Abstract For an infinite slab of strain gradient sensitive material subjected to plane-strain tensile loading, compu- tation established and analysis confirmed that passivation of the lateral boundaries at some stage ...Abstract For an infinite slab of strain gradient sensitive material subjected to plane-strain tensile loading, compu- tation established and analysis confirmed that passivation of the lateral boundaries at some stage of loading inhibits plastic deformation upon further loading. This result is not surprising in itself except that, remarkably, if the gradient terms contribute to the dissipation, the plastic deformation is switched off completely and only resumes at a clearly defined higher load, corresponding to a total strain ec, say. The analysis presented in this paper confirms the delay of plastic deformation following passivation and determines the exact manner in which the plastic flow resumes. The plastic strain rate is continuous at the exact point ec of resumption of plastic flow and, for the first small increment Ae = e - ec in the imposed total strain, the corresponding increment in plastic strain, AeP, is proportional to （Ae）2. The constant A in the relation AeP（0） = A（Ae）2, where AeP（0） denotes the plastic strain increment at the centre of the slab, has been determined explicitly; it depends on the hardening modulus of the material. The presence of energetic gradient terms has no effect on the value of ec unless the dissipative terms are absent, in which case passivation reduces the rate of plastic deformation but introduces no delay. This qualitative effect of dissipative gradient terms opens the possibility of experimen- tal discrimination of their presence or absence. The analysisemploys an incremental variational formulation that is likely to find use in other problems.展开更多
In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotationa...In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.展开更多
文摘Abstract For an infinite slab of strain gradient sensitive material subjected to plane-strain tensile loading, compu- tation established and analysis confirmed that passivation of the lateral boundaries at some stage of loading inhibits plastic deformation upon further loading. This result is not surprising in itself except that, remarkably, if the gradient terms contribute to the dissipation, the plastic deformation is switched off completely and only resumes at a clearly defined higher load, corresponding to a total strain ec, say. The analysis presented in this paper confirms the delay of plastic deformation following passivation and determines the exact manner in which the plastic flow resumes. The plastic strain rate is continuous at the exact point ec of resumption of plastic flow and, for the first small increment Ae = e - ec in the imposed total strain, the corresponding increment in plastic strain, AeP, is proportional to （Ae）2. The constant A in the relation AeP（0） = A（Ae）2, where AeP（0） denotes the plastic strain increment at the centre of the slab, has been determined explicitly; it depends on the hardening modulus of the material. The presence of energetic gradient terms has no effect on the value of ec unless the dissipative terms are absent, in which case passivation reduces the rate of plastic deformation but introduces no delay. This qualitative effect of dissipative gradient terms opens the possibility of experimen- tal discrimination of their presence or absence. The analysisemploys an incremental variational formulation that is likely to find use in other problems.
文摘In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.
