3D FEM simulations and experimental validation of plastic deformation of pure aluminum deformed by ECAP and combination of ECAP and direct extrusion

Rigid-viscoplastic3D finite element simulations(3D FEM)of the equal channel angular pressing(ECAP),thecombination of ECAP+extrusion with different extrusion ratios,and direct extrusion of pure aluminum were performed andanalyzed.The3D FEM simulations were carried out to investigate the load-displacement behavior,the plastic deformationcharacteristics and the effective plastic strain homogeneity of Al-1080deformed by different forming processes.The simulationresults were validated by microstructure observations,microhardness distribution maps and the correlation between the effectiveplastic strain and the microhardness values.The3D FEM simulations were performed successfully with a good agreement with theexperimental results.The load-displacement curves and the peak load values of the3D FEM simulations and the experimentalresults were close from each other.The microhardness distribution maps were in a good conformity with the effective plastic straincontours and verifying the3D FEM simulations results.The ECAP workpiece has a higher degree of deformation homogeneity thanthe other deformation processes.The microhardness values were calculated based on the average effective plastic strain.Thepredicted microhardness values fitted the experimental results well.The microstructure observations in the longitudinal andtransverse directions support the3D FEM effective plastic strain and microhardness distributions result in different formingprocesses.

Deformation Localization-A Review on the Maximum-Effective-Moment(MEM) Criterion

The essential difference in the formation of conjugate shear zones in brittle and ductile deformation is that the intersection angle between brittle conjugate faults in the contractional quadrants is acute （usually ～60°） whereas the angle between conjugate ductile shear zones is obtuse （usually 110°）. The Mohr-Coulomb failure criterion, an experimentally validated empirical relationship, is commonly applied for interpreting the stress directions based on the orientation of the brittle shear fractures. However, the Mohr-Coulomb failure criterion fails to explain the formation of the low-angle normal fault, high-angle reverse fault, and the conjugate strike-slip fault with an obtuse angle in the ~1 direction. Although it is ten years since the Maximum-Effective-Moment （MEM） criterion was first proposed, and increasingly solid evidence in support of it has been obtained from both observed examples in nature and laboratory experiments, it is not yet a commonly accepted model to use to interpret these anti- Mohr-Coulomb features that are widely observed in the natural world. The deformational behavior of rock depends on its intrinsic mechanical properties and external factors such as applied stresses, strain rates, and temperature conditions related to crustal depths. The occurrence of conjugate shear features with obtuse angles of -110~ in the contractional direction on different scales and at different crustal levels are consistent with the prediction of the MEM criterion, therefore -110° is a reliable indicator for deformation localization that occurred at medium-low strain rates at any crustal levels. Since the strain-rate is variable through time in nature, brittle, ductile, and plastic features may appear within the same rock.

Nakayama automorphisms of PBW deformations and Hopf actions

Poincaré-Birkhoff-Witt(PBW)deformations of Artin-Schelter regular algebras are skew CalabiYau.We prove that the Nakayama automorphisms of such PBW deformations can be obtained from their homogenizations.Some Calabi-Yau properties are generalized without Koszul assumption.We also show that the Nakayama automorphisms of such PBW deformations control Hopf actions on them.

Tensile properties and fractographs of Ti–2.5Al–1.5Mn foils at different temperatures

The tensile properties and fractographs of Ti- 2.5Al-1.5Mn foils at different temperatures were investi- gated. It is observed that material properties closely cor- relate with the thickness （T） to grain size （d） ratio and deformation temperature. Tensile analysis shows that local deformation is the main deformation feature in foils forming at room temperature, which may lead to premature fracture. The causes of inhomogeneous deformation behavior are the limited number of deformable grains contained in deformation zone and the weak transferability of hardening among different grains. Fracture analysis reveals that the size of dimples can represent the ductility of foils at room temperature. With the further increase of deformation temperature, the main plastic deformation mode of foils is transformed from intragranular disloca- tions and twin crystal to grain-boundary gliding and roll- ing. In conclusion, foil forming at elevated temperature can increase the hardening transferability and the number of deformable grains in deformation zone, which is an effective method to improve the formability and reduce the scatter of material properties.