Average Strain Rate Research Articles

Orientation and length of mammalian skeletal myocytes in response to a unidirectional stretch.

Effects of mechanical forces exerted on mammalian skeletal muscle cells during development were studied using an in vitro model to unidirectionally stretch cultured C2C12 cells grown on silastic membrane. Previous models to date have not studied these responses of the mammalian system specifically. The silastic membrane upon which these cells were grown exhibited linear strain behavior over the range of 3.6-14.6% strain, with a Poisson's ratio of approximately 0.5. To mimic murine in utero long bone growth, cell substrates were stretched at an average strain rate of 2.36%/day for 4 days or 1.77%/day for 6 days with an overall membrane strain of 9.5% and 10.6%, respectively. Both control and stretched fibers stained positively for the contractile protein, alpha-actinin, demonstrating muscle fiber development. An effect of stretch on orientation and length of myofibers was observed. At both strain rates, stretched fibers aligned at a smaller angle relative to the direction of stretch and were significantly longer compared to randomly oriented control fibers. There was no effect of duration of stretch on orientation or length, suggesting the cellular responses are independent of strain rate for the range tested. These results demonstrate that, under conditions simulating mammalian long bone growth, cultured myocytes respond to mechanical forces by lengthening and orienting along the direction of stretch.

Timing and duration of syn-magmatic deformation in the Mabel Downs Tonalite, northern Australia

Detailed outcrop mapping combined with microstructural and U–Pb SHRIMP zircon data indicate that emplacement of the Mabel Downs Tonalite spanned progressive regional D 3 deformation in the Palaeoproterozoic Halls Creek Orogen of northern Australia, and that the duration of magmatism exceeded the crystallisation time of the pluton had its entire volume been emplaced instantaneously (∼10 5 y). The pluton comprises several compositionally distinct phases, which show (i) a regional solid-state S 3a foliation-forming event, predated by a strongly deformed porphyritic monzogranite with a U–Pb SHRIMP zircon age of 1837.3±6.0 Ma (95% confidence level); and (ii) overprinting by the localised S 3b Ord River Shear Zone, which crosscuts a 1831.9±3.3 Ma foliated granodiorite and contains 1826.6±7.3 Ma undeformed felsic veins, providing a younger age limit for D 3 deformation. The protracted nature of deformation and magmatism during regional D 3 deformation is significant in the context of the evolution of Halls Creek Orogen, which is characterised by a prolonged thermal event spanning three regional deformation events ( D 2, D 3 and D 4) within a 30–40 million-year interval. The accumulated finite strain is more probably the product of relatively long-lived events (of the order of several millions of years) with low average crustal strain rates, rather than high crustal strain rates during short-lived deformation episodes (=10 5 y). Thus the partitioning of strain accumulation into discrete deformation events during the rapid development of the Halls Creek Orogen was probably not as pronounced as in orogenic belts characterised by higher accumulated strain or longer intervals between deformation events.

Chaotic behavior of an elastoplastic bar in tensile test over a wide range of strain rate: a numerical investigation

Numerical tensile tests of an elastoplastic cylindrical bar at various high strain rates are performed by the use of a dynamic explicit FEM code (DYNA3D, a public domain version). The effects of mass (inertia) of the body, strain rate and strainrate sensitivity exponent ( m-value) on the deformation pattern and the load curve are investigated. As for the material, strain-dependent nth power work hardening property is given by σ=Kε n(1+ ε ̇ ) m where ε ̇ is strain rate. The range of the prescribed average strain rate is 50–1000/s where the tensile tests with constant average strain rate and with constant tensile velocity are performed. Materials with higher density exert a greater influence on deformation mode at a high strain rate. Even if the tensile speed is less than that of plastic wave propagation, the deformation becomes non-uniform remarkably due to mass effect. It is unexpected that double necking occurs at certain computational conditions. The strain at maximum load point predicted by the numerical simulation does not coincide with the analytically predicted one. Maximum rate of decrease in cross sectional area within the straight portion of the bar is compared with Hart's instability criterion based on the imperfection in the cross section. In high-rate tension over ε ̇ =400/ s , deformation behavior is chaotic in the sense that it varies very sensitively with a trivial change in material properties and/or in the prescribed strain rate.

Measurement of apparent extensional viscosities of polyolefin melts from process contraction flows

The extensional characteristics of branched and linear polyolefin melts have been evaluated in slit die flow cells with abrupt contraction ratios of 4:1 and 15:1 on a single screw extruder. Apparent extensional viscosities of the melts in planar flows have been obtained by two routes, the first employing extensional strain rate data measured from particle velocimetry, the second using a continuum mechanics analysis based on the entry flow profile. The influence of flow geometry on apparent extensional viscosity of the polymer melts has been investigated. The measured in-process apparent extensional viscosities of the branched and linear polyolefin melts are found to be in good agreement, despite differences in the strain histories imposed by two contraction geometries (centre line extensional stress and corresponding average axial strain rates differ). Particle velocimetry was found to be better than the continuum mechanics approach in obtaining extensional strain rates due to a lower susceptibility to experimental errors. It appears that the in-process methods of assessing apparent extensional viscosity, with an abrupt 180° entry slit die, are geometry independent for the range of materials, strain and strain rates covered and provide a useful technique for ranking process-typical extensional behaviour of melts.

Equal channel angular extrusion of difficult-to-work alloys

The deformation and failure characteristics of several difficult-to-work alloys during equal channel angular extrusion (ECAE) were established. The behavior of commercial-purity titanium (CP Ti) and AISI 4340 steel (quenched and tempered to R c35) was determined under isothermal conditions at temperatures between 25 and 325°C and ram speeds producing average effective strain rates between 0.002 and 2 s −1. CP Ti was particularly susceptible to shear localization during ECAE; uniform flow occurred only at high temperatures and low strain rates. On the other hand, the 4340 steel deformed uniformly under all conditions except those comprising high temperature and high strain rate. Observations of shear banding and shear failure were interpreted in terms of the tendency for strain concentration as quantified by the flow localization (‘alpha’) parameter, or the ratio of the normalized flow softening rate to the strain-rate sensitivity. Similar observations of shear failure during non-isothermal ECAE of Ti-6Al-4V at hot-working temperatures were also explained in terms of the effect of temperature, strain rate, and deformation mode on the alpha parameter. Physical modeling (visioplasticity) and finite element method (FEM) modeling were applied to elucidate failure modes and the effects of chilling on non-uniform flow during non-isothermal ECAE. The understanding of the effect of material properties on the tendency for flow localization was used to develop processing alternatives to promote uniform flow during ECAE.

Characteristics of human fingertips in the shearing direction.

The shearing strain of the human fingertip plays an important role in the determination of the optimal grasping force and in the perception of texture. Most research concerned with the mechanical impedance of the human fingertips has treated the orthogonal direction to the tip surface, and little attention has been paid to the tangential direction. This paper describes impedance characteristics of the human fingertips in the tangential directions to the tip surface. In the experiment, step and ramp shearing forces were individually applied to the tips of the thumb, middle finger, and little finger. Dynamics of the fingertips were represented by the Kelvin model. Experimental results show that each fingertip had different properties with respect to the shearing strain versus the applied force, and that the thumb had the strongest shearing stiffness among these three digits. Moreover, the shearing stiffness depended on the direction of the applied force, and the stiffness in the pointing direction was stronger than that in the perpendicular direction. As the contact force in the orthogonal direction to the fingertip surface was increased, the shearing stiffness and viscosity increased without regard to the load speed of the shearing force. Furthermore, it is shown that the average strain rate of the fingertip in the tangential direction to the fingertip surface became slower and converged to a constant value with higher contact forces.

２層フィルムのドローレゾナンス現象

The forming process of a two-layer film is generally constituted by pulling through a variable air gap into a water-cooling bath after the two polymer melts are coextruded through a flat die. In this process, the film thickness often varied in a cyclic manner according to the process conditions. This phenomenon is referred to as draw resonance and is also observed in melt spinning and film processing.An experimental study was carried out to investigate the draw resonance in forming process of a two-layer film. The two-layer film in which the first layer consists of poly (vinylidene fluoride) (PVDF) and the second layer consists of poly (methyl methacrylate) (PMMA) or PMMA/PVDF was prepared, and the total film thickness was about 50μm. As the take-up velocity or the die land gap was increased and/or the air gap was decreased, the instability of film thickness was in-creased.The average elongational strain rate was calculated from the conditions of the film forming process. The instability of the film thickness increased abruptly at a critical point of the average strain rate, and the critical point changed with the composition of polymers. Through rheological mesurements on the polymer melts, we concluded that the instability is related to the elasticity of the second polymer layer.

Behavior of Oxide Scale on 9Cr–1Mo Steel Under Varying External Stresses

The effects of different external stresses on the oxidation behavior of9Cr–1Mo steel were investigated. Tensile specimens were subjected tostresses of 11, 20, 28, and 40 MPa and the oxidation behavior was studiedat a temperature of 973 K. The elongation of the specimen was determined byan extensometer. An acoustic-emission unit was employed to monitor theintegrity of the oxide scale. The oxide scale was found to undergo bucklingbefore spalling, in the case of unstressed specimens, and in the case ofthose specimens subjected to a stress up to 28 MPa. The specimen with 40 MPastress showed the development of cracks. The application of external stressup to 28 MPa (average strain rate for 28 MPa stress was1.2 x 10-7 s-1) had a beneficial effect with respectto the adherence of the oxide scale. The specimen with 40 MPa of stress(average strain rate of 5.2 x 10-77 s-1) showedsubstantial weight gain on oxidizing up to 140 hr. The unstressed specimenrevealed enhanced spallation when compared with the stressedones. Investigation by SEM revealed the spalling of the oxide scale when theduration of oxidation was higher than 70 hr at all stress levels employed inthe present investigation. Formation of cracks at 40 MPa exposed fresh areasto oxygen and caused accelerated oxidation. Analysis by energy-dispersiveX-ray spectrometry (EDS) revealed the segregation of chromium at the oxideridges. The segregation of silicon was also significant for the specimensubjected to a stress of 40 MPa. Analysis by XRD clearly revealed thepresence of oxides of chromium and iron (Cr2O3 andFe2O3) and spinel-type oxide (FeCr2O4).

THE ASSESSMENT OF TOTAL SEISMIC MOMENT

In this paper we address two problems: (a) the estimation of the total moment release for the calculation of average strain rates and (b) the assessment of the contribution to the total moment of earthquakes smaller than those available in regional or global catalogues. We also examine the bias associated with the different methods currently in use to estimate earthquake recurrence and total rate of seismic moment release, which are important considerations in engineering seismology and tectonics.

Damage evolution in creep bulging of thin sheet metal

The creeping motion of thin sheet metal, damaged by artificial cavities is observed in bulging tests and simulated ‘semi’-analytically. The sheet metal satisfies Norton’s Law for secondary creep and is subjected to a bi-directional stretch. The stretch is produced by creep bulging through elliptical dies with the virtue of sustaining nearly uniform background stress ratio for each aspect ratio of the die axes. In order to reach large deformations with significant shape evolution of the cavities, the tests were conducted at superplastic conditions. The sheet is double layered (only one layer is cavitated) made of Tin–Lead (50–50 Pb–Sn). The measured damage growth is compared to an approximate simulation. The simulation of the damage evolution, throughout its time history, makes repeated use of a so-called “Green-function solution” for the motion of a single isolated cavity in an infinite viscoplastic continuum. The solution is modified from Muskhelishvili’s elastic solution by replacing the elastic shear modulus by a “viscous-like” variable (“plastic shear modulus”) which depends (non-linearly) on the evolved average strain-rate. Similarly, the stresses in the ligaments between cavities were averaged to approximate the local stress concentrations. Due emphasis is given to the rotation of each elliptical cavity, beside its expansion (contraction) and elongation.

Fine details of the Wadati‐Benioff zone under Indonesia and its geodynamic implications

Using about 5200 handpicked P, S, pP, sP, PcP, and ScP phases from digitally recorded seismograms, together with International Seismological Centre reported phases, we obtain improved hypocentral locations for ∼1790 earthquakes, ∼983 of them having 90% confidence limits <30 km, at depths >50 km, in the period 1962 to September 1996, along the Indonesian subduction zone. We use an improved joint hypocenter determination method in which the solution is more stable than in the original one. We show that for deep earthquakes, use of the core‐reflected phases is as good as use of depth phases, and since such core phases often have larger amplitudes and sharper onsets than the depth phases, their arrival times can be read very accurately. The positions of the relocated hypocenters show that (1) a portion of the Indonesian arc between ∼110°E and 123°E longitude, and deeper than ∼500 km, is dipping southward at an angle of ∼75°, that is, in a direction opposite to the upper part of the north dipping slab, and (2) east of about 108°E, the seismic zone is wider near 670 km than near the 500 km depth. The first suggests southward lateral flow in the mantle, relative to the plate motion vector here. From the contortion of the seismic zone along the eastern portion of the Indonesian arc, we can estimate the average lateral shear strain rate in the 300 to 670 km depth range to be of the order of 10−16s−1, over the last 10–20 Myr.

Adiabatic shear localization in the dynamic punch test, part I: experimental investigation

Abstract The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during a dynamic punch test is investigated. Specifically, the possibility and affects of adiabatic shear localization are examined. The three materials are chosen to encompass a wide range of physical properties. Punch tests are conducted at average shear strain rates from 10 −3 to 10 4 s −1 on a servo-hydraulic compression machine, a mechanical press, and a Hopkinson bar apparatus. Experimental load displacement curves are obtained and fractographic and metallographic analysis is performed. Finite element simulations of punching operations are performed in the second part of this two part investigation to examine internal deformation not visible during experimental tests. More specifically, the role of adiabatic shear localization in burr formation is determined. Adiabatic shear localization occurs in the titanium alloy for the mechanical press and Hopkinson bar tests, while localization is not present for the 6061-T6 aluminum in any test. The 1018 steel begins to exhibit some transitional behavior toward shear localization in the Hopkinson bar experiments. It is seen that in the materials tested here, a combination of high strength and low strain hardening make a material more susceptible to adiabatic shear localization in punching operations.

Thermal explosion theory for shear localizing energetic solids

The behaviour of energetic solids subjected to simple shear loading is modelled to predict ignition. The model is transient, one dimensional and includes effects of thermal diffusion, plastic work and exothermic reaction with one-step irreversible Arrhenius kinetics. A common power-law constitutive model for shear stress which accounts for strain hardening, strain-rate hardening and thermal softening is used. For the energetic solid composite LX-14 subjected to an average strain rate of , the model predicts reactive shear localization after an induction time of approximately t=5 ms, in which regions of high strain rate () are confined to thin spatial zones. An approximate thermal explosion theory which enforces spatially homogeneous stress, temperature and reaction progress as well as accounting for the early-time dominance of plastic work over exothermic reaction allows the development of simple analytic expressions for the temporal evolution of all variables. The simple expressions give predictions which agree well with both: (a) numerical predictions of a spatially homogeneous theory which allows simultaneous influences of reaction and plastic work and (b) numerical predictions of a spatially inhomogeneous theory which accounts for spatial stress distributions, thermal diffusion and spatially localized reaction. In particular, the induction time to ignition is captured accurately by the approximate theory; hence, while reactive shear localization may accompany an ignition event, ignition causality is most dependent on plastic work done during the time of spatially homogeneous shear.

Unified interpretation of internal stress superplasticity models based on thermally- activated kinetics

Three main theoretical models of internal stress superplasticity proposed by Greenwood and Johnson [ Proc. R. Soc. A, 1965, 283, 403], Sherby et al. [ Mater. Sci. Technol., 1985, 1, 925], and Sato and Kuribayashi [ Acta metall. mater., 1993, 41, 1759] have been expanded to include the temperature dependence of the average strain rate. It is revealed that the constitutive equations of these models are equivalent regarding the thermally activated kinetics, and that the apparent activation energy of internal stress superplasticity is equal to 1/ n (where n is the stress exponent of isothermal power-law creep) times that of isothermal power-law creep. This theoretical prediction has been experimentally verified by the thermal cycling creep tests using the same temperature profiles with several equivalent temperatures in a Be particle-dispersed Al matrix composite. The obtained apparent activation energy was 22 kJ/mol, which is approximately 1/7 times that of isothermal creep.

A model with two micro-scales for the effects of geometrical distribution of material inhomogeneity

A general method is proposed to account for the geometrical distribution of material inhomogeneity. It consists in a two-step micro-macro transition. The randomly inhomogeneous material is envisaged as made of cells, each one with a definite distribution of material inhomogeneity, i.e. with a definite “state”. Only a finite number of different states is considered for the cells. In other words, many identical cells exist, though at random places in the material. In the first step, the behavior of each set of identical cells, i.e., the constitutive relation that relates the average stress in that set of cells to the average strain-rate in the same set, is obtained by periodic homogenization. In the second step, a variational model is used to get the macroscopic behavior of the material, i.e. to appropriately average over the different sets of cells. The method is theoretically justified. It is then applied to a fibre-reinforced mortar. It is efficient in predicting the mechanically measured reinforcement. The influences of the fibres arrangement and the friction coefficient are investigated: an arrangement is found to reinforce more effectively than does another one.

ＳｉＣ粒子強化２１２４アルミニウム合金の高速超塑性による箱形形状への成形

The forming test was performed at 773 K using a 250 mm × 250 mm blank sheet by the gas pressure, which was preset to achieve the average strain rate of 0.1/s. The rectanglar part is successfully formed with in about 10 seconds and the maximum thickness reduction strain is over 100% at the corner of the part. The high forming rate leads to the uniform thickness distributions of the formed part and it coincides with the bulge forming test conducted by authors in the previous work. From the results of measuring the change in contour shape and thickness distributions, the forming process is proved as follows. The sheet is bulged freely in the die at first and then attaches the bottom or side wall, finally formed along the corner of the die. The process coincides with the shape predicted in the calculation of the gas pressure pattern.

ＳｉＣ粒子強化２１２４アルミニウム合金複合材料の高速超塑性によるビードパネル成形

SiC particle reinforced 2124 aluminum alloy composite sheet was studied on high strain rate superplastic forming into three types of bead panels. The forming test was performed at 773 K using a 250 mm × 250 mm blank sheet by gas pressure, which was preset to achieve the average strain rate of 0.1/s. Three shapes were successfully formed in about 10 seconds and the formability into three-dimensional shapes were confirmed under high forming rate. In case of a box shape or a box shape with a shallow bead at the bottom, minimum thickness was seen at four corners of the box. For the multi narrow deep bead panel, however, it was seen at the side wall near the flange and the maximum thickness strain was 150 to 200%. The simple prediction method of gas pressure pattern used in this study is applicable to certain complex shapes.

Internal stress superplasticity in directionally solidified Al–Al 3Ni eutectic composite

Thermal cycling creep behavior in fiber-reinforced composites was investigated using a directionally solidified Al–Al 3Ni eutectic composite. A superplastic elongation of 120% was obtained during a thermal cycling tensile creep test. Compression creep tests were performed under an external stress applied either parallel or perpendicular to the growth direction. The average strain rates for the two directions exhibited the characteristics of internal stress superplasticity: those at low stresses were much higher than the corresponding isothermal creep rates and were proportional to the applied stress. In the case of transverse loading, the thermal cycling creep rate was explained quantitatively using the previously reported internal stress superplasticity model for particle-dispersed composite. In the case of longitudinal loading, it was much lower than that predicted using the model because of the difference in the stress state and the relaxation process. However, thermal cycling creep had very low activation energy, which is a unique characteristic of internal stress superplasticity.

Transformation superplasticity of zirconium

A tensile strain of 270 pct was achieved for coarse-grained zirconium subjected to transformation superplasticity conditions, where strain increments are accumulated upon repeated thermal cycling around the allotropic transformation temperature under the biasing effect of a uniaxial tensile stress. The strain increment per cycle was found to consist of two equal contributions from transformations on heating and cooling and to increase linearly with the applied stress. The measured strain increments are in good quantitative agreement with predictions based on the average internal stress during the transformation, which was determined independently from experimental transformation times. As the cycling frequency is raised, the average strain rate increases (a maximum value of 1.3·10−4 s−1 was measured), but the strain increment per cycle decreases above a critical cycling frequency, for which the sample gage section undergoes only a partial phase transformation. The resulting reduction in internal mismatch and increase in internal stress are modeled using the experimental observation that β-Zr deforms by a mixture of diffusional and dislocation creep in the stress range of interest.

Investigation of Reactive Shear Localization in Energetic Solids

The behavior of an energetic solid subjected to shear is modelled. Data from torsional splitHopkinson bar (TSHB) experiments are first reduced to calibrate a constitutive model for stress, accounting for the effects of strain and strain rate hardening, in an inert simulant, Mock 900–20, of the high explosive LX–14. This stress model is employed in a transient one dimensional model which includes effects of thermal softening, thermal diffusion, plastic heating, and exothermic reaction. For an event with an average strain rate of 2.8×103S-1, reactive shear localization with local strain rates and temperatures in excess of 5×104s-1 and 5000K, respectively, is predicted. It is predicted that within a domain of length comparable to that of the largest heterogeneities, around 250 µm, reaction evolves over sub-nanosecond times scales. Localization and ignition are found to be sensitive to changes in mechanical properties, specific heat. and activation energy, and insensitive to changes in kinetic rate constant, heat release, and thermal conductivity.