Creep and Long-Term Strength of a Laminated Thick-Walled Tube of Nonlinear Viscoelastic Materials Loaded by External and Internal Pressures

• Published in: Mechanics of composite materials Vol. 57; no. 6; pp. 731 - 748
• Main Author: Khokhlov, А. V.
• Format: Journal Article
• Language: English
• Published: New York Springer US 2022; Springer; Springer Nature B.V
• Subjects: Ceramics; Characterization and Evaluation of Materials; Chemistry and Materials Science; Classical Mechanics; Composite materials; Composites; Constitutive equations; Constitutive relationships; Creep (materials); Criteria; Exact solutions; External pressure; Functional equations; Glass; Integral equations; Internal pressure; Laminates; Materials Science; Mathematical analysis; Natural Materials; Nonlinearity; Operators (mathematics); Shear strain; Solid Mechanics; Stress distribution; Thick walls; Thickness; Tubes; Viscoelastic materials; Viscoelasticity; integral equations; relaxation modulus; long-term strength curve; Rabotnov constitutive equation; laminated composites; nonlinear viscoelasticity; fracture time; creep; multilayer thick-walled tubes
• ISSN: 0191-5665; 1573-8922
• DOI: 10.1007/s11029-022-09995-0

An exact solution to the creep and long-term strength problem for pressurized thick-walled tubes consisting of several layers of physically nonlinear viscoelastic materials obeying the Rabotnov constitutive equation with two arbitrary material functions for each layer (creep compliance and a function that governs the physical nonlinearity) was constructed and studied. All layer materials are homogeneous, isotropic, and incompressible, and the tube is loaded by internal and external pressures creating a plain strain state, i.e., zero axial displacements are given on the edge of tube cross sections. Closed expressions were found for displacement, strain, and stress fields in relation to the single unknown function of time and integral operators involving this function, pairs of (arbitrary) material functions of each tube layer, preset pressure values and ratios of tube layers radii, and an integral equation to determine this unknown function was derived. Expressions and three creep failure criteria with three measures of damage (the effective shear strain, the maximum shear strain, or the maximum principal strain) were used to derive formulas for the creep fracture time of a tube to mark the layer in which the fracture will occurs earlier and to find a simple strength parameter for the tube (depending on layers thicknesses and their fracture strains) which should be increased to enhance its long-term strength. Assuming that the relaxation moduli of layer materials are proportional to a single (arbitrary) function of time and the material functions that govern the nonlinearity coincide with a power function with a positive exponent, an exact solution of the resolving functional equation was constructed. All integrals involved in the general representation of the tube stress field were calculated and reduced to simple algebraic formulas convenient for an analysis. Explicit formulas were derived for the creep fracture time of the tube, and closed equations for the long-term strength curves based on three creep failure criteria mentioned above were found. The general properties of the long-term strength curves were studied for arbitrary material functions of the constitutive relation and compared with each other. It is proved that the long-term strength curves (fracture time as a function of pressures difference) are decreasing and convex down and that their shape is controlled mainly by the compliance functions of layer materials rather than by the radii of tube layers and the nonlinearity of the governing physical function, because they influence only the factor responsible for the long-term strength in tension along the pressure axis.