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.

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.

Fastener Tightening Beyond Yield

2004 ◽  
Author(s):  
Sayed A. Nassar ◽  
Payam H. Matin
Keyword(s):  
Equilibrium Point ◽  
Joint Stiffness ◽  
Cyclic Loads ◽  
Clamping Force ◽  
Bolted Joint ◽  
Permanent Set ◽  
Clamp Force ◽  
Service Load ◽  
The Mean ◽  
Initial Assembly

The effect of fastener tightening beyond yield on the amount of clamp load loss, due to the application of a separating force, is investigated for a system in which the bolted joint remains within its elastic range. After the initial assembly, the joint is subsequently subjected to a tensile separating force, which increases the tensile stress in the fastener further into the plastic range. Simultaneously, the separating force reduces the clamping force. Upon the removal of the separating service load from the system, the system reaches a new equilibrium point between the fastener tension and the joint clamping force. At the new equilibrium point, the tension in the fastener is reduced due to its plastic elongation. The reduction in fastener tension translates to a partial, yet permanent, reduction in the clamping force. Excessive loss of the clamp load is a failure mode that may lead to joint leakage, loosening, or fatigue failure. Additionally, the loss of the clamp force reduces the mean stress, which may significantly affect the fatigue performance of the system under subsequent cyclic loads. A discretized non-linear model is established in order to describe the fastener behavior, and to determine the clamp load loss due to the permanent set in the fastener. The effect of two non-dimensional variables on the amount of clamp load loss is investigated. The first variable is the fastener-to-joint stiffness ratio, and the second is the ratio of initial fastener tension to its yield strength. Analytical results are presented for a range of stiffness ratios that simulates both soft and hard joint applications.

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.

Clamp Load Loss due to Fastener Elongation Beyond its Elastic Limit

2005 ◽  
Vol 128 (3) ◽  
pp. 379-387 ◽  
Author(s):  
Sayed A. Nassar ◽  
Payam H. Matin
Keyword(s):  
Equilibrium Point ◽  
Elastic Limit ◽  
Clamping Force ◽  
Bolted Joint ◽  
Proportional Limit ◽  
Joint System ◽  
Analytical Results ◽  
Service Load ◽  
Permanent Loss ◽  
Joint Separation

The amount of clamp load due to an externally applied separating force is determined for a boiled assembly in which the fastener is elongated past its proportional limit, while the clamped joint remained within its elastic range. 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 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 that may lead to joint leakage, loosening, or fatigue failure. A nonlinear model is established 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. Two fastener materials with significantly different rates of strain hardening are used for modeling the behavior of the bolted joint system. The effect of three nondimensional variables on the amount of clamp load loss is investigated. The first variable is the stiffness ratio of the joint and the fastener. The second is the ratio of initial fastener tension to the fastener elastic limit, and the third variable is the ratio of the separating force to the force that causes joint separation to start. Analytical results are presented for a range of stiffness ratios that simulates both soft and hard joint applications. Experimental verification of the analytical results is presented.

Prediction of Clamp Load Loss Under Fully Reversed Cyclic Loads in Bolted Joints

2005 ◽  
Author(s):  
Payam H. Matin ◽  
Sayed A. Nassar
Keyword(s):  
Equilibrium Point ◽  
Strain Hardening ◽  
Compressive Force ◽  
Linear Range ◽  
Half Cycle ◽  
Clamping Force ◽  
Bolted Joint ◽  
Service Load ◽  
Non Linear ◽  
Reversed Cyclic

The amount of clamp load loss due to a fully reversed cyclic service load is determined for a bolted assembly in which both the fastener and the joint were initially tightened beyond their respective proportional limits. After the initial tightening of the fastener, the joint is subsequently subjected to a fully reversed cyclic load that acts as a tensile separating force in the first half cycle, and as a compressive force on the joints during the second half cycle of the loading. During the first quarter cycle, the separating force would increase the fastener tensile stress further into the non-linear range. Such separating force would simultaneously reduce the clamping force in the bolted joint. At the end of the following quarter of the cycle, the bolted joint system reaches a new equilibrium point between the fastener tension and the joint clamping force. At the new equilibrium point, the clamp load is reduced from its initial value, due to the plastic elongation of the fastener. In the third quarter of the cycle, the compressive service load would increase the joint compressive stress into the non-linear range. Similarly, the clamp load loss would be increased at the end of the second half cycle, due to the plastic compression in the joint. The total clamp load loss may significantly lead to joint leakage, loosening, or fatigue failure. A non-linear strain hardening model is implemented in order to determine the clamp load loss due to accumulative effect of the permanent set in the fastener and the joint after the service load had been removed. Various rates of strain hardening are used for modeling the behavior of the fastener and joint materials. The effect of three non-dimensional variables on the amount of clamp load loss is investigated. The variables include the joint-to-fastener stiffness ratio, the ratio of the initial fastener tension to its elastic limit, and the ratio of the external force to its maximum tensile value that would cause joint separation to start.

Bending Effect in Concentric Bolted Joints Under Transverse Load

2013 ◽  
Author(s):  
Yosef Amir ◽  
Saravanakumar Iyyanar ◽  
Aravind Devali ◽  
Muniratnam Kumar
Keyword(s):  
Closed Form ◽  
Potential Risk ◽  
Closed Form Solution ◽  
Form Solution ◽  
Bolted Joints ◽  
Transverse Load ◽  
Catastrophic Failure ◽  
Bending Stress ◽  
Bolted Joint ◽  
Bending Effect

Bending stress calculation in eccentric bolted joints is a well-known process in the design of bolted joints. However, in a concentric bolted joint with transverse load, the existence of bending stress is generally not considered as critical. But in reality, there is a possibility of catastrophic failure of the bolt occurring in a concentric bolted joint as a result of the bending stress even before the joint looseness or before the bolt fracture under tension. The aim of this paper is to propose a closed form solution to predict the potential risk of this failure that could be developed particularly at moderate preload of the bolt. Three concentric bolted joint cases with M12, M10 and M8 with transverse load and external tension load were investigated; FEA and experimental results validated the closed form calculation.

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.

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