Mechanical behavior of nanorubber reinforced epoxy over a wide strain rate loading

Nanorubber/epoxy composites containing 0,2,6 and 10 wt%nanorubber are subjected to uniaxial compression over a wide range of strain rate from 8×10^(-4) s^(-1) to~2×10^(4) s^(-1).Unexpectedly,their strain rate sensitivity and strain hardening index increase with increasing nanorubber content.Potential mechanisms are proposed based on numerical simulations using a unit cell model.An increase in the strain rate sensitivity with increasing nanorubber content results from the fact that the nanorubber becomes less incompressible at high strain,generating a higher hydro-static pressure.Adiabatic shear localization starts to occur in the epoxy under a strain rate of 22,000 s^(-1) when the strain exceeds 0.35.The presence of nanorubber in the epoxy reduces adiabatic shear localization by preventing it from propagating.

Present-day Upper-crustal Strain Rate Field in Southeastern Tibet and its Geodynamic Implications:Constraints from GPS Measurements with ABIC Method

The Earth’s surface kinematics and deformation are fundamental to understanding crustal evolution.An effective research approach is to estimate regional motion field and deformation fields based on modern geodetic networks.If the discrete observed velocity field is obtained,the velocity related fields,such as dilatation rate and maximum shear strain rate,can be estimated by applying varied mathematical approaches.This study applied Akaike's Bayesian Information Criterion(ABIC)method to calculate strain rate fields constrained by GPS observations in the southeast Tibetan Plateau.Comparison with results derived from other three methods revealed that our ABIC-derived strain rate fields were more precise.The maximum shear strain rate highlighted the Xianshuihe–Xiaojiang fault system as the main boundary for the outward migration of material in southeastern Tibet,indicating rotation of eastern Tibet material around the eastern Himalaya rather than whole extrusion along a fixed channel.Additionally,distinct dilatation rate patterns in the northeast and southwest regions of the fault system were observed.The northeast region,represented by the Longmenshan area,exhibited negative dilatational anomalies;while the southwest region,represented by the Jinsha River area north of 29°N,displayed positive dilatational anomalies.This indicates compression in the former and extension in the latter.Combined with deep geophysical observations,we believe that the upper and lower crusts of the Jinsha River area north of 29°N are in an entire expanding state,probably caused by the escape-drag effect of material.The presence of a large,low-viscosity region south of 29°N may not enable the entire escape of the crust,but instead result in a differential escape of the lower crust faster than the upper crust.

Spalling characteristics of high-temperature treated granitic rock at different strain rates

The dynamic spalling characteristics of rock are important for stability analysis in rock engineering.This paper presented an experimental investigation on the dynamic spalling characteristics of granite with different temperatures and strain rates.A series of dynamic spalling tests with different impact velocities were conducted on thermally treated granite at different temperatures.The dynamic spalling strengths of granite with different temperatures and strain rates were determined.A model was proposed to correlate the dynamic spalling strength of granite,high temperature and strain rate.The results show that the spalling strength of granite decreases with increasing temperature.Moreover,the spalling strength of granite with a higher strain rate is larger than that with a lower strain rate.The proposed model can describe the relationship among dynamic spalling strength of granite,high temperature and strain rate.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

Experimental and numerical study on dynamic mechanical behaviors of shale under true triaxial compression at high strain rate

High-energy gas fracturing of shale is a novel,high efficacy and eco-friendly mining technique,which is a typical dynamic perturbing behavior.To effectively extract shale gas,it is important to understand the dynamic mechanical properties of shale.Dynamic experiments on shale subjected to true triaxial compression at different strain rates are first conducted in this research.The dynamic stress-strain curves,peak strain,peak stress and failure modes of shale are investigated.The results of the study indicate that the intermediate principal stress and the minor principal stress have the significant influence on the dynamic mechanical behaviors,although this effect decreases as the strain rate increases.The characteristics of compression-shear failure primarily occur in shale subjected to triaxial compression at high strain rates,which distinguishes it from the fragmentation characteristics observed in shale under dynamic uniaxial compression.Additionally,a numerical three-dimensional Split Hopkinson Pressure Bar(3D-SHPB),which is established by coupling PFC3D and FLAC3D methods,is validated to replicate the laboratory characteristics of shale.The dynamic mechanical characteristics of shale subjected to different confining stresses are systematically investigated by the coupling PFC3D and FLAC3D method.The numerical results are in good agreement with the experimental data.

A novel fractal-statistical scaling model of rocks considering strain rate

The scaling-dependent behaviors of rocks are significant to the stability and safe operation of the structures built in or on rock masses for practical engineering.Currently,many size effect models are employed to connect laboratory measurements at small scales and engineering applications at large scales.However,limited works consider the strain rate effect.In this study,an fractal-statistical scaling model incorporating strain rate is proposed based on a weakest-link approach,fractal theory and dynamic fracture mechanics.The proposed scaling model consists of 8 model parameters with physical meaning,i.e.rate-dependent parameter,intrinsic material parameter,dynamic strain rate,quasi-static strain rate,quasi-static fracture toughness,micro-crack size,micro-crack intensity and fractal dimension,enabling the proposed scaling model to model the scaling behaviors under different external conditions.Theoretical predictions are consistent with experimental data on red sandstone,proving the reliability and effectiveness of the proposed scaling model.Thus,the scaling behaviors of rocks under dynamic loading conditions can be captured by the proposed fractal-statistical scaling model.The sensitivity analysis indicates that the nominal strength difference becomes more obvious with a higher strain rate,larger fractal dimension,smaller micro-crack size or lower micro-crack intensity.Therefore,the proposed scaling model has the potential to capture the scaling behaviors considering the thermal effect,weathering effect,anisotropic characteristic etc.,as the proposed scaling model incorporated model parameters with physical meaning.The findings of this study are of fundamental importance to understand the scaling behaviors of rock under dynamic loading condition,and thus would facilitate the appropriate design of rock engineering.

Strain Rate Effect of AE Characteristics in the Whole Process of Uniaxial Tensile of Mortar

We completed the uniaxial tensile test of mortar in the range of strain rate from 10^(-6)to 10^(-4)s^(-1)in the section containing softening,and carried out acoustic emission monitoring(AE)simultaneously.A series of AE parameters and spectrum analysis methods were used to identify the damage evolution process and cracking mechanism of mortar at different strain rates.The results show that,with the increase of strain rate,the peak stress and tensile elastic modulus of mortar increase obviously,and the stress level corresponding to the starting point of AE activity increases significantly as well,which indicates that the mechanical properties and AE characteristics of mortar have obvious strain rate effect.With the increase of strain rate,the cumulative AE hit decreases gradually,while the average AE hit rate increases significantly,indicating that the increase of strain rate reduces the damage degree of internal microstructure of the specimen,but the crack propagation speed increases.In the pre-peak stress stage,the average of AE ringing count and signal energy decreases with the increase of strain rate,while the average of duration increases;in the post-peak stress stage(f_(t)-30%f_(t)),the average of the three AE parameters all increase with the increase of strain rate,indicating that the strain rate effect on the damage process of mortar is different before and after peak stress,and the damage mechanism represented by different parameters is also different.In the whole process of uniaxial tensile of mortar,with the increase of strain rate,the scatter distribution of AE frequency-amplitude becomes more discrete,and the b-value shows a decreasing trend.In addition,the average level of AE peak frequency decreases with the increase of strain rate,while that of ca8 band wavelet energy spectrum coefficient increases.It is indicated that the increase of strain rate enables the crack propagation state of mortar specimen to become unstable,and the width of macrocrack increases but the proportion decreases.

Productive Traits and Triploid Rate Stability in Triploidy-Induced ‘Haida No. 2’ Strain of the Pacific Oyster, Crassostrea gigas

In order to evaluate the effects of triploidy induction on a selected strain‘Haida No.2’of the Pacific oyster Crassostrea gigas,which is characterized with golden shell color and high growth rate,the growth,survival rate and stability of triploid rate were analyzed at different development stages in the present study.Three different conditions inhibiting the release of polar body Ⅱ or polar body Ⅰ were tested:(A)Cytochalasin-B(CB),0.5mg L^(−1) at 10min post-insemination for 15 min;(B)CB,0.5mg L^(−1)at 15 min postinsemination for 20 min;and(C)CB,0.7mg L^(−1),at 15 min post-insemination for 20 min.The triploidy induction treatments significantly reduced the D-larvae and survival rates at the larvae stage but not at the juvenile and adult stages.Triploid rate dramatically decreased at the larval stage and did not significantly change at the juvenile and adult stages.Regarding the stability of the triploid rate,there was a significant difference between the three treatment groups.Larvae from the treatment A and control groups exhibited higher growth rates in shell height than those from the other two treatment groups at day 27.Triploid juveniles and adults from the treatment A group exhibited a higher wet weight than diploids from the control group and triploids from the other treatment groups.Triploidy induction did not affect the shell color of the progeny.The results obtained in the study demonstrate that triploidy induction has the potential to be used to increase the production of C.gigas variety‘Haida No.2’without modifying its golden shell color.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

The strain rate sensitive and anisotropic behavior of rare-earth magnesium alloy ZEK100 sheet

To overcome the limitation in formability at room temperature,manufacturers have developed magnesium alloys with remarkable properties by adding rare-earth elements.The rare-earth magnesium alloys behave differently from the conventional alloys,especially with respect to their coupled anisotropic and strain rate sensitive behavior.In the current work,such behavior of the rare-earth Mg alloy ZEK100 sheet at room temperature is investigated with the aid of the elastic viscoplastic self-consistent polycrystal plasticity model.Different strain rate sensitivities(SRSs)for various deformation modes are employed by the model to simulate the strain rate sensitive behaviors under different loading directions and loading rates.Good agreement between the experiments and simulations reveals the importance and necessity of using different SRSs for each deformation mode in hexagonal close-packed metals.Furthermore,the relative activities of each deformation mode and the texture evolution during different loadings are discussed.The anisotropic and strain rate sensitive behavior is ascribed to the various operating deformation modes with different SRSs during loading along different directions.

Strain-Rate Dependency of a Unidirectional Filament Wound Composite under Compression

This article presents the results of experimental studies concerning the dynamic deformation and failure of a unidirectional carbon fiber reinforced plastic(T700/LY113)under compression.The test samples were manufactured through the filament winding of flat plates.To establish the strain rate dependencies of the strength and elastic modulus of the material,dynamic tests were carried out using a drop tower,the Split Hopkinson Pressure Bar method,and standard static tests.The samples were loaded both along and perpendicular to the direction of the reinforcing fiber.The applicability of the obtained samples for static and dynamic tests was confirmed through finite elementmodeling and the high-speed imaging of the deformation and failure of samples during testing.As a result of the conducted experimental studies,static and dynamic stress-strain curves,time dependencies of deformation and the stress and strain rates of the samples during compression were obtained.Based on these results,the strain rate dependencies of the strength and elasticity modulus in the strain rate range of 0.001-6001/s are constructed.It is shown that the strain rate significantly affects the strength and deformation characteristics of the unidirectional carbon fiber composites under compression.An increase in the strain rate by 5 orders of magnitude increased the strength and elastic modulus along the fiber direction by 42%and 50%,respectively.Perpendicular loading resulted in a strength and elastic modulus increase by 58%and 50%,respectively.The average strength along the fibers at the largest studied strain rate was about 1000MPa.The obtained results can be used to design structural elements made of polymer composite materials operating under dynamic shock loads,as well as to build models of mechanical behavior and failure criteria of such materials,taking into account the strain rate effects.

Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory

To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity.

Effect of Strain Rate on Tensile Behavior of Sn-9Zn-xAg-ySb;{(x, y) = (0.2, 0.6), (0.2, 0.8), (0.6, 0.2), (0.8, 0.2)} Lead-Free Solder Alloys

The tensile properties of Sn-9Zn-xAg-ySb;{(x, y) = (0.2, 0.6), (0.2, 0.8), (0.6, 0.2), (0.8, 0.2)} lead-free solders were investigated. All the test samples were annealed at 150°C for 1 hour. The tests are carried out at room temperature at the strain rate of 4.17 × 10-3 s-1, 20.85 × 10-3 s-1, and 208.5 × 10-3 s-1. It is seen that the tensile strength increases and the ductility decrease with increasing the strain rate over the investigated range. From the strain rate change test results, the strain sensitivity values are found in the range of 0.0831 to 0.1455 due to the addition of different alloying elements.

Bending Failure Mode and Prediction Method of the Compressive Strain Capacity of A Submarine Pipeline with Dent Defects

A dent is a common type of defects for submarine pipeline.For submarine pipelines,high hydrostatic pressure and internal pressure are the main loads.Once pipelines bend due to complex subsea conditions,the compression strain capacity may be exceeded.Research into the local buckling failure and accurate prediction of the compressive strain capacity are important.A finite element model of a pipeline with a dent is established.Local buckling failure under a bending moment is investigated,and the compressive strain capacity is calculated.The effects of different parameters on pipeline local buckling are analyzed.The results show that the dent depth,external pressure and internal pressure lead to different local buckling failure modes of the pipeline.A higher internal pressure indicates a larger compressive strain capacity,and the opposite is true for external pressure.When the ratio of external pressure to collapse pressure of intact pipeline is greater than 0.1,the deeper the dent,the greater the compressive strain capacity of the pipeline.And as the ratio is less than 0.1,the opposite is true.On the basis of these results,a regression equation for predicting the compressive strain capacity of a dented submarine pipeline is proposed,which can be referred to during the integrity assessment of a submarine pipeline.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Based on governing equations of saturated porous media and Liapunov＇ s stability here, onset conditions matrix of porous media used by solid stress and Terzaghi＇s effective stress constitutive description under seepage flow state, are presented, which have different forms with different representation of the solid phase, matrix or skeleton, constitutive model of porous media. The main difference relates with how to describe the interaction between solid phase and liquid phase in constitutive model. The derived onset condition of strain localization under Terzaghi＇ s effective stress description can be used to interpret different failure types, piping effect, landslides and mudflows, by means of the type and the magnitude ratio of relative movement between solid phase and liquid phase. Examples here illuminate the onset condition of how to work.

Effect of Strain－Rate Sensitivity on Deformation Localization in Porous Materials

The deformation localization in strain-rate sensitive porous materials is analyzed based on the lower bound approach proposed by the author. The retarding effect of material viscosity on deformation localization and the influence of the material strain-rate sensitivity factor on the critical strain to localized necking and the shear localization are investigated. Consideration concerning the material inhomogeneity and the void nucleation effect is also given. Finally the fracture strains of the plane strain tension specimens of AISI4340 steels are calculated and the results are compared with those of the experiment and of Gurson's equations.

Strength characteristics of dry and saturated rock at different strain rates

The strength of rock materials is largely affected by water and loading conditions, but there are few studies on mechanical properties of saturated rocks at high strain rates. Through compressive tests on dry and saturated sandstone specimens, it was found that the dynamic compressive strength of both dry and saturated sandstone specimens increased with the increase of strain rates. The saturated rock specimens showed stronger rate dependence than the dry ones. The water affecting factor （WAF）, as the ratio of the strength under dry state to that under saturated state, was introduced to describe the influence of water on the compressive strength at different strain rates. The WAF under static load was close to 1.38, and decreased with the increase of strain rate. When the strain rate reached 190 s^-1, the WAF reduced to 0.98. It indicates that the compressive strength of saturated specimens can be higher than that of dry ones when the strain rate is high enough. Furthermore, the dual effects of water and strain rate on the strength of rock were discussed based on sliding crack model, which provided a good explanation for the experimental results.

Influence of strain rate on microstructure and formability of AZ31B magnesium alloy sheets

The effects of strain rate on microstructure and formability of AZ31B magnesium alloy sheets were investigated through uniaxial tensile tests and hemispherical punch tests with strain rates of 10^-4, 10^-3, 10^-2, 10^-1 s^-1 at 200℃. The results show that the volume fraction of dynamic recrystallization grains increases and the original grains are gradually replaced by recrystallization grains with the strain rate decreasing. A larger elongation and a smaller r-value are obtained at a lower strain rate, moreover the erichsen values become larger with the strain rate reducing, so the formability improves. This problem arises in part from the enhanced softening and the coordination of recrystallization grains during deformation.

Flow behavior and microstructure of ZK60 magnesium alloy compressed at high strain rate

Flow behavior and microstructure of a homogenized ZK60 magnesium alloy were investigated during compression in the temperature range of 250-400 ℃ and the strain rate range of 0.1-50 s^-1. The results showed that dynamic recrystallization （DRX） developed mainly at grain boundaries at lower strain rate （0.1-1 s^-1）, while in the case of higher strain rate （10-50 s^-1）, DRX occurred extensively both at twins and grain boundaries at all temperature range, especially at temperature lower than 350 ℃, which resulted in a more homogeneous microstructure than that under other deformation conditions. The DRX extent determines the hot workability of the workpiece, therefore, hot deformation at the strain rate of 10-50 s^-1 and in the temperature range of 250-350 ℃ was desirable for ZK60 alloy. Twin induced DRX during high strain rate compression included three steps. Firstly, twins with high dislocation subdivided the initial grain, then dislocation arrays subdivided the twins into subgrains, and after that DRX took place with a further increase of strain.