Analysis of Creep Strains and Stress Relaxation in Thin-Walled Tubular Members Made of Linear Viscoelastic Materials. 1.
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International Applied Mechanics, Vol. 56, No. 2, March, 2020
ANALYSIS OF CREEP STRAINS AND STRESS RELAXATION IN THIN-WALLED TUBULAR MEMBERS MADE OF LINEAR VISCOELASTIC MATERIALS. 1. SUPERPOSITION OF SHEAR AND VOLUME CREEP*
V. P. Golub, Ya. V. Pavlyuk, and V. S. Reznik
The problem of creep strains and stress relaxation analysis in thin-walled tubular members made of linear viscoelastic materials under combined tension and torsion loading is solved. The solution is obtained using viscoelastic models in the form of superposition of shear and volume creep. The creep and relaxation kernels are represented by fractional-exponential functions. The solutions are validated experimentally by analyzing longitudinal, transverse, and shear creep strains as well as the relaxation of normal and tangential stresses in thin-walled tubular members made of organic glass and high-density polyethylene. Keywords: thin-walled tubular member, linear viscoelastic material, tension and torsion, fractional-exponential functions, creep strain, stress relaxation, experimental validation Introduction. The wide application of polymers and polymer-based composites in critical members of modern structures has promoted their development and active usage in the strength design of linear and nonlinear viscoelasticity models [1, 4, 9, 10, 19]. The problems of analysis of creep strains and stress relaxation are most often considered for one-dimensional and combined stress–strain states. In using the principal approaches of viscoelasticity for describing the deformation of polymeric materials and compositions of them in the range of small stresses, satisfactory results can be obtained within the framework of the linear theory of viscoelasticity. These results refer to processes of deformation in one-dimensional stress state. The methods of determining mechanical parameters including parameters of hereditary kernels, which enter into the constitutive equations of the theory, can be considered as completely stated and experimentally validated. An example is the problems on creep and stress relaxation of non-uniformly aging bodies [1], rod systems, thin plates and cylindrical shells [19], reinforcing fibers, one-directional layered plastics, and polymer-concrete under constant and variable loading [2, 3, 11, 15], as well as in solving problems of the propagation of cracks in plates made of polymeric materials [5]. Analysis of creep and relaxation processes in linear viscoelastic materials in complex stress state is a much more complicated problem because there is even no consensus on the structure of constitutive equations. Particularly, in a number of the solutions obtained in [10, 12, 16, 18, 19] it was assumed that the creep in such materials is shape distortion without change in the volume. In this case, the kernel of the volume creep was assumed to be equal to zero. In reality, however, the volume strain also depends on time and loading history and is often commensurable with the elastic and creep strains related to shape distortion [4, 6, 10].
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