Theory and application of equivalent transformation relationships between plane wave and spherical wave

Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.

The Change of Orientation Relationships Between Austenite and α'-Martensite During Deformation in High Manganese TRIP Steel

In situ observation of electron backscattering diffraction technique was used to evaluate the orientation relationships between austenite and α′-martensite（α′-M） for high manganese transformation-induced plasticity steel.It was noted that different from the thermal martensite,which well obeyed K-S relationship with austenite,the orientation relationship between deformation-induced α′-M with austenite changed during deformation,namely K-S and N-W relations coexisted.No clear differences existed between α′-M variants with two kinds of relationships in terms of martensitic orientation,shape and the misorientation between α′-M variants.And this phenomenon happened in almost all austenitic grains with different orientations investigated in this study.An atom displacement mechanism through conjugate complex slips of partial dislocations in the distorted fcc lattice was applied in this article to interpret the coexistence of K-S and N-W relationships.

Quantitative Analysis of the Crystallographic Orientation Relationship Between the Martensite and Austenite in Quenching–Partitioning–Tempering Steels

The orientation relationships（ORs）between the martensite and the retained austenite in low-and medium-carbon steels after quenching–partitioning–tempering process were studied in this work.The ORs in the studied steels are identified by selected-area electron diffraction（SAED）as either K–S or N–W ORs.Meanwhile,the ORs were also studied based on numerical fitting of electron backscatter diffraction data method suggested by Miyamoto.The simulated K–S and N–W ORs in the low-index directions generally do not well coincide with the experimental pole figure,which may be attributed to both the orientation spread from the ideal variant orientations and high symmetry of the low-index directions.However,the simulated results coincide well with experimental pole figures in the high-index directions{123}_（bcc）.A modified method with simplicity based on Miyamoto’s work was proposed.The results indicate that the ORs determined by modified method are similar to those determined by Miyamoto’method,that is,the OR is near K–S OR for the low-carbon Q–P–T steel,and with the increase of carbon content,the OR is closer to N–W OR in medium-carbon Q–P–T steel.

UNIFORMIZATION OF MULTIGRANULAR LINGUISTIC LABELS AND THEIR APPLICATION TO GROUP DECISION MAKING

In multiple attribute group decision making （MAGDM） problems based on linguistic information, the granularities of linguistic label sets are usually different due to the differences of thinking modes and habits among decision makers. In order to deal with this inconvenience, the transformation relationships among multigranular linguistic labels （TRMLLs）, which are applied to unify linguistic labels with different granularities into a certain linguistic label set with fixed granularity, are presented in this paper. Furthermore, the reference tables are made according to TRMLLs so that the interrelated calculation will be less complicated, and the method of how to use them is explained in detail. At length, the TRMLLs are illustrated through an application example.