Equipment for testing of materials with the recording of completely equilibrium deformation diagrams

The analysis of the previous results of the study on concrete stress-strain behavior at elevated temperatures has been carried out. Based on the analysis, the main reasons for strength retrogression and elastic modulus reduction of concrete have been identified. Despite a significant amount of research in this area, there is a large spread in experimental data received, both as a result of compression and tension. In addition, the deformation characteristics of concrete are insufficiently studied: the coefficient of transverse deformation, the limiting relative compression deformation corresponding to the peak load and the almost complete absence of studies of complete deformation diagrams at elevated temperatures. The two testing chambers provided creating the necessary temperature conditions for conducting studies under bending compression and tension have been developed. On the basis of the obtained experimental data of physical and mechanical characteristics of concrete at different temperatures under conditions of axial compression and tensile bending, conclusions about the nature of changes in strength and deformation characteristics have been drawn. Compression tests conducted following the method of concrete deformation complete curves provided obtaining diagrams not only at normal temperature, but also at elevated temperature. Based on the experimental results, dependences of changes in prism strength and elastic modulus as well as an equation for determining the relative deformation and stresses at elevated temperatures at all stages of concrete deterioration have been suggested.

Improvement Of Curvilinear Diagrams Of Concrete Deformation

Promyshlennoe i Grazhdanskoe Stroitel stvo ◽

10.33622/0869-7019.2019.08.99-104 ◽

2019 ◽

pp. 99-104

Keyword(s):

Reinforced Concrete ◽

Peak Load ◽

Experimental Studies ◽

Concrete Structures ◽

Deformation Model ◽

Reinforced Concrete Structures ◽

Significant Difference ◽

Deformation Diagrams

Problems when calculating reinforced concrete structures based on the concrete deformation under compression diagram, which is presented both in Russian and foreign regulatory documents on the design of concrete and reinforced concrete structures are considered. The correctness of their compliance for all classes of concrete remains very approximate, especially a significant difference occurs when using Euronorm due to the different shape and sizes of the samples. At present, there are no methodical recommendations for determining the ultimate relative deformations of concrete under axial compression and the construction of curvilinear deformation diagrams, which leads to limited experimental data and, as a result, does not make it possible to enter more detailed ultimate strain values into domestic standards. The results of experimental studies to determine the ultimate relative deformations of concrete under compression for different classes of concrete, which allowed to make analytical dependences for the evaluation of the ultimate relative deformations and description of curvilinear deformation diagrams, are presented. The article discusses various options for using the deformation model to assess the stress-strain state of the structure, it is concluded that it is necessary to use not only the finite values of the ultimate deformations, but also their intermediate values. This requires reliable diagrams "s–e” for all classes of concrete. The difficulties of measuring deformations in concrete subjected to peak load, corresponding to the prismatic strength, as well as main cracks that appeared under conditions of long-term step loading are highlighted. Variants of more accurate measurements are proposed. Development and implementation of the new standard GOST "Concretes. Methods for determination of complete diagrams" on the basis of the developed method for obtaining complete diagrams of concrete deformation under compression for the evaluation of ultimate deformability of concrete under compression are necessary.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.1.05 ◽

2020 ◽

pp. 60-73

Author(s):

Yu V Nemirovskii ◽

S V Tikhonov

Keyword(s):

General Solution ◽

Least Squares ◽

Nonlinear Differential Equations ◽

Limit State ◽

Algebraic Equations ◽

Method Of Least Squares ◽

Elasticity Limit ◽

Limit Values ◽

Symbolic Calculations ◽

Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

Features of the kinetics of cyclic elastoplastic deformation diagrams at dwells in cycles and superimposition of variable stresses on them

Industrial laboratory Diagnostics of materials ◽

10.26896/1028-6861-2020-86-12-46-53 ◽

2020 ◽

Vol 86 (12) ◽

pp. 46-53

Author(s):

M. M. Gadenin

Keyword(s):

Experimental Data ◽

Elastoplastic Deformation ◽

Low Cycle Fatigue ◽

Cycle Fatigue ◽

Loading Cycle ◽

Additional Variable ◽

Dynamic Creep ◽

Variable Stresses ◽

Kinetics Of ◽

Deformation Diagrams

The goal of the study is determination of the regularities of changes in cyclic strains and related deformation diagrams attributed to the existence of time dwells in the loading modes and imposition of additional variable stresses on them. Analysis of the obtained experimental data on the kinetics of cyclic elastoplastic deformation diagrams and their parameters revealed that in contrast to regular cyclic loading (equal in stresses), additional deformations of static and dynamic creep are developed. The results of the studys are especially relevant for assessing the cyclic strength of unique extremely loaded objects of technology, including nuclear power equipment, units of aviation and space systems, etc. The experiments were carried out on the samples of austenitic stainless steel under low-cycle loading and high temperatures of testing. Static and dynamic creep deformations arising under those loading conditions promote an increase in the range of cyclic plastic strain in each loading cycle and also stimulate an increase in the range of elastoplastic strain due to active cyclic deformation. At the same time the existence of dwells on extrema of stresses in cycles without imposition of additional variable stresses on them most strongly affects the growth of plastic strain ranges in cycles. Imposition of additional variable stresses on dwells also results in the development of creep strains, but their growth turns out to be somewhat less than in the presence of dwells without stresses imposed. The diagrams of cyclic deformation obtained in the experiments are approximated by power dependences, their kinetics being described in terms of the number of loading cycles using corresponding temperature-time functions. At the same time, it is shown that increase in the cyclic plastic deformation for cycles with dwells and imposition of additional variable stresses on them decreases low cycle fatigue life compared to regular loading without dwells at the same stress amplitudes, moreover, the higher the values of static and dynamic creep, the greater decrease in low-cycle fatigue life. This conclusion results from experimental data and analysis of conditions of damage accumulation for the considered forms of the loading cycle using the deformation criterion of reaching the limit state leading to fracture.

Influence of Humidity of Concrete on Its Deformation Diagrams under Load at Low Negative (up to -70°C) Temperatures

Stroitel nye Materialy ◽

10.31659/0585-430x-2017-749-6-10-13 ◽

2017 ◽

Vol 749 (6) ◽

pp. 10-13 ◽

Cited By ~ 2

Author(s):

N.I. KARPENKO ◽

◽

V.N. YARMAKOVSKY ◽

D.Z. KADIEV ◽

◽

...

Keyword(s):

Deformation Diagrams

Numerical Modeling of Large Deformations for Porous Metals and Identification of Carcass Deformation Diagrams

Mechanics of Composite Materials ◽

10.1007/s11029-021-09920-x ◽

2021 ◽

Vol 56 (6) ◽

pp. 747-754

Author(s):

V. G. Bazhenov ◽

М. N. Zhestkov

Keyword(s):

Numerical Modeling ◽

Large Deformations ◽

Porous Metals ◽

Deformation Diagrams

On the nuclear equilibrium deformation and the moment of inertia of the band

Physics Letters B ◽

10.1016/0370-2693(71)90596-x ◽

1971 ◽

Vol 34 (4) ◽

pp. 255-256 ◽

Cited By ~ 5

Author(s):

S.A. Hjorth ◽

J. Oppelstrup ◽

G. Ehrling

Keyword(s):

Moment Of Inertia ◽

Equilibrium Deformation ◽

The Moment

DIFFERENTIAL EQUATIONS OF EQUILIBRIUM OF IDEALLY ELASTOPLASTIC CONTINUOUS MEDIUM FOR PLANE ONE-DIMENSIONAL DEFORMATION IN APPROXIMATION OF CLOSING EQUATIONS BY BIQUADRATIC FUNCTIONS

STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS ◽

10.37538/0039-2383.2021.2.37.45 ◽

2021 ◽

Vol 295 (2) ◽

pp. 37-45

Author(s):

S.V. Bakushev ◽

Keyword(s):

Differential Equations ◽

Shear Deformation ◽

Continuous Medium ◽

Strain Tensor ◽

Shear Deformations ◽

One Dimensional ◽

Volumetric Expansion ◽

Fractional Rational Function ◽

Secant Shear Modulus ◽

Deformation Diagrams

The present article considers the construction of differential equations of equilibrium of geometrically and physically nonlinear ideally elastoplastic in relation to shear deformations of continuous medium under conditions of one-dimensional plane deformation, when the diagrams of volumetric and shear deformation are approximated by biquadratic functions. The construction of physical dependencies is based on calculating the secant moduli of volumetric and shear deformation. When approximating the graphs of the volumetric and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations; the secant modulus of volumetric expansion-contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volumetric and shear deformation, the secant shear modulus is a fractional (rational) function of the shear strain intensity; the secant modulus of volumetric expansion-compression is a fractional (rational) function of the first invariant of the strain tensor. Based on the assumption of independence, generally speaking, from each other of the volumetric and shear deformation diagrams, five main cases of physical dependences are considered, depending on the relative position of the break points of the graphs of the diagrams volumetric and shear deformation. On the basis of received physical equations, differential equations of equilibrium in displacements for continuous medium are derived under conditions of plane one-dimensional deformation. Differential equations of equilibrium in displacements constructed in the present article can be applied in determining stress and strain state of geometrically and physically nonlinear ideally elastoplastic in relation to shear deformations of continuous medium under conditions of plane one-dimensional deformation, closing equations of physical relations for which, based on experimental data, are approximated by biquadratic functions.

Deformation Diagrams

Theory of Structures ◽

10.1002/9783433602638.ch15 ◽

2013 ◽

pp. 233-243

Keyword(s):

Deformation Diagrams