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Engineering Design Fundamentals and Single Flat Joint Characteristics 251

and Boothroyd proposed an expression to represent the hysteresis loop
on the basis of its schematic representation, already shown in Fig. 6-18. 14
Kpa
s/Phs
P h P hs (1 e ) (6-5)
where P h tangential load

s tangential displacement
K pa stiffness parameter. This value is of great interest in
understanding the dynamic behavior of the flat joint
subjected to the exciting force; however, its nature is not
fully clarified yet.
asymptotic value of tangential load (see Fig. 6-18)
P hs
In the hysteresis loop context, the marked observations are that the
energy loss per cycle is in inverse proportion to the value K , and that
pa
the maximum energy loss can be obtained by approaching the tangen-
tial force ratio to be close to the coefficient of friction and using the joint
surface with a low value of K pa and high coefficient of friction.
Obviously, Boothroyd et al. and Dekoninck provide us with the inform-
ative data, and thus we summarize the further major findings as follows.
1. Under dynamic tangential loading, the joint shows apparently the
nonlinear hysteresis loop in conjunction with the load-deflection
curve, and this loop has a slight time dependence: The damping is
larger in the commencement of loading.
2. The nonlinear hysteresis curve is derived from the interfacial
microslip, which shows linearity and nonlinearity at lower and larger
loads, respectively.
3. The energy loss at the joint is significant and changes considerably
depending on the applied load in the previous loading cycle.
4. The energy loss per cycle is independent of the excitation frequency
ranging from 5 to 200 Hz.
5. It is notable that larger values of D in Dekoninck’s expression can
be obtained for the joint with the adhesive, the same as the flat joint
subjected to the excitation force in the direction normal to the joint
surface.

14
Koizumi et al. proposed an empirical expression for the tangential microdeflection of
the single bolt-flange assembly under tangential loading. According to their proposal, the
tangential microdeflection is a function of the tangential force ratio, consisting of the
elastic deflection and microslip.
Koizumu, T., Y. Ito, and M. Masuko, “Experimantal Expression of the Tangential Micro-
displacement between Joint Surfaces,” Trans. of JSME, 1978, 44(384): 2861–2870.