A new form of the coherency energy in pseudoelasticity

In some previous papers [1], [2] pseudoelasticity in tensile experiments has been treated thermodynamically under the assumption that the relevant constitutive ingredients are

饱和黏弹性多孔介质中的平面波及能量耗散

研究了流体饱和不可压黏弹性多孔介质中的非均匀平面波及其能量流和能量耗散规律. 在流 相和固相物质微观不可压、固相骨架宏观服从积分型本构关系和小变形的假定下，利用 Helmholtz分解，得到了饱和黏弹性多孔介质中非均匀平面波的一般解以及纵波、横波相速 度和衰减率等的解析表达式，分析了平面波传播矢量和衰减矢量之间的关系. 数值结果表明 孔隙流体与固相骨架间的相互作用以及固相骨架的黏性对波的相速度、衰减率等有着显著的 影响. 同时，得到了饱和黏弹性多孔介质的能量方程，给出了能量流矢量和能量耗散率. 对 非均匀平面纵波和横波，推导了平均能量流矢量和平均能量耗散率的解析表达式.     

Interfacial energy and dissipation in martensitic phase transformations. Part II: Size effects in pseudoelasticity

This paper is a continuation of the Part I (H. Petryk, S. Stupkiewicz, Interfacial energy and dissipation in martensitic phase transformations. Part I: Theory. J. Mech. Phys. Solids, 2010, doi:10.1016/j.jmps.2009.11.003). A fully three-dimensional model of an evolving martensitic microstructure is examined, taking into account size effects due to the interfacial energy and also dissipation related to annihilation of interfaces. The elastic micro-strain energy at microstructured interfaces is determined with the help of finite element computations and is approximated analytically. Three interface levels are examined: of grain boundaries attained by parallel martensite plates, of interfaces between austenite and twinned martensite, and of twin interfaces within the martensite phase. Minimization of the incremental energy supply, being the sum of the increments in the free energy and dissipation of the bulk and interfacial type at all levels, is used as the evolution rule, based on the theory presented in Part I. An example of the formation and evolution of a rank-three laminated microstructure of finite characteristic dimensions in a pseudoelastic CuAlNi shape memory alloy is examined quantitatively.     

Equilibrium thermodynamics of pseudoelasticity and quasiplasticity

Motivated by recent experimental results by Glasauer [1], a thermodynamic theory of shape memory alloys is proposed, which includes not only the high temperature – pseudoelastic – behavior but also the low temperature range of quasiplasticity. Due to the occurance of three different phases – austenite and two martensitic variants – several cases of two-phase equilibria and a three-phase equilibrium have to be taken into account. Their relevance is determined by minimization of the total free energy and subsequently illustrated by the construction of phase charts. A special point of interest is the influence of interfacial energy effects on these phase charts, resulting in phenomena like, for example, the apparent violation of Gibbs' phase rule. Furthermore, the role of interfacial energies in the hysteretic load-displacement behavior is discussed in the light of the additional quasiplastic case. Received June 12, 1996     

Phase mixtures in dynamics of pseudoelasticity

We give a numerical treatment of phase mixtures in pseudoelasticity from a purely mathematical point of view. It is based on a surprising result that the approximate solution may consist of persistent oscillations in strain which resemble the experimentally observed interface patterns. Such a solution is obtained from a sequence of solutions for a rate-type viscoelastic problem with a non-monotone equilibrium stress-strain relation, for which in the limit as the viscosity tends to infinity the viscoelastic problem reduces to the rate-independent elastic problem describing phase transitions. In this manner, it seems to give yet another perspective for the phase mixture from dynamic point of view as the evolution of an unstable state, in contrast to the traditional treatment from stability analysis for phase equilibrium.     

INTERNAL VARIABLES AND THERMODYNAMIC MODELLING OF PSEUDOELASTICITY

ＩＮＴＥＲＮＡＬＶＡＲＩＡＢＬＥＳＡＮＤＴＨＥＲＭＯＤＹＮＡＭＩＣＭＯＤＥＬＬＩＮＧＯＦＰＳＥＵＤＯＥＬＡＳＴＩＣＩＴＹＨｕｏＹｏｎｇｚｈｏｎｇ（霍永忠）（ＲｅｃｅｉｖｅｄＦｅｂ．２．１９９６；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＺｈｅｎｇＱｉａｎｓｈｕｉ）...     

On the size of the hysteresis in pseudoelasticity

Pseudoelasticity is a phenomenon that occurs in alloys with shape memory: In a loading-unloading cycle a body will return to its original configuration, but its path in a load-deformation diagram will run through a hysteresis loop.Pseudoelastic behaviour can be modelled by statistical mechanics which produces a non-monotone load-deformation isotherm. Once such a nonmonotone curve has been calculated there is the possibility of a phase transition that is connected with a hysteresis loop.The paper describes a method for the calculation of the width of the hysteresis. It comes to the conclusion that this width is determined by the interfacial energy associated with domain boundaries between the phases. The bigger that energy is the bigger is the hysteresis loop.     

Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys

Transformation pseudoelasticity and shape memory effect of alloy materials are investigated from the thermomechanical point of view. The thermomechanical constitutive equations and the kinetics of transformation established by the theory are applied to explain the stress-strain-temperature behavior of the material. Numerical illustrations for the uniaxial stress state are given.     

The temperature dependence of yield

A theoretically rigorous expression is derived from the fundamental equation of rate processes to describe the temperature dependence of the upper and lower yield stress in terms of physical quantities. The effect of the activation volume and activation energy on the yield behavior was investigated over a wide temperature range. The analysis shows that the yield stress is a sensitive function of the temperature when the activation volume is small and that the temperature sensitivity is relatively weak at activation volumes V _f>10³ b ³. The theory predicts that the yield drop has a maximum at an intermediate temperature range and vanishes both at very low and very high temperatures. The calculated behavior was found to be in good qualitative agreement with the results of the measurements obtained by several investigators. It is concluded that the proposed theory can explain fully the temperature dependence of the yield behavior.     

Simulation of temperature fields in arc and beam welding

 Heat and mass transfer in arc and beam welding is considered. The main objectives are analysis of the heat transfer in the weld pool and the workpiece and to demonstrate how computer simulation can be used as a tool to predict the temperature distribution as the determining element of the heat effects of welding. Simulation results of two particular welding processes are compared and validated with measurements. Received on 26 July 1999     

Transient temperature fields and residual stress fields of metallic materials under welding

Based on the situation of welding thermal conduction and thermo-elasto-plasticityresearch,Ms paper explores some problems in this field.First,the boundary elementmethod for nonlinear problems is improved by linearization of nonlinear problems and usedin welding thermal conduction analysis.Second,the thermo-elasto-plastic finite elementmethod is used for the welding stress calculation,in which the phase transformation isconsidered by the"equivalent linear expansion coefficient method".The comparison of the calculated results with experimental data shows that themethods provided in this paper are available.     

Pressure dependence of glass transition temperature in polymers

The pressure dependencedT _g /dP of glass transition temperatureT _g has received considerable interest due to its connection with solid state thermodynamic properties and theories of glass transition. Free volume considerations (1, 2) led to an estimate of the pressure effect onT _g , showing thatdT _g /dP had to depend on thermal expansion and compressibility changes atT _g through the equation: [1] $$\frac{{dT_g }}{{dP}} = \frac{{\Delta \beta }}{{\Delta \alpha }}$$ whereΔβ=β _e ?β _g andΔα=α _e ?α _g Later work (3, 4, 5, 6) has shown that eq. [1] is not verified by experimental facts, the ratioΔβ/Δα being much larger than (dT _g /dP) exp. Recent analysis of the properties of glasses obtained under different pressures have complicated the situation, showing that the experimental value ofdT _g /dP depends, of course, on the polymer usedbut also on the experimental procedure used in its determination. Since it is obvious that in order to measure anyΔT _g -value we need to operate on at leasttwo glasses, these should be identical in all properties which could influenceT _g except pressure. Any difference in morphology,which could lead to a change in T _g at constant pressure, should therefore be avoided in order to get a sound value for the pure pressure effectdT _g /dP. To reveal this effect, we have performed (7)dT _g /dP determinations on two polymers, polyvinylacetate (PVAC) and polyvinylchloride (PVC), following three different procedures:

1. Measurement of the changeΔT _g induced by application of a pressure incrementΔP on the liquid polymer (T>T _g ). This is the procedure normally used; the liquid is cooled down at a fixed rate of temperature change (～5 °C/day) andT _g is dilatometrically recorded at 1 atmosphere. Then the polymer is taken again to the liquid state, pressure ΔP is applied and, at the same rate, the system is cooled down isobarically; the newT _g is recorded anddT _g /dP calculated.
2. Measurement of the change ΔT_g induced by application of a pressure increment ΔP on the glassy polymer (T _g ). Once determinedT _g at 1 atmosphere, pressureΔP is applied on the glass, time is given to the system to equilibrate; then the glass is heated isobarically. Intersection of the glassy line to the liquid line in a volume/temperature plot gives the newT _g and therefore allows the calculation ofdT _g /dP.
3. Measurement ofΔT _g during the heating of a glass along an isochor (5, 8). Here the polymer glass is heated at constant volume, by application of an increasing pressure at increasing temperatures given by(?P/?T) _v . By repeating this procedure two times, starting from two different specific volumes of the glass, two values ofT _g at different pressures can be recorded anddT _g /dP calculated.

   Table 1 shows the result of this work     

   16.

   Stability of curvilinear Euler-Bernoulli beams in temperature fields     

   《International Journal of Non》2017

   In this work, stability of thin flexible Bernoulli-Euler beams is investigated taking into account the geometric non-linearity as well as a type and intensity of the temperature field. The applied temperature field T(x,z) is yielded by a solution to the 2D Laplace equation solved for five kinds of thermal boundary conditions, and there are no restrictions put on the temperature distribution along the beam thickness. Action of the temperature field on the beam dynamics is studied with the help of the Duhamel theory, whereas the motion of the beam subjected to the thermal load is yielded employing the variational principles.The heat transfer (Laplace equation) is solved with the use of the finite difference method (FDM) of the third-order accuracy, while the integrals along the beam thickness defining the thermal stress and moments are computed using Simpson's method. Partial differential equations governing the beam motion are reduced to the Cauchy problem by means of application of FDM of the second-order accuracy. The obtained ordinary differential equations are solved with the use of the fourth-order Runge-Kutta method.The problem of numerical results convergence versus a number of beam partitions is investigated. A static solution for a flexible Bernoulli-Euler beam is obtained using the dynamic approach based on employment of the relaxation/set-up method.Novel stability loss phenomena of a beam under the thermal field are reported for different beam geometric parameters, boundary conditions, and the temperature intensity. In particular, it has been shown that stability of the flexible beam during heating the beam surface essentially depends on the beam thickness.     

   17.

   Studying temperature fields and thermal stresses in corrugated laminates     

   Yu. N. Nemish 《International Applied Mechanics》1982,18(5):422-428

        

   18.

   Optimization of temperature fields and stresses in a doubly-connected plate     

   Ya. I. Burak  Ya. P. Romanchuk  B. M. Trishch 《International Applied Mechanics》1986,22(1):56-61

        

   19.

   The temperature dependence of non-linear creep and recovery in oriented polypropylene     

   C.J. MorganI.M. Ward 《Journal of the mechanics and physics of solids》1971

   This paper describes creep, recovery and load superposition experiments on an oriented polypropylene monofilament in the temperature range 28–60 C. Although the monofilament exhibited non-linear behaviour, the results for different temperatures were found to be related by simple time/temperature equivalence.     

   20.

   Calculation of nonlinear temperature fields in complex two-dimensional regions     

   A. I. Bobrik  V. N. Mikhailov 《International Applied Mechanics》1976,12(4):378-382

        

Stability of curvilinear Euler-Bernoulli beams in temperature fields

In this work, stability of thin flexible Bernoulli-Euler beams is investigated taking into account the geometric non-linearity as well as a type and intensity of the temperature field. The applied temperature field T(x,z) is yielded by a solution to the 2D Laplace equation solved for five kinds of thermal boundary conditions, and there are no restrictions put on the temperature distribution along the beam thickness. Action of the temperature field on the beam dynamics is studied with the help of the Duhamel theory, whereas the motion of the beam subjected to the thermal load is yielded employing the variational principles.The heat transfer (Laplace equation) is solved with the use of the finite difference method (FDM) of the third-order accuracy, while the integrals along the beam thickness defining the thermal stress and moments are computed using Simpson's method. Partial differential equations governing the beam motion are reduced to the Cauchy problem by means of application of FDM of the second-order accuracy. The obtained ordinary differential equations are solved with the use of the fourth-order Runge-Kutta method.The problem of numerical results convergence versus a number of beam partitions is investigated. A static solution for a flexible Bernoulli-Euler beam is obtained using the dynamic approach based on employment of the relaxation/set-up method.Novel stability loss phenomena of a beam under the thermal field are reported for different beam geometric parameters, boundary conditions, and the temperature intensity. In particular, it has been shown that stability of the flexible beam during heating the beam surface essentially depends on the beam thickness.     

The temperature dependence of non-linear creep and recovery in oriented polypropylene

This paper describes creep, recovery and load superposition experiments on an oriented polypropylene monofilament in the temperature range 28–60 C. Although the monofilament exhibited non-linear behaviour, the results for different temperatures were found to be related by simple time/temperature equivalence.