This article presents a detailed derivation of the constitutive relations for a linear viscoelastic isotropic model to describe the creep of P110 steel used in the production of oil and gas tubular goods (OCTG). Using the generalized Hooke’s law and the hereditary Boltzmann relations, the time dependence of the material’s mechanical behavior is taken into account. The resulting tensor relations are reduced to a one-dimensional case, an important step for practical application, in particular, for approximating the relaxation modulus in the Maxwell–Wiechert viscoelastic model in case of uniaxial tension. Furthermore, the paper formulates the key assumptions adopted in using this model. The mechanical model can be applied to metals operating at high temperatures, in particular to oil and gas tubular goods with premium threaded connections. The sealability of the connections is provided by a special design element — a radial seal, the sealing characteristics of which are significantly affected by metal creep during operation in high-temperature wells under prolonged loading. As part of the study, creep tests were conducted at the NUST MISIS laboratory on the coupling blank of a threaded connection made from P110 grade steel. Model coefficients were obtained to approximate the experiment creep curves using Monte–Carlo method. The resulting model with assumptions introduced allows for predicting the service life of premium threaded connections operating under prolonged load in high-temperature wells. 

Kirill S. Strelkov, Scientific Researcher; e-mail: ks.strelkov@yandex.ru; https://orcid.org/0009-0001-9203-9599