Description of Residual Stresses in Autofrettaged Open-Ended Cylinders Made of High-Strength Steel.

The elastic range in loading-unloading processes is often reduced with a Bauschinger effect. This material property may have a high impact on residual stresses and, as a result, on the performance of autofrettaged cylinders under service conditions. The objective of the present paper is to demonstrate this impact using a material model that accounts for the response of typical high-strength steel. The solution is semi-analytic and, therefore, can be used for fast and accurate analysis of the process of autofrettage. A numerical example illustrates the general solution. This example shows that the Bauschinger effect has a significant impact on the residual circumferential stress in the vicinity of the inner radius of the cylinder. This stress is the most significant quantity of autofrettaged cylinders. Therefore, the main result obtained suggests that even a moderate Bauschinger effect should be taken into account in analyses of the process of autofrettage.

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers.

The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.

An accurate upper bound solution for plane strain extrusion through a wedge-shaped die.

An upper bound method for the process of plane strain extrusion through a wedge-shaped die is derived. A technique for constructing a kinematically admissible velocity field satisfying the exact asymptotic singular behavior of real velocity fields in the vicinity of maximum friction surfaces (the friction stress at sliding is equal to the shear yield stress on such surfaces) is described. Two specific upper bound solutions are found using the method derived. The solutions are compared to an accurate slip-line solution and it is shown that the accuracy of the new method is very high.