Construction Of Constitutive Equations Research Articles

Effect of nano-scaled Al2O3 particles on dynamic recrystallization behavior and microstructure evolution of pure copper in hot deformation

The unusual dynamic recrystallization (DRX) behavior and microstructure evolution during compression deformation at 400–800 °C of a Cu–Al2O3 alloy were investigated herein. The calculation of activation energy (Q) and critical strain for DRX (εc), as well as the prediction of the volume fraction of DRX, are achieved through the construction of constitutive equations and a kinetic model of DRX. The nano-scaled Al2O3 particles are found to exert a significant pinning effect on dislocations and grain boundaries, significantly increasing the dislocation density. The Cu–Al2O3 exhibits a higher work hardening rate and stress compared to pure Cu under the same deformation conditions. The peak stresses of Cu–Al2O3 at 400 °C and 800 °C are 319.7 MPa and 155.4 MPa, respectively, 80.4 % and 243.1 % higher than those of pure Cu. The addition of nano-scaled Al2O3 particles reduces Q and εc of DRX, promoting the transition from low-angle to high-angle grain boundaries during high-temperature deformation. Additionally, distortion zones induced by Al2O3 particles as potential nucleation sites for DRX. While the addition of these particles promotes DRX of pure Cu, the initial DRX rate of Cu–Al2O3 is suppressed by the strong pinning effect of Al2O3 particles.

Hot deformation behavior and processing workability of a powder forged Fe-2.1Cu-0.5C alloy

Hot deformation behavior of as-sintered Fe-2.1Cu-0.5C alloy was evaluated through the construction of constitutive equations and a hot processing map. The hot deformation behavior was investigated at different temperatures and strain rates and microstructure observations were subsequently conducted. Flow stress for the initiation of dynamic recrystallization mechanism was determined. Tensile and fatigue strength tests were conducted at room temperature. It was observed that the microstructure of the alloy forged at lower temperature exhibited smaller grain size and its grain size increased with higher forging temperatures. Mechanical testing results revealed that an increase in the forging temperature led to a lower tensile strength and a higher fatigue strength. This change can be attributed to the larger grain sizes and the reduction of microcracks. A forging temperature at 1050 °C was recommended to achieve optimal mechanical properties for powder forged Fe-2.1Cu-0.5C products. These results might give some hints for optimizing process conditions and improving mechanical properties of powder metallurgy alloys by the use of constitutive equations and thermal processing maps.

On the Construction of Constitutive Equations for Orthotropic Materials with Different Properties under Tension and Compression in Creep

On the Construction of Constitutive Equations for Orthotropic Materials with Different Properties under Tension and Compression in Creep

Experimental study on construction of constitutive equation of PMMA resin and PC resin

Experimental study on construction of constitutive equation of PMMA resin and PC resin

Bauschinger Effect Prediction in Thick-Walled Autofrettaged Cylindrical Pressure Vessels

The paper addresses the Bauschinger effect under complex stress state in materials with deformation-induced anisotropy whose strain hardening is described by the isotropic–kinematic (translational) type hardening hypothesis. The Bauschinger effect is analyzed using the model based on the yield surface conception and graphical–analytical method of construction of constitutive equations under complex loading. As an example, cylindrical pressure vessels with closed and open ends subjected to autofrettage are considered. The tension–compression Bauschinger effect in the axial and hoop directions as well as the Bauschinger effect under reversed torsion with respect to the longitudinal axis is determined. The role of such factors as the level of prestraining under autofrettage, relation between isotropic and kinematic components of the strain hardening, and chemical composition of the material is analyzed. The results obtained are presented in the form of plots.

Construction of constitutive equations for deformable media under complex loading in terms of steel 40X test data

The author analyzes the data of triaxial tension test of 40X steel carried out in the Institute of Mining. An eigentensor basis, where relations between increments of stresses and strains are independent of the type of loading and additional loading, is found.

A study of the elastoplastic properties of polymer-silicate nanocomposites with allowance for the change in their volumes during deformation

The results of experimental and theoretical studies of the elastoplastic properties of medium-density polyethylene and nanocomposites formed on its basis with a filler of layered clay minerals are described. It is found that the deformation of these materials is accompanied by a significant change in their volumes, which is primarily caused by the development of internal damage of the system (the formation of pores and cracks at the microlevel). A component that takes into account the change in volume during deformation is introduced into the previously proposed model of a heterogeneous medium that can undergo significant non-linear elastic and plastic deformations. For this purpose, we use a differential approach to the construction of constitutive equations and an additive decomposition of the total strain-rate tensor of the medium into strainrate tensors of the elastic and plastic components. Using an improved model, we describe the experimental curves of uniaxial stretching for pure PE and two PE-based polymer-silicate nanocomposites. The introduction of filler particles into the polymer matrix leads to enhancement of the role of two structural mechanisms in the formation of plastic properties: The presence of the filler contributes to the development of internal structural damage; the same particles decrease the orientation ability of the PE matrix, thereby hindering the development of plastic deformations in it. The use of tensor variables in the model makes it appropriate for describing not only stretching but also other types of loading of the material.

Deformation bands, the LEDS theory, and their importance in texture development: Part II. Theoretical conclusions

The facts regarding “regular” deformation bands (DBs) outlined in Part I of this series of articles are related to the low-energy dislocation structure (LEDS) theory of dislocation-based plasticity. They prompt an expansion of the theory by including the stresses due to strain gradients on account of changing selections of slip systems to the previously known dislocation driving forces. This last and until now neglected driving force is much smaller than the components considered hitherto, principally due to the applied stress and to mutual stress-screening among neighbor dislocations. As a result, it permits a near-proof of the LEDS hypothesis, to wit that among all structures which, in principle, are accessible to the dislocations, that one is realized which has the lowest free energy. Specifically, the temperature rises that would result from annihilating the largest DBs amount to only several millidegrees Centigrade, meaning that they, and by implication the entire dislocation structures, are close to thermodynamical equilibrium. This is in stark contrast to the assumption of the presently widespread self-organizing dislocation structures (SODS) modeling that plastic deformation occurs far from equilibrium and is subject to Prigogine’s thermodynamics of energy-flow-through systems. It also holds out promise for future rapid advances in the construction of constitutive equations, since the LEDS hypothesis is the principal basis of the LEDS theory of plastic deformation and follows directly from the second law of thermodynamics in conjunction with Newton’s third law. By contrast, all other known models of metal plasticity are in conflict with the LEDS hypothesis. In regard to texture modeling, the present analysis shows that Taylor’s criterion of minimum plastic work is incorrect and should be replaced by the criterion of minimum free energy in the stressed state. Last, the LEDS hypothesis is but a special case of the more general low-energy structure (LES) hypothesis, applying to plastic deformation independent of the deformation mechanism. It is thus seen that plastic deformation is one of nature’s means to generate order, as a byproduct of the entropy generation when mechanical work is largely converted into heat.

Constitutive equations of plastic deformation of a two-phase composite medium

The construction of effective constitutive equations for a composite medium on the basis of the known properties of the components is a necessary condition for the development of new materials with given characteristics and makes possible a considerable reduction of experimental studies. For composites with plastic components the construction of constitutive equations at the macrolevel should be based on the law of averaging permanent deformations. 1. Let us examine a two-phase elastoplastic composite medium such that the characteristic volume V = V(I ) + V(2 ), and v i = V(i)/V is the coefficients of the volume content of the components. We will consider homogeneous boundary conditions [1, 2], determined by a constant stress ~ or strain e tensor, to be given on the surface of a characteristic volume. We write the operations of averaging over the volume:

One approach to the construction of constitutive equations in creep theory

One approach to the construction of constitutive equations in creep theory

Frame-invariance of turbulence constitutive relations

The applicability of the principle of material frame-indifference to turbulence and its consequences for turbulence modelling are considered. By introducing a distinction between arbitrary time-dependent orthogonal transformations of (i) the fluid motion, and (ii) the observer, we find that frame-invariant tensorial measures of the absolute angular velocity and acceleration can be defined. This follows from consideration of a four-dimensional formulation of classical mechanics which formally possesses the property of invariance under arbitrary changes of frame of the observer. These tensors allow the construction of constitutive equations which depend, for example, on the absolute angular velocity of the fluid, and which also satisfy the principle of material frame-indifference. The results of this analysis have application outside the field of turbulence modelling. The invariance properties of some previously published Reynolds stress transport turbulence models are examined and modifications are suggested.

Shock Thickness in Viscoplastic Solids

In this paper a system of constitutive relations for plane-strain finite deformation in strain-rate sensitive elastic-plastic materials is developed. A method is presented for computing the main features of steady-state one-dimensional plastic-strain waves by elementary numerical techniques in materials of this type. This method is applicable to a wide variety of material constitutive relations and provides an alternative to computing complete wave profiles for investigators interested primarily in the effects of certain numerical parameters on the principal features of waves. The method is illustrated by use of particular constitutive relations but is applicable to a much wider class of relations. Maximum normal stress, pressure, and shear stress are computed, using this method, as a function of wave speed. For two different plastic strain-rate relations the maximum plastic strain rate and total strain are computed as a function of wave speed. Making use of these results, estimates are provided for the wave-front thickness in terms of wave speed and the parameters of the particular viscoplastic constitutive equations used. These results suggest ways in which plastic wave experiments can be used to motivate the construction of constitutive equations for finite deformation in strain-rate sensitive plastic solids.