Derivation of Plastic Work Rate Done per Unit Volume for Mean Yield Criterion and Its Application

In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate done per unit volume were derived. A generalized worked example of slab forging was analyzed by the criterion and its corresponding plastic work rate done per unit volume. Then, the precision of the solution was compared with those by Mises and Twin shear stress yield criterions, respectively. It turned out that the calculated results by MY criterion were in good agreement with those by Mises criterion.

APPLICATION OF NONLOCAL FRICTION IN SEVERAL KINDS OF PLASTIC FORMING PROBLEMS

The nonlocal friction law proposed by Oden et al. was adopted in order to consider the nonlocal friction effect of the asperities on the rough contact surface between the die and the workpiece in several kinds of metal plastic forming problems. The mechanical equilibrium equations with the integral-differential form were obtained by using the engineering method or slab method, and solved approximately by using the perturbation method. The normal stress distributions on the contact surfaces in metal forming problems with nonlocal friction were obtained, and the factors which affect the nonlocal friction effect were analyzed.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Crack Properties of Lean Duplex Stainless Steel 2101 in Hot Forming Processes

The crack behavior of LDX 2101 by hot compression tests in the temperature range of 950 to 1150 ℃ and strain rate range of 0.01 to 30 s-1 was studied.The hot workability map of LDX 2101 was constructed and the alloy exhibited a better crack resistance at higher temperature and lower strain rate.Microvoids initiated and coalesced into crack at subsurface on the equatorial plane of bulge surface under secondary tensile condition.The cracks were orientated at an angle of approximately 45° with respect to the compression axis due to the secondary tensile stress.Microcracks easily initiated on the interface of ferrite and austenite and propagated within ferrite.The predicted results using specific plastic work approach were matched well with the free surface cracks.