Showing papers on "Strain rate published in 1998"

Real-time strain rate imaging of the left ventricle by ultrasound

Abstract: The regional function of the left ventricle can be visualized in real-time using the new strain rate imaging method. Deformation or strain of a tissue segment occurs over time during the cardiac cycle. The rate of this deformation, the strain rate, is equivalent to the velocity gradient, and can be estimated using the tissue Doppler technique. We present the strain rate as color-coded 2-dimensional cine-loops and color M-modes showing the strain rate component along the ultrasound beam axis. We tested the method in 6 healthy subjects and 6 patients with myocardial infarction. In the healthy hearts, a spatially homogeneous distribution of the strain rate was found. In the infarcted hearts, all the infarcted areas in this study showed up as hypokinetic or akinetic, demonstrating that this method may be used for imaging of regional dysfunction. Shortcomings of the method are discussed, as are some possible future applications of the method. (J Am Soc Echocardiogr 1998;11:1013-9.)

Review of Strain Rate Effects for Concrete in Tension

Abstract: A literature review was conducted to determine the extant data characterizing the effects of strain rate on the tensile strength of concrete. In particular, additional new data by Ross and colleagues were considered. These data support the dynamic increase factor (DIF) being a bilinear function of the strain rate in a log-log plot, with no increases for strain rates below 0.000001 with a slope change at a strain rate of 1/s. A DIF of approximately 7 was obtained at the highest reported experimental strain rate of 157/s. The DIF formulation recommended by the European CEB was described, together with its origins. It was found that the data differed somewhat from the CEB recommendations, mostly for strain rates beyond 1/s. Therefore, an alternate formulation was proposed based on the experimental data.

Processing maps for hot working of titanium alloys

Abstract: In recent years, processing maps are being used to design hot working schedules for making near-net shapes in a wide variety of materials. In this paper, the results obtained on the characterization of hot working behavior of titanium and its alloys using the approach of processing maps are described. In commercial purity α titanium, dynamic recrystallization (DRX) domain occurs at 775°C and 0.001 s−1 with an efficiency of power dissipation [2m/(m+1) where m is the strain rate sensitivity of flow stress] of 43%. The DRX domain shifts to higher strain rates when the interstitial impurity content is lowered. In the near-α and α-β alloys like IMI 685, Ti–6Al–4V, the preform microstructure has a significant influence on the processing maps. For example, in the transformed β (Widmanstatten) preform microstructures, these alloys exhibit a domain of spheroidization at lower temperature and a domain of β superplasticity at higher temperatures, both occurring at slow strain rates. These domains merge at the β transus because of the occurrence of damage processes which lower the tensile ductility. On the other hand, processing maps on alloys with equiaxed preform microstructure exhibit a clear superplasticity domain in the α-β range and the β phase undergoes DRX with a power dissipation efficiency of ≈45–55%. Titanium materials in general, exhibit wide flow instability regimes due to adiabatic shear bands formation at higher strain rates and hence careful process design has to be adopted for successful forging and microstructural control.

Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures

Abstract: This study investigates the plastic deformation and fracture behaviour of titanium alloy (Ti–6Al–4V) under high strain rates and various temperature conditions. Mechanical tests are performed at constant strain rates ranging from 5×102 to 3×103 s−1 at temperatures ranging from room temperature to 1100°C by means of the compressive split-Hopkinson bar technique. The material's dynamic stress–strain response, strain rate, temperature effects and possible deformation mechanisms are discussed. Furthermore, the plastic flow response of this material is described by a deformation constitutive equation incorporating the effects of temperature, strain rate, strain and work hardening rate. The simulated results based on this constitutive equation are verified. The fracture behaviour and variations of adiabatic shear band produced by deformation at each test condition are investigated with optical microscopy and scanning electron microscopy. The results show that the flow stress of Ti–6Al–4V alloy is sensitive to both temperature and strain rate. Nevertheless, the effect on flow stress of temperature is greater than that of strain rate. Fracture observations reveal that adiabatic shear banding turns out to be the major fracture mode when the material is deformed to large plastic strain at high temperature and high strain rate.

Review of static and dynamic properties of steel reinforcing bars

Abstract: A literature review of the effects of high strain rates on the properties of steel reinforcing bars was conducted. Static and dynamic properties were gathered for bars satisfying ASTM A615, A15, A432, A431, and A706, with yield stresses ranging from 42 ksi (290 MPa) to 103 ksi (710 MPa). Strength enhancement with strain rate was expressed in the form of a dynamic increase factor (DIF) defined as the ratio of the dynamic to static yield (or ultimate) stress. It was observed that the DIF would increase for lower reinforcing bar yield stress. A simple relationship is proposed that gives the DIF (for both yield and ultimate stress) as a function of strain rate and yield stress. This relationship is of importance for the analysis of reinforced concrete structures subjected to blast or highly dynamic loads.

Analyses of slow high-concentration flows of granular materials

Abstract: A theory intended for slow, dense flows of cohesionless granular materials is developed for the case of planar deformations. By considering granular flows on very fine scales, one can conveniently split the individual particle velocities into fluctuating and mean transport components, and employ the notion of granular temperature that plays a central role in rapid granular flows. On somewhat larger scales, one can think of analogous fluctuations in strain rates. Both kinds of fluctuations are utilized in the present paper. Following the standard continuum approach, the conservation equations for mass, momentum and particle translational fluctuation energy are presented. The latter two equations involve constitutive coefficients, whose determination is one of the main concerns of the present paper. We begin with an associated flow rule for the case of a compressible, frictional, plastic continuum. The functional dependence of the flow rule is chosen so that the limiting behaviours of the resulting constitutive relations are consistent with the results of the kinetic theories developed for rapid flow regimes. Following Hibler (1977) and assuming that there are fluctuations in the strain rates that have, for example, a Gaussian distribution function, it is possible to obtain a relationship between the mean stress and the mean strain rate. It turns out, perhaps surprisingly, that this relationship has a viscous-like character. For low shear rates, the constitutive behaviour is similar to that of a liquid in the sense that the effective viscosity decreases with increasing granular temperature, whereas for rapid granular flows, the viscosity increases with increasing granular temperature as in a gas. The rate of energy dissipation can be determined in a manner similar to that used to derive the viscosity coefficients. After assuming that the magnitude of the strain-rate fluctuations can be related to the granular temperature, we obtain a closed system of equations that can be used to solve boundary value problems. The theory is used to consider the case of a simple shear flow. The resulting expressions for the stress components are similar to models previously proposed on a more ad hoc basis in which quasi-static stress contributions were directly patched to rate-dependent stresses. The problem of slow granular flow in rough-walled vertical chutes is then considered and the velocity, concentration and granular temperature profiles are determined. Thin boundary layers next to the vertical sidewalls arise with the concentration boundary layer being thicker than the velocity boundary layer. This kind of behaviour is observed in both laboratory experiments and in granular dynamics simulations of vertical chute flows.

Analysis of fault slip inversions: Do they constrain stress or strain rate?

Abstract: Fault slip data commonly are used to infer the orientations and relative magnitudes of either the principal stresses or the principal strain rates, which are not necessarily parallel or equal. At the local scale of an individual fault, the shear plane and slip direction define the orientations of the local principal strain rate axes but not, in general, the local principal stress axes. At a large scale, the orientations of P and T axes maxima for sets of fault slip data do not provide accurate inversion solutions for either strain rate or stress. The quantitative inversion of such fault slip data, however, provides direct constraints on the orientations and relative magnitudes of the global principal strain rates. To interpret the inversion solution as constraining the global principal stresses requires that (1) the fault slip pattern must have a characteristic symmetry no lower than orthorhombic; (2) the material must be mechanically isotropic; and (3) there must be a linear constitutive relationship between the global stress and the global strain rate. Isotropic linear elastic constitutive equations are appropriate to describe the local deformation surrounding an individual slip discontinuity. Fault slip inversions, however, constrain the characteristics of a large-scale cataclastic flow, which is described by constitutive equations that are probably, but to an unknown degree, anisotropic and nonlinear. Such material behavior would not strictly satisfy the requirements for the stress interpretation. Thus, at the present state of knowledge, fault slip inversion solutions are most reliably interpreted as constraining the principal strain rates.

Dynamic Increase Factors for Concrete

Abstract: : For reinforced concrete structures subjected to blast effects, response at very high strain rates (up to 1000 s(-1)) is often sought. At these high strain rates, the apparent strength of concrete can increase significantly. The dynamic increase factor (DIF), i.e. the ratio of the dynamic to static strength, is normally reported as function of strain rate. For concrete, the DIF can be more than 2 in compression, and more than 6 in tension. Knowledge of the DIF is of significant importance in the design and analysis of structures for explosives safety. DIF curves for concrete have been published in manuals by the Tri-Services, the Defense Special Weapons Agency, the Air Force, and the Department of Energy. However, these curves are typically based on limited data. A literature review was conducted to determine the extant data to characterize the effects of strain rate on the compressive and tensile strengths of concrete. This data support the dynamic increase factor (DIF) being a bilinear function of the strain rate in a log-log plot. The DIF formulation recommended by the European CEB was described, together with its origins. For tension, it was found that the data differed somewhat from the CEB recommendations, mostly for strain rates beyond 1 s(-1), and an alternate formulation was proposed based on the experimental data.

Ring-shear studies of till deformation: Coulomb-plastic behavior and distributed strain in glacier beds

Abstract: A ring-shear device was used to study the factors that control the ultimate (steady) strength of till at high shear strains. Tests at a steady strain rate and at different stresses normal to the shearing direction yielded ultimate friction angles of 26.3 and 18.6° for tills containing 4% and 30% clay-sized particles, respectively. Other tests at steady normal stresses and variable shear-strain rates indicated a tendency for both tills to weaken slightly with increasing strain rate. This weakening may be due to small increases in till porosity. These results provide no evidence of viscous behavior and suggest that a Coulomb-plastic idealization is reasonable for till deformation. However, viscous behavior has often been suggested on the basis of distributed shear strain observed in subglacial till. We hypothesize that deformation may become distributed in till that is deformed cyclically in response to fluctuations in basal water pressure. During a deformation event, transient dilation ofdiscrete shear zones should cause a reduction in internal pore-water pressure that should strengthen these zones relative to the surrounding till, a process called dilatant hardening. Consequent changes in shear-zone position, when integrated over time, may yield the observed distributed strain.

Adiabatic shear bands in a TI-6Al-4V titanium alloy

Abstract: Dynamic (γ≈103⧹sec) torsional experiments were performed to investigate the process of initiation and formation of adiabatic shear bands in Ti-6Al-4V alloy. In this study, thin-wall tubular specimens were deformed dynamically in a torsional Kolsky bar (torsional split Hopkinson bar) . Through high-speed photography of a grid pattern previously printed on the specimens outer surface, the local strain and the local strain rate were found to be in the range of 75%–350% and 8.0×104⧹sec, respectively. The width of the shear bands ranged from 12–55 μm. In addition, an array of infrared detectors was employed to measure the local temperature rise during the deformation process. A peak temperature of 440–550°C was found in the various tests. The fracture surface of the shear band material was characterized by (1) regions of elongated dimples within which no second phase particles were observed, and (2) regions with a relatively flat and smeared appearance. There was no clear evidence based either on the appearance of the shear band in SEM or the measured temperature rise to suggest that the material within the shear band had undergone a phase transformation.

On the development of instability criteria during hotworking with reference to IN 718

Abstract: A simple instability condition based on the Ziegler’s continuum principles as applied to large plastic flow, is developed for delineating the regions of unstable metal flow during hot deformation. It can be used for any type of the flow stress versus strain rate curve. This criterion has been validated using the flow stress data of IN 718 with microstructural observations. The optimum hot working conditions for the superalloy IN 718 are suggested based on the instability map.

Low-frequency shear attenuation in polycrystalline olivine: Grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology

Abstract: The high-temperature (1200–1285°C) torsional dynamic attenuation (10−3–100 Hz) and unidirectional creep behavior of a fine, uniform grain sized (d ≈ 3 μm) olivine (∼Fo92) aggregate have been measured. In all cases, the material is found to be mechanically linear (i.e., γ(t), γ ∝ σxy1), indicating that diffusional processes dominate the deformation kinetics in these experiments. The creep response displays a large decelerating transient in the strain rate leading to a nominally constant “steady state.” The attenuation behavior displays a band in QG−1 that is moderately dependent on frequency (QG−1 ≈ f−0.35) and temperature with −1.5

Strain-rate-dependent constitutive equations for concrete

Abstract: This paper summarizes the results of a comprehensive experimental study to quantify the effects of strain rate on concrete compressive and tensile strengths. Direct compression and splitting tensile tests were conducted at quasi-static rates (between 10{sup {minus}7}/s and 10{sup {minus}5}/s) in a standard MTS machine to establish the static properties. These same tests were conducted at high strain rates (between 10{sup {minus}1}/s and 10{sup 3}/s) on a split-Hopkinson pressure bar (SHPB) to determine the dynamic material properties. A statistical analysis was performed on the data and strain-rate-dependent constitutive equations, both for compression and tension, were developed. These constitutive equations were subsequently employed to modify an existing quasi-static, nonlinear concrete material model.

A generalized law for brittle deformation of Westerly granite

Abstract: A semiempirical constitutive law is presented for the brittle deformation of intact Westerly granite. The law can be extended to larger displacements, dominated by localized deformation, by including a displacement-weakening break-down region terminating in a frictional sliding regime often described by a rate- and state-dependent constitutive law. The intact deformation law, based on an Arrhenius type rate equation, relates inelastic strain rate to confining pressure Pc, differential stress σΔ, inelastic strain ei and temperature T. The basic form of the law for deformation prior to fault nucleation is lne˙i=c-(E*/RT)+(σΔ/aσo)sin-a(πei/2eo) where σo and eo are normalization constants (dependent on confining pressure), a is rate sensitivity of stress, and α is a shape parameter. At room temperature, eight experimentally determined coefficients are needed to fully describe the stress-strain-strain rate response for Westerly granite from initial loading to failure. Temperature dependence requires apparent activation energy (E* ∼ 90 kJ/mol) and one additional experimentally determined coefficient. The similarity between the prefailure constitutive law for intact rock and the rate- and state-dependent friction laws for frictional sliding on fracture surfaces suggests a close connection between these brittle phenomena.

Strain rate behavior of composite materials

Abstract: The effect of strain rate on the compressive and shear behavior of carbon/epoxy composite materials was investigated. Strain rate behavior of composites with fiber waviness was also studied. Falling weight impact system and servohydraulic testing machine were used for dynamic characterisation of composite materials in compression at strain rates up to several hundred per second. Strain rates below 10 s −1 were generated using a hydraulic testing machine. Strain rates above 10 s −1 were generated using the drop tower apparatus developed. Seventy-two-ply unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions and [(0 8 /90 8 ) 2 /0 8 ] s crossply laminates were characterised. Off-axis (30 and 45°) compression tests of the same unidirectional material were also conducted to obtain the in-plane shear stress–strain behavior. The 90° properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The shear stress–strain behavior, which is also matrix-dominated, shows high nonlinearity with a plateau region at a stress level that increases significantly with increasing strain rate. The 0° and crossply laminates show higher strength and strain values as the strain rate increases, whereas the modulus increases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases the dynamic stress–strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal case and highest in the transverse and shear cases. Unidirectional and crossply specimens with fiber waviness were fabricated and tested. It is shown that, with severe fiber waviness, strong nonlinearity occurs in the stress–strain curves due to fiber waviness with significant stiffening as the strain rate increases.

Shape Fixity and Shape Recovery in a Film of Shape Memory Polymer of Polyurethane Series

Abstract: The shape fixity and recovery in a film of shape memory polymer of polyurethane series were investigated by the thermomechanical cycling tests with loading at various temperatures. The results are summarized as follows: (1) Strain is recovered at temperatures in the vicinity of the glass transition temperature Tg for loading above Tg, but it is recovered at temperatures in the vicinity of the midpoint temperature of glass transition for loading below Tg. (2) The rate of strain fixity is 98% for loading above Tg, while it decreases with increasing cycles for loading below Tg. (3) The rate of strain recovery for loading above Tg is 98% except for the early cycles. (4) The thermomechanical properties of materials with different Tg are quite alike in spite of the difference in Tg.

Dynamic Increase Factors for Steel Reinforcing Bars

Abstract: : For reinforced concrete structures subjected to blast effects, response at very high strain rates (up to 1000 s-1) is often sought. At these high strain rates, the reinforcing bars yield stress can increase by 100%, or more, depending on the grade of steel used. The dynamic increase factor (DIF), i.e. the ratio of the dynamic to static value, is normally reported as function of strain rate. Knowledge of the DIF is of significant importance in the design and analysis of structures for explosives safety. DIF curves for both yield and ultimate strengths have been derived and published in manuals by the Tri-Services, the Defense Special Weapons Agency, the Air Force, and the Department of Energy. However, these curves are typically based on limited data, and even on data from steel bars of a different grade. A literature review of the effects of high strain rates on the properties of steel reinforcing bars (rebars) was conducted. Static and dynamic properties were gathered for bars satisfying ASTM A615, A15, A432, A431, and A706, with yield stresses ranging from 42 to 103 ksi (290 to 710 MPa). The data indicates that the DIF decreases for higher rebar yield stress, and that the DIF is higher for yield stress than for ultimate stress. A simple relationship is proposed that gives the DIF (for both yield and ultimate stress) as a function of strain rate and yield stress.