Study of the viscoelastoplastic deformation of an element of a body with a three-branch loading path

Abstract

The studies [3, 7-9, I 1] proposed governing equations of the theory of thermoviscoelasticity to describe features of the deformation of elements for a body in complex nonisothermal loading processs occurring along arbitrary paths. The studies also described methods of specifying the functionals that enter into these equations. The ~vorks of [2, 3,[7][8][9][10][11][12][13] examined features of the inelastic deformation of certain structural steels and alloys and empirically substantiated the above-mentioned governing equations in the complex isothermal and non-isothermal loading of elements of a body over paths in the form of twobranch broken lines including straight and curved sections. In contrast to this, here we present results of studies of the viscoelastic loading of a structural element at high temperatures along a three-branch path located within one plane of the the space of II'yushin [5J.We used the method proposed in [4, 10] to perform complex active loading along a three-branch path at 700~ The second and third branches were curvilinear. Tubular specimens of alloy E1 437 that had been heated to 700~ were first subjected to tension by an axial force to the plastic stress c(n)zz = 0.0133. They were then twisted with a simultaneous reduction in the tensile force. The tensile force was increased at a certain moment and the turning moment was decreased. The rate of loading of the specimen over the path was constant and was equal to .':; = 25.105 Pa/sec. Loading time was 8.3 min. Here, creep strain at this temperature and loading rate corresponded at the end of the given process to roughly 50% of the total strains. The results of our tests are shown in Table 1, where azz, a~, z are components of the stress tensor and ezz, tr t~,z are components of the strain tensor.We will describe this process using the stress-strain relations in [3, 7, 9, 10], which in the given case of loading specimens by a tensile force and turning moment have the form Here, No = 1" sin 13 . N 1 = P V2-sin (a --13) " " (2) -ff " sin a ' sin ~z ; a = arccos sz=Szz q-2sw~s~~ + 2s,~s~z .% + 2e~ = 9"0(1 --2v)We used the following notation in (1)-(3): I" is shear-strain intensity; S is shear-stress intensity; a is the angle between the stress vector -~ and a tangent to the loading path; /3 is the angle between the strain vector E and this tangent; s is the arc coordinate of the loading path; % is the mean normal stress; t o is the mean relative elongation; G and v are the shear modulus and Poisson's ratio, dependent on temperature; a dot above a letter denotes differentiation with respect to the arc coordinate s.Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev.