A Finite Element to Perform 3D Shakedown Analysis for Limited Kinematic Hardening Materials

The use of the Design by Analysis (DBA) route is a modern trend in pressure vessel and piping international codes in mechanical engineering. However, to apply the DBA to structures under variable mechanical and thermal loads, it is necessary to assure that the plastic collapse modes, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. The tool available to achieve this target is the shakedown theory. Unfortunately, the practical numerical applications of the shakedown theory result in very large nonlinear optimization problems with nonlinear constraints. Precise, robust and efficient algorithms and finite elements to solve this problem in finite dimension has been a more recent achievements. However, to solve real problems in an industrial level, it is necessary also to consider more realistic material properties as well as to accomplish 3D analysis. Limited kinematic hardening, is a typical property of the usual steels and it should be considered in realistic applications. In this paper, a new finite element with internal thermodynamical variables to model kinematic hardening materials is developed and tested. This element is a mixed ten nodes tetrahedron and through an appropriate change of variables is possible to embed it in a shakedown analysis software developed by Zouain and co-workers for elastic ideally-plastic materials, and then use it to perform 3D shakedown analysis in cases with limited kinematic hardening materials

The Influence of Limited Kinematic Hardening in Shakedown Analysis

The use of the Design by Analysis concept is a trend in modern pressure vessel and piping calculations. DBA flexibility allow us to deal with unexpected configurations detected at in-service inspections. It is also important, in life extension calculations, when deviations of the original standard hypotesis adopted initially in Design by Formula, can happen. To apply the DBA to structures under variable mechanic and thermal loads, it is necessary that, alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case), be precluded. These are two basic failure modes considered by ASME or European Standards in DBA. The shakedown theory is the tool available to achieve this goal. In order to apply it, is necessary only the range of the variable loads and the material properties. Precise, robust and efficient algorithms to solve the very large nonlinear optimization problems generated in numerical applications of the shakedown theory is a recent achievement. Zouain and co-workers developed one of these algorithms for elastic ideally-plastic materials. But, it is necessary to consider more realistic material properties in real practical applications. This paper shows an enhancement of this algorithm to dealing with limited kinematic hardening, a typical property of the usual steels. This is done using internal thermodynamic variables. A discrete algorithm is obtained using a plane stress, mixed finite element, with internal variable. An example, a beam encased in an end, under constant axial force and variable moment is presented to show the importance of considering the limited kinematic hardening in a shakedown analysis.

A Comparati ve Study of Mechanical and Tribological Properties of AISI-304 and AISI-316 Submitted to Glow Discharge Nitriding

Mechanical and tribological properties of AISI 304 and AISI 316 stainless steels submitted to glow discharge ion nitriding are reported. The atmosphere was 20:80 - N2:H2 with substrate temperatures ranging from 300 to 500 °C. Treatment at 300 °C produced expanded austenite (γN) in both steels. Increasing the temperature, the phases γ′-Fe4N and ε- Fe2+xN were present and the latter is the major phase for AISI 304. At 500 °C, the CrN phase was also identified in both steels. Hardnesses of about 13-14 GPa at near surface regions were obtained in both steels. Moreover, AISI 316 nitrided at 500 °C has the deepest hard layer. Tribological tests showed that wear can be reduced by up to a factor of six after the nitriding processes, even for a working temperature of 300 °C. The profiles during and after nanoscratch tests did not reveal significant differences after nitriding processes in both steels.

A Comparative Study of Mechanical and Tribological Properties of AISI-304 and AISI-316 Submitted to Glow Discharge Nitriding

Mechanical and tribological properties of AISI 304 and AISI 316 stainless steels submitted to glow discharge ion nitriding are reported. The atmosphere was 20:80 - N2:H2 with substrate temperatures ranging from 300 to 500 °C. Treatment at 300 °C produced expanded austenite (γN) in both steels. Increasing the temperature, the phases γ′-Fe4N and ε- Fe2+xN were present and the latter is the major phase for AISI 304. At 500 °C, the CrN phase was also identified in both steels. Hardnesses of about 13-14 GPa at near surface regions were obtained in both steels. Moreover, AISI 316 nitrided at 500 °C has the deepest hard layer. Tribological tests showed that wear can be reduced by up to a factor of six after the nitriding processes, even for a working temperature of 300 °C. The profiles during and after nanoscratch tests did not reveal significant differences after nitriding processes in both steels.

Microstructure characterization of 316L deformed at high strain rates using EBSD

Specimens from split Hopkinson pressure bar experiments, at strain rates between ~ 1000–9000 s− 1 at room temperature and 500 °C, have been studied using electron backscatter diffraction. No significant differences in the microstructures were observed at different strain rates, but were observed for different strains and temperatures. Size distribution for subgrains with boundary misorientations > 2° can be described as a bimodal lognormal area distribution. The distributions were found to change due to deformation. Part of the distribution describing the large subgrains decreased while the distribution for the small subgrains increased. This is in accordance with deformation being heterogeneous and successively spreading into the undeformed part of individual grains. The variation of the average size for the small subgrain distribution varies with strain but not with strain rate in the tested interval. The mean free distance for dislocation slip, interpreted here as the average size of the distribution of small subgrains, displays a variation with plastic strain which is in accordance with the different stages in the stress-strain curves. The rate of deformation hardening in the linear hardening range is accurately calculated using the variation of the small subgrain size with strain.