Simulation of Buckling Instability of a Large Deformation Twisting Operation
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abstract
The twisting of flat bars to create the shape of an auger has been used by blacksmiths for many centuries. Easily recognizable examples of such work include twisted square rods used in wrought iron gates, and hand crafted twist drills. To this day, a large variety of long drills used in the mining industry are created by twisting flat bars of appropriate cross-section. In all of these examples, the edges of the material form a helical pattern which may be characterized by the diameter to pitch ratio. In practice, a pitch ratio of unity is typical, as this ensures sufficient axial motion of material. This pitch ratio is obtained without difficulty as long as the cross-section of the bar is not very slender. In an effort to manufacture augers intended for moving granular material rather than for drilling, thin and wide sections are desirable. This is mainly to save weight and material cost. However, such slender geometry may be prone to non-uniform deformations prior to achieving the desired pitch ratio. Apparently, for a given thickness, the ability to produce an acceptable final product is diminished as the width is increased. Nonuniform deformation in the form of folding or curling as shown in Figure 1 is the main concern for the wide and thin bars. The folding response may be recognized as instability of the system under the action of the applied torsion. Buckling of rods due to torsional loading has been studied theoretically by Ziegler [ 1 ] for the case of circular cross-sections and elastic deformation. Thin walled beam sections are considered by Timoshenko and Gere [2], and Bazant and Cedolin [3] with deformations limited to small strain elasticity. Twisting an auger necessarily requires very large strains and plastic response of the material. Furthermore, the twisting operation involves several parameters, such as temperature, axial tension and twisting rate. The success of the process and the range of its applicability may be improved if the optimum conditions are established. For this purpose, numerical modelling of the process is applied to many variations of the parameters to establish an understanding of the limitations, and how to best control the operation.
