弾塑性論に基づく速度・状態依存性摩擦構成式の提案と境界値問題への適用

• Material Type: 博士論文
• Title: 弾塑性論に基づく速度・状態依存性摩擦構成式の提案と境界値問題への適用
• Author/Editor: 尾崎, 伸吾
• Author Heading: 尾崎, 伸吾
• Publication Date: 2013-09-30
• Publication Date (W3CDTF): 2013-09-30
• Alternative Title: Proposal of elastoplastic analogy constitutive equation for rate- and state-dependent friction and its application to boundary value problems
• Degree grantor/type: 横浜国立大学
• Date Granted: 2013-09-30
• Date Granted (W3CDTF): 2013-09-30
• Dissertation Number: 乙第390号
• Degree Type: 博士(工学)
• Conferring No. (Dissertation): 乙第390号
• Text Language Code: jpn
• NDLC: UT51
• Target Audience: 一般
• Note (General): In various fields of engineering, it is important to clarify the frictional sliding behavior for a wide range of scales from microscopic elements to continental plates. Especially, when two solid bodies in contact slide slowly past each other without lubrication, an intermittent vibration phenomenon might be observed. Such rate-dependent frictional behaviors are referred to as stick-slip motions, and such motions can impair the stability of machines and structures. The aim of this study is to propose a rate- and state-dependent constitutive equation for friction and is also to propose a numerical approach for analyzing frictional contact boundary value problems including rate-dependency and anisotropy. The proposed friction model and the numerical approach are referred to herein as the rate-dependent subloading friction model and the rate form approach, respectively. It is widely known that a high friction coefficient is first observed as a sliding between bodies commences, which is called the static friction. Then, the friction coefficient decreases approaching the lowest stationary value, which is called the kinetic friction. Thereafter, if the sliding stops for a while and then it starts again, the friction coefficient recovers and a similar behavior as that in the first sliding is reproduced. In this study, based on the elastoplastic theory, the constitutive model for friction was formulated by extending the conventional friction model so as to describe the above-mentioned rate- and state-dependent frictional sliding behaviors. Fundamental features of proposed model are as follows: 1. The process for the rising of friction coefficient up to the static-friction and the subsequent reduction to the kinetic-friction is formulated in the unified way as the isotropic softening process due to the plastic-sliding based on the concept of subloading surface describing the smooth elastic-plastic transition, although only the rising process has been discussed and it has been described as the isotropic hardening process in the past models . 2. The process for the recovery from the kinetic- to static-friction is formulated as the isotropic hardening due to the creep deformations of surface asperities, while it has been formulated by the irrational equation involving the elapsed time after the stop of sliding. 3. The smooth elastic-plastic transition is depicted and the cyclic sliding behavior can be described by incorporating the concept of the sliding-subloading surface in which the plastic-sliding velocity due to the rate of contact traction inside the sliding-yield surface is described exhibiting the smooth elastic-plastic transition. It is inevitable for the prediction of the loosing of screws, bolts and piles, the smooth stress/strain distribution at contact surface and the increase of traction with slip in wheel rotation on a solid surface for instance. 4. The reduction of friction coefficient with the increase of normal contact traction is described by incorporating the nonlinear sliding surface, i.e., the normal traction dependency of frictional criterion. 5. A judgment whether or not the sliding surface is fulfilled is not required in the loading criterion for the plastic sliding velocity. This advantage is of importance especially for the analysis of cyclic friction phenomena in which a loading and an unloading are repeated. These fundamental properties could be described by the concisely unified formulation in the proposed model. The qualitative property of the present model was examined and its adequacy was verified by the numerical experiments of linear sliding phenomenon. Further, the quantitative predictability of the present model was also be verified by comparing with the various basic test results. Next, I demonstrated the numerical analysis of the stick-slip instability based on the rate-dependent subloading-friction model with Coulomb’s condition. As the first stage of the analysis of general contact boundary value problems, the one-degree-of-freedom spring-mass system was used for examinations. The validity of the present approach was examined by numerical experiments of stick-slip motions under various dynamic characteristics of the system, such as the mass, the spring stiffness and the driving velocity, and various frictional properties. The flexibility of present rate form approach was verified by demonstrating the capability of describing qualitative trends in experimental reports for the stick-slip motion. Moreover, the stick-slip instability was confirmed to have a strong correlation to not only the dynamic conditions of the system, but also the properties related to the variation rate of the friction coefficient and the preliminary microscopic sliding before macroscopic sliding. I also discussed the transition between the stick-slip and the stable sliding modes, and propose simple criteria using the friction coefficient difference and/or the spring elongation. The effectiveness of proposed criterial method was demonstrated using the numerical analysis results when the dynamic conditions change roughly. Finally, the quantitative predictability of the present numerical approach was verified by comparing it to experimental results of one-degree-of-freedom system in the range of the examined conditions. The capability of the rate-dependent friction model was shown not only for various combinations of test materials but also for dynamical conditions, i.e., the stiffness, driving velocity, and mass of system. Then, I formulated an anisotropic friction model with the orthotropy and rotation of the sliding surface based on the elastoplastic theory. This model can also describe preliminary microscopic sliding and rate-dependent frictional response. First, the qualitative property of the present model was examined and its adequacy was verified by numerical experiments on the linear sliding phenomenon. The flexibility of the friction model was shown not only for fundamental anisotropic behavior but also for rate-dependency. Furthermore, the quantitative predictability of the present model was verified by comparing it with the basic experimental results in the range of the examined conditions. To analyze practical contact boundary value problems, the rate-dependent friction model was then implemented in the FEM using the user subroutine of the commercial software package. A typical FE analysis of rate-dependent frictional sliding behavior, including stick-slip motion, was conducted to examine the effect of Young's modulus, the geometric properties, and boundary conditions on the numerical results. The present FE approach using the rate-dependent friction model considers not only the properties of friction and materials but also variations in boundary conditions. In addition, the responses of the friction force and displacement of a target body but also the stress and strain states in bulk can be grasped. Moreover, the anisotropic friction model was implemented to FEM by using the user subroutine of the commercial software package. Then, the typical FE analysis was carried out and the effect of parameters prescribing the anisotropy on the numerical results was examined. From the results of the FE analyses, I suggest that the present FE approach is applicable to the practical contact boundary value problems, including the stick-slip motion, anisotropic frictional sliding and the microscopic sliding. In the present FE analyses, however, the simple FE model that includes the rigid body was adopted. Examinations of stick-slip motion should be investigated using more general FE models, involving nonlinear material property such as plasticity and hyperelasticity and several deformed bodies having complex geometries in frictional contact. It should be noted that further discussion on the application of CAE is necessary because frictional sliding sometimes represents system and environmental dependencies. However, systematic investigations using CAE with CAD are useful for design, control, and maintenance of assembled bodies and tribological conditions at contact surfaces, to suppress stick-slip motion.
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• Date Accepted (W3CDTF): 2016-08-04T09:59:51+09:00
• Date Created (W3CDTF): 2016-09-16
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• Periodical Title (URI): http://hdl.handle.net/10131/8482; https://ynu.repo.nii.ac.jp/records/4625
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