-strain behavior. One effect of dislocation drag is to produce a region of tensile instability at small strains for any strain rate. At sufficiently high strain rates there is no region of tensile stability. However, computation of a decreased strain for tensile instability at strain rates greater than 103 s−1, in opposition to experimental measurements, provides evidence that the strong upturn reported for the flow stress of copper is not caused by dislocation drag. The likely explanation is an enhanced rate of dislocation generation.

On the gradient-dependent theory of plasticity and shear banding

Abstract: After a brief review of a recently developed gradient-dependent theory of plasticity various questions related to the yield function and the loading-unloading condition in the presence of higher order strain gradients and the determination of the corresponding phenomenological coefficients are addressed. For rate-independent materials, we construct as before an analytical solution for the strain profile in the postlocalization regime providing the shear band thickness and strain within it but we now compare these results to recently obtained experimental data by assigning appropriate values to the gradient coefficients. We also address some questions recently raised in the literature regarding our nonlinear shear band analysis. For rate-dependent materials, the resulting spatio-temporal differential equation for the strain is solved numerically using the finite difference method. It is shown that the band width does not depend on the grid size, as long as the the grid size is smaller than a certain characteristic length. Various initial imperfections of different amplitudes and sizes are examined, and the possibility of simultaneous development of two shear bands and their interaction is investigated.

Cyclic Plasticity and Low Cycle Fatigue Life of Metals

Abstract: 1 Introduction 2 Stress and Strain in Cyclic Loading Monotonic stress-strain curve Stress-strain relationship in cyclic loading Hysteresis loop Cyclic hardening/softening curves Cyclic stress-strain curve 3 Cyclic Plasticity and Microstructure Metals and simple alloys with fcc structure Metals and single phase alloys with bcc structure Other metals and single phase alloys Multiphase materials 4 Dislocation Mechanisms in Cyclic Plastic Straining Athermal mechanisms in fcc metals Thermally activated cyclic straining Dislocation mechanisms in particle strengthened metals 5 Statistical Description of Cyclic Stress-Strain Response Internal and effective stress in an elementary volume Statistical approach 6 Experimental Investigation of the Dynamics of Cyclic Plastic Straining Stress-dip method Stress and strain relaxation Strain rate changes Analysis of hysteresis loop shape Evaluation of results using individual methods 7 Cyclic Creep Relevant experimental investigations Dislocation arrangements Mechanisms and models 8 Fatigue Crack Initiation Observation of surface relief evolution Models of surface relief evolution Mechanisms of crack initiation Role of grain boundaries Role of inclusions 9 Growth of Fatigue Cracks Fracture mechanics approach to fatigue crack growth Crack growth under small scale yielding General yield fatigue crack growth Short crack growth 10 Fatigue Life of Smooth Bodies Strain controlled cycling Plastic strain controlled cycling Stress controlled cycling Energy criterion Evaluation of fatigue life of a smooth body using the fatigue process model 11 Fatigue Life of Notched Bodies Stress and strain concentration in a notched body Fatigue life evaluation 12 Variable Amplitude Loading Phenomenological description Analysis of load history Sudden changes of strain amplitude Cyclic plasticity in repeated block loading Hypothesis of cumulative damage Fatigue life prediction 13 Effect of Depressed Temperature Cyclic plasticity Fatigue life 14 High Temperature Low Cycle Fatigue Cyclic plasticity at elevated temperatures Fatigue life and its evaluation Damage mechanisms Fatigue life prediction 15 Thermal and Thermomechanical Fatigue The effect of temperature changes under constraint Reversed plasticity and thermal cracking Thermal ratchetting 16 Multiaxial Loading Multiaxial stress and strain Cyclic stress-strain response Fatigue life 17 Computer Controlled Fatigue Testing Role of the digital computer Low cycle fatigue test Crack growth test Variable amplitude test Other tests 18 Characterisation of Low Cycle Fatigue Resistance of Metallic Materials Basic characteristics Review of materials properties References Subject Index

Nanoindentation of nanocrystalline ZnO

Abstract: A number of nanocrystalline ceramics have been fabricated by the gas phase condensation technique. The mechanical properties of one of the first ceramics produced by this method, nanophase TiO{sub 2},have been discussed in an earlier study. This paper reports a similar study undertaken to examine the properties of nanocrystalline ZnO. Nanoindenter techniques are used to determine hardness, Young's modulus, and strain rate sensitivity in ultra-fine grained ZnO. Significant properties variations are experienced within a given sample, indicating a large degree of microstructural inhomogeneity. Nevertheless, a distinct evolution in properties can be observed as a function of sintering temperature. Young's modulus and hardness values increase almost linearly with increasing sintering temperature, and, in addition, there also appears to be a linear correlation between the development of the two materials properties. In contrast, strain rate sensitivity is shown to have an inverse dependence on sintering temperature. This dependence appears to be linked to the strong influence of grain size on strain rate sensitivity, so that the lower sintering temperatures, which provide the finer grain sizes, tend to promote strain rate sensitivity. The results of this study are strikingly similar to those obtained earlier for nanophase TiO{sub 2}, and they indicate that themore » earlier results could probably be generalized to a much broader range of nanocrystalline ceramics.« less

Rheology and deformation mechanisms of an isotropic mica schist

Abstract: We have investigated the transitional, semibrittle deformation of a mica schist (∼75 % biotite) by shortening cylinders cored at 0°, 45°, and 90° to foliation to varying strains, at confining pressures Pc to 500 MPa, constant strain rates e from 1.5 × 10−7 to 1.6 × 10−4 s−1 and temperatures T from 25° to 400°C. Deformation is concentrated within one or more throughgoing, millimeter-wide shear zones at all conditions; these localize at low strains (e < 2%) through the nucleation and coalescence of dense sets of intragranular microkink bands (MKBs). Despite distinct differences in the relative number of mica grains oriented favorably for slip and kinking in different loading directions, the differential stresses required for shear zone development vary little with fabric orientation. Biotite schist undergoes a transition from strain-softening to steady strength mechanical response at confining pressures in the range 75 to 150 MPa. The pressure sensitivity of strength (characterized by the slope μ of the Mohr envelope) decreases from μ ∼0.5 (at Pc <100 MPa) to μ < 0.1 at pressures greater than 200 MPa, reflecting the increasing contribution of glide and kinking in biotite at higher pressures. However, dilatancy associated with microcracking and void formation along MKB boundaries persists to at least 500 MPa. Within the pressure-insensitive regime (200 ≤ Pc ≤ 500 MPa), temperature and strain rate dependencies of strength determined in stepping tests reveal a strong history dependence to flow that cannot strictly be described by a steady state constitutive law. Samples deformed in steps from low to high temperatures or fast to slow strain rates consistently exhibit stronger temperature and strain rate sensitivities than those deformed along T decreasing or e increasing paths. Path-dependent effects may reflect differences in the degree to which inherited dislocation substructures are utilized or overprinted during later deformation increments. By assuming an exponential relationship between differential stress σd and strain rate e of the form e = C exp(ασd) exp (−Q/RT), we fit the data with two end-member flow laws with a single activation energy Q = 89 kJ/mol, and exponential constants αss = 0.15 ± 0.01 MPa−1 and αws=0.55 ± 0.04 MPa−1 that account for the different responses observed along stepping paths that are strongly sensitive or weakly sensitive to T and e, respectively. Application of the results to crustal deformation suggests that mica-rich aggregates are weaker than other common rock types throughout a broad midcrustal depth range, supporting the inference that retrograde reaction to phyllosilicates may be important in localizing crustal deformations within large faults and shear zones.

Mechanical behavior and interface design of MoSi2-based alloys and composites

Abstract: The mechanical behavior of hot pressed MoSi2-based composites containing M05Si3, SiO2, CaO and TiC as reinforcing second phases was investigated in the temperature regime 1000-1300 °C. The effects of strain rate on the flow stress for M05Si~-, SiO2- and CaO-containing composites are presented. Effects of several processing routes and microstructural modifications on the mechanical behavior of MoSi2-M05Si ~ composites are given. Of these four composite additions, M05Si 3 and CaO produce strengthening of MoSi 2 in the temperature range investigated. SiO 2 greatly reduces the strength, consistent with the formation of a glassy phase at interface and interphase boundaries. TiC reduces the flow stress of MoSi 2 in a manner that suggests dislocation pumping into the MoSi 2 matrix. The strain rate effects indicate that dislocation creep (glide and climb) processes operate over the temperature range investigated, with some contribution from diffusional processes at the higher temperatures and lower strain rates. Erbium is found to be very effective in refining the microstructures and in increasing the hardness and fracture properties of MoSi2-MosSi 3 eutectics prepared by arc melting. Initial results on microstructural modeling of the deformation and fracture of MoSi2-based composites are also reported.

Transient Behaviour of Laminar Counterflow Hydrogen-Air Diffusion Flames with Complex Chemistry

Abstract: The nonsteady behaviour of counterflow diffusion hydrogen-air flames is studied in this article, using a finite difference implicit method and a complex kinetics model. The flame responses to step and sinusoidal strain rale variations are obtained for flames submitted to moderate strain rates and also to strain rates corresponding to extinction conditions. Frequency response curves are obtained for both cases and for different values of the equivalence ratio. The behaviour of flame characteristics like the maximum temperature, the heat release rate and typical species mass fraction profiles is examined. It is found that H2O and OH radicals change approximately like the maximum temperature while hydrogen atom H mass fraction exhibits larger excursion. The dynamics of the flame are governed by the imposed mean strain rate on one hand and by the critical extinction strain rate on the other. Far from the extinction limit the cut-off frequency is set by the mean strain rate and the flame behaviour is ...

Effect of Strain Hardening and Rate Sensitivity on the Dynamic Growth of a Void in a Plastic Material

Abstract: The problem studied in this paper concerns the dynamic expansion of a spherical void in an unbounded solid under the action of remote hydrostatic tension. The void is assumed to remain spherical throughout the deformation and the matrix to be incompressible. The effects of inertia, strain hardening, and rate sensitivity on the short and long-term behavior of the void, as well as on its response to ramp loading, are investigated in detail.

Creep Mechanism of Polycrystalline Yttrium Aluminum Garnet

Abstract: The high-temperature deformation behavior of a fine-grained polycrystalline yttrium aluminum garnet (YAG) was studied in the temperature range of 1400° to 1610°C using constant strain rate compression tests under strain rates ranging from 10−5/s to 10−3/s. The stress exponent of the creep rate, the activation energy in comparison with that for single-crystal YAG, and the grain size dependence suggest that Nabarro–Herring creep rate limited by the bulk diffusion of one of the cations (Y or Al) is the operative mechanism.

On the measurement of local strain and temperature during the formation of adiabatic shear bands

Abstract: A series of experiments was performed to study the process of adiabatic shear band initiation and formation in steels. The steels include a low carbon cold-rolled steel and three martensitic steels (HY-100 and two tempers of AISI 4340 VAR steel of varying hardness). In each case the specimens are machined as thin-walled tubes that are deformed dynamically in a torsional Kolsky bar (torsional split Hopkinson bar). Shear band initiation and formation are observed by ultrahigh-speed photography of a fine grid pattern deposited on the specimen's surface. It is shown that the critical strain for shear band initiation depends on the magnitude of a preexisting defect, in accordance with the predictions of Molinari and Clifton, J. Appl. Mech., 54 (1991) 806–812. Ultrahigh-speed photographs of the grid pattern show that local strains of 100–1000% may be attained and that the local strain rates reach 10 5 s −1 . In addition, the local temperature in the shear band is measured by employing an array of small high-speed infrared detectors that provide a plot of temperature as a function of time and position. Within the shear band region, temperatures of 600 °C have been measured.

One-dimensional consolidation testing of soft clay from Bothkennar

Abstract: The one-dimensional consolidation behaviour of Bothkennar clay has been examined by testing high quality intact and reconstituted specimens recovered using the Laval sampler. The collaborative test programme consisted of incremental load, constant rate of strain, and restricted flow tests. During the test programme the variation of yield stress with depth, the effect of strain rate on the observed yield stress, the creep behaviour and the variability in soil compressibility were investigated. It was noted that the yield stress is influenced by the strain rate, with faster rates resulting in higher values of yield stress. When this was taken into account, it was found that specimens taken from a single depth showed reasonably consistent behaviour independent of the type of test. Creep occurred in the incremental load tests, with the maximum rate just after yield, indicating a clear linkage between creep and the structural breakdown at yield. The vertical permeability of the specimens was determined by flow...

Pressure-shear impact investigation of strain rate history effects in oxygen-free high-conductivity copper

Abstract: A combined experimental and computational investigation of the behavior of oxygen-free high-conductivity copper under very high shear rates is presented. Pressure-shear plate impact is used for conducting constant strain rate tests and strain rate change texts in which the specimen is strained at shear rates up to 106s−1 for 1μs and then strained at substatially lower shear rates for another microsecond. The specimen is sandwiched between two hard elastic plates to impose conditions of simple shear at very high strain rates and constant hydrostatic pressure. Marked increases in flow stresses are observed at strain rates of 105s−1 and higher. Flow stresses decrease gradually after a sharp drop in strain rate in all strain rate change tests. Homogeneous equiaxed dislocation cells are found as the predominant substructure in the deformed specimens. Theoretical analyses of the nonlinear wave propagation within the specimen are carried out using a general internal variable formulation in which the hardening rate depends on the rate of deformation. The governing system of hyperbolic partial differential equations is solved using a finite-difference scheme; computational results are compared with the experimental results. Both small- and finite-deformation formulations are considered. Only the internal variable model which incorporates a strong rate sensitivity of strain hardening is successful in describing the observed response to the change in strain rate. The enhanced rate sensitivity at high strain rates is concluded to be related primarily to the rate sensitivity of strain hardening, not the rate sensitivity of the flow stress at constant dislocation structure. The generation and evolution of dislocation cells appears to be the dominant micromechanical process during the high- rate deformation of pure metals.

Creep of Power-Law Material Containing Spherical Voids

Abstract: Finite element calculations have been carried out for spherical unit cells containing a concentric spherical hole to characterize the power law creep of a material containing voids. Axisymmetric states of macroscopic stress were applied to the unit cells ranging from purely hydrostatic loading to purely deviatoric stressing. The results of the unit cell calculations are approximated well by a creep potential for the macroscopic behavior of a porous material. This potential agrees with the unit cell results for purely hydrostatic stress and purely deviatoric stress and involves a simple elliptical interpolation in between. The model predicts quite well the ratio of transverse to axial strain rate in uniaxial compression tests.

Constitutive modeling and simulation of energy absorbing polyurethane foam under impact loading

Abstract: The compressive-stress strain response of polyurethane foam under uniaxial compressive impact loading has been studied. The development of a uniaxial constitutive model from strain rate controlled compression tests is detailed. Density and temperature functions have been added to the integral power model proposed by Schwaber, Meincke, and Nagy. The model assumes that the effects of density, temperature, strain and strain rate on stress are separable functions. The model correlated well with actual static compression tests and was used successfully to predict the impact response of energy absorbing polyurethane foam under uniaxial compressive loading.

Constitutive Modeling and Simulation of Energy Absorbing Polyurethane Foam Under Impact Loading

Abstract: The compressive-stress strain response of polyurethane foam under uniaxial compressive impact loading has been studied. The development of a uniaxial constitutive model from strain rate controlled compression tests is detailed. Density and temperature functions have been added to the integral power model proposed by Schwaber, Meincke and Nagy. The model assumes that the effects of density, temperature, strain and strain rate on stress are separable functions. The model correlated well with actual static compression tests and was used successfully to predict the impact response of EA polyurethane foam under uniaxial compressive loading.

An Improved Method for Compressive Stress-Strain Measurements at Very High Strain Rates

Abstract: This paper describes a modification of the split Hopkinson pressure bar, to allow compression testing of high strength metals at a strain rate of up to about 10$^{5}$ s$^{-1}$. All dimensions are minimized to reduce effects of dispersion and inertia, with specimens of the order of 1 mm diameter. Strain is calculated from the stress record and calibrated with high-speed photography. Particular attention has been paid to the accuracy of the technique, and errors arising from nonlinearity in the instrumentation, dispersion, frictional restraint and inertia have all been quantitatively assessed. Stress-strain results are presented of Ti 6A14V alloy, a high strength tungsten alloy, and pure copper.

Nonlinear strain measures for general biaxial extension of polymer melts

Abstract: Starting from the idea of equilibration, i.e., assuming that all molecular tensions are evenly distributed onto short and long chains in polydisperse polymer melts, we derive a general strain measure from a slip‐link model. By specifying disentanglement and slip of polymer chains, the strain measures of Lodge, Wagner, Doi, and Marrucci are shown to be special cases of this general strain measure. Predictions are compared to experimental data of uniaxial, planar, ellipsoidal, and equibiaxial extensions of a well‐characterized polydisperse polyisobutylene melt. The data do not support Doi’s assumption that the tube diameter remains unchanged by deformation. The relative tube diameter and its inverse, the molecular stress function, can be extracted directly from the data. The tension of the average polymer chain increases with increasing deformation, i.e., the polymer chain is stretched. At small strains, the relative cross section of the tube is inversely proportional to the average stretch of the tube.

An analysis of the isothermal hot compression test

Abstract: The nominally isothermal, uniaxial hot compression test has been analyzed with special reference to the effects of temperature nonuniformities and friction on sample deformation and flow stress estimates. A simple one-dimensional analysis was used to establish the influence of initial temperature nonuniformities, strain rate, and the temperature dependence of the flow stress on flow localization tendencies. Noticeable strain concentrations were predicted to occur only at high strain rates (∼10 s−1) in materials such as titanium alloys, but not in steels, for typical values of the initial temperature nonuniformity. More extensive numerical (finite element method) simulations of the compression test with various values of the friction shear factor corroborated the conclusions of the flow localization analysis. In addition, it was established that initial temperature nonuniformities, as well as friction, have an almost negligible effect on flow stress data deduced from measurements of average pressurevs true height strain, at least for reductions of the order of 50 pct. The analysis results were supported by observations of the deformation behavior of a near-gamma titanium aluminide and a low-alloy steel.

A rheological view of high-strain-rate superplasticity in alloys and metal-matrix composites

Abstract: Recent studies have indicated that superplasticity can occur at extremely high strain rates, yielding tensile elongations of the order of 1250 percent at a strain rate of 1/s. This phenomenon, presently designated 'high strain rate superplasticity' (HSRS), has been reported in alloys, metal-matrix composites (MMCs), and mechanically-alloyed materials; all materials exhibiting HSRS have extremely fine, about 1-micron grain size, and the phenomenon is observed at high homologous matrix temperatures that are in some cases higher than the matrix solidus temperature. Attention is presently given to the rheological factor in HSRS. It is suggested that the presence of a liquid phase or a low melting point region due to solute segregation, as at the whisker-matrix interface of an MMC, is responsible for HSRS. 24 refs.