Showing papers on "Strain rate published in 1997"

Single Polymer Dynamics in an Elongational Flow

Abstract: The stretching of individual polymers in a spatially homogeneous velocity gradient was observed through use of fluorescently labeled DNA molecules. The probability distribution of molecular extension was determined as a function of time and strain rate. Although some molecules reached steady state, the average extension did not, even after a ∼300-fold distortion of the underlying fluid element. At the highest strain rates, distinct conformational shapes with differing dynamics were observed. There was considerable variation in the onset of stretching, and chains with a dumbbell shape stretched more rapidly than folded ones. As the strain rate was increased, chains did not deform with the fluid element. The steady-state extension can be described by a model consisting of two beads connected by a spring representing the entropic elasticity of a worm-like chain, but the average dynamics cannot.

Mechanotransduction in bone: osteoblasts are more responsive to fluid forces than mechanical strain.

Abstract: Mechanical force applied to bone produces two localized mechanical signals on the cell: deformation of the extracellular matrix (substrate strain) and extracellular fluid flow. To study the effects of these stimuli on osteoblasts, MC3T3-E1 cells were grown on type I collagen-coated plastic plates and subjected to four-point bending. This technique produces uniform levels of physiological strain and fluid forces on the cells. Each of these parameters can be varied independently. Osteopontin (OPN) mRNA expression was used to assess the anabolic response of MC3T3-E1 cells. When fluid forces were low, neither strain magnitude nor strain rate was correlated with OPN expression. However, higher-magnitude fluid forces significantly increased OPN message levels independently of the strain magnitude or rate. These data indicate that fluid forces, and not mechanical stretch, influence OPN expression in osteoblasts and suggest that fluid forces induced by extracellular fluid flow within the bone matrix may play an important role in bone formation in response to mechanical loading.

Strain hardening regimes and microstructural evolution during large strain compression of low stacking fault energy fcc alloys that form deformation twins

Abstract: Constant true strain rate simple compression tests were conducted on annealed, polycrystalline samples of α-brass and MP35N, and the evolution of the true stress (σ)-true strain (e) response was documented. From these data, the strain hardening rate was numerically computed, normalized with shear modulus (G), and plotted against both (σ − σ 0)/G (σ0 being the initial yield strength of the alloy) and e. Such normalized plots for α-brass and MP35N were found to be almost identical to each other, and revealed four distinct stages of strain hardening: stage A, with a steadily decreasing strain hardening rate up to a true strain of about −0.08; stage B, with an almost constant strain hardening rate up to a true strain of about −0.2; stage C, with a steadily decreasing strain hardening rate up to a true strain of about −0.55; and a final stage D, again with an almost constant strain hardening rate. Optical microscopy and transmission electron microscopy (TEM) were performed on deformed samples. The results suggested that stage A corresponded to stage III strain hardening (dynamic recovery) of higher stacking fault energy (SFE) fcc metals such as copper. The onset of stage B correlated with the first observation of deformation twins in the microstructure. Further straining in stage B was found to produce clusters of parallel twins in an increasing number of grains. Stage C correlated with the development of severe inhomogeneity of deformation within most grains, and with the development of significant misorientation between the twin/matrix interface and the {111} plane in the matrix of the grain, i.e., the matrix/twin interface lost coherency with continued deformation. Stage D correlated with extensive formation of secondary twins that resulted in twin intersections in many grains. Early in stage D, some strain localization in the form of shear bands was observed. Although formation of these shear bands had no detectable effect on the macroscopic strain hardening rate, it did correlated with a marked change in texture evolution. Based on these experimental observations, we have developed and presented a physical description of the microstructural phenomena responsible for the various strain hardening stages observed in low SFE fcc alloys.

Logarithmic strain, logarithmic spin and logarithmic rate

Abstract: Two yet undiscovered relations between the Eulerian logarithmic strain inV and two fundamental mechanical quantities, the stretching and the Cauchy stress, are disclosed. A new spin tensor and a new objective tensor-rate are accordingly introduced. Further, new rate-form constitutive models based on this objective tensor-rate are established. It is proved that (i). an objective corotational rate of the logarithmic strain inV can be exactly identical with the stretching and in all strain measures only inV enjoys this property, and (ii). InV and the Cauchy stress σ form a work-conjugate pair of strain and stress.

Creep, stress relaxation, and plastic deformation in Sn-Ag and Sn-Zn eutectic solders

Abstract: Because of the high homologous operation temperature of solders used in electronic devices, time and temperature dependent relaxation and creep processes affect their mechanical behavior In this paper, two eutectic lead-free solders (965Sn-35Ag and 91Sn-9Zn) are investigated for their creep and stress relaxation behavior The creep tests were done in load-control with initial stresses in the range of 10-22 MPa at two temperatures, 25 and 80°C The stress relaxation tests were performed under constant-strain conditions with strains in the range of 03-24% and at 25 and 80°C Since creep/relaxation processes are active even during monotonie tensile tests at ambient temperatures, stress-strain curves at different temperatures and strain rates provide insight into these processes Activation energies obtained from the monotonic tensile, stress relaxation, and creep tests are compared and discussed in light of the governing mechanisms These data along with creep exponents, strain rate sensitivities and damage mechanisms are useful for aiding the modeling of solder interconnects for reliability and lifetime prediction Constitutive modeling for creep and stress relaxation behavior was done using a formulation based on unified creep plasticity theory which has been previously employed in the modeling of high temperature superalloys with satisfactory results

Hypo-Elasticity Model Based upon the Logarithmic Stress Rate

Abstract: Recently these authors have proved [46, 47] that a smooth spin tensor Ωlog can be found such that the stretching tensor D can be exactly written as an objective corotational rate of the Eulerian logarithmic strain measure ln V defined by this spin tensor, and furthermore that in all strain tensor measures only ln V enjoys this favourable property This spin tensor is called the logarithmic spin and the objective corotational rate of an Eulerian tensor defined by it is called the logarithmic tensor-rate In this paper, we propose and investigate a hypo-elasticity model based upon the objective corotational rate of the Kirchhoff stress defined by the spin Ωlog, ie the logarithmic stress rate By virtue of the proposed model, we show that the simplest relationship between hypo-elasticity and elasticity can be established, and accordingly that Bernstein's integrability theorem relating hypo-elasticity to elasticity can be substantially simplified In particular, we show that the simplest form of the proposed model, ie the hypo-elasticity model of grade zero, turns out to be integrable to deliver a linear isotropic relation between the Kirchhoff stress and the Eulerian logarithmic strain ln V, and moreover that this simplest model predicts the phenomenon of the known hypo-elastic yield at simple shear deformation

Constitutive equations for high temperature flow stress of aluminium alloys

Abstract: Constitutive equations for the relationship between stress, strain, strain rate, and temperature are an essential input for modelling thermomechanical processing. Hot plane strain compression testing was used to deform commercial purity aluminium, Al-1Mn, and Al-1Mg alloys at temperatures of 300, 400, and 500°C and equivalent strain rates of 0.25, 2.5, and 25 s−1, to an equivalent strain of 2. Flow stress data obtained from these tests were analysed using the Sah et al. and hyperbolic sine forms of relationships. Values of constants in the constitutive equations were obtained and were shown to provide an accurate description of the experimental stress-strain curves, including the effect of temperature rise due to deformational heating and the effect of changing strain rate. The application and limitations of the relationships are discussed.

Nonlinear mechanical response of high density polyethylene. Part II: Uniaxial constitutive modeling

Abstract: Based on the experimental data presented in Part I, two uniaxial constitutive models are constructed. The first, a nonlinear viscoelastic (NVE) model, is formulated using the mechanical analogy consisting of one independent spring and six Kelvin elements in series. Creep data are used to determine the model parameters. The second model, a viscoplastic (VP) formulation, is developed using the viscoplastic theory proposed by Bodner to characterize the uniaxial viscoplastic behavior of metals. Inelastic strain rate is introduced into the state variable in addition to inelastic work to depict the strong rate dependent behavior of HDPE. Experimental data from constant strain rate tests are employed to construct the material functions of the model. Limitations in the application of each model are discussed in conjunction with possibilities for future work.

Shear localization and recrystallization in high-strain, high-strain-rate deformation of tantalum

Abstract: Tantalum was subjected to high plastic strains (global effective strains between 0 and 3) at high strain rates (>104 s−1) in an axisymmetric plane strain configuration. Tubular specimens, embedded in thick-walled cylinders made of copper, were collapsed quasi-uniformly by explosively-generated energy; this was performed by placing the explosive charge co-axially with the thick-walled cylinder. The high strains achieved generated temperatures which produced significant microstructural change in the material; these strains and temperatures were computed as a function of radial distance from the cylinder axis. The microstructural features observed were: (i) dislocations and elongated dislocation cell (eeff 2.5, T > 1000 K). Whereas the post-deformation (static) recrystallization takes place by a migrational mechanism, dynamic recrystallization is the result of the gradual rotation of subgrains coupled with dislocation annihilation. A simple analysis shows that the statically recrystallized grain sizes observed are consistent with predicted values using conventional grain-growth kinetics. The same analysis shows that the deformation time is not sufficient to generate grains of a size compatible with observation (0.1–0.3 μm). A mechanism describing the evolution of the microstructure leading from elongated dislocation cells, to subgrains, and to micrograins is proposed. Grain-scale localization produced by anisotropic plastic flow and localized recovery and recrystallization was observed at the higher plastic strains (eeff > 1). Residual tensile ‘hoop’ stresses are generated near the central hole region upon unloading; this resulted in ductile fracturing along shear localization bands.

Nonlinear mechanical response of high density polyethylene. Part I: Experimental investigation and model evaluation

Abstract: The nonlinear behavior of high density polyethylene (HDPE) is investigated for samples cut from thick-walled HDPE pipe. Extensive experimental work has been performed to characterize the non-linear time-dependent response of the material tested under uniaxial compression. Tests were conducted under conditions of constant strain rate, creep, stress relaxation, constant loading rate, abrupt change of strain rate, creep-recovery, cyclic strain rate, and various combinations of these loading conditions. Creep and stress relaxation response after strain reversal and the effect of the transient response on the following stress-strain behavior is examined. Permanent strains for the test specimens and their dependence on loading histories are investigated. Specimens cut at various orientations from the pipe are used to quantify the small amounts of local anisotropy in the pipe specimen. The experimental work has been used to develop both nonlinear viscoelastic (NVE) and viscoplastic (VP) constitutive models in a companion paper. Both the test results and the corresponding model predictions are reported in this paper. It is found that the VP model reproduces the nonlinear viscoelastic-viscoplastic behavior of HDPE very well provided that the current strain is not below the maximum strain imposed (there is no strain reversal). The NVE model predicts the material behavior reasonably well for some loading conditions, but inadequately for others.

Collective behavior and spacing of adiabatic shear bands

Abstract: The failure of metals subjected to high strain rates is frequently related to the collective development of adiabatic shear bands which results in a patterning depending on the material properties and the loading conditions. In this paper, the spacing between adiabatic shear bands is characterized by analytical means in a one-dimensional formulation. Using a perturbation analysis, a dominant instability mode can be characterized, whose wavelength is related to the shear-band spacing. Explicit solutions are found for materials with no strain hardening. Asymptotic developments are used to obtain results that account for strain hardening. Comparisons are made with experimental results and other existing models.

Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization

Abstract: The formalism for rate and state friction is extended to represent fault zones where temperature, porosity, effective normal traction, and strain rate are functions of position (measured across the fault zone). A traditional form for the instantaneous coefficient of friction is retained, where μ0 is the steady state coefficient of friction at shear strain rate , a and b are small constants, is the shear strain rate, ψ is a state variable that represents damage, and ψ0 a normalizing factor. Percolation theory of cracked solids is used to justify a relation between porosity and the state variable of ψ=exp[(ϕ0-f)/Cϵ], where cϵ is a dimensionless constant, and ϕ0 is the porosity at a reference steady state strain rate ϵ0 and at a reference temperature where Δ≡0 and a reference effective normal traction ΔP0. These relationships and percolation theory imply an evolution law for porosity of the (normalized) form where t is time, ΔP is the effective normal traction, Cη is a material property (related to compaction viscosity) that depends on the temperature difference ΔT from reference condition, 0 indicates reference conditions, and η is a power law rheology exponent. The first term represents creation of porosity by frictional dilatancy while the second term represents closure of porosity by compaction. The effects of transient changes of pressure and temperature on the coefficient of friction are represented when the normalizing factor ψ0 is ΔPnCη(0)/ΔPn0Cη(ΔT). The theory is complete in the sense that the complete earthquake cycle is represented and that there are no unmeasurable state parameters. The theory was applied to investigate earthquake quenching by fluid pressure decreases associated with frictional dilatancy and the related topic of strain localization and delocalization within fault zones. It was found that strain localization will occur when b>a. Such strain localization tends to destabilize sliding within drained faults by reducing the effective value of the critical displacement. Fault zones that are hydraulically sealed from the country rock but internally hydraulically connected are also destabilized because strain localization reduces the fluid pressure decrease from frictional dilatancy. Two mechanisms that delocalize strain once sliding is well underway were investigated. Strain rate strengthening at high-strain rates leads to a high strain zone that gradually broadens throughout an earthquake. An increase in the coefficient of friction with temperature leads to a high strain rate zone that moves through the fault zone from hot regions created by frictional heating to cold regions.

Experimental investigation of superplastic behaviour in magnesium alloys

Abstract: Constant strain rate tensile tests have been conductedfor fine grained Mg-Al-Zn (AZ91) and Mg-Zn-Zr (ZK60 and ZK61) alloys processed by powder metallurgy (PM) and ingot metallurgy (IM) routes. The experimental results revealed that the strain rate was inversely proportional to the cube of the grain size and that the activation energy for superplastic flow was higher than that for grain boundary diffusion. The PM Mg alloys showed superplastic behaviour at higher strain rates than the IM Mg alloys. This is because of smaller grain sizes of the PM Mg alloys. The origin of the high strain rate superplasticity for the PM Mg alloys is unlikely to be associated with the presence of a liquid phase.

Influence of Ferrite Rolling Temperature on Microstructure and Texture in Deformed Low C and IF Steels

Abstract: Single pass rolling experiments were carried out on two low carbon steels and an IF grade at temperatures between ambient and 700°C. The main aim was to investigate the transition from the well known behavior observed under cold rolling conditions to the less understood warm rolling behavior. Three aspects of the deformed state were examined: the occurrence of in-grain shear banding at angles of 30°-35°(and 17°-20°) to the rolling plane; the stored energy of deformation; and the final texture. These were chosen because of their effect on recrystallization. In-grain shear bands were evident, to one degree or another, in all samples. Their sensitivity to deformation temperature, however, was markedly different in the two low C grades compared to the IF grade. In the low C material, the frequency of banding was high at low temperatures but virtually nil at high temperatures. The degree of banding remained constant with temperature in the IF steel. These observations are explained in terms of strain rate sensitivity differences. The stored energy measurements were consistent with results in the dynamic strain aging literature. The deformation textures obtained were also in line with typical ferrite rolling textures. The overall sharpness of the rolling textures of the low C grades, however, increased markedly with temperature. This is ascribed to a drop in the texture weakening caused by in-grain shear banding.

A finite element analysis of the squeeze flow of an elasto-viscoplastic paste material

Abstract: A finite element analysis of squeeze flow has been implemented for a material that exhibits elasto-viscoplasticity. The formulation is based upon the assumption that linear elastic deformation occurs prior to yield and that the yield surface is strain rate hardening as defined by an associated viscoplastic flow rule. Both no-slip and lubricated wall boundary conditions are considered. The numerical simulation results are compared with experimental measurements involving a model elasto-viscoplastic material for which the material parameters were derived from tensile and ram extrusion measurements. Satisfactory agreement was obtained for the compressive forces as a function of displacement, the radial displacement fields and the wall normal and shear stress distributions.

Toward an experimental study of deep mantle rheology: A new multianvil sample assembly for deformation studies under high pressures and temperatures

Abstract: A new sample assembly for the multianvil high-pressure apparatus has been developed that results in high-strain plastic deformation at high pressures and temperatures with minimal deformation during the initial pressurization stage. In this assembly, the sample is a thin disk which is sandwiched between two pistons and oriented at 45° to their long axis. The sample and pistons are surrounded by a Pt tube and a polycrystalline MgO cylinder. Upon pressurization, a uniaxial stress develops because of the anisotropy of mechanical properties. Deformation during initial pressurization, which occurred in previous studies, is minimized by locating soft materials at the ends of the pistons and by the simple shear deformation geometry (as opposed to uniaxial compression) that allows sliding at the sample-piston interfaces at low pressures. Large plastic strains, up to ∼100% shear strain, have been achieved in (Mg,Fe) 2 SiO 4 phases at high pressures (up to 15 GPa) and high temperatures (up to 1900 K). A theoretical analysis has been made to evaluate the relative contributions to sample deformation from the relaxation of elastic strain in the sample column and from continuing advancement of the multianvil guide blocks. The observed dependence of strain on time, pressure and temperature suggests that deformation in the present experiments occurred mostly as a relaxation process rather than at a constant strain rate caused by continuous piston movement. A comparison of the creep strength of olivine inferred from the strain relaxation data at ∼15 GPa and ∼1900 K with low-pressure data provides an estimate of the activation volume for creep of V* = 14 ( ±1) x 10 -6 m 3 mol -1 . The theoretical analysis shows that constant strain rate deformation could result from the advancement of the guide blocks after complete stress relaxation, although the total strain will be much less than that attained in the relaxation process. Possible applications of this technique to studies of high-pressure rheology and deformation microstructures in high-pressure minerals are discussed, and strategies for future deformation experiments under high pressures and temperatures are proposed.

Shear flow of wormlike micelles in pipe and cylindrical Couette geometries as studied by nuclear magnetic resonance microscopy

Abstract: The nonlinear viscosity of the wormlike surfactant system cetyl pyridinium chloride/sodium salicylate (60 mM/100 mM in water) has been investigated in both pipe and cylindrical Couette geometries, using nuclear magnetic resonance to image both velocity and diffusion In pipe flow we observe transitions from Newtonian to non-Newtonian viscosity, to spurt, to unstable flow, and then to a regime where fluctuations are rapid on the timescale of a few milliseconds In the Couette cell we observe apparent slip at the inner wall as well as a high shear rate band located away from the wall in the body of the fluid The banding phenomenon, which has its counterpart in the pipe flow, is consistent with double valuedness in the stress versus rate of strain relationship for this fluid

Surface strain accumulation and the seismic moment tensor

Abstract: Although the scalar moment accumulation rate within the seismogenic zone beneath a given area is sometimes deduced from the observed average surface strain accumulation rate over that same area (e.g., Working Group on California Earthquake Probabilities, 1995), the correspondence between the two is very uncertain. The equivalence between surface strain accumulation and scalar moment accumulation is based on Kostrov's (1974) relation between the average strain rate over a volume and the moment-rate tensor for that volume. The average strain rate over the volume is replaced by the average strain rate measured at the free surface to deduce an approximate moment-rate tensor. Only in exceptional circumstances will that moment-rate tensor correspond to a double-couple mechanism, a mechanism that can be represented by a scalar moment accumulation rate. More generally, the moment tensor must be resolved into the superposition of two or more double-couple mechanisms, and that resolution can be done in many ways, each with its own scalar moment rate. Thus the resolution is not unique. This is demonstrated by deducing scalar moment accumulation rates for a GPS network that covers most of California south of San Francisco. It is shown that resolutions into different double-couple mechanisms lead to scalar moment accumulation rates differing by factors of ∼2. We suggest that the minimum scalar moment rate equivalent to principal surface strain rates ɛ 1 and ɛ 2 acting over the area A is M (min) = 2 μHA Max (¦ ɛ 1¦, ¦ ɛ 2¦, ¦ ɛ 1 + ɛ 2¦), where μ is the rigidity and H the depth of seismogenic zone, and the function Max is equal to the largest of its arguments. Within the uncertainites of measurement, the scalar moment accumulation rate in southern California based on that approximation is in balance with the average historic seismic moment release rate so that no current earthquake deficit need be accumulating.