Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation. This work presents an analysis u...Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation. This work presents an analysis using the theory of phase transformation. The jump of deformation gradient across the interface between two phases and the Maxwell relation are considered. Governing equations for the phase transformation are derived. The analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique, real and physically acceptable solution. The equations are solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress, the stresses and strains inside both austenite and martensite phases, and the transformation-front orientation angle are determined to be in reasonably good agreement with experimental observations.展开更多
The stress-induced phase transformation in incompressible materials and the interfacial stability of multi-phase deformation were studied. The existence of multi-phase deformation was determined through exploring whet...The stress-induced phase transformation in incompressible materials and the interfacial stability of multi-phase deformation were studied. The existence of multi-phase deformation was determined through exploring whether the material would lose the strong ellipticity at some deformation gradient. Then, according to the stability criterion which is based on a quasi-static approach, the stability of the multi-phase deformation in incompressible materials was investigated by studying the growth/decay behaviour of the interface in the undeformed configuration when it is perturbed. At last, the way to define multi-phase deformation in incompressible materials was concluded and testified by a corresponding numerical example.展开更多
The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod...The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.展开更多
基金the National Natural Science Foundation of China(No.10272079)the joint grant from the National Natural Science Foundation of China and the Royal Society
文摘Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation. This work presents an analysis using the theory of phase transformation. The jump of deformation gradient across the interface between two phases and the Maxwell relation are considered. Governing equations for the phase transformation are derived. The analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique, real and physically acceptable solution. The equations are solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress, the stresses and strains inside both austenite and martensite phases, and the transformation-front orientation angle are determined to be in reasonably good agreement with experimental observations.
基金Supported by National Natural Science Foundation of China(No.10272079)the Joint Grant from National Natural Science Foundation of China andthe Royal Society, UK(No.10511130192) .
文摘The stress-induced phase transformation in incompressible materials and the interfacial stability of multi-phase deformation were studied. The existence of multi-phase deformation was determined through exploring whether the material would lose the strong ellipticity at some deformation gradient. Then, according to the stability criterion which is based on a quasi-static approach, the stability of the multi-phase deformation in incompressible materials was investigated by studying the growth/decay behaviour of the interface in the undeformed configuration when it is perturbed. At last, the way to define multi-phase deformation in incompressible materials was concluded and testified by a corresponding numerical example.
基金Supported by National Natural Science Foundation of China(No. 10272079)joint grant from National Natural Science Foundation of Chinathe Royal Society of UK under their Joint Project Scheme
文摘The crucial effect of compressibility of rods on their instability is novelly demonstrated via singularity theory. It is shown that the critical load of compressible rod is always greater than the one of the Euler rod, and a subcritical pitchfork bifurcation, which cannot occur for the Euler rod, may occur for a compressible rod. A whole bifurcation diagram of compressible rods is as follows ： when the original slenderness ratio of a compressible rod, $o is smaller than （1 ＋ v/3 √3π/2,, the rod does not buckle; when So∈ [1＋ v/3）3√3π/2 ,（1＋v/5）5 5√5π/4）,the rod may undergo a subcritical pitchfork bifurcation and a collapse may occur; when So ∈ [1＋ v/5）5√5π/4 ＋ ∞）, the rod may undergo a supercritical pitchfork bifurcation. The deformation of cross section of rods causes a little shift of bifurcation points towards to the one corresponding to larger slenderness ratio.
