## 1 Introduction  
Polyetheretherketone (PEEK) is a thermoplastic semi-crystalline polymer that is actively used in modern industries due to a unique combination of a number of operational properties [1], thermo, heat, and fire resistance, low hygroscopicity, radiation and chemical resistance, good mechanical and dielectric properties, and biocompatibility [2; 3; 4]. It is known from [5; 6] that the crystallization temperature of PEEK, depending on the manufacturer, varies from 287 to 311 \({}^{\circ}\)C, the melting temperature varies from 339 to 347 \({}^{\circ}\)C, the decomposition temperature varies from 567 to 589 \({}^{\circ}\)C, and the glass transition temperature varies from 140 to 148 \({}^{\circ}\)C, the upper limits of the operating temperatures being from 230 to 290 \({}^{\circ}\)C, respectively. It is known from [7] that the PEEK density is a function of the degree of crystallinity and can be assumed constant for a material in the amorphous \(\rho_{a}\) = 1262.6 Kg/m\({}^{3}\) and crystallized state \(\rho_{K}\) = 1400.6 Kg/m\({}^{3}\). Similarly to [7], the coefficient of thermal expansion can be considered a constant value at the temperature intervals of the glassy \(\alpha_{c}\) = 100 \(\times\) 10\({}^{-6}\) 1/\({}^{\circ}\)C and highly elastic states \(\alpha_{B}\) = 670 \(\times\) 10\({}^{-6}\) 1/\({}^{\circ}\)C.  
The dependences of thermophysical characteristics of PEEK on temperatnse are known from [8; 9] and represent non-monotonic curves over the studied temperature range from 25 to 330 \({}^{\circ}\)C. In the range from 25 to 100 \({}^{\circ}\)C, a decrease in the specific heat capacity from \(C_{p}=1242\) J/(kg K) to 1.181 J/(kg K) and a subsequent return to the previous level is observed for the curves. Similarly, for thermal conductivity: from \(\lambda=0.268\) W/(m K) to 0.157 W/(m K). In the temperature range from 100 to 300 \({}^{\circ}\)C, an almost linear increase in the described characteristics is observed from \(C_{p}=1282\) J/(kg K) to \(2412\) J/(kg K) and from \(\lambda=0.230\) W/(m K) to 0.264 W/(m K), respectively. When the crystallization temperature is reached, a sharp increase in both characteristics is observed up to the limit values of \(C_{p}=3248\) J/(kg K) and \(\lambda=0.357\) W/(m K) with their further decrease as the melting temperature is reached. At the same time, when solving a number of problems (for example, calculating the stress-strain state of the structure [7]), the mentioned thermophysical properties of the material can be assumed constant and equal to \(C_{p}=1300\) J/ (kg K) and \(\lambda=0.25\) W/(m K). There are a number of comparative calculations on the mechanical behavior of PEEK in extreme operating conditions (with the transition to plastic) [10]. To describe the thermal deformation of the PEEK material and calculate the stress-strain state of the structure, the Johnson-Cook model is mainly used. This model allows taking into account plastic deformation, strain rate, viscous effects, and the thermal softening of the material [11; 12; 13; 14; 15]. However, this model has some drawbacks. It is convenient to use in software packages with an explicit scheme for calculating non-stationary problems. We had an extremely poor convergence of the solution when trying to implement it in ANSYS Mechanical APDL. In addition, the validity of using this model to describe polymers remains an open question. Moreover, it should be noted that in the process of layer-by-layer growth, the material works under normal conditions, not associated with large active deformations, but in a wide temperature range. In this case, the main hypothesis of the formation of residual deflections [7] is the assumption of the prevailing contribution of the incompatibility of deformations in individual layers due to the non-synchronous solidification of the thermoviscoelastic material. A similar mechanism is used in the production of prestressed glass. For this reason, a viscoelastic model was chosen.