Change in thickness in curved fold model for axial crushing of tubes

A partly inside and partly outside curved fold model with variable straight length and stepped variation in the thickness of tube during folding has been developed in the present paper. The variation of circumferential strain during the formation of fold has been taken into consideration. All model parameters viz. size of fold, optimal value of folding parameter, maximum hinge angle and the final radius of curvature of fold have been evaluated analytically. An expression has been derived for determining the variation of crushing load during the formation of a fold. The total outside and total inside fold models can be easily derived from the present model. The results have been compared with experiments and reasonably good agreement has been observed. The incorporation of change in thickness of tube during folding has been found to reduce the folding parameter thus bringing it closer to the experiments. Some parametric studies by varying the length of straight portion of the fold have also been conducted. The results are of help in understanding the phenomenon of actual fold formation.