Study of thermoviscoelastoplastic processes in the deformation of structural elements

Shevchenko, Yu. N.

doi:10.1007/bf02682281

Cited by 32 publications

(72 citation statements)

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“…Thus, the error of this formula is d e = | |/ max 100. We also calculated the strains for processes 2, 4, and 5 using the conventional constitutive equations describing deformation along small-curvature paths [6], which disregard the stress mode. It was established that the maximum difference between the calculated and experimental strains at the end of process 2 is 16%.…”

Section: Algorithm To Analyze the Deformation Of Tubular Specimensmentioning

confidence: 99%

“…These functions should be determined from tests on tubular specimens proportionally (at different constant stress mode angles) loaded by tension and internal pressure. If the functions are assumed independent of the stress mode angle and determined in tension tests, the equations transform into the equations of deformation along small-curvature paths [6].To validate the above assumptions, test data for tubular specimens subject to tension and internal pressure were used in [13][14][15]. The specimens were made of Kh18N10T steel and preliminarily annealed.…”

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Constitutive equations of elastoplastic isotropic materials that allow for the stress mode

2009

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The constitutive equations describing the elastoplastic deformation of an isotropic material and taking into account the stress mode are validated against available experimental data. We propose a method for the approximate determination of the base functions appearing in the constitutive equations and relating the first and second invariants of the stress tensors and the linear components of finite strains. The strain components obtained by this method are compared to experimental data Keywords: isotropic material, elastoplastic deformation, constitutive equations Introduction. In formulating constitutive equations for isotropic materials [1, 2, 6, 12, 16, etc.], the conventional theories of plasticity [4, 5, 9-11, etc.] assume, as a rule, that the relationships between the invariants of stress and strain tensors are independent of the stress mode. This assumption agrees with experimental data at small strains (to 6-10%) [7] and is invalid if strains are large [3,8]. The papers [13,14] propose constitutive equations that describe the elastoplastic deformation of isotropic materials along small-curvature paths and take into account the stress mode. These equations relate the components of the stress tensor and the linear components of the strain tensor in Euler's coordinate system, can be used at both small and large strains, and are based on the assumption that the directional deviators of stresses and plastic strain differentials coincide and the mean plastic strain is nonzero. The equations include two functions, one relating the mean stress and strain and the stress mode angle and the other relating the intensities of tangential stresses and shear strains and the stress mode angle. These functions should be determined from tests on tubular specimens proportionally (at different constant stress mode angles) loaded by tension and internal pressure. If the functions are assumed independent of the stress mode angle and determined in tension tests, the equations transform into the equations of deformation along small-curvature paths [6].To validate the above assumptions, test data for tubular specimens subject to tension and internal pressure were used in [13][14][15]. The specimens were made of Kh18N10T steel and preliminarily annealed. It was established that the relations between the intensities of tangential stresses and shear strains obtained at the same stress mode angle and different ratios of principal stresses agree to within the scatter of experimental data. These base functions were calculated in [15] for the following stress mode angles: w p p s = 0 6 3 , / , / . The radial strain needed to calculate the functions and not measured in these tests was determined approximately. In [13][14][15], however, the strains were not determined based on the proposed constitutive equations and these functions and were not compared with experimental data.In contrast to [13][14][15], the present paper proposes a different approximate approach to determine the radial strain and finds new values of base functions. We u...

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Section: Algorithm To Analyze the Deformation Of Tubular Specimensmentioning

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Constitutive equations of elastoplastic isotropic materials that allow for the stress mode

2009

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“…Next, we use this function and the intensity of tangential stresses S (1.9) at the end and beginning of the current step of loading to determine the intensity of shear strains G. After that, we use formula (1.16) to calculate the intensity of plastic shear strains G (p) and the increment D G Thus, the above algorithm allows approximate calculation of the components of the strain tensor for a tubular specimen under loading of given type assuming that only the function F 2 (1.11) is dependent on the stress mode. If the function F 2 (1.11) is considered independent of the stress mode and equal to the base function at w p/ s = 3 (i.e., when the specimen is subject to uniaxial tension), then this algorithm may be used to determine the components of the strain tensor based on the theory of deformation along small-curvature paths [4,5].…”

Section: Calculation Of Base Functionsmentioning

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Approximate description of the inelastic deformation of an isotropic material with allowance for the stress mode

2010

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The elastoplastic deformation of an isotropic material is described using constitutive equations and allowing for the stress mode. The equations include two nonlinear functions that relate the first and second invariants of the stress and linear-strain tensors to the stress mode angle. It is proposed to use a linear rather than nonlinear relationship between the first invariants of the tensors. This simplification is validated by comparing calculated and experimental strains under loading with constant and variable stress mode angle Keywords: isotropic material, elastoplastic deformation, constitutive equations, stress mode angle Introduction. Constitutive equations describing the elastoplastic deformation of isotropic materials along small-curvature paths and allowing for the stress mode were proposed in [10,11]. These equations relate the stress components and the linear strain components and can be used both at small and large strains. It was assumed that stress deviators and differentials of plastic strains are coaxial. The equations contain two nonlinear functions that depend on a stress mode parameter. For this parameter, the stress mode angle was used in [3]. One function relates the mean stress and strain and the stress mode angle, while the other function relates the intensities of tangential stresses and shear strains and the stress mode angle. These functions are determined from tests on tubular specimens under tension and internal pressure increased proportionally, i.e., at several constant stress mode angles. When these functions are assumed independent of the stress mode angle and determined from uniaxial-tension tests, the above equations transform into the standard equations of the theory of deformation along small-curvature paths [2, 4, 5, 13], which are widely used to solve boundary-value problems [6-9, etc.].The assumptions underlying the constitutive equations were validated in [10][11][12] against the data of tests on tubular specimens subject to tension and internal pressure. The specimens were made of Kh18N10T steel and preliminarily annealed.An approximate method to calculate the above functions from test data for stress mode angles w p p s = 0 6 3 , / , / (base functions) was proposed in [1]. For intermediate values of w s , linear interpolation was used. The base functions and the algorithm developed in [1] were used to analyze several deformation processes for tubular specimens for different stress mode angles. The calculated strains were in satisfactory agreement with experimental data.In support of [10][11][12] and in contrast to [1], the present paper uses a more simple approximate approach to describe the inelastic deformation of isotropic materials with allowance for the stress mode. This approach assumes that the relationship between the mean stress and the mean strain is independent of the stress mode, while the relationship between the intensities of tangential stresses and shear strains is dependent on the stress mode. The approach will be tested against specific examples.1. Co...

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“…This parameter is taken to be the stress mode angle [2]. If we replace the former nonlinear function by a linear relation between the first invariants of the stress and strain tensors and assume that the latter function is independent of the stress mode and determined from simple-tension tests, then the constitutive equations go over into those describing deformation along paths of small curvature [4], which in the case of active loading coincide with the equations of incremental plasticity [2, 8, etc.] associated with the von Mises yield criterion.…”

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Method of successive approximations for solving boundary-value problems of plasticity with allowance for the stress mode

Babeshko

Shevchenko

2010

Int Appl Mech

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A method for solving boundary-value problems of plasticity with allowance for the stress mode is developed. To describe the elastoplastic deformation of an isotropic material, use is made of constitutive equations that include two nonlinear functions dependent on the stress mode and determined experimentally. The elastoplastic state of a thin cylindrical shell under axisymmetric loading is calculated as a numerical example. The numerical results demonstrate good convergence of the method. The effect of the stress mode on the strain distribution in a cylindrical shell is assessed Keywords: boundary-value problems of plasticity, stress mode, third stress invariant, thin cylindrical shell Introduction. Constitutive equations describing the elastoplastic deformation of isotropic materials along paths of small curvature were proposed and experimentally validated in [7,[10][11][12]. These equations relate the components of the stress tensors and linear strains and assume that the strains have elastic and plastic components and the stress deviators and plastic strain differentials are coaxial. The equations include two nonlinear functions determined experimentally, one relating the mean stress and mean strain to the stress mode parameter, while the other relating the shear-stress and shear-strain intensities to the same parameter. This parameter is taken to be the stress mode angle [2]. If we replace the former nonlinear function by a linear relation between the first invariants of the stress and strain tensors and assume that the latter function is independent of the stress mode and determined from simple-tension tests, then the constitutive equations go over into those describing deformation along paths of small curvature [4], which in the case of active loading coincide with the equations of incremental plasticity [2, 8, etc.] associated with the von Mises yield criterion.To linearize the constitutive equations [10-12], the method of additional stresses was used in [10], where the general process of successive approximations for solving boundary-value static problems was outlined. Simplified constitutive equations [10-12] were considered in [1], where the former nonlinear function was replaced by a linear relation between the mean stress and mean strain and the possibility of such a replacement was justified. The simplified constitutive equations were used in [9] to solve a spatial problem of plasticity for a body of revolution based on the method of successive approximations. Unlike [9] and further to [10], the present paper details the algorithm of successive approximations based on the simplified constitutive equations that include the two nonlinear functions mentioned above and allow for unloading. The algorithm will be tested by solving a problem for a thin shell under axisymmetric loading. The method will be analyzed for practical convergence. Problem Formulation and Governing Equations.Consider an isotropic body (its mechanical properties are similar in all directions, the stress mode parameter being constan...

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Study of thermoviscoelastoplastic processes in the deformation of structural elements

Cited by 32 publications

References 2 publications

Constitutive equations of elastoplastic isotropic materials that allow for the stress mode

Constitutive equations of elastoplastic isotropic materials that allow for the stress mode

Approximate description of the inelastic deformation of an isotropic material with allowance for the stress mode

Method of successive approximations for solving boundary-value problems of plasticity with allowance for the stress mode

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