Nonlinear Viscoelastic-Plastic Creep Model of Rock Based on Fractional Calculus

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long-term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic-plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user-defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic-plastic creep model. Through sensitivity analysis of the fractional order β2 and viscoelastic coefficient ξ2, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic-plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long-term engineering stability research.

An Improved Bingham Model and the Parameter Identification of Coal (Rock) Containing Water Based on the Fractional Calculus Theory

The rheological properties of coal (rock) containing water cannot be characterized by the traditional Bingham model. This problem was addressed in this study through theoretical analysis and experimental research. Based on fractional calculus theory, a fractional calculus soft element was introduced into the traditional Bingham model. An improved Bingham model creep equation and a relaxation equation were obtained through theoretical derivations. Triaxial creep experiments of coal (rock) with different moisture contents were conducted. The parameters of the improved Bingham model were obtained by the least-squares method. Conclusions are as follows: (1) in the improved Bingham model, the stage of nonlinear accelerated creep could be characterized by the creep curves of the soft element; (2) with the increasing moisture content of the coal (rock), the transient strain and the slope of the steady creep stage increased and the total creep time showed a decreasing trend; and (3) the parameters of the creep model were obtained by nonlinear fitting of experimental data, and the fitted curve could better describe the whole creep process. The rationality of the improved creep model was verified. It can provide a theoretical basis for the study and engineering analysis of coal (rock).

Implementation of a viscoplastic substrate creep model in the thermomechanical simulation of the WAAM process

This research work focusses on the implementation of a viscoplastic creep model in the thermomechanical simulation of the wire arc additive manufacturing (WAAM) process for Ti-6Al-4 V structures. Due to the characteristic layer by layer manufacturing within the WAAM process, viscoplastic material effects occur, which can be covered by implementing a creep model in the thermomechanical simulation. Experimental creep tests with a wide temperature, load and time range were carried out to examine short-term creep behaviour in particular. A Norton-Bailey creep law is used to accurately fit the experimental data and describe the base material’s creep behaviour. Subsequently, the fitted Norton-Bailey creep law was implemented in the thermomechanical simulation of the WAAM process. Finally, to determine the effect of creep on global distortion and local residual stress state in the substrate, simulations of a simplified linear, three-layer WAAM structure, with and without applying the implemented creep law, were carried out and compared to experimental data. The thermomechanical simulation with implemented creep model reveals a significant improvement in the numerical estimation of distortion and residual stress state in the substrate. The maximum distortion is reduced by about 13% and respectively the mean absolute percentage error between simulation and experiment decreases by about 34%. Additionally, the estimation accuracy with respect to the local residual stress state in the substrate improved by about 10%.

Creep Behavior of Saturated Clay in Triaxial Test and a Hyperbolic Model

As one of the basic mechanical properties of soil, the creep property of a given type soil is related to stress path, and stress level. In this paper, triaxial shear creep tests under different deviatoric stress levels were performed on both intact sample and the reconstituted sample of clay taken from Hangzhou, China. Based on the Boltzmann linear superposition principle, the creep curves of the clay sample under different levels of deviatoric stress were obtained, and the creep characteristics of the intact sample and the reconstituted sample were compared in both total stress creep analysis and effective stress creep analysis. Furthermore, the creep curves were fitted using a hyperbolic creep model. The results show that (1) under the same stress level, the creep of intact sample evolves more than that of reconstituted sample; (2) the hyperbolic creep model is suited to describe the creep characteristics of intact and reconstituted clay, and the model parameters A s and B s can be linearly correlated to the stress level D r ; (3) for the application of the hyperbolic model, the total stress analysis works better, and the model parameters A s and B s can be determined by a linear relationship with Dr.

Magnetic and electronic properties of iron-based superconducting systems

<p>This thesis is motivated by the large variety of high-temperature superconductors that contain iron in the superconducting layer. This number has grown rapidly since the discovery in 2008 of the iron-pnictides (and chalcogenides), where iron and arsenic form the superconducting layer. Also of interest are the iron-cuprate hybrid materials, where one out of three copper atoms is replaced by iron. The aim is to understand the superconducting, magnetic and electronic properties of these materials in respect to their iron content. This thesis describes some of these properties for the iron-pnictide compounds of CeFeAsO₁₋xFx and AFe₂As₂ (A=Ba, Sr), and for the ironcuprate hybrids of FeSr₂YCu₂O₆₊y and FeSr₂Y₂₋xCexCu₂O₁₀₋y. Here it has been found that CeFeAsO₁₋xFx follows a 3D fluctuation conductivity above the superconducting transition and the thermal activation energy is correlated to the critical current density within a two fluid-flux creep model below the superconducting transition. NMR measurements show that there is considerable charge disorder within the superconducting doping region. The AFe₂As₂ show a positive magnetoresistance, which could be interpreted through three-carrier transport. Superconducting samples of SrFe₂As₂ display a large enhancement in the magnetoresistance below the superconducting transition up to 1600 %, which is due to three-carrier transport through metallic and superconducting regions in an inhomogeneous state. The superconducting properties of the iron-cuprate FeSr₂YCu₂O₆₊y in respect to the location of iron was studied under the influence of electron and hole doping and with additional magnetic impurities. FeSr₂Y₂₋xCexCu₂O₁₀₋y shows a disorder induced spin-glass state and strong localization depending on the doping.</p>