Transient longitudinal waves in a strain-softening rod has been investigated. For rate-dependent materials, the governing equations are proved to be hyperbolic, thereby indicating that the stress waves in softening st...Transient longitudinal waves in a strain-softening rod has been investigated. For rate-dependent materials, the governing equations are proved to be hyperbolic, thereby indicating that the stress waves in softening state still propagate along the rod. A transient solution for a semi-infinite rod subjected to an axial impact has been obtained, which shows that there exists a finite softening region in the rod and it travels along the rod. It is indicated that the length of the softening region and the plastic wave speed are pertinent to the rate sensitivity as well as to the softening character of materials.展开更多
Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic-viscoplastic constitutive relation with various hardening-softening-hardenin...Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic-viscoplastic constitutive relation with various hardening-softening-hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip. On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening (or softening-hardening) has a particularly strong effect on the near crack tip stress and deformation fields.展开更多
The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy ...The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy and a stress parameter, independent of stress history. The modified plastic strain energy approach was developed based on results from a series of drained plastic strain compression tests along various stress paths on saturated dense Toyoura sand with accurate stress and strain measurements. The proposed model is coupled with an isotropically work-hardening and softening, non-associtated, elasto-plastic material description. The constitutive model concerns the inherent and stress system-induced cross-anisotropic elastic deformation properties of sand. It is capable of simulating the deformation characteristics of stress history and stress path, the effects of pressure level, anisotropic strength and void ratio, and the strain localization.展开更多
The effect of strain hardening and strain softening behavior of flow stress changing with temperature on welding residual stress, plastic strain and welding distortion of ATN0 1-T4 aluminum alloy was studied by finite...The effect of strain hardening and strain softening behavior of flow stress changing with temperature on welding residual stress, plastic strain and welding distortion of ATN0 1-T4 aluminum alloy was studied by finite simulation method. The simulation results show that the weld seam undergoes strain hardening in the temperature range of 180-250 ℃, however, it exhibits strain softening at temperature above 250 ℃ during welding heating and cooling process. As a result, the strain hardening and strain softening effects counteract each other, introducing slightly influence on the welding residual stress, residual plastic strain and distortion. The welding longitudinal residual stress was determined by ultrasonic stress measurement method for the flat plates of A7N01-T4 aluminum alloy. The simulation results are well accordant with test ones.展开更多
An experimental investigation was carried out on the flow characteristic and hardening of steel 40 subjected to complex combined axial-torsional cyclic straining. For a specific cyclic strain path, the steel has mainl...An experimental investigation was carried out on the flow characteristic and hardening of steel 40 subjected to complex combined axial-torsional cyclic straining. For a specific cyclic strain path, the steel has mainly cyclic softening behavior when the strain amplitude is small. While with an increase of the effective strain amplitude, the softening becomes small, but there is the cyclic softening even though the steel is subjected to the cyclic loading by a square strain path. However, the steel has cyclic additional hardening by a nonproportional path, compared with the proportional cycling. Generally, the additional hardening is small and its historical effect is not obvious at small strain amplitude. The additional hardening is remarkable by a cross-triangular strain path of large strain amplitude. The memory of the history of nonproportional cyclic loading, the direction of plastic flow and the plastic modulus of the steel were also studied.展开更多
Fault rockburst is treated as a strain localization problem under dynamicloading condition considering strain gradient and strain rate. As a kind of dynamic fracturephenomena, rockburst has characteristics of strain l...Fault rockburst is treated as a strain localization problem under dynamicloading condition considering strain gradient and strain rate. As a kind of dynamic fracturephenomena, rockburst has characteristics of strain localization, which is considered as aone-dimensional shear problem subjected to normal compressive stress and tangential shear stress.The constitutive relation of rock material is bilinear (elastic and strain softening) and sensitiveto shear strain rate. The solutions proposed based on gradient-dependent plasticity show thatintense plastic strain is concentrated in fault band and the thickness of the band depends on thecharacteristic length of rock material. The post-peak stiffness of the fault band was determinedaccording to the constitutive parameters of rock material and shear strain rate. Fault bandundergoing strain softening and elastic rock mass outside the band constitute a system and theinstability criterion of the system was proposed based on energy theory. The criterion depends onthe constitutive relation of rock material, the structural size and the strain rate. The staticresult regardless of the strain rate is the special case of the present analytical solution. Highstrain rate can lead to instability of the system.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Transient longitudinal waves in a strain-softening rod has been investigated. For rate-dependent materials, the governing equations are proved to be hyperbolic, thereby indicating that the stress waves in softening state still propagate along the rod. A transient solution for a semi-infinite rod subjected to an axial impact has been obtained, which shows that there exists a finite softening region in the rod and it travels along the rod. It is indicated that the length of the softening region and the plastic wave speed are pertinent to the rate sensitivity as well as to the softening character of materials.
文摘Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic-viscoplastic constitutive relation with various hardening-softening-hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip. On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening (or softening-hardening) has a particularly strong effect on the near crack tip stress and deformation fields.
基金The project supported by the Association of International Education of Japan
文摘The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy and a stress parameter, independent of stress history. The modified plastic strain energy approach was developed based on results from a series of drained plastic strain compression tests along various stress paths on saturated dense Toyoura sand with accurate stress and strain measurements. The proposed model is coupled with an isotropically work-hardening and softening, non-associtated, elasto-plastic material description. The constitutive model concerns the inherent and stress system-induced cross-anisotropic elastic deformation properties of sand. It is capable of simulating the deformation characteristics of stress history and stress path, the effects of pressure level, anisotropic strength and void ratio, and the strain localization.
基金Project(2007DFR70070) supported by China-Russia Government-to-Government Scientific and Technical Cooperation Foundation
文摘The effect of strain hardening and strain softening behavior of flow stress changing with temperature on welding residual stress, plastic strain and welding distortion of ATN0 1-T4 aluminum alloy was studied by finite simulation method. The simulation results show that the weld seam undergoes strain hardening in the temperature range of 180-250 ℃, however, it exhibits strain softening at temperature above 250 ℃ during welding heating and cooling process. As a result, the strain hardening and strain softening effects counteract each other, introducing slightly influence on the welding residual stress, residual plastic strain and distortion. The welding longitudinal residual stress was determined by ultrasonic stress measurement method for the flat plates of A7N01-T4 aluminum alloy. The simulation results are well accordant with test ones.
基金The project supported by National Natural Science Foundation of China
文摘An experimental investigation was carried out on the flow characteristic and hardening of steel 40 subjected to complex combined axial-torsional cyclic straining. For a specific cyclic strain path, the steel has mainly cyclic softening behavior when the strain amplitude is small. While with an increase of the effective strain amplitude, the softening becomes small, but there is the cyclic softening even though the steel is subjected to the cyclic loading by a square strain path. However, the steel has cyclic additional hardening by a nonproportional path, compared with the proportional cycling. Generally, the additional hardening is small and its historical effect is not obvious at small strain amplitude. The additional hardening is remarkable by a cross-triangular strain path of large strain amplitude. The memory of the history of nonproportional cyclic loading, the direction of plastic flow and the plastic modulus of the steel were also studied.
基金This work was financially supported by the National Natural Science Foundation of China (No.50309004) Liaoning Technical University (No. 02-38).
文摘Fault rockburst is treated as a strain localization problem under dynamicloading condition considering strain gradient and strain rate. As a kind of dynamic fracturephenomena, rockburst has characteristics of strain localization, which is considered as aone-dimensional shear problem subjected to normal compressive stress and tangential shear stress.The constitutive relation of rock material is bilinear (elastic and strain softening) and sensitiveto shear strain rate. The solutions proposed based on gradient-dependent plasticity show thatintense plastic strain is concentrated in fault band and the thickness of the band depends on thecharacteristic length of rock material. The post-peak stiffness of the fault band was determinedaccording to the constitutive parameters of rock material and shear strain rate. Fault bandundergoing strain softening and elastic rock mass outside the band constitute a system and theinstability criterion of the system was proposed based on energy theory. The criterion depends onthe constitutive relation of rock material, the structural size and the strain rate. The staticresult regardless of the strain rate is the special case of the present analytical solution. Highstrain rate can lead to instability of the system.
