A simple bolted joint was analyzed to calculate bolt clampup relaxation for a graphite/epoxy (T300/5208) laminate. This study was based on a viscoelastic finite-element analysis of a double-lap joint with a steel bolt. Clampup forces were calculated for various steady-state temperature-moisture conditions using various exposure durations.

The finite-element analysis predicted that clampup forces would relax even for the room-temperature dry (RTD) condition. The relaxations were 8, 13, 20, and 31% for exposure durations of 1 day, 1 month, 1 year, and 20 years, respectively. As expected, elevated temperature and moisture levels each increased the relaxation rate. The viscoelastic effects of elevated temperature and moisture appeared to be additive.

Based on the finite-element results, a simple empirical equation was developed for clampup force relaxation. First, the equation was postulated to have the same functional form as the inverse of the material compliance in the thickness direction. Second, the two constants in the equation were fitted, by a least-square regression analysis, to the RTD results, Finally, the equation was generalized to include temperature- and moisture-dependent viscoelastic effects by using material hygrothermal shift factors. This generalized equation was used to calculate clampup forces for the same temperature-moisture conditions as used in the finite-element analysis. The two sets of calculated results agreed well.

The clampup equation was further evaluated by comparing calculated and measured clampup forces. Instrumented (strain-gaged) bolts were monitored throughout a 100-day test period. Three steady-state test environments were used: RTD, room temperature with a laboratory ambient moisture level (0.46%), and an elevated-temperature (66°C) dry case. The equation agreed reasonably well with the test data.