An approach to predict free surface fracture in bulk forming
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I. INTRODUCTION
THE forming limit diagram is a useful tool for the synthesis of successful bulk forming processes such as forging, bending, and rolling. Surface strain measurements at sites of expected cracking are made on selected test pieces undergoing deformation modes such as plane strain tension, upsetting, and slab bending.[1,2] Although the stress state is generally one of compression in bulk forming processes, secondary tensile stresses may develop because of friction and geometry defects, leading to initiation of cracks and premature fracture. A plot of the limit tensile strain components versus the compressive ones for different loading paths sets up the required formability curve for the tested alloy. The data available in the literature for metallic alloys that are obtained experimentally[3–8] led to suggesting an empirical workability criterion in the form of a straight line with a slope of 1/2 that passes through the plane strain fracture point for the given material and conditions. Other semiempirical fracture conditions based on macromechanical perspective have been suggested.[9,10,11] For instance, Cockcroft and Latham[9] postulated that fracture is controlled by the maximum principal tensile stress integrated over the strain path. Modification to this condition was proposed by others[10,11] to include an explicit dependence on the mean stress. Several investigators[3,7,8] have applied the Cockroft-Latham fracture criterion[9] with varying degrees of success to predict the onset of cracking in bulk forming processes. Wifi et al.[12] presented a critical review comparing various workability criteria in bulk forming processes. They emphasized A.R. RAGAB, Professor, is with the Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, Giza, 12316, Egypt. Contact e-mail: [email protected] Manuscript submitted April 6, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
the need to determine the range of applicability best suitable for each criterion. A recent investigation[13] assessed several of the most commonly used fracture criteria experimentally and numerically. It was concluded that fracture is controlled by shear mode for negative stress triaxialities, whereas void growth is the dominant failure mode for large positive triaxialities. Numerous analytical models to predict the forming limit curve for sheet metal stretching are based on the assumption of Marciniak and Kuczynski[14] by introducing a thickness inhomogeneity in the sheet metal. Lee and Kuhn[4] derived the bulk formability curve by applying the local necking analysis of Marciniak and Kuczynski.[14] Kuhn and his coworkers[2,4,7,15] consider a material element with an initial thickness inhomogeneity that undergoes deformation into the tension-compression range. In addition to the difficulty in assuming a realistic thickness inhomogeneity, the model predicts only the essential features rather than the magnitude of the limit strain curve. Thomason[8] as well as Kuhn and Lee[7] observed subsurface void form
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