PSI - Issue 24

Guido Violano et al. / Procedia Structural Integrity 24 (2019) 251–258

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G. Violano and L. A ff errante / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 1: The force vs penetration relation predicted by the JKR theory (black solid line) for a single asperity contact. The red solid line represents the unloading path predicted by Muller model. The yellow and gray areas are the EAH and VAH contributions respectively.

2. Detachment of viscoelastic spheres

Moving from the basic relations of JKR theory, Muller (1999) proposed a numerical approach to describe the detachment process of a viscoelastic sphere from a rigid half-space. Under the assumption of a constant pull-o ff rate, for a sphere of radius R in contact over a circular area of radius a , Muller proposed a two-parameter equation to include the e ff ect of viscoelasticity in the detachment process (1) where we have defined the following dimensionless quantities ¯ a = a / a 0 and ¯ δ = δ/δ 0 ,with a 0 = 3 R π ∆ γ 0 / (6 E ∗ R ) 1 / 3 and δ 0 = R π ∆ γ 0 / (6 E ∗ R ) 2 / 3 . In eq. (1), β is a parameter depending on the viscoelastic and adhesive properties of the bodies, and it is proportional to the pull-o ff rate V = − d δ/ dt . The second parameter n is a characteristic constant of the elastomer, and it may be determined experimentally. In general, n ranges from 0 . 1 to 0 . 8. The classical JKR equations relating load, contact radius and approach can be rewritten in dimensionless form as ¯ a = 1 2 1 + 1 + ¯ P 1 / 2 2 / 3 (2) ¯ δ = ¯ a 2 + ¯ P 2¯ a (3) where ¯ P = P / P 0 , with P 0 = 1 . 5 π R ∆ γ 0 . Given the load P i reached at the end of the loading process, eqs. (2) and (3) can be used to calculate the values of the contact radius a i and penetration δ i at the beginning of the unloading phase. With these initial conditions, eq. (1) can be solved to obtain the contact radius vs penetration relation. The dimen sionless contact load is then calculated by ¯ P = 2¯ a ¯ δ − ¯ a 2 . (4) 3. Experimental tests We performed normal contact loading-unloading tests between an optically glass lens and rubber substrates. The spherical glass indenter presents a radius of curvature of 103 . 7 mm. The rubber substrate is made of PolyDiMethyl- d ¯ a d ¯ δ = 1 β   ¯ a 3 1 − ¯ δ 3¯ a 2 2 − 4 9   1 / n