Study Of Axial Quasi-static And Dynamic Buckling Properties Of TiNi Phase Transformation Cylindrical Shells

Phase transformation(PT) can greatly affect the mechanical responses of materials and structures.It is one of the basic problems and major research fields of solid mechanics and material science.Study of the mechanical behavior of shape memory alloy(SMA) cylindrical shells under impact inevitably involves the study of the effect of phase transformation on the structures because SMA is a typical phase transformation material.In this paper,the quasi-static axial compression and impact response of the pseudo-elastic phase transformation cylindrical shells(PTCS) are systematically investigated experimentally and numerically.Some interesting phenomena and regularities are found and in-depth understanding is gained:(ⅰ).static buckling instability properties of the PTCS with different sizes under different boundary conditions;(ⅱ).the formation and development regularities of the phase transformation hinges(PTHs);(ⅲ).dynamic buckling response and energy absorbing ability of the PTCS under single loading.The conclusions can provide the basis for its engineering applications.Static buckling instability characteristics of PTCS are related to martensitic transformation,the behavior of phase transformation hinges,and recovery upon unloading which is significantly different from elastic-plastic cylindrical shells (EPCS).The diameter-thickness ratio(DTR) and length-diameter ratio(LDR) of the PTCS is closely related to its buckling mode.With the same length-diameter ratio,the number of its circumferential folds increases with the increasing diameter-thickness ratio.The static specific energy S_c of the PTCS has a relationship with its geometry and buckling mode,and decreases with the increasing DTR as the LDR is smaller.The static specific energy S_e is the largest with the buckling mode of three hinges,the next is that with the buckling mode of two hinges or mixed-mode,and the smallest is that with the buckling mode of four hinges at the same axial height.As the LDR of the PTCS is 2.5,the DTR is 30,and the buckling mode is three hinges at the same axial height,the static specific energy is the largest and reaches 2257.62J.Kg^-1.Using a simplified ideal PE constitutive model,the behavior of circumferential phase transformation hinges(CPTH) of the PTCS section is theoretically analyzed. Regularity of PT zone development and evolvement as well as of phase boundaries motion is disclosed,and corresponding analytic expression is given.The energy dissipation due to PT of the shell section during a complete loading-unloading cycle is given.Experimental investigation was conducted on PTCSs with different LDR and boundary conditions under single pulse loading using a modified split Hopkinson pressure bar(SHPB) apparatus.It is found that PTCSs with different LDR and boundary conditions have different buckling modes.The PTH of the PTCS is characterized by the following:1.Recoverability;2.the phase-change hinge appears on the microsecond time scale that is coupled with the fluctuation effect and its deformation increase is fluctuant;3.there are a number of PTHs in the PTCS under impact loading.The area of the dynamic hysteresis curve is much larger than that of the static compression,so energy absorption efficiency can be much higher.Numerical simulation on the semi-infinite PTCSs subject to step loading is studied.When the step loading amplitude is lower than the initial stress inducing martensite transformation(σ_MS),there is only transmission of an elastic P-wave and no phase transition buckling in the shell.When the step loading is aboveσ_MS, two-wave structure of elastic P-wave and PT shock wave occur according to theoretical analysis and numerical simulation indicates axial symmetry bucking ripples occur at the zone corresponding to the PT shock wave after the elastic wave. Propagating speed of buckling boundary is about 460-500m/s.Bending disturbances produced by the influence of lateral inertia,sudden softening of material module in the PT zone and higher axial load under rapid impact loading are the physical mechanisms that induce phase transformation buckling of PTCS.Simulation result of the experiment shows that unloading and recovery process of PTCS is not consistent with the local stress redistribution and concentration.It can be divided into four phases:1.local stress unloads first in the middle of PTCS;2. stress continues to unload near the incident bar.3.Stress continues to unload near the transmission bar,the first and second layer PT buckling rumple disappear;4.the whole PTCS vibrates elastically.Martensite fraction distribution along the wall thickness of CPTH is the most non-uniformly,that of axial phase transformation hinge takes second place,and that of the phase transformation diagonal hinge is the most uniform.