Strain Rate Dependence Of Strength Research Articles

Effect of Displacement Rate on Sharp Millimeter Indentation

Indentation is widely used to investigate the elastic and plastic properties of materials, which include strain rate dependence. However, the results of the general micro-indentation test were affected by the microscopic scale of materials (e.g., surface roughness, and crystal grain size distribution), since the displacement was small. In the present study, we develop the sharp millimeter indention expanded displacement without the microscopic scale of materials. Furthermore, the effect of displacement rate on the sharp millimeter indentation was evaluated using the quasi-static and impact indentation test. In this study, high purity aluminum, with 99.99 mass%, was selected as the material with strain rate dependence of strength. The quasi-static indentation test was performed using the universal testing machine at the displacement rate of 8.3×10-7 m/s, 8.3×10-6 m/s, and 8.3×10-5 m/s. The impact indention was carried out at the displacement rate of approximately 3×100 m/s. The loading curvature decreased with increasing displacement immediately after indentation, and then this value was convergent, regardless of the displacement rate. It was clear that this convergent value was affected by the displacement rate.

An Extended Mohr–Coulomb Model for Fracture Strength of Intact Brittle Materials Under Ultrahigh Pressures

An extended Mohr–Coulomb model is proposed to represent the pressure‐dependent strength of intact structural ceramics under quasi‐static and dynamic loading rates at high pressures. A plot of normalized shear stress versus hydrostatic pressure for a range of structural ceramics revealed that despite the differences in material properties, test methods, and strain rates, the failure strength data fall in a narrow range, which can be represented by a unified model. The overall deformation behavior of structural ceramics and their strain rate dependence of strength in multiaxial loading at high pressure beyond Hugoniot elastic limit (HEL) can be explained by an exponential pressure dependence in the Mohr–Coulomb model. The analysis also suggests that the influence of strain rate on strength of a ceramic diminishes with increase in confinement pressure.

Effect of dynamic strain rate on micro-indentation properties of pure aluminum

Indentation is widely used to investigate the elastic and plastic properties of mechanical materials, which includes the strain rate sensitivity. The indentation exhibits an inhomogeneous strain distribution in contrast to compression and tensile tests with homogeneous deformation. Thus, the strain rate of the indentation may form the inhomogeneous distribution. Therefore, the effect of strain rate distribution of the indentation on pure aluminum with respect to the strain rate dependence of strength in order to clarify the effect of the strain rate on the indentation technique. First, the numerical simulation was established using the Cowper-Symonds equation as the dynamic constitutive equation. Secondary, the strain rate distribution was calculated from the equivalent plastic strain distribution. The strain rate distribution was quite different from the strain distribution, which showed that the strain rate at the crater rim was higher than that beneath the indenter. Finally, we try to perform the averaging of strain rate distribution in order to make an index of strain rate in the indentation. The average of strain rate distribution was calculated using the equivalent plastic strain above a boundary value that is the critical strain and the representative strain. There is correlation between the average strain rate and the loading curvature, which shows that the average strain rate can express as the representative of strain rate for the indentation technique.

鋭い圧子押込みにおける応答曲面法を用いたCowper-Symonds構成式定数の決定

Instrumented indentation is widely used to investigate the elastic and plastic properties of mechanical materials. During an indentation experiment, a rigid indenter penetrates normally into a homogeneous solid, where the indentation load and the displacement are continuously recorded during loading and unloading. It was known that the micro-indentation test was strongly affected by the strain rate in the materials with strain rate dependence of strength. In the second report, the new approach for the evaluation of the strain rate dependence of materials was developed using the loading curvature-displacement relation obtained from the sharp indentation. Therefore, we attempted to use the response surface method in order to determine the constants for Cowper-Symonds constitutive equation (dynamic constants). First, the relationship between the dynamic constants and the loading curvature was constructed by the response surface, and then those were determined using the inverse analysis. It was confirmed that the dynamic constants could be obtained by substituting the result of the micro-indentation for the unknown materials into the response surface up to the strain rate of 102 s-1. By using this method, it is possible to evaluate the strain rate dependence of materials in such a strain rate range.

Selected Topics on Material Strength and Thermally Activated Deformation Processes

Thermally activated deformation processes are discussed with reference to the studies done by the present author and his coworkers. First, dislocation motion in one- and two-dimensional periodic stress fields is analyzed to understand the deformation mechanisms of bcc metals and spinodally decomposed alloys. The role of the thermally activated kink-pair formation on the temperature and strain-rate dependence of strength is also discussed. Secondly, diffusion-controlled processes pertinent to high-temperature deformation are discussed by applying a unified and fundamental rate equation derived previously. Thirdly, mechanisms for the temperature and strain-rate dependence of polycrystals and ultrafinegrained and nanocrystalline materials are introduced. A proposed model taking into account the thermally activated dislocation depinning at grain boundaries is discussed. [doi:10.2320/matertrans.M2014386]

Characterization of Kota Sandstone Under Different Strain Rates in Uniaxial Loading

Quasi-static to dynamic compression behavior of Kota sandstone is investigated herein under low (0.00001–0.1/s) and medium (1/s) strain rates in order to characterize the rate-dependent stress–strain response of the sandstone found in the region of Kota in India. Both quasi-static and dynamic tests are performed in a universal testing machine. From the stress–strain response of Kota sandstone, the effect of strain rate on peak stress, failure strain and modulus of elasticity have been studied. It is observed that with the increase in strain rate, the peak stress of sandstone increases. The failure strain and the modulus of elasticity also increase with increase in strain rate. Conversely, peak stress decreases for the tests which are carried out at a rate slower than usual static test. The strength increase factor of Kota sandstone, namely the dynamic increase factor (DIF) has been calculated. Based on the results obtained from the tests conducted on the sandstone, an empirical equation has been developed for correlating the DIF with the applied strain rates. Further, effect of rock sample diameter and aspect ratio on strain rate dependent strength of rock has been studied. Correction equations have been developed for taking into account the effect of sample sizes as per the ASTM D7012-13 on the peak stress in Kota sandstone.

Molecular Dynamics Simulations and Continuum Modeling of Temperature and Strain Rate Dependent Fracture Strength of Graphene With Vacancy Defects

We investigated the temperature and strain rate dependent fracture strength of defective graphene using molecular dynamics and an atomistic model. This atomistic model was developed by introducing the influence of strain rate and vacancy defects into the kinetics of graphene. We also proposed a novel continuum based fracture mechanics framework to characterize the temperature and strain rate dependent strength of defective sheets. The strength of graphene highly depends on vacancy concentration, temperature, and strain rate. Molecular dynamics simulations, which are generally performed under high strain rates, exceedingly overpredict the strength of graphene at elevated temperatures. Graphene sheets with random vacancies demonstrate a singular stress field as in continuum fracture mechanics. Molecular dynamics simulations on the crack propagation reveal that the energy dissipation rate indicates proportionality with the strength. These findings provide a remarkable insight into the fracture strength of defective graphene, which is critical in designing experimental and instrumental applications.

Impact Compressive Properties of Foamed Film with Closed Cell

The compressive properties of foamed polyethylene (PE) film with a closed cell for electronic devices have been investigated. A commercial closed cell foamed PE film with a density of 330 kg/m3 was used. Quasi-static testing was carried out at strain rates of 10−3 to 10−1 s−1. The strain rate of the impact test was approximately 105 s−1 by means of split Hopkinson pressure bar method. Within the set of experiments, the compressive stress increased with the strain rate in both the quasi-static and impact test. In particular, the flow stress increased substantially with the increasing strain rate in the impact deformation. At strains of less than 0.4, the trapped air was locally compressed within the cells, which led to the strain rate dependency of strength in the quasi-static test and the impact test.

材料強度と熱活性化変形過程に関する若干の考察

Thermally activated deformation processes are discussed with reference to the studies done by the present author and his coworkers. First, dislocation motion in one- and two-dimensional periodic stress fields is analyzed to understand the deformation mechanisms of bcc metals and spinodally decomposed alloys. The role of the thermally activated kink-pair formation on the temperature and strain-rate dependence of strength is also discussed. Secondly, diffusion-controlled processes pertinent to high-temperature deformation are discussed by applying a unified and fundamental rate equation derived previously. Thirdly, mechanisms for the temperature and strain-rate dependence of polycrystals and ultrafinegrained and nanocrystalline materials are introduced. A proposed model taking into account the thermally activated dislocation depinning at grain boundaries is discussed. [doi:10.2320/matertrans.M2014386]

Effect of High Strain Rate on Indentation in Pure Aluminum

The indentation properties of pure aluminum (99.9%, 3N aluminum) and high purity aluminum (99.999%, 5N aluminum) with respect to the strain rate dependence of strength are experimentally investigated in order to clarify the effect of strain rate on the micro-indentation test. A micro-indentation test using a Berkovich indenter was performed at loading rates of 0.7, 7, and 70 mN/s. In all of the specimens, the indenter was loaded to a maximum value of 1200 mN, and then was maintained for 30 s. In the 3N specimen, the dependence of the loading rate on the load was slight at loading rates of 0.7 and 7 mN/s, whereas the load at the loading rate of 70 mN/s was higher than the loads at loading rates of 0.7 and 7 mN/s. On the other hand, the load for the 5N specimen increased with the increasing loading rate. Thus, the effect of the loading rate on the load-displacement curve for the 3N and 5N specimens was similar to the strain rate dependence of strength for theses metals. In addition, the micro-indentation test was demonstrated to be strongly affected by high strain rate at a loading rate of 70 mN/s.

Interaction forces between pipelines and submarine slides — A geotechnical viewpoint

Assessment of interaction forces between deep water pipelines and potential submarine slides, debris flows and turbidity currents is an important aspect of geohazard studies. Historically, interaction forces have tended to be expressed in terms of drag factors, within a traditional fluid mechanics framework, with the drag factors depending strongly on an equivalent Reynolds number for the non-Newtonian debris material. Here, we have followed a more geotechnical approach, allowing the interaction forces to be expressed in terms of a strain-rate dependent shear strength of the debris material, and with the inclusion of a drag term (with fixed drag coefficient) for high velocity, low strength, combinations. This superposition approach treats separately the interaction forces that arise from the strain-rate dependent strength and the inertia of the debris, rather than combining them into a single drag force. A failure envelope is proposed, allowing axial and normal interaction forces to be estimated for any angle of attack of the debris flow.

GS20 押込試験による強度のひずみ速度依存性評価の試み

A strain rate effect on load-displacement relation by instrumented a sharp indentation was investigated for pure Aluminum which has high strain rate dependence of strength. When micro-indentation tests were carried out by using a sharp indenter (Berkovich type) at a loading rate of 07-70mN/s the indentation load rose with the loading rate. Finite Element Method was used for the indentation analysis in comparison with experiment. The load increase behavior could be simulated by dynamic FEM with the Cowper-Simonds constitutive equation which includes the strain rate dependence of strength. The FE simulation showed the strain rate under the indenter reaches dynamic range and it caused the load increase. The strain rate under the indenter depends on not only the loading rate but also the indenter angle. If the relationship between the load increase and the indentation test condition is constructed, the strain rate dependence of strength may be evaluated by indentation test.

Effect of high strain rate on micro-indentation test in pure aluminum

The indentation properties of pure aluminum (99.9%, 3N aluminum) and high purity aluminum (99.999%, 5N aluminum) with respect to the strain rate dependence of strength are experimentally investigated in order to clarify the effect of strain rate on the micro-indentation test. A micro-indentation test using a Berkovich indenter was performed at loading rates of 0.7, 7, and 70 mN/s. In all of the specimens, the indenter was loaded to a maximum value of 1200 mN, and then was maintained for 30 s. In the 3N specimen, the dependence of the loading rate on the load was slight at loading rates of 0.7 and 7 mN/s, whereas the load at the loading rate of 70 mN/s was higher than the loads at loading rates of 0.7 and 7 mN/s. On the other hand, the load for the 5N specimen increased with the increasing loading rate. Thus, the effect of the loading rate on the load-displacement curve for the 3N and 5N specimens was similar to the strain rate dependence of strength for theses metals. In addition, the micro-indentation test was demonstrated to be strongly affected by high strain rate at a loading rate of 70 mN/s.

Determination of strain rate dependent through-thickness tensile properties of textile reinforced thermoplastic composites using L-shaped beam specimens

The presented work focuses on a methodology to characterise strain rate dependent strength and elastic properties of textile reinforced composites in laminate through-thickness direction. Here, for the characterisation L-shaped beam specimens are used. The investigated composite is a fabric reinforced thermoplast made of hybrid E-glass/polypropylene yarns. The analytical solution for the determination of the through-thickness tensile strength as proposed by Lekhnitskii and Shivakumar is verified by means of an optical deformation analysis and is extended for thew determination of the through-thickness elastic modulus. Finally, the possibility of the strain rate dependent characterisation is investigated and a Johnson–Cook based modelling approach is used to represent the apparent strain rate dependency of the through-thickness failure onset. The methodology is successfully used to capture the material strain rate effects with the according strength values and model parameters over a strain rate range of 10 −4 s −1 to 10 s −1 as well as the elastic modulus.

MP-43 純銅の微小押込試験におけるひずみ速度の効果(ポスターセッション)

In order to elucidate the effect of strain rate on indentation load, relationship between micro-indentation test using sharp indenter (Berkovich type) and finite element method (FEM) analysis was investigated in pure copper (rolled and annealed copper). It was shown that the load-displacement curve obtained form the static FEM analysis was inconsistent with that obtained form the micro-indentation test in both the rolled and annealed coppers. On the other hand, in the dynamic FEM analysis (LS-DYNA), Cowper-Symonds model included the strain rate dependency of strength were employed. The calculated load-displacement curves by Cowper-Symonds model showed good agreement with the experimental result in both the coppers.

Plastic bulging of sheet metals at high strain rates

The biaxial bulge test is a material test for sheet metals to evaluate formability and determine the flow stress diagram. Due to the biaxial state of stress induced in this test, the maximum achievable strain before fracture is much larger than in the uniaxial tensile test. A new dynamic bulge testing technique is simulated and analyzed in this study which can be performed on a conventional split Hopkinson pressure bar (SHPB) system to evaluate the strain-rate dependent strength of material at high impact velocities. Polyurethane rubber as pressure carrying medium is used to bulge the OFHC copper sheet. The use of hyperelastic rubber instead of fluid as a pressure medium makes the bulge test simple and easy to perform. The input bar of SHPB is used to apply and measure the bulging pressure. The finite element simulation using ABAQUS/explicit and analytical analysis are compared and show good correlation with each other. The results clearly show that as the strain-rate increases, the strength of the OFHC copper increases. From the study, a robust method to determine the material behavior under dynamically biaxial deformation conditions has been developed.

Thermally activated dislocation depinning at a grain boundary in nanocrystalline and ultrafine-grained materials

As an attempt to understand the temperature and strain-rate dependence of strength in nanocrystalline and ultrafine-grained materials, thermally activated depinning process has been incorporated into a dislocation bow-out model from a grain boundary. Such quantities as activation energy, activation volume, strain-rate sensitivity and yield strength are discussed and compared with experimental results available in literature. It is found that the present model analysis can reasonably explain the observed characteristics of these quantities.

Precipitation in ductile Fe–18Al–5Cr alloys with additions of Mo, W and C and effects on high-temperature strength

The strength of a Fe–Al-based alloy containing small additions of Mo, W and C has been determined from room temperature up to 800 °C, and the strain rate dependence of strength examined. Strength of the as-cast material is maintained at above 600 °C, but it is lost at higher temperatures, especially at slow strain rates. This behaviour is largely explained by solute hardening effects, with no sign of any precipitates forming. After a solution treatment, annealing material at 800 °C leads to the appearance of Fe–Mo–W carbides which provide better strength under conditions of high temperature and slow strain rate. The possibilities for improving high-temperature strength and creep behaviour by the formation of carbide or intermetallic precipitates are discussed.

Temperature–time response of a polymer bonded explosive in compression (EDC37)

The compressive strength of the energetic composition EDC37 has been measured at a temperature of 293 ± 2 K over a range of strain rates from 10−8 to 103 s−1, and at a strain rate of 10−3 s−1 over a range of temperatures from 208 to 333 K. The results show that failure stress is a monotonic function of applied strain rate or temperature, which is dominated by the relaxation properties of the polymeric binder; this is confirmed by dynamic mechanical thermal analysis performed on both EDC37 and its binder. Similarities between the compressive strain rate/temperature data sets can be understood by temperature–time superposition; data collected at a strain rate of 10−3 s−1 over a temperature range 208 to 333 K were mapped onto a plot of strain rate dependent strength at 293 K, using an empirically determined sensitivity of −13.1 ± 0.3 K per decade of strain rate. Sample size was noted to have a modest effect on the stress–strain behaviour; small length to diameter ratios gave results consistent with an increased degree of confinement. Samples taken to large strains exhibited strain localization in the form of shear bands.

Strain rate dependent strength and stress–strain characteristics of a welded tuff

Results of 61 uniaxial compression tests on the welded Topopah Spring tuff are presented. The tests were carried out under constant strain rates at room temperature. Stress–strain analysis indicates that dilatancy and compaction start at about 50% of ultimate strength. A sudden stress drop occurs at about 90% of the ultimate strength, which indicates the onset of specimen failure. Both strength and peak axial strain decrease with strain rate as power functions. Based on the strain rate dependence of strength and peak axial strain, it is inferred that the elastic modulus is strain rate dependent. A relationship between stress, axial strain, and axial strain rate is developed. The parameters in this relation are estimated using multivariate regression to fit stress–axial strain–strain rate data.