Dynamic Constitutive Behavior And Fracture Of Some Rare Earth Elements

Few data is currently available on dynamic constitutive behavior and fracture of Rare Earth(RE) elements. This study provided dynamic constitutive equations and fracture behavior ofneodymium (Nd), lanthanum (La) and praseodymium-neodymium (Pr-Nd), which had beenpublished in Journal of Applied Physics, Material Science and Engineering：A, Journal ofRare Earth and Internationaol Journal of Nonlinear Sciences and Numerical Simulation. Theinnovations in this thesis are as follows:1) Dynamic compressive constitutive equations of metallic Nd, La and Pr-Nd weredetermined and examined.Based on compressive test, static on810material test system (MTS) and dynamic on thefirst compressive loading in split Hopkinson pressure bar (SHPB) for Nd, La and Pr-Ndcylinder specimens at high strain rates and temperatures, Johson-Cook (J-C) type [G. R.Johson and W. H. Cook, in proceeding of seventh international symposium on Ballistics (TheHague, The Netherlands,1983). pp.541-547] compressive constitutive equations of Nd, Laand Pr-Nd were determined. The determined dynamic compressive constitutive equationswere examined by using the numerical simulation of SHPB tests. The reflected andtransmitted pulses of SHPB tests computed with the determined constitutive equations ofthose specimen materials could be consistent with the experimental data to a certain extent.2) Dynamic tensile constitutive equations of metallic Nd, La and Pr-Nd were determinedand examinedFor tensile split Hopkinson bar (TSHB) tests, the most difficult problem is that thespecimen is subjected to non-uniform deformation due to mass effect in split of its desireduniformity which is necessary to obtain the tensile properties of the specimen material. Thenumerical simulations of TSHB tests for Nd and La sheet specimens were performed by usingLS-DYNA [J. O. Hallquist. LS-DYNA keywords use’s manual (Version970), LSTC, USA.2003, April] with determined dynamic compressive constitutive equations of Nd and La tostudy the influence of specimens geometry on TSHB tests and to optimize TSHB tests. Basedon tensile tests, static on MTS and dynamic on the first tensile loading in optimized TSHBtests for Nd, La and Pr-Nd sheet specimens at high strain rates, J-C type andHolmquist-Johnson type [T. J. Holmquist, G. R. Johnson, Journal of Physics I,1991,C3-853-C-860] tensile constitutive equations for La, Pr-Nd and Nd were determined,respectively. The computed transmitted and reflected pulses of TSHB tests for Nd, La andPr-Nd sheet specimens by using the determined tensile constitutive equations for Nd, La andPr-Nd and strain rate dependent fracture strain fcould be consistent with the experimental data.3) The pressure effect and the effect of Lode angle parameter on dynamic constitutive behavior of some rare earth elements were shownStatic and dynamic compressive tests for Nd, La and Pr-Nd cylinder specimens have different stress triaxialities η(η=p/σ, p pressure, σ flow stress) and Lode angles θ (cos(3θ)=(r/σ)3, r=(9/2[s]·[s]:[s])1/3,[s] the deviatoric stress tensor) in comparison with static and dynamic tensile tests for Na, La and Pr-Nd sheet specimens. The pressure effect and Lode angle effect on dynamic constitutive behavior of Nd, La and Pr-Nd were shown in static and dynamic experiments, obviously. The effects of hydrostatic pressure on dynamic constitutive behavior of Nd, La and Pr-Nd do not have to be linear while the effects of Lode angle do change the shape of the dynamic yield surface.4) Dynamic compressive fractures of metallic Nd, La and Pr-Nd were investigatedThe multi-compressive loading in SHPB tests for metallic Nd and La cylinder specimens were recorded by a high-speed camera and were used to investigating large deformations of Nd and La specimens. However, it is difficult to describe the deformation history dependency of the dynamic constitutive equation by using physically based models. We made an empirical approach to non one-dimensional dynamic deformation of Nd and La cylinder specimens:the flow stress σ as a function of strain ε, strain rate ε and temperature T maintains its form with variable parameters during multi-compressive pulses in SHPB tests. By using the approach, we successfully modeled the large deformations of Nd and La cylinder specimens in SHPB tests. It was recorded by the high speed camera that the Nd and La cylinder specimens fractured during the multi-compressive loadings in SHPB tests while the Pr-Nd cylinder specimens fractured during the first compressive loading in SHPB tests. The results of3D Super Depth Digital Microscope (SDDM) investigation of the recovered metallic Nd and Pr-Nd cylinder specimens showed the shearing fracture. The shearing instability strains in dynamic compressive deformation of metallic Nd and Pr-Nd cylinder specimens were estimated with the obtained constitutive equations according to the criterion given by Batra and Wei [R. C. Batra, Z. G. Wei, International Journal of Impact Engineering,34(2007):448-463], and were compared with the average strain of recovered specimens.5) Dynamic tensile fractures of metallic Nd, La and Pr-Nd were investigatedThe Nd and La sheet specimens fractured during the first tensile loading in TSHB tests. The experimental transmitted and reflected pulses of TSHB tests for Nd and La sheet specimens could be explained with numerical simulation involving fracture of Nd and La sheet specimens. The dynamic fracture strength of Nd and La metal was found to be dependent on the strain rate. In general, the dynamic fracture strength is assumed to be dependent to the local strain rate, and the relation between the dynamic fracture strength and strain rate was taken as an intrinsic property of materials. The dynamic loading-carrying capacity σe of materials under dynamic tensile loads derived by Ou et al.[Z. C. Ou, Z. P. Duan, F. L. Huang. International Journal of Impact Engineering,37(2010):942-945] was investigated for Nd and La metal. It was noted that the effects of the incubation time, the intrinsic critical failure length on σe are severe. The fractured Nd and La sheet specimens of tensile tests were investigated by using scanning electron microscope (SEM). It was found that a transition from random to deterministic damage evolution patterns (from brittle to ductile) was notable as the strain rates increase for La sheet specimens while the transition unobserved for Nd sheet specimens.6) The pressure effect and the effect of Lode angle parameter on dynamic fracture of some rare earth elements were shownDynamic compressive fracture of Nd, La and Pr-Nd cylinder specimens have different stress triaxialities η and Lode angles θ in comparison with dynamic tensile fracture of Nd, La and Pr-Nd sheet specimens. The hydrostatic pressure is one of the most important parameters that controls material ductility while the effect of Lode angle parameter on fracture initiation becomes weak in high η region. If the fracture locus is symmetric with respect to θ (θ=1-(6θ)/π) as postulated by Wierzbicki et al.[T. Wierzbicki, Y. Bao, Y. W. Lee, Y Bai, International Journal of Mechanical Sciences,47(2005):719-743], then the fracture strain of cylinders upsetting tests (θ=-1) should lay on the extrapolated curve of fracture locus calibrated by notched round bars tensile tests (η≥1/3,θ=1). The dynamic compressive fracture strains of Nd, La and Pr-Nd cylinders should lay on the extrapolated curves of εf versus η for Nd, La and Pr-Nd, respectively, which pass the dynamic tensile fracture strains of Nd, La and Pr-Nd sheets.