Showing papers on "Strain rate published in 1990"

Evolution of dislocation densities and the critical conditions for the Portevin-Le Châtelier effect

Abstract: A model is proposed for the critical strains associated with the Portevin-Le Châtelier effect (PLC) in terms of the strain dependence of the densities of mobile and forest dislocations. The classical critical condition for the onset of the PLC effect, viz. that of vanishing of the strain rate sensitivity of flow stress under the influence of dynamic strain aging is reexamined. The analysis takes into account the strain dependence of a key quantity: the elementary strain produced when all mobile dislocations perform a successful thermally activated step through the forest obstacles. This elementary strain is estimated by studying a system of coupled differential equations for the evolution of the two densities. Results are obtained in semi-quantitative form and compared with available data. It is shown that the following effects are consistently explained: the occurrence of critical strains for the onset and termination of jerky flow, occasional observation of two PLC regimes within the same deformation curve, the behaviour of the critical strains at high strain rates and low temperatures and, possibly, the particular behaviour exhibited by some alloys at low strain rates and high temperatures. Consequences for the “friction” and “forest” models of dynamic strain aging are discussed.

Mechanical properties of nanophase TiO 2 as determined by nanoindentation

Abstract: Nanoindenter techniques have been used to determine the hardness. Young’s modulus, and strain rate sensitivity of nanophase TiO2, which is currently available only in very small quantities and which cannot be tested by most conventional techniques. Hardness and Young’s modulus both increase linearly with sintering temperature over the range 25–900°C but come to within only 50–70% of the single crystal values. Strain rate sensitivity, on the other hand, is measurably greater for this material than for single crystal rutile, and the value of strain rate sensitivity increases as the grain size and the sintering temperature are decreased. In its as-compacted form, the strain rate sensitivity of nanophase TiO2 is approximately a quarter that of lead at room temperature, indicating a potential for significant ductility in these ceramic materials. Finally, a significant scatter in hardness values has been detected within individual nanophase samples. This is interpreted as arising from microstructural inhomogeneity in these materials.

Non-Newtonian Rheology of Igneous Melts at High Stresses and Strain Rates: Experimental Results for Rhyolite, Andesite, Basalt, and Nephelinite

Abstract: The stress-strain rate relationships of four silicate melt compositions (high-silica rhyolite, andesite, tholeiitic basalt, and nephelinite) have been studied using the fiber elongation method. Measurements were conducted in a stress range of 10–400 MPa and a strain rate range of 10−6 to 10−3 s−1. The stress-strain rate relationships for all the melts exhibit Newtonian behavior at low strain rates, but non-Newtonian (nonlinear stress-strain rate) behavior at higher strain rates, with strain rate increasing faster than the applied stress. The decrease in calculated shear viscosity with increasing strain rate precedes brittle failure of the fiber as the applied stress approaches the tensile strength of the melt. The decrease in viscosity observed at the high strain rates of the present study ranges from 0.25 to 2.54 log10 Pa s. The shear relaxation times τ of these melts have been estimated from the low strain rate, Newtonian, shear viscosity, using the Maxwell relationship τ = η s /G ∞. Non-Newtonian shear viscosity is observed at strain rates ( ɛ ˙ = time - 1 ) equivalent to time scales that lie 3 log10 units of time above the calculated relaxation time. Brittle failure of the fibers occurs 2 log10 units of time above the relaxation time. This study illustrates that the occurrence of non-Newtonian viscous flow in geological melts can be predicted to within a log10 unit of strain rate. High-silica rhyolite melts involved in ash flow eruptions are expected to undergo a non-Newtonian phase of deformation immediately prior to brittle failure.

Basal slip and mechanical anisotropy of biotite

Abstract: The basal slip systems of biotite and their mechanical expressions have been investigated by shortening single crystals oriented to maximize and minimize shear stresses on (001). Samples loaded at 45° to (001) exhibit gentle external rotations associated with dislocation glide. High-angle kink bands in these samples, unlike those developed in micas loaded parallel to (001), are limited to sample corners. Samples shortened perpendicular to (001) show no evidence of nonbasal slip and fail by fracture over all conditions tested. The mechanical response of biotite shortened at 45° to (001) is nearly perfectly elastic-plastic; stress-strain curves are characterized by a steep elastic slope, a sharply defined yield point, and continued deformation at low (mostly 1%. Stresses measured beyond the yield point are insensitive to confining pressure over the range 200 to 500 MPa and exhibit weak dependencies upon strain rate and temperature. Assuming an exponential relationship between differential stress σd and strain rate e˙ of the form e˙=Cexp(ασd)exp(−Q/RT), the data collected over strain rates and temperatures of 10−7 to 10−4 s−1 and 20° to 400°C, respectively, are best fit by an exponential constant α of 0.41±0.08 MPa-1 and an activation energy Q of 82±13 kJ/mol. A power law fits the data equally well with n = 18±4 and Q = 51±9 kJ/mol. Samples oriented favorably for slip in directions [100] and [110] are measurably weaker than those shortened at 45° to [010] and [310], consistent with the reported Burgers vectors 〈100〉, 1/2 〈110〉, and 1/2 〈110〉. The anisotropy of biotite is further revealed by contrasting these plastic strengths with results of samples deformed parallel and perpendicular to (001). Previous studies have shown that biotite loaded in the (001) plane is strong prior to the nucleation of kink bands. The strength of biotite shortened perpendicular to (001) exceeds that measured parallel to (001) and is pressure dependent. Application of the results to deformation within the continental crust suggests that biotite oriented favorably for slip is much weaker than most other silicates over a wide range of geologic conditions. Its presence within foliated rocks and shear zones may limit locally the stresses that can be supported.

An experimental and anaiytical investigation of the large strain compressive and tensile response of glassy polymers

Abstract: In this investigation, the plastic flow of polycarbonate (PC) was examined by obtaining true stress-strain data over a range of strain rates at room temperature through homogeneous, uniaxial, constant strain rate compression testing to strains as high as 125 percent. Uniaxial compressive loading conditions give rise to a planar molecular orientation process which results in the observed strain hardening in compression. Uniaxial tensile tests on PC were also conducted. The necked region of the tensile specimen is being cold drawn resulting in a uniaxial state of orientation. Therefore, the observed macroscopic strain hardening in uniaxial tension distinctly differs from that obtained In uniaxial compression, giving different stress-strain curves. The major differences experimentally obtained between the large strain response in compression and tension indicate a need for an orientation-based model of the strain hardening process. The experimental program also acts to uncouple the effects of strain softening and strain rate providing more accurate data for future modeling of the true strain softening process. A constitutive law which directly relates the strain hardening response to the state of molecular network stretch in the polymer is used to model and analyze the experiments. The model is found to simulate the observed rate dependent yield and post yield strain softening and hardening of the compressive data over the entire range of strain rates very well. The model is then utilized in a finite element analysis of the tensile tests on PC. Numerical results compared favorably with the experimental data including: load vs, contraction curves, natural draw ratio, and the axial stress-strain response of the cold drawing region.

The brittle compressive fracture of ice

Abstract: The brittle compressive fracture under uniaxial loading of fresh-water, granular ice Ih has been studied. Measurements are reported of the fracture stress at temperatures from −10 to −50°C at strain rates of 10 −3 and 10 −1 s −1 for grain sizes from approximately 1 to 10 mm. Also a summary is reported of measurements by Jones et al . (unpublished) of the kinetic coefficient of friction for ice on ice at temperatures from −10 to −40°C at sliding velocities from 5 × 10 −7 m s −1 to 5 × 10 −2 ms −1 . Observations via high speed photography of internal cracking during loading are included. The strength, albeit scattered, increases with decreasing grain size, with decreasing temperature and at −10°C with decreasing strain rate. Similarly, the coefficient of friction increases with decreasing temperature and at −10°C with decreasing sliding velocity. Wing cracks were observed on some inclined cracks nucleated during loading. The results are explained in terms of the frictional crack sliding-wing crack model [as developed by Ashby and Hallam, Acta metall. 34, 497 (1986)] of compressive fracture. Finally, a simple model is presented for the transition from ductile to brittle behavior. It is based upon the competition between the building up and the relaxation of internal stresses within the vicinity of the internal cracks, and it leads to a transition strain rate which can be expressed in terms of the fracture toughness, the creep rate, the kinetic coefficient of friction and the microstructural scale of the material.

Description of tantalum deformation behavior by dislocation mechanics based constitutive relations

Abstract: Dislocation mechanics based constitutive equation constants are determined for temperature, strain rate, work hardening, and polycrystal grain size influences on the deformation behavior of various tantalum materials. An analysis of the maximum load point strain provides a useful method of determining the work hardening constants. Different athermal stress constants and thermal activation related constants are obtained for certain groupings of the different tantalum materials. The variations are correlated with the annealing history of the materials and related to dislocation model parameters involved in the thermal activation strain rate analysis. Computed tantalum deformation results based on these constants are shown to agree with Gourdin’s reported expanding ring test measurements and with the deformed shape of a Taylor cylinder impact test specimen.

Geometric factors affecting the internal stress distribution and high temperature creep rate of discontinuous fiber reinforced metals

Abstract: The creep deformation behavior of metal-matrix composites has been studied by a continuum mechanics treatment utilizing finite element techniques. The objective of the work has been to understand the underlying mechanisms of fiber reinforcement at high temperatures and to quantify the importance of reinforcement phase geometry on the overall deformation rate. Internal stress distributions are presented for a material that consists of stiff elastic fibers in an elastic, power law creeping matrix. Results indicate that large triaxial stresses develop in the matrix, and that these stresses have a strong effect on reducing the creep rate of the composite. Reinforcement phase geometry, as measured by the fiber volume fraction, aspect ratio, separation, and overlap, greatly influences the degree of constraint on the flowing matrix material and the overall deformation rate. Theoretical predictions from this modeling are compared to experimental results of creep deformation in metal-matrix composite systems with varying degrees of agreement.

Superelastic behaviour of a fine-grained, yttria-stabilized, tetragonal zirconia polycrystal (Y-TZP)

Abstract: The microstructure and deformation characteristics of a fine-grained superelastic yttria-stabilized tetragonal zirconia polycrystal (Y-TZP) have been investigated. Both hot indentation and tensile tests were carried out at temperatures between 1273 and 1923K over the strain rate range from 2.7 × 10−5 to 2 × 10−3 s−1. It was found that the material exhibited extensive plasticity at temperatures higher than 1473K; a maximum tensile elongation of over 800% was recorded. Microstructural examination did not indicate the presence of a glassy phase at grain boundaries. Yttrium, however, was found to segregate to the grain boundaries. The microstructure of the Y-TZP was thermally unstable and appreciable grain growth was observed at emperattures higher than 1723 K; the grain growth was enhanced by external stresses, i.e. dynamic grain growth was observed. Grain growth at elevated temperatures resulted in apparent strain rate sensitivity exponents of approximately 0.33 at 1723K. This value decreased with increasing temperature. The grain size-compensated strain rate, however, was found to depend approximately on the square of the flow stress, i.e. to exhibit a true strain sensitivity value of 0.5, which suggests a grain boundary sliding mechanism. Microstructures from samples that were deformed superelastically indicated that grains remained equiaxed; this observation is consistent with a grain boundary sliding mechanism. The activation energy for superplasticity, under the conditions of constant structure, in Y-TZP was calculated to be 720 kJ/mol.

Mechanical properties and microstructures of Al-Mg-Sc alloys

Abstract: The mechanical properties of Al-(Mg)-0.5Sc alloys have been investigated. Room-temperature tensile and toughness properties were found to reflect a superposition of the properties of Al-Mg and Al-0.5Sc alloys and are quite competitive with high-performance Al alloys. A combination of substructure refinement by Mg and stabilization by Al3Sc precipitates produces exceptional superplasticity as exemplified by superplastic forming (SPF) elongations in excess of 1000 pct at a strain rate of 0.01 s-1. Overall, these alloys demonstrate an extremely attractive combination of strength, toughness, density, and SPF fabricability.

Mixed‐Mode Fracture of Concrete Subjected to Impact Loading

Abstract: An analytical and experimental investigation of mode I (tensile) and mixed mode (combined tensile and shear) fracture of concrete subjected to impact loading was conducted. The rate of loading ranged from a slow strain rate of 10\u-\u6/s to an impact strain rate of 0.5/s. Mixed-mode tests were conducted using beams with notches at different locations along the span of the beam. A new clip gage was developed to measure crack-opening displacement at slow and impact rates of loading. A nonlinear fracture-mechanics model was developed to predict the rate sensitivity of mode I and mixed-mode fracture of concrete. This approach was based on the observation that the prepeak nonlinearity may be attributed to prepeak stable crack growth and that this prepeak crack growth decreased with an increase in the rate of loading. The mixed-mode-fracture-mechanics study used finite element analysis with singular quarter-point elements at the crack tip. Mixed-mode experimental and analytical results indicate that impact loading could result in brittle diagonal tension-shear failure of concrete structures as opposed to ductile flexural failure at a slow rate of loading.

The relationship between plate velocity and trench viscosity in Newtonian and power‐law subduction calculations

Abstract: The relationship between oceanic trench viscosity and oceanic plate velocity is studied using a Newtonian rheology by varying the viscosity at the trench. The plate velocity is a function of the trench viscosity for fixed Rayleigh number and plate/slab viscosity. Slab velocities for non-Newtonian rheology calculations are significantly different from slab velocities from Newtonian rheology calculations at the same effective Rayleigh number. Both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate. Non-Newtonian rheology eliminates the need for imposed weak zones and provides a self-consistent fluid dynamical mechanism for subduction in numerical convection models.

Viscoelastic material characterization and modeling for polyethylene

Abstract: An extensive set of stress relaxation and constant strain rate tests for characterizing the mechanical responses of a medium density polyethylene and a high density polyethylene that are commonly used in natural gas distribution piping is described and analyzed. The development of coherent master curves for the relaxation modulus, maximum stress, and the time-to-failure for pressurized pipes through a combination of both horizontal and vertical shifting is presented. The relaxation data are used to develop a nonlinear Viscoelastic material model. The model is assessed by making comparisons of the predicted stress-strain response with the measured response in the constant strain rate tests.

The stability of elliptical vortices in an external straining flow

Abstract: Subject to uniform strain, an elliptical patch of vorticity in an in viscid, incompressible, two-dimensional fluid generally rotates or nutates and extends or compresses while retaining a precisely elliptical shape (the Kida solutions) This result is of interest because the uniform strain idealizes the leading-order distortional influence of distant vortices in a flow with many vortices Because of the unsteady motion of the distant vortices, both the strain rate and the rotation rate of the strain axes typically vary with time In the special case that the strain rate and rotation rate are steady, and when the strain rate is not too large, periodic motion of an elliptical vortex is possible Larger strain rates lead to indefinite extension of the vortexUniform strain, however, only approximately mimics the effect of distant vortices The local variations- in the strain field around a vortex disturb the vortex, preventing it from retaining a simple, elliptical shape These disturbances may amplify because of instabilities In this paper, we examine the stability of periodic elliptical motion to small boundary disturbances, for the case of steady, uniform strain and rotation rate, first by linear Floquet theory and then by direct, high-resolution, nonlinear numerical integrations It is discovered that a significant portion of the periodic solutions are linearly unstable Instability can occur even when the strain rate is arbitrarily small and the basic motion arbitrarily close to circular Extended nonlinear calculations exhibit recurrence, in some cases, and attrition of the vortex by repeated wave amplification, steepening, and breaking in others

Strain-rate sensitive behavior of cement paste and mortar in compression

Abstract: The strain-rate sensitivity of the cement paste and mortar constituents of concrete is studied experimentally. Saturated cement paste and mortar specimens are loaded in compression to 15,000 microstrains, 27 to 29 days after casting, using strain rates ranging from 0.3 to 300,000 microstrains/sec. Water-cement ratios of 0.3, 0.4, and 0.5 are used. Strain-rate sensitivity of the material is measured in terms of the initial elastic moduli, maximum stress, and corresponding strain. The initial elastic moduli and the strength of cement paste and mortar increase by 7% and 15%, respectively, with each order of magnitude increase in strain rate. The strain at the maximum stress is the greatest for the lowest strain rate. With an increase in strain rate, the strain at the maximum stress first decreases and then increases.

Thermo-Mechanical Fatigue of Mar-M247: Part 1—Experiments

Abstract: Isothermal fatigue tests, out-of-phase and in-phase thermo-mechanical fatigue tests were performed on Mar-M247 nickel-based superalloy. The experiments were conducted in the temperature range 500°C to 871°C. Results indicate that the lives differ with strain-temperature phasing and with strain rate. The results of out-of-phase thermo-mechanical tests correspond well with strain-life data of isothermal tests conducted at the peak temperature (871°C). However, the in-phase thermo-mechanical results differed depending on the strain amplitude. Significant surface and crack tip oxidation and gamma prime depletion has been observed based on metallographic and Auger Spectroscopic analyses. These changes were measured as a function of time. The environment induced changes significantly influenced the fatigue lives in isothermal and out-of-phase thermo-mechanical fatigue cases. In these cases transgranular cracking was observed. Grain boundary crack nucleation and grain boundary crack growth dominated the in-phase thermo-mechanical fatigue cases. Based on these observations the requirements for a life prediction model are outlined. The life prediction model and the predictions are given in Part 2 of this paper.

The optical and mechanical response of flexible polymer solutions to extensional flow

Abstract: The optical and mechanical responses of dilute and semidulute solutions of flexible polymer molecules to extensional flow are measured. The optical property of interest, the birefringence, is sensitive to the local orientation of the polymer coil, whereas the mechanical property investigated, the effective extensional viscosity, is sensitive to the overall deformed length of the molecule. These two properties are simultaneously measured as a function of the rate of strain by using an opposing jets apparatus. Solutions ranging from 50 to 300 ppm by weight polystyrene dissolved in both tri-cresyl phosphate, a good solvent at 22°C, and di-octyl phthalate, a theta solvent at 22°C, were studied. The results show that the response of the flexible polymer is dependent on the solvent quality. Both the local orientation and the deformed length of the molecule increase with increasing strain rate at low rates of strain for both solvents. However, in the theta solvent at high rates of strain the birefringence saturates, while the effective extensional viscosity drops with increasing strain rate. This indicates a decrease in the overall deformed length of the molecule at high strain rates due to the decrease in the residence time of the coil in the flow field. In the good solvent, molecular entanglements begin to affect the extensional viscosity at high strain rates if the concentration and molecular weight are sufficiently large. The response of flexible polymers to extensional flow is qualitatively compared to numerical simulations based on bead-spring and bead-rod models. Although these models are able to capture the saturation of birefringence under conditions where the extensional viscosity is still changing, they do not predict the observed maxima in extensional viscosity as a function of strain rate.

Performance of epoxy and polyester polymer concrete

Abstract: The behavior of epoxy and polyester concretes was studied under various curing conditions, temperatures, and strain rates. The influence of aggregate size and distribution on the mechanical properties of polymer concrete (PC) was also investigated. The strain rate was varied between 22 and 120 C (72 and 248 F). The strength, failure strain, modulus, and stress-strain per minute, and the temmperature between 22 and 120 C (72 and 248 F). The strength , failure strain, modulus, and stress-strain relationship of polymer concrete systems are influenced by the curing method, testing temperature, and strain rate to varying degrees. The influence of test variables on the mechanical properties of polymer concrete systems are quantified. Compared to the uniformly graded fine aggregates, the gap-graded aggregates produced polymer concrete with better mechanical properties. The compressive modulus and splitting-tensile strength of polymer concrete are related to their compressive strength. It was found that the property relationsips recommended by ACI codes and others specifically developed for high-strength cement concrete are not directly applicable to the PC systems investigated in this study. A new constitutive model is proposed to predict the complete compressive stress-strain behavior of epoxy and polyester polymer concrete systems. Analytical expressions relating the parameters of the constitutive model to the testing temperature and strain rate are derived.

Differential stress‐induced melt migration: An experimental approach

Abstract: A gradient in the dilatational component of a differential state of stress will cause migration of the melt phase in a texturally (quasi)equilibrated partial melt. An experimental approach to image such deformation-induced melt migration is presented. Two-phase, solid-liquid aggregate beams (prepared by a glass-ceramic technique) having a primary crystalline phase of MgSiO3 (orthoenstatite with a limited amount of clinoenstatite intergrowths) in chemical and textural equilibrium with a sodium aluminosilicate glass are subjected to four-point flexure; a first-order thermodynamic analysis, based on the energy balance between grain boundaries (solid-solid interfaces) and solid-liquid interfaces, indicates that the melt phase flows from that side of the specimen under a compressive principal stress to the specimen side under a tensile principal stress. When the solid-liquid aggregate is characterized by a Newtonian rheology (i.e., the deformation occurs via a solution-precipitation-enhanced diffusional creep mechanism), the melt migration is easily observed as a large deformation transient accompanying the flexural flow of a specimen. The melt migration is thus characterized as a completely recoverable, anelastic strain in the two-phase system; the rheology of the partially molten beams is well modelled by eT(t)=e0[1−exp(−Bt)]+e˙sst where eT is the total inelastic strain, e0 is the total anelastic strain due to melt migration, e˙ss is the steady-state strain rate for the two-phase aggregate, t is time and B is a function of either the viscosity of the liquid phase or of the rheology (viscosity) of the two-phase aggregate. In the experiments reported here, the melt migration is shown to be rate limited by the kinetics of compaction and/or dilation of the crystalline residuum. The impact of the experimental approach on compaction-based models of melt transport and segregation is discussed.

1990 Plenary Lecture: Strain Rate Effects in Stress Corrosion Cracking

Abstract: Slow strain rate testing (SSRT) was initially developed as a rapid, ad hoc laboratory method for assessing the propensity for metals and environments to promote stress corrosion cracking. It is now clear, however, that there are good theoretical reasons why strain rate, as opposed to stress per se, will often be the controlling parameter in determining whether or not cracks are nucleated and, if so, are propagated. The synergistic effects of the time dependences of corrosion-related reactions and microplastic strain provide the basis for mechanistic understanding of stress corrosion cracking in high-pressure pipelines and other structures. However, while this may be readily comprehended in the context of laboratory slow strain tests, its extension to service situations may be less apparent. Nevertheless, laboratory work involving realistic stressing conditions, including low-frequency cyclic loading, shows that strain or creep rates give good correlation with thresholds for cracking and with crac...