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.

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.

Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Anisotropic dynamic permeability model for porous media

Based on the tortuous capillary network model,the relationship between anisotropic permeability and rock normal strain,namely the anisotropic dynamic permeability model(ADPM),was derived and established.The model was verified using pore-scale flow simulation.The uniaxial strain process was calculated and the main factors affecting permeability changes in different directions in the deformation process were analyzed.In the process of uniaxial strain during the exploitation of layered oil and gas reservoirs,the effect of effective surface porosity on the permeability in all directions is consistent.With the decrease of effective surface porosity,the sensitivity of permeability to strain increases.The sensitivity of the permeability perpendicular to the direction of compression to the strain decreases with the increase of the tortuosity,while the sensitivity of the permeability in the direction of compression to the strain increases with the increase of the tortuosity.For layered reservoirs with the same initial tortuosity in all directions,the tortuosity plays a decisive role in the relative relationship between the variations of permeability in all directions during pressure drop.When the tortuosity is less than 1.6,the decrease rate of horizontal permeability is higher than that of vertical permeability,while the opposite is true when the tortuosity is greater than 1.6.This phenomenon cannot be represented by traditional dynamic permeability model.After the verification by experimental data of pore-scale simulation,the new model has high fitting accuracy and can effectively characterize the effects of deformation in different directions on the permeability in all directions.

Mechanical properties and fracture surface roughness of thermally damaged granite under dynamic splitting

In order to understand the mechanical properties and the fracture surface roughness characteristics of thermally damaged granite under dynamic splitting,dynamic Brazilian splitting tests were conducted on granite samples after thermal treatment at 25,200,400,and 600℃.Results show that the dynamic peak splitting strength of thermally damaged granite samples increases with increasing strain rate,showing obvious strain‐rate sensitivity.With increasing temperature,thermally induced cracks in granite transform from intergranular cracks to intragranular cracks,and to a transgranular crack network.Thermally induced damages reduce the dynamic peak splitting strength and the maximum absorbed energy while increasing the peak radial strain.The fracture mode of the thermally damaged granite under dynamic loads is mode Ⅱ splitting failure.By using the axial roughness index Z2 a,the distribution ranges of the wedge‐shaped failure zones and the tensile failure zones in the fracture surfaces under dynamic Brazilian splitting can be effectively identified.The radial roughness index Z_(2)^(r)is sensitive to the strain rate and temperature.It shows a linear correlation with the peak splitting strength and the maximum absorbed energy and a linear negative correlation with the peak radial strain.Z_(2)^(r)can be used to quantitatively estimate the dynamic parameters based on the models proposed.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Strain effects on Li^(+) diffusion in solid electrolyte interphases:A molecular dynamics study

Dilithium ethylene dicarbonate(Li_(2)EDC) and dilithium butylene dicarbonate(Li_(2)BDC) are the common organic compositions of the solid electrolyte interphase(SEI) layers in rechargeable lithium-ion batteries.The Li^(+) diffusion in the amorphous and ordered phases of Li_(2) EDC and Li_(2) BDC under various strains has been investigated by using molecular dynamics simulations.It is found that different strains lead to diverse changes in Li^(+) diffusivity.The tensile strain makes the Li+diffusion coefficients increase in amorphous and ordered Li_(2)EDC or Li_(2) BDC,and the compressive strain makes the Li+diffusion coefficients decrease in them.The average Li+coordination number calculation,ion conductivity calculation and the calculation of the residence autocorrelation function in amorphous and ordered Li_(2)EDC or Li_(2)BDC are performed to further analyze the strain effects on Li^(+) transport in them.The factors influencing Li^(+) diffusion in amorphous and ordered Li_(2)EDC or Li_(2) BDC under the strain are discussed.

Molecular dynamics study on the dependence of thermal conductivity on size and strain in GaN nanofilms

The thermal conductivity of GaN nanofilm is simulated by using the molecular dynamics(MD)method to explore the influence of the nanofilm thickness and the pre-strain field under different temperatures.It is demonstrated that the thermal conductivity of GaN nanofilm increases with the increase of nanofilm thickness,while decreases with the increase of temperature.Meanwhile,the thermal conductivity of strained GaN nanofilms is weakened with increasing the tensile strain.The film thickness and environment temperature can affect the strain effect on the thermal conductivity of GaN nanofilms.In addition,the analysis of phonon properties of GaN nanofilm shows that the phonon dispersion and density of states of GaN nanofilms can be significantly modified by the film thickness and strain.The results in this work can provide the theoretical supports for regulating the thermal properties of GaN nanofilm through tailoring the geometric size and strain engineering.

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

This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.

Effect of Dynamic Strain Aging on Hardness in the Heat-Affected Zone of SUS316 Steel Welds

DSA(dynamic strain aging)phenomenon in SUS316 steel was investigated using isothermal and non-isothermal tensile tests of simulated HAZ(heat-affected zone)thermal cycles.Isothermal tensile tests were performed on SUS316 in the peak temperature range of 20-700°C,with strain rates varying from 4.2×10^(-3)to 4.2×10^(-5)s^(-1).Based on the appearance of discontinuous plastic flows,expressed as serrations,and the hardening phenomenon of the tensile samples,the conditions for the occurrence of DSA in the SUS316 steel were investigated.Furthermore,the extent of hardening due to DSA was evaluated by comparing the hardness values of the SUS316 and SUS316EHP steels after the tensile tests.To confirm the effect of DSA on hardness in the HAZ of the welded SUS316 steel,non-isothermal tensile tests of the simulated HAZ thermal cycles were performed using a Thermec Master.The relationship between the increase in Vickers hardness due to DSA and the strain in the HAZ was determined;the effect of DSA on hardness in the HAZ could be predicted.The DSA in SUS316 steel was found to be mainly attributed to the dynamic interaction of dislocations with C and N interstitial atoms during high-temperature deformation.

Modeling of strain hardening and dynamic recrystallization of ZK60 magnesium alloy during hot deformation

The flow stress behavior of ZK60 alloy at elevated temperature was investigated. The strain hardening and dynamic recrystallization of the alloy were modeled by Kocks-Meching model and Avrami equation, respectively. A new constitutive equation during hot deformation was constructed to predict the flow stress considering the dynamic recrystallization. The results show that the flow stress curves predicted by the proposed equation have high correlation coefficients with the experimental data, which confirms that the developed model is accurate and effective to establish the flow stress equation of ZK60 magnesium alloy during hot deformation. Microstructure observation shows that dynamic recovery occurs in the initial stage of hot deformation. However, the microstructure turns to recrvstallization structure as the strain increases.

Molecular dynamics study on temperature and strain rate dependences of mechanical tensile properties of ultrathin nickel nanowires

Based on the EAM potential, a molecular dynamics study on the tensile properties of ultrathin nickel nanowires in the （100〉 orientation with diameters of 3.94, 4.95 and 5.99 nm was presented at different temperatures and strain rates. The temperature and strain rate dependences of tensile properties were investigated. The simulation results show that the elastic modulus and the yield strength are gradually decreasing with the increase of temperature, while with the increase of the strain rate, the stress--strain curves fluctuate more intensely and the ultrathin nickel nanowires rupture at one smaller and smaller strain. At an ideal temperature of 0.01 K, the yield strength of the nanowires drops rapidly with the increase of strain rate, and at other temperatures the strain rate has a little influence on the elastic modulus and the yield strength. Finally, the effects of size on the tensile properties of ultrathin nickel nanowires were briefly discussed.

Nucleation mechanisms of dynamic recrystallization in Inconel 625 superalloy deformed with different strain rates

The effects of strain rates on the hot working characteristics and nucleation mechanisms of dynamic recrystallization (DRX) were studied by optical microscopy and electron backscatter diffraction (EBSD) technique. Hot compression tests were conducted using a Gleeble-1500 simulator at a true strain of 0.7 in the temperature range of 1000 to 1150 °C and strain rate range of 0.01 to 10.00 s?1. It is found that the size and volume fraction of the DRX grains in hot-deformed Inconel 625 superalloy firstly decrease and then increase with increasing strain rate. Meanwhile, the nucleation mechanism of DRX is closely related to the deformation strain rate due to the deformation thermal effect. The discontinuous DRX (DDRX) with bulging of original grain boundaries is the primary nucleation mechanism of DRX, while the continuous DRX (CDRX) with progressive subgrain rotation acts as a secondary nucleation mechanism. The twinning formation can activate the nucleation of DRX. The effects of bulging of original grain boundaries and twinning formation are firstly gradually weakened and then strengthened with the increasing strain rate due to the deformation thermal effect. On the contrary, the effect of subgrain rotation is firstly gradually strengthened and then weakened with the increasing strain rate.

Dynamic behavior of frozen soil under uniaxial strain and stress conditions

The split Hopkinson pressure bar （SHPB） method is used to investigate the dynamic behavior of the artificial frozen soil under the nearly uniaxial strain and uniaxial stress conditions. The tests are conducted at the temperatures of -3 ℃, -8 ℃, -13℃, -17℃, -23℃, and -28℃ and with the strain rates from 900 s^-1 to 1500 s^-1. The nearly uniaxial stress-strain curves exhibit an elastic-plastic behavior, whereas the uniaxial stress-strain curves show a brittle behavior. The compressive strength of the frozen soil exhibits the positive strain rate and negative temperature sensitivity, and the final strain of the frozen soil shows the positive strain under the nearly uniaxial strain is greater rate sensitivity. The strength of the frozen soil than that under the uniaxial stress. After the negative confinement tests, the specimens are compressed, and the visible cracks are not observed. However, the specimens are catastrophically damaged after the uniaxial SHPB tests. A phenomenological model with the thermal sensitivity is established to describe the dynamic behavior of the confined frozen soil.

Improving Tribological Performance of Gray Cast Iron by Laser Peening in Dynamic Strain Aging Temperature Regime

A high and stable brake disc friction coefficient is needed for automobile safety, while the coefficient degrades due to elevated temperature during the braking process. There is no better solution except changes in material composition and shape design optimization. In the dynamic strain aging（DSA） temperature regime of gray cast iron, micro-dimples with different dimple depth over diameter and surface area density are fabricated on the material surface by laser peening（LP） which is an LST method. Friction behavior and wear mechanism are investigated to evaluate the effects of surface texturing on the tribological performance of specimens under dry conditions. Through LP impacts assisted by DSA, the friction coefficients of the LPed specimens increase noticeably both at room temperature and elevated temperature in comparison to untreated specimens. Moreover, the coefficient of specimen with dimple depth over diameter of 0.03 and surface area density of 30% is up to 0.351 at room temperature, which dramatically rises up to 1.33 times that of untextured specimen and the value is still up to 0.3305 at 400℃ with an increasing ratio of 35% compared to that of untreated specimen. The surface of textured specimen shows better wear resistance compared to untreated specimen. Wear mechanism includes adhesive wear, abrasive wear and oxidation wear. It is demonstrated that LP assisted by DSA can substantially improve wear resistance, raise the friction coefficient as well as its stability of gray cast iron under elevated temperatures. Heat fade and premature wear can be effectively relieved by this surface modification method.

Effect of Temperature and Strain Rate on Dynamic Properties of Low Silicon TRIP Steel

The dynamic tensile test of 0.11C-0.62Si-1.65Mn TRIP steel was carried out at different strain rates and test temperatures. The results show that both temperature and strain rate affect the retained austenite transformation. At high strain rates, the uniform elongation decreases, whereas the total elongation and energy absorption increase. The tensile strength is less strain rate sensitive. With raising test temperature, the tensile strength is reduced and the mechanical properties generally deteriorate, especially at 110℃,However, excellent mechanical properties were obtained at 50℃ and 75℃.

Influences of Stress Wave Propagation upon Studying Dynamic Response of Materials at High Strain Rates

How the wave propagation analysis plays a key role in the studies of dynamic response of materials at high strain rates is analyzed. For the wave propagation technique, the followings are important: the loading and unloading constitutive relation presumed, the positions of the sensors embedded, the interactions between loading waves and unloading waves. For the split Hopkinson pressure bar (SHPB) technique, the assumption of one-dimensional stress wave propagation and the assumption of stress uniformity along the specimen should be satisfied. When the larger diameter bars are employed, the wave dispersion effects should be considered, including the high frequency oscillations, non-uniform stress distribution across the bar section, increase of rise time, and amplitude attenuation. The stress uniformity along the specimen is influenced by the reflection times in specimen, the wave impedance ratio of the specimen and the bar, and the waveform.

Experimental investigation of rigid confinement effects of radial strain on dynamic mechanical properties and failure modes of concrete

In this study,to confirm the effect of confining pressure on dynamic mechanical behavior and failure modes of concrete,a split Hopkinson pressure bar dynamic loading device was utilized to perform dynamic compressive experiments under confined and unconfined conditions.The confining pressure was achieved by applying a lateral metal sleeve on the testing specimen which was loaded in the axial direction.The experimental results prove that dynamic peak axial stress,dynamic peak lateral stress,and peak axial strain of concrete are strongly sensitive to the strain rate under confined conditions.Moreover,the failure patterns are significantly affected by the stress-loading rate and confining pressure.Concrete shows stronger strain rate effects under an unconfined condition than that under a confined condition.More cracks are created in concrete subjected to uniaxial dynamic compression at a higher strain rate,which can be explained by a thermal-activated mechanism.By contrast,crack generation is prevented by confinement.Fitting formulas of the dynamic peak stress and dynamic peak axial strain are established by considering strain rate effects(50–250 s-1)as well as the dynamic confining increase factor(DIFc).

Dynamic recrystallization,texture and mechanical properties of high Mg content Al−Mg alloy deformed by high strain rate rolling

The Al−Mg alloy with high Mg addition(Al−9.2Mg−0.8Mn−0.2Zr-0.15Ti,in wt.%)was subjected to different passes(1,2 and 4)of high strain rate rolling(HSRR),with the total thickness reduction of 72%,the rolling temperature of 400℃and strain rate of 8.6 s^(−1).The microstructure evolution was studied by optical microscope(OM),scanning electron microscope(SEM),electron backscattered diffraction(EBSD)and transmission electron microscope(TEM).The alloy that undergoes 2 passes of HSRR exhibits an obvious bimodal grain structure,in which the average grain sizes of the fine dynamic recrystallization(DRX)grains and the coarse non-DRX regions are 6.4 and 47.7mm,respectively.The high strength((507±9)MPa)and the large ductility((24.9±1.3)%)are obtained in the alloy containing the bimodal grain distribution.The discontinuous dynamic recrystallization(DDRX)mechanism is the prominent grain refinement mechanism in the alloy subjected to 2 passes of HSRR.

Dynamic compressive property and failure behavior of extruded Mg-Gd-Y alloy under high temperatures and high strain rates

For the purpose of investigating the dynamic deformational behavior and failure mechanisms of magnesium under high strain rates,the Split Hopkinson Pressure Bar(SHPB)was used for investigating dynamic mechanical properties of extruded Mg-Gd-Y Magnesium alloy at ambient temperature(300 K),200℃(473 K)and 300℃(573 K)temperature.The samples after compression were analyzed by scanning electron microscope(SEM)and metallographic microscope.Dynamic mechanical properties,crack performance and plastic deformation mechanism of extruded Mg-Gd-Y Magnesium alloy along the extrusion direction(ED)were discussed.The results show that,extruded Mg-Gd-Y Magnesium alloy has the largest dynamic compressive strength which is 535 MPa at ambient temperature(300 K)and strain rate of 2826 s^(−1).When temperature increases,dynamic compressive strength decreases,while ductility increases.The dynamic compression fracture mechanism of extruded Mg-Gd-Y Magnesium alloy is multi-crack propagation and intergranular quasi-cleavage fracture at both ambient temperature and high temperature.The dynamic compressive deformation mechanism of extruded Mg-Gd-Y Magnesium alloy is a combination of twinning,slipping and dynamic recrystallization at both ambient temperature and high temperature.