Slip line field theory

In the BOC fan the slip lines undergo a smooth rotation from BO to CO by an angle Af = ujl, which, according to slip-line-field theory, results in a monotonic change with of the mean normal stress by... 

Based on the slip-line field theory [e.g., see Hill (1950)], Adachi and Yoshioka (1973) also extended the analysis of Ansley and Smith (1967) for spheres to include the creeping cross-flow over cylinders and obtained the following approximation expression for X ... 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

Several researchers tried to replace the single-shear plane model by a shear zone model. Lee and Shaffer (1951) provided a slip-line solution by applying the theory of plasticity. In the slip-line model, the metal is assumed to flow along the line of maximum shear lines. The slip-line field solution cannot be applied easily to three-dimensional as well as strain-hardening cases. Sidjanin and Kovac (1997) applied the concept of fracture mechanics in chip formation process. Atkins (2003) demonstrated that the work for creation of new surfaces in metal cutting is significant. He also points out that Shaw (1954) has shown this work to be insignificant. However, when this work is included based on the modem ductile fracture mechanics, even the Merchant analysis provides reasonable results. 

The actual behavior of the blunting crack requires for its analysis numerical approaches that we consider below. However, here we try first to capture the essential features of the flow pattern from the ideally plastic, non-hardening material solutions using slip-line-field approaches of plasticity theory. 

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