Body Centered Cubic Fe In Uniaxial Or Hydrostatic Pressure Under The Action Of The Structural Stability Study

The lattice stability of a perfect crystal under tensile or pressure loading is not only one of the most important issues in elasticity but also an essential consideration in analysis of the structural responses and the theoretical strength of the crystals.The theoretical strength of a material is defined as the stress at which a homogeneously deformed perfect crystal becomes elastically unstable with respect to internal displacements.Mechanical properties of structural sensitivity,any small variety of structure will put effort to the mechanical properties significantly.Therefore,the study of the structural stability and theoretical strength of solids have long been an interesting subject and widely investigated with plentiful advancing experimental and theoretical methods.The theoretical strength of a material offers a theoretical basis for analysis the inherent ductility or brittleness,estimation the fracture properties,and modification properties and design of the materials,especially for the design of the high Strength materials.In this paper,we derived analytical expressions of the normal stresses and elastic constants by combining the MAEAM and the modified Born criteria,assessed the structural responses including equal and unequal distortion along the lattice parameters under uniaxial or hydrostatic loading, calculated the cohesive energy,normal stress and elastic constants as a function of lattice parameters and determined the elastic stable region and the corresponding theoretical strength of the selected BCC metals Fe.The conclusions are summarized as follows:(1) While BCC crystal Fe loaded in direction,in tensile region,even if an orthorhombic path is applied,the deformation is always along the tetragonal Bain path.While in compressive region,the deformation first follows the tetragonal Bain path till the branching point ofλ₁=0.9064. Furthermore,the branched orthogonal path is preferred over the conventional tetragonal Bain path since the lower compressive stressσ₁ and energy E is needed.Although a stress-free FCC phase with a local maximum energy of -4.2186eV appearing either in compressive region or in tensile region,it is unstable and would slip spontaneously into its near neighbor stress-free mBCT phase with a local minimum energy of -4.2270eV.The stable region ranges fromλ₁=0.9064 with the corresponding theoretical strength of -79.7eV/nm³ in compression toλ₁=1.1788 with the corresponding theoretical strength of 30.6eV/nm³ in tension.(2) While BCC crystal Fe loaded in direction,even if an orthorhombic path is applied, the deformation is spontaneous along the tetragonal path while b₁≤0.3449nm in compressive region. In addition to the initial BCC phase,a BCT phase and the other BCC phase appear also at stress-free states.The BCT phase with the local maximum internal energy of -4.227eV is unstable and would slip spontaneously into the appeared BCC phase with the same minimum internal energy of -4.280eV as the initial BCC phase.The stable region ranges for the theoretical strength from -43.78eV/nm³ with a corresponding strain-7.34%under compression to 44.06eV/nm³ with a corresponding strain 6.49%under tension along orthorhombic path.(3) For all four BCC crystals Fe,V,Nb and Ta under hydrostatic loading,as expected whether compressive or tensile loading from initial state,the internal energy per atom E_i are all increased. The failures occur while the conditionμ＞0 is violated in compressive region andκ＞0 is violated in tensile region.The stable regions are determined to be 0.9269～1.1495,0.9270～1.1545,0.9268～1.1449 and 0.9268～1.1427 in the lattice stretchλfor Fe,V,Nb and Ta.