The Studies Of Phase Transformations Kinking In Rocks Based On Elastoplastic Constitutive Theories

Rock kink bands have been widely observed in nature. Rock kinking involves important information of the earth's crust movement. Many researchers have devoted their work to experimental research on rock kinking, but no theoretical model has been given so far to reveal its formation mechanism and to predict it exactly. Regarded as a result of stress-induced phase transition for the formation of kink bands in sedimentary rocks, an elastoplastic phase transition model is suggested in the present paper. The precise studies to the rock mineral phase transition discovered some of the deformation process is truly plastic thus concluded that kink bands are the marks of geologic structure resulted from stress-induced phase transitionThe theoretical studies discovered that phase transition may occur to superelastic materials having non-convex strain energy function. Further analysis revealed phase transition may occur in such elastoplastic materials with strain softening behavior and the Maxwell stress and the strains inside both elastic phase and elastoplastic phase are all determined after phase transformation has occured. It is proved that for any assumed strain-softening curve the algebraic sum of areas enclosed by the Maxwell stress straight line and strain-softening cure is always equal to zero that agrees with the result given by Ericksen for the analysis of phase transformations in nonlinearly elastic bars.Considering the discontinuity of deformation gradient and stress across interfaces between kink band and un-kinked areas, imposing the continuity of traction across interfaces and the Maxwell relation the phase transformation control function under planar strain is established in this paper. With the control function and the elastoplastic constitutive equation for sedimentary rocks, the phase transition analysis model for rocks kinking formation is provided. With the aid of phase transition model, kinking analysis is transferred into seeking the minimum first principal value of the stress tensor on which the equations reduced by phase transition conditions and the constitutive laws have a unique, physically acceptable real solution which can be found by homotopy continuation methods. The results solved numerically depend on the constitutive laws selected so the elasoplastic constitutive laws both based on Drucker-Prager yield criteria for rock definite deformation and embodied rock transverse isotropy by incorporating a microstructure tensor are applied respectively. The numerical example of planar strain state illustrated that critical kinking stress, stress and strain in and out the kink bands, both the inclination angle of the kink band and the kink orientation can all be predicted which are accordance with the experimental measurements. As is shown by the calculations that the smaller the rate of plasticity tangent module to elasticity module the larger the strain jump quantity across phase transformation interface is, which verified the kink band formation was due to rock subjected ductile shear in high confine pressure. The conclusions that phase transformation occurrence was dependent with material behavior, mean pressure and stress deviator was drawn.