Viscoelastic Strain Hardening Model for Gasket Creep Relaxation

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Antoine Abboud ◽  
Sayed A. Nassar
Keyword(s):  
Strain Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Duration ◽  
Experimental Procedure ◽  
Hardening Model ◽  
Pressure Step ◽  
Viscoelastic Strain ◽  
Step Loading ◽  
Gasket Material

This paper proposes a novel strain hardening model for investigating gasket creep relaxation under compressive step-loading at room temperature. A closed form solution is developed for predicting the steady-state gasket pressure. Step-loading of the gasket may be directly achieved and controlled, or indirectly estimated through the bolt tightening and retightening torque. The effect of gasket material, time duration at each stress level, as well as the geometric parameters of the gasket are investigated. An experimental procedure and test setup are used to validate the proposed gasket model.

Formulation of a Strain Hardening Model for Gasket Creep Relaxation

2011 ◽  
Author(s):  
Antoine Abboud ◽  
Sayed A. Nassar
Keyword(s):  
Strain Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Duration ◽  
Experimental Procedure ◽  
Hardening Model ◽  
Pressure Step ◽  
Step Loading ◽  
Gasket Material ◽  
Set Up

This paper proposes a novel strain hardening model for investigating gasket creep relaxation under compressive step-loading at room temperature. A closed form solution is developed for predicting the steady-state gasket pressure. Step-loading of the gasket may be directly achieved and controlled, or indirectly estimated through the bolt tightening and re-tightening torque. The effect of gasket material, time duration at each stress level, as well as the geometric parameters of the gasket is investigated. An experimental procedure and test set-up are used to validate the proposed gasket model.

A Proposed Model for Predicting Clamp Load Loss Due to Gasket Creep Relaxation in Bolted Joints

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Basil A. Housari ◽  
Ali A. Alkelani ◽  
Sayed A. Nassar
Keyword(s):  
Joint Stiffness ◽  
Closed Form Solution ◽  
Load Level ◽  
Form Solution ◽  
Bolted Joints ◽  
Experimental Procedure ◽  
Proposed Model ◽  
Gasket Material ◽  
Improved Model ◽  
Over Time

An improved mathematical model is proposed for predicting clamp load loss due gasket creep relaxation in bolted joints, taking into consideration gasket behavior, bolt stiffness, and joint stiffness. The gasket creep relaxation behavior is represented by a number of parameters which has been obtained experimentally in a previous work. An experimental procedure is developed to verify the proposed model using a single-bolt joint. The bolt is tightened to a target preload and the clamp load loss due to gasket creep relaxation is observed over time under various preload levels. The experimental and analytical results are presented and discussed. The proposed model provides a prediction of the residual clamp load as a function of time, gasket material and thickness, bolt stiffness, and joint stiffness. The improved model can be used to simulate the behavior of creep relaxation in soft joints as the joint stiffness effect is considered. Additionally, a closed form solution is formulated to determine the initial clamp load level necessary to provide the desired level of a steady state residual clamp load in the joint, by taking the gasket creep relaxation into account.

A Proposed Model for Predicting Residual Clamp Load in Gasketed Bolted Joints

2010 ◽  
Author(s):  
Basil A. Housari ◽  
Ali A. Alkelani ◽  
Sayed A. Nassar
Keyword(s):  
Joint Stiffness ◽  
Closed Form Solution ◽  
Load Level ◽  
Form Solution ◽  
Relaxation Behavior ◽  
Bolted Joints ◽  
Experimental Procedure ◽  
Proposed Model ◽  
Gasket Material ◽  
Improved Model

An improved mathematical model is proposed for predicting the residual clamp load in gasketed bolted joints, taking into consideration gasket creep relaxation behavior, bolt stiffness, and joint stiffness. The gasket creep relaxation behavior is represented by a number of parameters which has been obtained experimentally in a previous work. An experimental procedure is developed to verify the proposed model using a single-bolt joint. The bolt is tightened to a target preload and the clamp load loss due to gasket creep relaxation is observed over time under various preload levels. The experimental and analytical results are presented and discussed. The proposed model provides a prediction of the residual clamp load as a function of time, gasket material and thickness, bolt stiffness, and joint stiffness. The improved model can be used to simulate the behavior of creep relaxation in soft joints as the joint stiffness effect is considered. Additionally, a closed form solution is formulated to determine the initial clamp load level necessary to provide the desired level of a steady state residual clamp load in the joint, by taking the gasket creep relaxation into account.

A Proposed Model for Creep Relaxation of Soft Gaskets in Bolted Joints at Room Temperature

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Ali A. Alkelani ◽  
Basil A. Housari ◽  
Sayed A. Nassar
Keyword(s):  
Mathematical Model ◽  
Room Temperature ◽  
Closed Form Solution ◽  
Load Level ◽  
Form Solution ◽  
Bolted Joints ◽  
Experimental Procedure ◽  
Proposed Model ◽  
Gasket Material ◽  
Over Time

A mathematical model is proposed for predicting the residual clamp load during creep and∕or relaxation in gasketed joints. An experimental procedure is developed to verify the proposed model for predicting the gasket relaxation under a constant compression, gasket creep under a constant stress, and gasket creep relaxation. To study gasket creep relaxation, a single-bolt joint is used. The bolt is tightened to a target preload and the clamp load decay due to gasket creep relaxation is observed over time under various preload levels. Experimental and analytical results are presented and discussed. The proposed model provides an accurate prediction of the residual clamp load as a function of time, gasket material, and geometric properties of the gasket. A closed form solution is formulated to determine the initial clamp load level necessary to provide the desired level of a steady state residual clamp load in the joint, by taking the gasket creep relaxation into account.

Nonlinear Strain Hardening Model for Predicting Clamp Load Loss in Bolted Joints

2005 ◽  
Vol 128 (6) ◽  
pp. 1328-1336 ◽  
Author(s):  
Sayed A. Nassar ◽  
Payam H. Matin
Keyword(s):  
Equilibrium Point ◽  
Strain Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Clamping Force ◽  
Bolted Joint ◽  
Proportional Limit ◽  
Hardening Model ◽  
Nonlinear Strain ◽  
Initial Assembly

Closed form solution for the amount of clamp load loss due to an externally applied separating force is determined for a bolted assembly in which the fastener is initially tightened beyond its proportional limit. The joint may or may not have been yielded at initial assembly, however. After the initial tightening of the fastener, the joint is subsequently subjected to a tensile separating force, which further increases the fastener tensile stress into the nonlinear range. Such a separating force will simultaneously reduce the clamping force in the bolted joint. Upon the removal of the separating service load, the bolted joint system reaches a new equilibrium point between the fastener tension and the joint clamping force. At the new equilibrium point, the fastener tension is reduced from its value at initial assembly, due to the plastic elongation of the fastener. The reduction in fastener tension translates into a partial—yet permanent—loss of the clamping load, which may lead to joint leakage, loosening, or fatigue failure. A nonlinear strain hardening model is implemented in order to describe the fastener behavior past the proportional limit of its material, and to determine the clamp load loss due to the permanent set in the fastener after the separating force has been removed. In order to study the effect of strain hardening, various rates of strain hardening are used for modeling the behavior of the fastener material. The effect of three nondimensional variables on the amount of clamp load loss is investigated. This includes the joint-to-fastener stiffness ratio, the ratio of initial fastener tension to its elastic limit, and the ratio of the separating force to its maximum value that would cause joint separation to start. Analytical results are presented for a range of stiffness ratios that simulates both soft and hard joint applications.

Effect of Separating Load Eccentricity on the Clamp Load Loss in a Bolted Joint Using a Strain Hardening Model

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Sayed A. Nassar ◽  
Mohan Ganganala
Keyword(s):  
Equilibrium Point ◽  
Strain Hardening ◽  
Elastic Limit ◽  
Closed Form Solution ◽  
Tensile Load ◽  
Load Level ◽  
Form Solution ◽  
Clamping Force ◽  
Bolted Joint ◽  
Load Rate

A nonlinear model is proposed for studying the effect of the eccentricity of applied tensile forces on the clamp load loss in bolted joints that were initially tightened beyond the bolt elastic limit while the joint remained in the elastic range. A closed form solution is obtained for the amount of clamp load loss due to a cyclic separating force. The proposed model takes into account two sources of nonlinearity, namely, the strain hardening behavior of the yielded bolt material as well as the nonlinear deformation behavior of the clamped plates under an external separating load. After the initial tightening of the fastener past its elastic limit, the subsequent application of a tensile separating force on the joint tends to increase the fastener tension in a nonlinear fashion, and, simultaneously, reduce the clamping force in the bolted joint from its initial value. Upon the removal of the cyclic tensile load, the bolted joint system reaches a new equilibrium point between the residual fastener tension and the joint clamping force. At the new equilibrium point, the fastener tension is reduced from its preload due to its plastic elongation; simultaneously, a partial yet permanent loss in the clamp load level takes place. Excessive clamp load loss may lead to joint leakage, fastener loosening, or fatigue failure. For a known amplitude of the external cyclic tensile load, the increase in bolt tension and corresponding reduction in the joint clamp load are highly sensitive to the eccentricity of the tensile load (from the bolt center). Variables studied include the eccentricity value of the separating load, rate of strain hardening of the bolt material, compressive and tensile stiffness of the clamped plates, bolt stiffness, bolt preload, and magnitude of the separating tensile load.

scholarly journals DRL-Assisted Resource Allocation for NOMA-MEC Offloading with Hybrid SIC

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 613
Author(s):  
Haodong Li ◽  
Fang Fang ◽  
Zhiguo Ding
Keyword(s):  
Resource Allocation ◽  
Interference Cancellation ◽  
Multiple Access ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Duration ◽  
User Grouping ◽  
Sixth Generation ◽  
Multi Access ◽  
Delay Tolerant

Multi-access edge computing (MEC) and non-orthogonal multiple access (NOMA) are regarded as promising technologies to improve the computation capability and offloading efficiency of mobile devices in the sixth-generation (6G) mobile system. This paper mainly focused on the hybrid NOMA-MEC system, where multiple users were first grouped into pairs, and users in each pair offloaded their tasks simultaneously by NOMA, then a dedicated time duration was scheduled to the more delay-tolerant user for uploading the remaining data by orthogonal multiple access (OMA). For the conventional NOMA uplink transmission, successive interference cancellation (SIC) was applied to decode the superposed signals successively according to the channel state information (CSI) or the quality of service (QoS) requirement. In this work, we integrated the hybrid SIC scheme, which dynamically adapts the SIC decoding order among all NOMA groups. To solve the user grouping problem, a deep reinforcement learning (DRL)-based algorithm was proposed to obtain a close-to-optimal user grouping policy. Moreover, we optimally minimized the offloading energy consumption by obtaining the closed-form solution to the resource allocation problem. Simulation results showed that the proposed algorithm converged fast, and the NOMA-MEC scheme outperformed the existing orthogonal multiple access (OMA) scheme.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

scholarly journals Effect of Strain Hardening Laws on Solution Behavior Near Frictional Interfaces in Metal Forming Processes: A Simple Analytical Example

Processes ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1471
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Pierre-Yves Manach
Keyword(s):  
Strain Hardening ◽  
Metal Forming ◽  
Equivalent Stress ◽  
Qualitative Difference ◽  
Closed Form Solution ◽  
Equivalent Strain ◽  
Form Solution ◽  
Thin Layers ◽  
Qualitative Behavior ◽  
Constitutive Parameters

The main objective of the present paper is to compare, by means of a problem leading to a closed-form solution, the qualitative behavior of solutions based on three strain hardening laws: Swift’s law, Ludwik’s law, and Voce’s law. The boundary value problem involves the maximum friction law as one of the boundary conditions. Such features of the solutions as nonexistence and singularity are emphasized. An important feature of Swift’s and Ludwik’s laws is that the equivalent stress approaches infinity as the equivalent strain approaches infinity. On the contrary, Voce’s law involves saturation stress as one of the constitutive parameters. This qualitative difference in the equivalent stress behavior as the equivalent strain approaches infinity results in the qualitative difference in solutions’ behavior. In particular, Swift’s and Ludwik’s hardening laws are compatible with the regime of sticking independently of other conditions. In the case of Voce’s law, the solution under sticking conditions may break down. Moreover, Voce’s law predicts intensive strain levels near the friction surface at sliding, and the other strain hardening laws do not. Thin layers of intensive plastic deformation often occur near frictional interfaces in metal forming processes. Voce’s law predicts the occurrence of such layers without any additional assumptions.

Effect of Load Eccentricity on the Behavior of a Bolted Joint With a Yielded Fastener

2009 ◽  
Author(s):  
Sayed A. Nassar ◽  
Mohan Ganganala
Keyword(s):  
Equilibrium Point ◽  
Strain Hardening ◽  
Elastic Limit ◽  
Closed Form Solution ◽  
Tensile Load ◽  
Load Level ◽  
Form Solution ◽  
Clamping Force ◽  
Bolted Joint ◽  
Tensile Forces

A nonlinear model is proposed for studying the effect of the eccentricity of applied tensile forces on the clamp load loss in bolted joints that were initially tightened beyond the bolt elastic limit. The joint may not have been yielded at initial assembly, however. A closed form solution is obtained for the amount of clamp load loss due to a cyclic separating force. The proposed model takes into account two sources of nonlinearity; namely, the strain hardening behavior of the yielded bolt material as well as the nonlinear deformation behavior of the clamped plates under an external separating load. After the initial tightening of the fastener past its elastic limit, the subsequent application of a tensile separating force on the joint tends to increase the fastener tension in a nonlinear fashion, and simultaneously reduce the clamping force in the bolted joint from its initial value. Upon the removal of the cyclic tensile load, the bolted joint system reaches a new equilibrium point between the residual fastener tension, and the joint clamping force. At the new equilibrium point, the fastener tension is reduced from its preload due to its plastic elongation; simultaneously, a partial-yet permanent-loss in the clamp load level takes place. Excessive clamp load loss may lead to joint leakage, fastener loosening, or fatigue failure. For a known amplitude of the external cyclic tensile load, the increase in bolt tension and corresponding reduction in the joint clamp load are highly sensitive to the eccentricity of the tensile load (from the bolt center). Variables studied include the eccentricity value of the separating load, the rate of strain hardening of the bolt material, compressive and tensile stiffnesses of the clamped plates, bolt stiffness, bolt preload, and the magnitude of the separating tensile load.

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