Flow behaviour constitutive model of CuCrZr alloy and 35CrMo steel based on dynamic recrystallization softening effect under elevated temperature

In order to study the effect of dynamic recrystallization on the metal flow behavior during thermal deformation,the elevated temperature compression experiments of CuCrZr alloy and 35CrMo steel are carried out using Gleeble-3810 thermal simulator.It is proved that the samples underwent obvious dynamic recrystallization behavior during thermal deformation by microstructure observation of deformed specimens.The size of recrystallized grains increases as the temperature improved and the strain rate decreased.Meanwhile,the net softening rate caused by dynamic recrystallization is determined based on the stress-dislocation relationship.It can be found that the value of net softening rate increases quadratically as the Z parameter decreases,and the dynamic recrystallization net softening rate of CuCrZr alloy and 35CrMo steel are calculated to be 21.9%and 29.8%,respectively.Based on the dynamic recrystallization softening effect proposed,the novel elevated temperature flow constitutive models of two different alloys are proposed,and the related parameters are well defined and solved in detail.The predicted values of the obtained models are agreed well with the experimental values.

Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.

The Evolution of Elliptic Flow Under First Order Phase Transition

Elliptic flow for non-central Au＋Au collisions at √SNN=200 GeV is investigated with a 2＋1 dimensional hydrodynamic model. We analyze the softening effect by the velocity along the axis. The contribution of the elliptic flow from the QGP phase, mixed phase and hadron gas phase is studied. The relation between the sound horizon and evolution of the elliptic flow is discussed.

A nonlinear explicit dynamic GBT formulation for modeling impact response of thin-walled steel members

A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impulsive loads.Considering the rate strengthening and thermal softening effects on member impact behavior,a modified Cowper-Symonds model for constructional steels is utilized.The element displacement field is built upon the superposition of GBT cross-section deformation modes,so arbitrary deformations such as cross-section distortions,local buckling and warping shear can all be involved by the proposed model.The amplitude function of each cross-section deformation mode is approximated by the cubic non-uniform B-spline basis functions.The Kirchhoff s thin-plate assumption is utilized in the construction of the bending related displacements.The Green-Lagrange strain tensor and the second Piola-Kirchhoff(PK2)stress tensor are employed to measure deformations and stresses at any material point,where stresses are assumed to be in plane-stress state.In order to verify the effectiveness of the proposed GBT model,three numerical cases involving impulsive loading of the thin-walled parts are given.The GBT results are compared with those of the Ls-Dyna shell finite element.It is shown that the proposed model and the shell finite element analysis has equivalent accuracy in displacement and stress.Moreover,the proposed model is much more computationally efficient and structurally clearer than the shell finite elements.

Compressive Mechanical Properties of Normalized 10^#Low Carbon Steel

Compressive mechanical properties of 10^# lowcarbon steel with normalizing heat treatment are studied. A Gleeble system is adopted to analyze the quasi-static properties and thermal softening effects of heat treated 10^# steel,while a Hopkinson bar apparatus is used to investigate its dynamic characteristics under different strain rates. The results showthat yield stress of heat treated 10^# steel is more than that of untreated one at room temperature. When the specimens are tested at different temperatures,yield stresses decrease with increasing temperature except 573 K. Moreover,the influence of strain rate on yield stress are verified,which shows that the yield stress increases sharply from 500 s^-1 to 1 890 s^-1,while it changes a little from 1 890 s^-1 to 4 850 s^-1. The results indicate that yield stress is mainly influenced by hardening effect at lowstrain rate and controlled by both thermal softening effect and strain rate hardening effect at high strain rate.

On the consistency of two-phase local/nonlocal piezoelectric integral model

In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.

Vertical dynamic response characteristics of single pile in non-homogeneous soil layers

A computational method and a mechanical model for evaluating the vertical dynamic harmonic response characteristics of a single pile embedded in non-homogeneous soil layers and subjected to harmonic loadings were established based on a certain assumption and the improved dynamic model of beam-on-Winkler foundation by using the principle of soil dynamics and structure dynamics. Both non-homogeneity of soil strata and softening effect of soil layer around the pile during vibration were simultaneously taken into account in the proposed computational model. It is shown through the comparative study on a numerical example that the numerical results of dynamic response of the single pile computed by the proposed method are relatively rational and can well agree with the numerical results computed from the well-known software of finite element method. Finally the parametric studies were conducted for a varied range of main parameters to discuss the effects of relevant factors on dynamic responses of the single pile embedded in non-homogeneous layered soils excited by harmonic loading with different frequencies.

Thrust force model for ultrasonic-assisted micro drilling of DD6 superalloy

As a typical refractory material,the DD6 nickelbased single-crystal superalloy has important applications in the aviation industry.Ultrasonic-assisted drilling is an advanced machining method that significantly improves machining of refractory materials.The drilling thrust force influences the hole surface quality,burr height,and bit wear.Therefore,it is necessary to predict the thrust force during ultrasonic-assisted drilling.However,there are few reports on the modeling of the thrust force in the ultrasonicassisted drilling of micro-holes.A thrust force prediction model for ultrasonic-assisted micro-drilling is proposed in this study.Based on the basic cutting principle,the dynamic cutting speed,dynamic cutting thickness,and acoustic softening effect caused by ultrasonic vibrations are factored into this model.Through model calibration,the specific friction force and specific normal force coefficients were determined.The model was verified through ultrasonic-assisted drilling experiments conducted at different feed rates,spindle speeds,frequencies,and amplitudes.The maximum and minimum errors of the average thrust force were 10.5%and 2.3%,respectively.This model accurately predicts the thrust force based on the parameters used for ultrasonic-assisted micro-hole drilling and can assist in the analysis and modeling of DD6 superalloy processing.