Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.展开更多
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 ...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.展开更多
Surface yielding of metallic material was measured with strain gage and X-ray diffraction methods. The results show that.when the residual stress in the transverse direction is involved,the surface yield strength shou...Surface yielding of metallic material was measured with strain gage and X-ray diffraction methods. The results show that.when the residual stress in the transverse direction is involved,the surface yield strength should be evaluated with biaxial Mises criterion.For a medium carbon high strength steel, the yield strength of the bulk material is 581 MPa and the surface yield strengths for 0.05% and 0.1%plastic strain are about 436 MPa and 463 MPa respectively.The 0.05% yield strength will approximately increase to 788 MPa after shot peening.In the early stage of plastic deformation, strain hardening in the surface layer is quite different from that of the bulk sample.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
基金supported by the National Science Foundation of China (41072071)
文摘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.
文摘Surface yielding of metallic material was measured with strain gage and X-ray diffraction methods. The results show that.when the residual stress in the transverse direction is involved,the surface yield strength should be evaluated with biaxial Mises criterion.For a medium carbon high strength steel, the yield strength of the bulk material is 581 MPa and the surface yield strengths for 0.05% and 0.1%plastic strain are about 436 MPa and 463 MPa respectively.The 0.05% yield strength will approximately increase to 788 MPa after shot peening.In the early stage of plastic deformation, strain hardening in the surface layer is quite different from that of the bulk sample.
