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

[+] Author and Article Information
Sayed A. Nassar, Payam H. Matin

Fastening and Joining Research Institute, Department of Mechanical Engineering, Oakland University, Rochester, MI 48309

J. Mech. Des 128(6), 1328-1336 (Dec 19, 2005) (9 pages) doi:10.1115/1.2214736 History: Received October 07, 2004; Revised December 19, 2005

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.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Bolted joint model

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Figure 2

Effect of external separating force in the elastic range

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Figure 3

Fluctuations in Fb and Fc corresponding to fluctuations in Fe(5)

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Figure 4

Nonlinear joint diagram (only fastener yielded)

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Figure 5

Nonlinear joint diagram (joint yielded—fastener not yielded)

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Figure 6

Nonlinear joint diagram (both fastener and joint yielded)

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Figure 7

Fastener tension versus elongation for austenitic stainless steel fastener

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Figure 8

Effect of the separating force on clamp load loss for stainless steel fastener predicted by the different methods

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Figure 9

Effect of the stiffness ratio on clamp load loss for stainless steel fastener with Fe∕Femax=1 predicted by different methods

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Figure 10

Theoretical and experimental clamp load loss versus separating force

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Figure 11

True stress—true strain curves for the materials simulated to show different amounts of strain hardening rates

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Figure 12

Effect of strain hardening on clamp load loss predicted by the different proposed methods

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Figure 13

Effect of preload level on clamp load loss for the material with different amounts of strain hardening rates



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