Strain Rate Relationship Research Articles

Evaluation of rate-dependent forming limit for AA7075 sheets under pneumatic stretching method at elevated temperatures

The forming limit of aluminum alloy (AA) 7075 sheets depending on the deformation mode, the strain-rate, and the temperature was evaluated under the pneumatic stretching technique at elevated temperatures. In order to perform the pneumatic stretching test and to prevent the unfavorable fracture on the edge with the targeted strain-rate, the previously introduced die shape designs were utilized with the pressure-time profile. The two different kinds of strain-rate and temperature-sensitive forming limits were determined, where one is the necking-based forming limit (NFL) and the other is the fracture-based forming limit (FFL). The results show that FFL is highly deviated from NFL at 400 °C than those at 470 °C due to abrupt strain localization, which leads to high dome height at the pneumatic forming during the relatively lower elevated temperature. The microscopical analysis (optical and scanning electron) reveals that higher temperature condition, 470 °C, has early fracture due to the high diffusion of micro-voids and faster coalescence of the voids. The well-known three parameters fracture criteria e.g. Johnson-Cook (J-C), Modified Mohr-Coulomb (MMC3), Lou, and Hu fracture model were multiplicatively extended to strain-rate relationships based on the suggested general equation and independently characterized for each elevated temperature with the error analysis.

Multiscale Approaches Including ANN and M5P-Tree with SI and OBJ Assessment Tools to Predict the Shear Thinning of Bentonite Drilling Muds Modified with Clay Nanosize at Various Elevated Temperatures

Improving the flowability behavior of the water-based drilling mud (WBM) using bentonite under high-temperature conditions is significant in the drilling borehole operations. In this study, the influence of bentonite and clay nanoparticle (CNP) contents on the non-Newtonian fluid (rheology) properties such as initial shear stress and fluid’s resistance to flow (viscosity) under high-temperature conditions were tested and quantified. The shear stress and shear strain rate relationships of WBM were simulated using two new rheological models of the vapor pressure and modified Hoerl models, and the modeling outcomes were validated with the Herschel–Bulkley (HB) model. This study also analyzed and formulated more than 268 data sets, including observational data and data obtained from previously published studies ranging with bentonite in the drilling muds from 2% to 8% (%wt. of water), 0% to 1% of CNP (%wt. of bentonite), and heating temperatures were ranging from 25°C to 100°C. The HB rheological model predicted initial shear stress better than the other two rheological models depending on several statistical assessments. The initial shear stress of drilling muds can be predicted well based on bentonite, CNP contents, and temperature using various simulation techniques. According to several statistical tests, the nonlinear regression and artificial neural network (ANN) performed stronger than other model techniques to predict the yield stress of WBM as a function of bentonite, CNP contents, and temperature.

Nusselt number-turbulent strain rate relationship: Forced convection of a flat surface downstream of a pair of side-by-side rectangular strips

The turbulent strain rate generated by a pair of 25.4 mm tall and 12.7 mm wide (W) rectangular strips at a Reynolds number based on the strip width of 8500 was measured using a 3D hotwire probe in a wind tunnel. The strips were placed side-by-side separated by 3 W, 2 W, and 1 W. The convective heat transfer enhancement, denoted by the normalized Nusselt number (Nu/Nu0), was correlated with turbulence fluctuation, Taylor microscale, turbulent strain rate and integral-Taylor scale ratio. With the effects of both turbulence fluctuation and eddy scale incorporated, the turbulent strain rate correlated most strongly with Nu/Nu0, with an R-square value of 0.82. Comparatively, the R-square for Nu/Nu0 - velocity fluctuation and Nu/Nu0 - Taylor microscale were 0.77 and 0.64, respectively. Furthermore, the turbulent strain rate was found to have the most significant impact on heat transfer augmentation, more so than the individual effects of turbulent fluctuation and Taylor microscale.

Reduced preload increases Mechanical Control (strain-rate dependence) of Relaxation by modifying myosin kinetics

Rapid myocardial relaxation is essential in maintaining cardiac output, and impaired relaxation is an early indicator of diastolic dysfunction. While the biochemical modifiers of relaxation are well known to include calcium handling, thin filament activation, and myosin kinetics, biophysical and biomechanical modifiers can also alter relaxation. We have previously shown that the relaxation rate is increased by an increasing strain rate, not a reduction in afterload. The slope of the relaxation rate to strain rate relationship defines Mechanical Control of Relaxation (MCR). To investigate MCR further, we performed in vitro experiments and computational modeling of preload-adjustment using intact rat cardiac trabeculae. Trabeculae studies are often performed using isometric (fixed-end) muscles at optimal length (Lo, length producing maximal developed force). We determined that reducing muscle length from Lo increased MCR by 20%, meaning that reducing preload could substantially increase the sensitivity of the relaxation rate to the strain rate. We subsequently used computational modeling to predict mechanisms that might underlie this preload-dependence. Computational modeling was not able to fully replicate experimental data, but suggested that thin-filament properties are not sufficient to explain preload-dependence of MCR because the model required the thin-filament to become more activated at reduced preloads. The models suggested that myosin kinetics may underlie the increase in MCR at reduced preload, an effect that can be enhanced by force-dependence. Relaxation can be modified and enhanced by reduced preload. Computational modeling implicates myosin-based targets for treatment of diastolic dysfunction, but further model refinements are needed to fully replicate experimental data.

A multiscale micromorphic model with strain rate relationship between MD simulations and macroscale experimental tests and dynamic heterogeneity for glassy polymers

This paper proposes a micromorphic simulation model with novel strain rate relationships between MD simulations and macroscale experiments at the ductile-brittle (DB) transition of glassy polymer and dynamic heterogeneity of deformation. Novelties of this paper are on the strain rate relationship between two different scale regions and investigations on the effects of molecular weight on the relationship. From molecular dynamics model having realistically entangled polymer networks and experiments, the strain rate relationships are derived and then realized through a two-scale multiscale continuum model based on the micromorphic theory. The investigation on the effects of molecular weights on the relationship yields that the relationship is maintained when the molecular weight is higher than the entanglement length. The relationship confirmed that the dynamic heterogeneity alleviates as the polymer enters into the plastic flow above the glass transition temperature and disappears above the melting temperature. These findings will be a basis for developing the constitutive relationship of glassy polymers through a multiscale approach that can incorporate the heterogeneous dynamics of molecules.

Mechanical Behavior of Lead at High Strain Rates

This paper presents a study on the material behaviors and constitutive models of lead at high strain rates. Quasi-static compressive tests and split Hopkinson pressure bar (SHPB) tests were conducted at room temperature. The results of the SHPB tests were verified by high-speed photography, and the error of strain is less than 3% at high strain rate (5000/s). Our results show that the yield stress and flow stress increase at high strain rates. This result indicates that lead is sensitive to the strain rate at high strain rates, but the dependence is not linear during 3000-5000/s. The strain-rate dependence of lead was fitted by a quadratic polynomial curve. To describe the nonlinear strain-rate relationship of lead, modified Johnson–Cook and Cowper–Symonds material models were used to fit the experimental stress–strain curves. The modified Cowper–Symonds model agrees better with the experimental results and can better describe the dynamic mechanical behavior of lead under high strain rates.

Material properties of human lumbar intervertebral discs across strain rates

BACKGROUND CONTEXTThe use of finite element (FE) methods to study the biomechanics of the intervertebral disc (IVD) has increased over recent decades due to their ability to quantify internal stresses and strains throughout the tissue. Their accuracy is dependent upon realistic, strain-rate dependent material properties, which are challenging to acquire. PURPOSEThe aim of this study was to use the inverse FE technique to characterize the material properties of human lumbar IVDs across strain rates. STUDY DESIGNA human cadaveric experimental study coupled with an inverse finite element study. METHODSTo predict the structural response of the IVD accurately, the material response of the constituent structures was required. Therefore, compressive experiments were conducted on 16 lumbar IVDs (39±19 years) to obtain the structural response. An FE model of each of these experiments was developed and then run through an inverse FE algorithm to obtain subject-specific constituent material properties, such that the structural response was accurate. RESULTSExperimentally, a log-linear relationship between IVD stiffness and strain rate was observed. The material properties obtained through the subject-specific inverse FE optimization of the annulus fibrosus (AF) fiber and AF fiber ground matrix allowed a good match between the experimental and FE response. This resulted in a Young modulus of AF fibers (—MPa) to strain rate (ε˙, /s) relationship of YMAF=31.5ln(ε˙)+435.5, and the C10 parameter of the Neo-Hookean material model of the AF ground matrix was found to be strain-rate independent with an average value of 0.68 MPa. CONCLUSIONSThese material properties can be used to improve the accuracy, and therefore predictive ability of FE models of the spine that are used in a wide range of research areas and clinical applications. CLINICAL SIGNIFICANCEFinite element models can be used for many applications including investigating low back pain, spinal deformities, injury biomechanics, implant design, design of protective systems, and degenerative disc disease. The accurate material properties obtained in this study will improve the predictive ability, and therefore clinical significance of these models.

On the upturn phenomenon in the strength vs. strain-rate relations of metals

The dynamic response of metals and their alloys to high strain-rate loading is examined in this work. Particularly, we focus on the controversy surrounding a claim, made by several authors, that the flow stresses of various materials experience a very large increase (the “upturn” phenomenon) at strain rates in the range of 103–104 s−1. This claim was contradicted by other workers who did not find such an “upturn” behavior for the same materials, at this range of strain rates. We review some of these works and identify possible reasons for this discrepancy, focusing on the differences between the experimental techniques which were used in the various studies.

Rheological behaviors and model of fresh concrete in vibrated state

The rheological behavior of fresh concrete under vibration is very different from that in static state. In this study, the relationship between shear strain rate and shear stress of fresh concrete under vibration was theoretically analyzed based on Eyring rate process theory and vibration damping theory, and the constitutive equations were gotten. At low shear strain rates, vibrated fresh concrete is a Bingham liquid, even Newtonian when vibrating time is enough long. However, at high shear strain rates, the shear stress - shear strain rate relationship is a logarithmic function. The shear deformation resistance decreases with increasing vibrating time, but increases with the distance from vibrator or the thickness of concrete. The rheological measurement in vibrated state was also conducted by using a ring shear type rheometer, into which a rod vibrator is integrated. The experimental results of shear stress - shear strain rate relationship were well consistent with the theoretical equations.

Temperature-dependent phase transformation of ice-1h under ultrafast uniaxial compression: A molecular dynamics simulation

The temperature and strain rate-dependent compressive behaviour of ice-1h was investigated through molecular dynamics simulations. The ice strength increased in response to a decrease in the initial temperature and an increase in the strain rate. Various deformation mechanisms depended on the ice’s initial temperature. Solid-liquid phase transformation was more likely to at a relatively high temperature. However, solid-solid phase transformation and dislocation-like glide were observed at relatively low temperatures. Experimental observations on the strength versus strain rate relationship of ice could be interpreted based on a prior study by Wu and Prakash [1].

Salt contamination and temperature impacts on the rheological and electrical resistivity behaviors of water based drilling mud

ABSTRACTThe impacts of up to 3% salt contamination and temperature in the range of 25°C to 75°C on the bentonite drilling muds were investigated. The rheological and resistivity properties of 2% and 8% bentonite based drilling muds were experimentally measured and modeled. The shear thinning stress-shear strain rate relationship was measured and modeled. Finally, a nonlinear model was used to predict the electrical resistivity (ρ), yield shear stress (τo), maximum shear stress (τmax) and the parameters of the drilling mud model to the bentonite content, temperature and salt content and the predictions agreed well with the experimental results.

On the Nuances in the Power Law Description and Interpretation of High Homologous Temperature Creep and Superplasticity Data

“Power law’’ representation is used to describe minimum creep rate and “steady state” superplastic deformation. In creep isothermal log stress – log strain rate relationship is linear for so long as the rate controlling mechanism remains unchanged. During optimal superplastic flow the slope of this curve changes even when there is no change in the rate controlling mechanism, i.e. the stress exponent, n, at a constant temperature and grain size is a function of strain rate. For a constant rate controlling mechanism, in both the phenomena, n decreases with increasing temperature. Grain size has no effect on creep, but its effect is significant in superplasticity. Therefore, analyzing creep and superplasticity data by treating n for any given mechanism as a constant independent of stress and temperature is questionable. In this analysis stress is normalized with respect to a reference stress, rather than the shear modulus. The microstructure dependence comes through the Buckingham Pi theorem. When contribution from microstructure terms to isothermal strain rate is constant, Laurent’s theorem helps generate a set of values for n. It is shown that the simplest solution, viz. n is independent of stress, but is a linear function of temperature, describes steady state creep. (The case n is independent of both stress and temperature follows as a special case.) The second simplest solution, viz. n is a linear function of both temperature and stress corresponds to steady state superplasticity. Using the equations, the values of n, activation energies for the rate controlling processes and strain rates at different temperatures and stresses could be estimated for both creep and superplasticity. The analysis is validated using experimental results concerning many systems. iiThis lecture is dedicated to the sacred memory of late Prof. Oleg D. Sherby.

Deformation behavior of thermoplastic elastomer specimens: Observation of the strain behavior in a wide range of tensile speeds

During the tensile testing of thermoplastic elastomers it is difficult to obtain true stress–strain curves because of necking phenomenon. Thus, we conducted a high‐speed tensile testing of Thermoplastic polyester elastomer's (TPC) notched specimens with strain measurement using digital correlation and reported the true stress–strain relations under various tensile speeds in this study. Because notched specimens enable control necking position, TPCs vary depending on the composition and composition ratio of the basic composition of the hard and soft segments. TPCs with two different hardness values (D52 and D57; ASTM D2240) were investigated. In typical TPCs using in this study, the hard and soft segments are composed of a polybutylene terephthalate chain and a polytetramethylene glycol chain, respectively. Because the strain rate and yield stress relationship are known to strongly influence the internal structure of TPCs, the relaxation time behavior depends TPCs' internal structure. In this study, we investigated the strain speed dependence in a TPCs. From the results, we could discuss quantitatively about influence on mechanical properties by changes in the internal structure depended on hard segment and soft segment in necking. POLYM. ENG. SCI., 58:E151–E157, 2018. © 2018 Society of Plastics Engineers

Creep behaviour of intact and remoulded fibrous peat

This paper presents the creep behaviour of intact and remoulded specimens of fibrous peat obtained from a field site near Anzac, Alberta, Canada. The creep behaviour was investigated by means of long-term drained and undrained triaxial tests. The development of volumetric, axial, and undrained axial strain and strain rate during drained and undrained creep tests under variable stress conditions is presented. The stress – strain – strain rate (p′–e v– $$\dot{\varepsilon }_{\text{v}}$$ ) relationship is found to be unique for different stress and loading durations. The p′–e v– $$\dot{\varepsilon }_{\text{v}}$$ relationship is analysed and represented by creep isotaches. The applicability of different creep models developed for normally consolidated clay is discussed and applied to define the development of creep strain in fibrous peat under varying isotropic and deviator stresses. The secondary consolidation coefficient for evaluating the volumetric strain rate of peat is found to be applicable with some limits. The drained creep behaviour of remoulded peat specimens differs from the behaviour shown by Shelby tube specimens, whereas the undrained creep behaviour in remoulded and Shelby tube specimens is similar.

Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment

This paper presents an extensive laboratory investigation of the non-linear rheological mechanical characteristics of hard rock under cyclic incremental loading and unloading. A data processing algorithm is proposed to analyze the experimental data, determine the instantaneous elastic and plastic strain components, visco-elastic and visco-plastic strain components from the total strain, and separate the visco-elastic and visco-plastic strain curves from the total creep strain curves. The elasto-viscoplastic rheological behavior of iherzolite specimens at various confining pressures is thoroughly studied using the obtained experimental data. Based on the data, a non-linear elasto-viscoplastic rheological model containing various deformation components is proposed, by connecting a Hooke body, a parallel combination of Hooke and plastic slide bodies, a Kelvin body, and a generalized Bingham body.The proportion of instantaneous plastic strain component in the total instantaneous strain has increasing tendency with higher deviatoric stress on a whole. The instantaneous elastic modulus of specimen tends to increase with higher deviatoric stress and confining pressure, the instantaneous plastic modulus of specimen is decreased with higher deviatoric stress at confining pressures of 3 and 6MPa on the whole, however, has no evident relationship with deviatoric stress, when confining pressure is increased to 9 and 16MPa. The proportion of the visco-plastic strain component in the creep strain is increased with higher deviatoric stress. The steady-state creep strain rate versus deviatoric stress relationship can be well described with an exponential expression. The elasto-viscoplastic characteristics of radial creep is similar to that of axial creep, but radial creep strain is only 25–30% of axial creep strain, steady-state creep rate in radial direction is about 35% of that in axial direction.

Deformation, diffusion and ductility during creep – continuous void nucleation and creep-fatigue damage

It is shown that the assumption of unit (negative) slope in the well known Monkman–Grant plot of time to failure against minimum creep rate is too restrictive. By acknowledging observed slopes in the range 0.8–1, a ductility–strain-rate relation is deduced where ductility decreases with reducing strain rate. This in turn has implications for the ductility exhaustion method as applied during stress relaxation in the dwell period of low cycle fatigue tests of austenitic steels at elevated temperature. The simple method is used to calculate the cyclic creep damage in typical tests on austenitic steels in the region 550–650 °C and is compared to other calculations as employed in the R5 high temperature assessment procedure. The assumption of a uniform nucleation rate of grain boundary voids with creep strain goes some way to predicting the slope of the ductility–strain-rate relation. Both the ‘unconstrained’ and ‘constrained’ (lower shelf) regions of void growth are discussed.

Isotach Elastoplasticity: A Case Study on Osaka Bay Clay

The theory of isotach elastoplasticity (IEP) is applied to investigate the strain rate and time effects in Osaka Bay clay from Japan. The IEP theory considers geomaterials like clays as an overdamped oscillatory physical system, for which the strain rate (analogous to the vibration frequency) decays in an exponential manner. This feature can be captured by a characteristic strain rate and time relationship. The evolutionary change of strain rate is found to affect the mechanical response of soft clays in an isotach manner. A loading–isotach (LI) yield curve is proposed in the stress and strain rate plane. Combination of the characteristic strain rate and time relationship in an isotach manner into the framework of critical state soil mechanics renders an isotach (rate-dependent) elastoplastic (IEP) constitutive model. A total of 9 model parameters is required, and their values can be properly determined via conventional laboratory tests. The validity of the proposed IEP is demonstrated using experimental data for Osaka Bay clay under various stress paths and strain rates, namely, long-term creep, constant rate of strain loading, relaxation, and their combination. Comparison of the model predictions and experimental results demonstrates that the theory of isotach elastoplasticity can be successfully applied to capture the strain rate and time effects on the mechanical behaviour of Osaka Bay clay.

Material Model for Creep-Assisted Microcracking Applied to S2 Sea Ice

A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.

An isotach elastoplastic constitutive model for natural soft clays

The time and strain rate dependency observed in natural soft clays is formulated within the framework of conventional elastoplasticity. Creep of soft clays is essentially like the response of an overdamped oscillatory system, i.e., the strain rate decays in an exponential manner. A characteristic strain rate and time relationship is presented based on data from creep tests on a large number of different soft clays. The evolutionary change of strain rate is found to affect the mechanical response of soft clays in an isotach manner. Taking strain rate as another stress-like variable, a loading–isotach (LI) yield curve is proposed, which describes the combined hardening mechanisms of loading and variation of strain rate. Incorporation of this LI yield curve into critical state soil mechanics results in an isotach elastoplastic (IEP) model in triaxial stress–strain–strain rate space, which has been dubbed ‘Hunter Clay’. The effects of fabric anisotropy and inter-particle cementation, which are typical features of natural soft clays, are also introduced to produce an advanced hierarchical constitutive model for soft clay. Qualitative predictions are first described and compared with the characteristic behaviour of natural soft clays. Experimental validations using test data for two soft clays are then carried out, and comparisons of the model predictions and experimental data demonstrate the capability of the model in reproducing realistic behaviour of natural soft clays. This work confirms that the complex mechanical behaviour of natural soft clays can be reproduced satisfactorily within the general framework of classical plasticity theory.

Closure to “Settlement of the Kansai International Airport Islands” by G. Mesri and J. R. Funk

Closure to “Settlement of the Kansai International Airport Islands” by G. Mesri and J. R. Funk