PSI - Issue 73

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Jakub Flodr et al. / Procedia Structural Integrity 73 (2025) 9–13 Jakub Flodr, Petr Lehner, Dominik Gřešica, Martin Krejsa / Structural Integrity Procedia 00 (2025) 000–000

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where: , ,

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design value of longitudinal normal stress, design value of transverse normal stress,

,

design value of shear stress,

declared yield strength of the base material, partial load capacity factor of the clinch connection, design value of the displacement (vertical) force,

design value of bending moment, design value of the normal force,

reduced shear area of the intermediate ring, full cross-sectional area of the annulus,

elastic section modulus.

3. Calculation examples 3.1. Assessment of a clinch joint loaded with shear

As a first example, a 3.45 mm thick sheet metal joint was selected for shear testing. During the experimental evaluation of such a joint, an average value of 8.80 kN was achieved. The following values were considered for the calculation: • thickness of the joined material t = 3.45 mm, • inner diameter of the clinch joint d 1 = 9.00 mm, • width in section t 1 = 1.13 mm, • width in section t 2 = 1.17 mm, • outer diameter d 2 = d 1 + t 1 + t 2 = 11.30 mm, • bending arm h 0 = 3.45 mm, • full area of the annulus A s = 36.67 mm 2 , • reduced area of the annulus A w,s = 24.56 mm 2 (shear area reduction factor for annulus = 0.67), • design value of bending moment = 16 387 Nm, • elastic section modulus = 84.65 mm 3 , and the following resulting values were calculated: • shear stress according to formula (2) = 193.3 MPa, • normal stress according to formula (3) , = 193.6 MPa, • von Mises stress according to formula (1) = 386.8 MPa ≤ f y = 390 MPa. The analytical calculation achieved a value of 4.80 kN through an iterative method. The difference between the analytically calculated value and the experimental data was 45%. 3.2. Assessment of a clinch joint loaded with tensile As a second example, a tensile test was used, where two sheets of 2.00 mm thick were connected. The average value of the experimental solution was 2.50 kN. The following values were considered for the calculation: • thickness of the joined material t = 2.00 mm, • inner diameter of the clinch joint d 1 = 4.30 mm, • width in section t 1 = 0.34 mm, • width in section t 2 = 0.32 mm, • outer diameter d 2 = d 1 + t 1 + t 2 = 4.96 mm, • full area of the annulus A s = 4.80 mm 2 , And the following resulting values were calculated: • normal stress according to formula (4) , = 385.0 MPa, • von Mises stress according to formula (1) = 385.0 MPa ≤ fy = 390 MPa.