Inelastic Constitutive Equation Research Articles

ニッケル基単結晶および一方向凝固超合金の多軸応力下における繰返し構成関係

This paper studies yield surface and stress amplitude ellipse for Nickel-base single crystal (SC) superalloy CMSX-2 and directionally solidified (DS) superalloy Mar-M247LC under multiaxial cyclic loadings. Mises' strain controlled tension/torsion cyclic loading tests were carried out at 1173K in air and the stress-strain relations were obtained experimentally. The inelastic constitutive equation based on slip theory, taking account of {111} ‹110› octahedral and {100} ‹110› cube slip systems, was developed. The yield surface and stress amplitude ellipse obtained from the slip theory were compared with the experimental results. The theory well explained the plastic deformation behavior for SC and DS superalloys, where somewhat different plastic deformation behavior was found between the two superalloys, caused by the different contribution of the two slip systems. Coaxiality between the Mises' stress and strain was extensively discussed based on the slip theory.

Extensive modeling of high temperature deformation for cyclically softening material

A unified inelastic constitutive equation is proposed to describe the cyclic inelastic deformation of 2 1 4 Cr-1Mo steel at an elevated temperature of 550°C. In the present study, the evolution of overstress is discussed which is shown to lead to a time-independent term in the inelastic strain rate. This term is proportional to the stress rate. Another significant point proposed in this study is the distinction of the inelastic deformation depending on the evolution of overstress. A mathematical model has been developed based on these assumptions. Many numerical experiments were conducted to examine the validity of the present model, and in comparison with the experimental results, the present model has been shown to give good descriptions for a wide variety of loading conditions, including rate-dependent plasticity, stress relaxation, and cyclic softening.

Extensive Modeling of High-Temperature Deformation Based on Unified Approach

A unified inelastic constitutive equation is proposed to describe the cyclic inelastic deformation of 2 1/4Cr-1Mo steel at 550°C. In the present study, an evolution of the overstress is discussed which leads the time-independent term into the inelastic strain rate. A mathematical model is developed and some examples of the numerical simulation are presented.

Influence of Prestraining and Deformation Rate on Strain Aging of Metal Materials. The Case of SUS 316 and A7075-T6 under Uniaxial Loading.

It is suggested that strain aging is one of the important factors for deriving the inelastic constitutive equation of metal materials used in structure. To investigate the effect of aging on the flow stress level in plastic deformation, under uniaxial loading using SUS316 stainless steel, which is a typical metal used in structure, and A7075-T6 aluminum-alloy, which shows a strong strain aging, the authors analyzed the intensity of temporary hardening after stress relaxation and calculated the behavior. The intensity behaves as a function of prestraining history, and calculated results agree with experimental responses.

Study on tne Unified Inelastic Constitutive Equation Considering the Evolution Equation of the Overstress.

The unified inelastic constitutive equation suggested in the previous report is extended to cyclic inelastic deformation and creep deformation of 2 1/4 Cr-1 Mo steel at 550°C. Two of the parameters in the monotonic model decrease with respect to the accumulated inelastic strain, resulting in cyclic softening of the internal stress and the overstress. To describe creep deformation, rate-dependent strain hardening of the internal stress is investigated and introduced into its evolution equation. Through several numerical simulations, the agreement is again found to be good.

Effect of Temperature and Hydrostatic Pressure on the Viscosity of Liquid : A Study on the Inelastic Constitutive Equation

The constitutive relation between the viscosity, temperature and hydrostatic pressure of liquid materials is investigated by the inelastic deformation theory (combined mechanism model) proposed in the previous paper in order to explain the inelastic behavior of solid materials. The constitutive relation of water and some other liquid materials is well explained quantitatively by the theory. The following are obtained : liquid flow due to several mechanisms, which are thermal activation processes similar to those of solid materials; the liquid region in a pressure-temperature diagram divided into several (mainly three) subregions classified by flow mechanism; a proposed constitutive equation containing hydrostatic pressure.

Non-Newtonian viscous flow of liquid. A study of an inelastic constitutive equation.

In this paper, the flow curve (the constitutive relation between shear stress and rate of shear) of a non-Newtonian fluid (liquid) is investigated on the basis of the first author's inelastic deformation theory. The theory is the combined deformation mechanism model and was proposed to explain the inelastic behavior of solids in the previous paper. The application of the theory to the flow curves of Newtonian, pseudoplastic, Bingham, plastic, and dilatant fluids leads to the possibility of the systematic explanation for these flow curves. The effect of temperature on the flow curve is also well explained. The theoretical considerations of the measurement values obtained by various researchers lead to the establishment of a maximum limit of rate of shear, which is assumed in the proposed constitutive equation.

Inelastic Constitutive Equation on the Basis of Distribution Function of Yield Stress : (Basic Equation and Parameter for Work Hardening and Softening)

In this paper, we propose the distribution function of the yield stress to characterize the inelastic behavior of metals. This inelastic model consists of infinitely small cells which have perfectly elastoplastic properties. The distribution function of the yield stress means the content of infinitely small cells. The integral constituitve equation for this model is derived under the combined stress state. To give the effect of the work hardening and softening to the model, we propose the scalar parameter which is the integrated value of inner products of incremental plastic strain vectors along the plastic strain path. This parameter is elaborated by the experimental data of the tensile stress-strain curve and the uniaxial cyclic curves for SUS 304 stainless steel. Biaxial stress-strain relations are calculated with the constitutive equation, including this parameter. It is shown that the work hardening and softening phenomena can be simulated with this constitutive equation and this parameter.

Effect of temperature and hydrostatic pressure on the viscosity of liquid. A study on inelastic constitutive equation.

The constitutive relation between viscosity, temperature and hydrostatic pressure of liquid materials is investigated by the inelastic deformation theory (combined mechanism model) proposed in the previous paper in order to explain the inelastic behavior of solid materials. The constitutive relation of water and some other liquid materials is well-explained quantitatively by the theory. The following are obtained : liquid flow due to several mechanisms, which are the thermal activation processes similar to those of solid materials ; the liquid region in a pressure-temperature diagram is divided into several (mainly three) subregions classified by flow mechanism ; a proposed constitutive equation containing hydrostatic pressure.

An inelastic constitutive equation on the basis of the distribution function of yield stress. 3rd report. The effect of viscoplasticity.

A unified constitutive equation is formulated to determine the plastic-creep behavior of metals under a combined state. The elastoplastic constitutive equation with a distribution function of yield stresses is extended by including the viscoplastic property. This theory is applied to predict the plasticity-creep stress-strain relation of SUS304 stainless steel. Two different nonlinear visco-plastic models are proposed for an elevated temperature and room temperature. The steady-state creep term is added into the elevated-temperature model. It is found that the properties of primary creep and the effect of creep on plasticity arise from the plasticity-creep interaction caused by the distribution of internal stresses. The rate sensitivity with over stress is considered for the room-temperature model. The time-dependent stress-strain relation, cyclic creep behavior and biaxial creep behavior are calculated and compared with the experimental results of SUS304 stainless steel.

Inelastic constitutive equation on the basis of the distribution function of yield stress. 2nd Report. Parameter for work hardening and softening.

To characterize the work hardening and softening in plastic deformation, we proposed the scalar parameter which is the integrated value of inner products of incremental plastic strain vectors along the strain path. This parameter was elaborated by the experimental data of the tensile stress-strain curve and the uni-axial cyclic curves of SUS 304 stainless steel. Bi-axial stress-strain relations and bi-axial cyclic plastic deformation were calculated with the constitutive equation including this parameter. The work hardening and softening phenomena were simulated for the bi-axial monotonic and cyclic plastic behavior.

Inelastic constitutive equation on the basis of the distribution function of yield stress. 1st Report. Formulation of plastic constitutive equation.

In this paper, we propose the distribution function of the yield stress to characterize the inelastic behavior of metal. This inelastic model is consisted with infinite small cells of the ideal plastic material, which are placed in parallel. The distribution function of the yield stress means the content of infinite small cells. The integral constitutive equation for this model is derived under combined stress state. The stress strain relations for several strain histories, which include the sharp corner of the strain paths, are calculated. It is shown that this constitutive equation can simulate Bauschinger's effect and the delay phenomenon.

An admissible form of an inelastic constitutive equation—I. General theory

From the viewpoint of irreversible thermodynamics an admissible form of rate-type constitutive equation of inelastic materials is given. The displacement gradient tensor F referred to the temporarily fixed reference frame which coincides with the Euler frame at the instant of the reference time is decomposed linearly into elastic and inelastic parts so that the procedure of formulation is simplified and clarified. The inelastic deformation rate is directly related to the internal production rate of entropy. The existence of an inelastic potential of the usual sense is not assumed, though the result can be understood to include the conventional flow theory based on an inelastic potential. An example of an elastoviscoplastic constitutive equation is given and some properties of yield surfaces are discussed.

An admissible form of an inelastic constitutive equation—II. Examples of elastoplastic constitutive equation

Some examples of elastoplastic constitutive equation are presented using the general theory reported in the preceding paper (Part I). Some examinations of them are given to show that the theory is self-consistent and useful especially for anisotropic materials or materials with anisotropy resulting from plastic deformation. Mises' and Yoshimura's yield functions and a kind of quadratic function are adopted as the yield function. Formulae of r-value after arbitrary pre-straining are given which are of paramount importance in the field of press-forming of sheet metals. Several examples of stress-strain curves for various loading paths are also given.