Logarithm Of Strain Rate Research Articles

Mechanical properties of geopolymer concrete exposed to dynamic compression under elevated temperatures

Through adoption of a self-designed high temperature SHPB apparatus herein, an experimental study is made on the mechanical properties of geopolymer concrete (GC) exposed to dynamic compression under elevated temperatures. As the results have turned out, the weight loss is remarkable within temperature ranges from room temperature to 200°C as well as from 600°C to 800°C. The dynamic compressive strength of GC grows higher at 200°C than at room temperature, but suffers a dramatic drop at 800°C. The critical strain is higher at elevated temperature than that at room temperature. At 200°C and 600°C, respectively, its energy absorption property is superior to that at room temperature. However, at 400°C and 800°C, respectively, it is inferior to that at room temperature. The strain rate effect of the dynamic increase factor (DIF) obtained from test data can reflect the inherent nature of GC. The DIF assumes a linear relationship with the logarithm of strain rate.

Comparison of the fracture toughness of Cu6Sn5 intermetallic compound as measured by nanoindentation and other methods

In this work, nanoindentation tests using a three-sided Berkovich indenter were performed for a Cu6Sn5 intermetallic compound (IMC) in interfacial specimens of lead-free Sn–3Ag–0.5Cu solder ball joints at room temperature to investigate effect of the strain rate on the mechanical properties of this IMC. The fracture toughness was found to have an approximately linear relationship with the logarithmic nanoindentation strain rate, implying that the fracture toughness decreased in a range of (1.64–0.63) MPam0.5 with an increase in the strain rate ranging from 0.01s−1 to 0.33s−1. This characteristic was similar to the KC values of Cu6Sn5 under shear or tensile tests. It was, however, when measured by nanoindentation tests, found to be less sensitive to the strain rate compared to measurements gained through shear or tensile tests. The results here were discussed and compared to those from other studies.

Determination of Instability in Zr-2.5Nb-0.5Cu Using Lyapunov Function

Hot workability of Zr-2.5Nb-0.5Cu alloy has been investigated by means of hot compression test using Gleeble-3800®, in the temperature and strain rate range of 700 to 925°C and 0.01-10s-1, respectively. Deformation behavior was characterized in terms of flow instability using peak stress with the help of Lyapunov Function. The true stress-strain curves shows that softening occurs at all lower temperature and for entire strain rates of deformation. The instable flow was suggested by negative m value at deformation condition of 700°C (5 and 10 s-1), while s value at 925°C (10 s-1). The combined result of rate of change of m and s with respect to log strain rate suggest that the deformation condition ranges from 725-780°C (10-2- 10-1 s-1) and 700°C (1-10 s-1) representing safe domain for stable flow.

A Modified Eyring Equation for Modeling Yield and Flow Stresses of Metals at Strain Rates Ranging from 10−5to 5 × 104 s−1

In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5to 5 × 104 s−1). This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.

Strain Rate Effect on the Mechanical Behaviour of Sandstones with Different Grain Sizes

Sandstone specimens with different grain sizes were tested under uniaxial compression at a range of strain rates to investigate the coupled influence of strain rate and grain size on the mechanical behaviour of sandstone. Average grain sizes of sandstones were 105.4 µm (fine grained, FG), 228 µm (medium grained, MG) and 321 µm (coarse grained, CG), and the considered strain rates were 10−6, 10−5, 10−4 and 10−3 S−1. We used an optical deformation and strain measuring system for all the tests to determine the deformation characteristics of specimens during loading. The peak strength was observed to increase non-linearly with an increasing gradient against logarithmic strain rate for FG sandstone, while the trend was a linear increase for MG sandstone and unsystematic for CG sandstone. The relationships of elastic modulus versus logarithmic strain rate for the three types of sandstones showed similar trends as for the peak strength. This observation suggests that the FG sandstones are more responsive to strain rate compared to coarser-grained sandstones and this was attributed to the differences in micro-crack development patterns of sandstones with different grain sizes. A surprising behaviour was observed for CG sandstone, which displayed an increase of strength at the slowest strain rate, reversing the general decreasing trend of strength with decreasing strain rate. Stress redistribution associated with grain fracturing was proposed as a possible mechanism to explain this counter-intuitive behaviour. Finally, the results of this paper suggest that the size of constituent grains is a critical parameter that needs to be incorporated in considerations of the mechanical behaviour of sandstones under different strain rates.

Analysis of solidification microstructure and hot ductility of Fe–22Mn–0·7C TWIP steel

The characteristics and evolution of the solidification microstructure of a Fe–0·7C–22Mn (wt-%) TWIP steel was experimentally analysed. The primary dendrite arm space was about 1–2 mm while the diameter of equiaxed grains was about 2–4 mm. Decreasing the Mn concentration was proved beneficial to grains refinement and interdendrite soundness improvement. The tensile strength and yield strength of the concerning TWIP steel were found to be higher than that of C–Mn HSLA steel under as cast conditions above 1073 K, according to the comparison of hot tensile experiment results. It is inferred the solution strengthening effect should be the main explanation for that. The hot ductility of this TWIP steel was observed to be not very favourable, since most of the reduction rates of area were lower than 40%. Obvious drop of the hot ductility within the temperature range from 1073 to 1223 K of this Fe–0·7C–22Mn TWIP steel was determined. Intragranular MnS inclusions and grain boundaries sliding at elevated temperatures should be the main reason, according to the experimental results of optical microscope (OM), scanning electron microscope (SEM) and X-ray diffraction (XRD). Besides, both strength and ductility increased linearly as logarithmic strain rate increased, attributed to the combined effect of strain hardening, dynamic strain aging and dynamic recrystallisation.

Problems associated with use of the logarithmic equivalent strain in high pressure torsion

The logarithmic "equivalent" strain is frequently recommended for description of the experimental flow curves determined in high pressure torsion (HPT) tests. Some experimental results determined at -196 and 190 °C on a 2024 aluminum alloy are plotted using both the von Mises and logarithmic equivalent strains. Three types of problems associated with use of the latter are described. The first involves the lack of work conjugacy between the logarithmic and shear stress/shear strain curves, a topic that has been discussed earlier. The second concerns the problems associated with testing at constant logarithmic strain rate, a feature of particular importance when the material is rate sensitive. The third type of problem involves the "history dependence" of this measure in that the incremental logarithmic strain depends on whether the prior strain accumulated in the sample is known or not. This is a difficulty that does not affect use of the von Mises equivalent strain. For these reasons, it is concluded that the qualifier "equivalent" should not be used when the logarithmic strain is employed to describe HPT results.

Characterization and modeling of polymeric matrix under multi-axial static and dynamic loading

A polymeric foam commonly used in composite sandwich structures was characterized under multi-axial loading at strain rates varying from quasi-static to dynamic. Tests were conducted under uniaxial compression, tension, pure shear and combinations of normal and shear stresses. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson pressure bar (Kolsky bar) system made of polycarbonate bars having an impedance compatible to that of the foam material. The typical compressive stress-strain behavior of the polymeric foam exhibits a linear elastic region up to a yield point, a nonlinear elastic-plastic region up to an initial peak or “critical stress” corresponding to collapse initiation of the cells, followed by strain softening up to a local minimum (plateau or saddle point stress) and finally, a strain hardening region up to densification of the foam. The characteristic stresses of the stress-strain behavior vary linearly with the logarithm of strain rate. A general three-dimensional elastic-viscoplastic model, formulated in strain space, was proposed. The model expresses the multi-axial state of stress in terms of an effective stress, incorporates strain rate effects and includes the large deformation region. Stress-strain curves obtained under multi-axial loading at different strain rates were used to develop and validate the elastic-viscoplastic constitutive model. Excellent agreement was shown between model predictions and experimental results.

Effect of Strain Rate on Tensile Properties of Miniature Size Specimens of Several Lead-Free Alloys

The effect of strain rate on tensile properties of several lead-free solder was investigated using miniature size specimens. High-temperature lead-free solder which are Sn-Cu and Sn-Sb alloys were prepared. Moreover, low-Ag lead-free solder which are Sn-1Ag-0.7Cu (SAC107, mass%) based alloys were prepared. Sn-3Ag-0.5Cu (SAC305) was also prepared for comparison. Tensile strength is proportion to the logarithm of strain rate in all solder investigated. Although 0.1% proof stress decreases at high strain rate in high-temperature solder, it scarcely changes in low-Ag solder. Elongation somewhat increases with increasing strain rate in high-temperature solder. It increases with increasing strain rate in low-Ag solder although it is lower than that of SAC305. Chisel point fracture mainly occurred except Sn-13Sb. In Sn-13Sb, brittle fracture occurred and thus elongation was lower than those of other solder. Sn-8.5Sb and Sn-1Ag-0.7Cu-1Bi-0.2In show mechanical properties similar to SAC305.

Inclusion of Strain-Rate Effects in Low Velocity Impact Simulation of Laminated Composites

Composite materials are widely used in aircraft, automotive, marine and railway applications and are exposed to impact loads, in particular low velocity impact. As material properties of composites are affected by strain-rate [, finite element analysis (FEA) by using static properties would not predict their impact behaviour accurately. Thus, the objective of this study was to include strain-rate effects in the simulation of composite laminates under low velocity impact. This was achieved using ABAQUS anisotropic damage model (ADM) by taking account of material properties changes as a function of log strain-rate using user-defined ABAQUS/VUSDFLD subroutine Strain-Rate Dependent ADM (SRD ADM). Results obtained from SRD ADM were validated using simple tensile test done by Okoli [. Subsequently a three-point bending impact event of a simple composite laminate beam by a cylindrical steel impactor was simulated using both the original ABAQUS Static ADM and the user-defined SRD ADM, and compared with experimental impact test results done by [. The results show that reductions in errors of predicted maximum impact reaction force (compared to experimental data) were achieved from 29% using Static ADM to 14% using SRD ADM and from 35% using Static ADM to 15% using SRD ADM respectively for impactor speeds of 2 ms-1 and 5 ms-1.

The Material Behavior and Fracture Mechanism of a Frangible Bullet Composite

The quasi-static and dynamic compressive mechanical properties of a bullet composite are investigated using the scattered spot technique, an electronic universal testing machine, and a Split—Hopkinson pressure bar. The stress-strain curves under static and dynamic loading are also obtained, and the strain rate effect is analyzed. The rupture structure is observed under a scanning electron microscope, and the microscopic damage mechanism of the bullet composite is examined. Results show that the composite is sensitive to the strain rate, such that the compressive strength of the composite increases with increased strain rate. The relationship of the compressive strength and elastic modulus with the logarithmic strain rate is nonlinear.

Molecular dynamics investigation of the thermomechanical behavior of monolayer GaN

Molecular dynamics simulations are performed on monolayer gallium nitride to study their mechanical behavior at various temperatures in the range of 10 to 1700 K. The transition from brittle to ductile nature has been illustrated from the evolution of fracture at two different temperatures of 700 and 1300 K. Brittle to ductile transition temperatures TBDT are obtained from the plots of logarithm of yield stress and inverse temperature at different strain rates and compared qualitatively with the same system in the presence of single and diatomic vacancies. Logarithm of strain rate against inverse of TBDT thus obtained represents an Arrhenius plot, the slope of which corresponds to the activation energy of dislocation glide that is found to be approximately 2.0 ± 0.05 eV for the present case. This suggests that the brittle to ductile transition is controlled by the dislocation mobility as in the case of other semiconductors like silicon and germanium. This behavior is found to be consistent with the presented underlying models. In addition, thermal conductivities are obtained over a temperature range of 300 to 2000 K from the equilibrium Green-Kubo formulations and compared with the (25,0) nanotube that is generated from the same system of monolayer GaN. The values are found to be decreased in both the cases as compared to the bulk gallium nitride, and the reduction in the values of thermal conductivity can be attributed to the finite size effects, increased surface inelastic scattering, and change of phonon spectrum at low dimensions, respectively.

Characterization and modeling of stain-rate-dependent behavior of polymeric foams

A polymeric foam was characterized under quasi-static and dynamic loading and a constitutive model was proposed to describe its nonlinear behavior at varying strain rates. Four characteristic properties were identified in the compressive stress–strain curves: (1) yield stress, (2) peak or “critical” stress corresponding to collapse initiation of the cells, (3) plateau stress following the initial collapse of the cells, and (4) strain hardening stress at the end of the plateau region and before the onset of densification. All of the above characteristic stresses vary linearly with the logarithm of strain rate. A strain-based nonlinear constitutive model was proposed. A unified (master) constitutive model with built-in strain rate dependence was formulated and was shown to be in very good agreement with experimental results. The master stress–strain response was modeled in two parts, a power law and one consisting of two exponential terms.

Flow Stress Prediction of High-Nb TiAl Alloys under High Temperature Deformation

In this work, a back propagation artificial neural network (BP-ANN) model is conducted to predict the flow behaviors of high-Nb TiAl (TNB) alloys during high temperature deformation. The inputs of the neural network are deformation temperature, log strain rate and strain whereas flow stress is the output. There is a single hidden layer with 7 neutrons in the network, and the weights and bias of the network were optimized by Genetic Algorithm (GA). The comparison result suggests a very good correlation between experimental and predicted data. Besides, the non-experimental flow stress predicted by the network is shown to be in good agreement with the results calculated by three dimensional interpolation, which confirmed a good generalization capability of the proposed network.

Experimental Study on Impact Compression and Spliting of Granite

In order to systematically study on dynamic mechanics character of granite, impact compression experiments and impact flattened Brazilian disc specimens of granite have been investigated with modified split Hopkinson pressure bar (SHPB) experimental facility, curve about stress versus strain and other parameter at strain rates of 23.9/s～108.4/s were obtained from impact compression. The dynamic tensile strength and critical tensile failure strain at strain rates of 2.3/s～25.6/s were obtained from impact flattened Brazilian. The experimental result show that dynamic compression strength , elastic modulus and failure strain，dynamic tensile strength significantly increase comparing to quasi-static experiment, and the above mechanics parameter include dynamic strength etc will increase with strain rate increasing, granite have the character of impact harding and ductility enhancement. The failure degree of failure will increase with increasing strain rate under impact compression; the failure configurations of the specimens present an center splitting mode under impact flattened Brazilian experiments. Whether impact compression or impact splitting under strain rate including this paper ’s experiments, the relationship between the DIFC or DIFT and the logarithm of strain rate is linear.

Dynamic Tensile Properties of Plastics over a Wide Range of Strain Rates

Dynamic tensile properties of a variety of plastics, were studied over a wide range of strain rates from 10-2 s-1 to 103 s-1 by using the Sensing Block Type High Speed Material Testing System (SBTS). The plastics were composed of seven kinds of polycarbonate, eight kinds of polyamide, one kind of polypropylene and acrylic-butadiene-styrene (ABS). It was observed for all the tested plastics, that the flow stress at each plastic strain increased monotonically with the logarithmic strain rate, and also increased linearly over the strain rates from 0.01s-1 to 32 s-1. It was observed that the strain rate sensitivity of the flow stress of these plastics decreased monotonously with the enhanced quasi-static flow stress. These phenomena are similar to those observed frequently for many metallic materials. The plastics were classified tentatively into three groups based on the rate sensitive characteristics. The possibility of expressing these dynamic properties for each group by using Tanimura-Mimura model was discussed.

Investigation on Finite Strain Constitutive Model with Logarithmic Strain Based on Torsion Experiments

In this paper, a finite strain constitutive model was proposed by the additive decomposition of the logarithmic strain rate and the generalization of small deformation constitutive model and a complete analysis was made for an isotropic hardening J2 flowing finite strain constitutive model based on torsion experiments. Logarithmic strain and Jaumann stress rate were discussed in solid circular shaft torsion deformation. Utilizing the results obtained from solid circular shaft torsion experiments, the plastic rigidity function in constitutive model was determined. The simple shear problem was studied by using the constitutive model given in this paper. The results shows that the plastic rigidity function corresponding to logarithmic strain was different from one to Green strain and finite strain constitutive model should be analyzed by logarithmic strain and torsion experiments.

Mechanical Properties of Bulk Nanocrystalline Silver-Using Compression Tests

In this paper, the compression test on the bulk nanocrystalline sliver ( n Ag) with average grain size of 50 nm was made. The stress-strain curves under different strain rates were obtained by test. The test results show that the mechanical behavior of n Ag is rate-dependent, and the dynamic compress yield stress are about 1.5 times of that n Ag in static test condition; The effect of strain harding on n Ag is smaller than that of coarse-grained silver (c Ag) in plastic deformation; The relationship between the yield strength and the logarithm of strain rate is approximately linear.

A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes

A simple phenomenological constitutive model has been proposed to describe dynamic deformation behavior of various metals in wide strain rate, strain, and temperature regimes. The formulation of the model is, σ=[A+B{1−exp(−Cε)}][D ln(ε̇/ε̇0)+exp(E⋅ε̇/ε̇0)][1−(T−Tref)/(Tm−Tref)]m, where σ is the flow stress, ε is the strain, ε̇ is the strain rate, ε̇0 is the reference strain rate, T is the temperature, Tref is the reference temperature, Tm is the melting temperature, and A, B, C, D, E, and m are the material parameters. The proposed model successfully describes not only the linear rise of flow stress with logarithmic strain rate for many metals, but also the upturn of the flow stress at strain rate over about 104 s−1 for the case of copper. It can also describe the exponential increase in the flow stress with logarithmic strain rate for the case of tantalum, and is capable of predicting thermal softening of various metals at high as well as low temperature. The current model can be used for the practical simulation of many high-strain-rate events with improved precision and as a more rigorous comparison standard in the development of a physical model.

Flexural properties and orthotropic swelling behavior of bagasse/thermoplastic composites

The flexural properties of commercial bagasse-filled polyethylene (PE) and polypropylene (PP) composites were determined as a function of strain rate at room temperature. The applied strain rates were 1.5 ×10-4, 3.75×10-4, 7.5×10-4, and 1.5×10-3 s-1. The flexural modulus tended to increase linearly for the two types of composites with the logarithm of strain rate. The bending strength of polypropylene composite also behaved in a similar manner, but the polyethylene composite exhibited different behavior in which the MOR values of polyethylene composite didn’t alter appreciably as a function of strain rate. The flexural response of a polypropylene-based composite was found to exhibit higher dependency on strain rate than a polyethylene-based composite. Water absorption of both composites followed the kinetics of a Fickian diffusion process. Water absorption and dimensional instability of PE-based composites were lower than those of PP-based composites. The highest swelling took place in the thickness of the samples, followed by the width and length, respectively.