MORDICA LECTURE Peierls stress of the iron lattice (BCC steels) is about 15 MPa at room temperature and moderate strain rate3, i.e., it contributes with about 45 MPa to the tensile plastic flow stress of ferritic steels on the assumption of the following orientation factor: For pure FCC metals, the ratio τi/σicl , is so small that the inequality (2) is never met (but for iridium) at any temperature. In short, the absolute bounds for the maximum tensile strength of a metallic crystalline material are given by Eq. (3) Its contribution to the plastic flow stress at room temperature of refractory metals (W, Ta, etc.) can indeed be much higher. To have an idea of the maximum value such a contribution can reach, the order of magnitude of the zero Kelvin limit of τp of BCC or HCP materials is 5·10-3 G* 3; for BCC iron, such limit is τp ≅ 365 MPa (i.e., a contribution of about 1 GPa to the tensile flow stress of ferritic steels at 0° Kelvin). The ideal shear stress ti can only be quantitatively predicted using atomistic numerical calculations. It turns out that results of rigorous atomistic calculations4-7 lead to near the same value obtained from the classical order of magnitude calculation of Frenkel8: Eq. (1) For <111> simple shear of BCC iron at room temperature, G* = 64 GPa3, and atomistic calculations yield τi = 6.4 GPa5. Similarly, for simple shear of FCC copper, τi = 4.2 GPa6,7. Summarizing, there is plenty of room between the lower and upper bounds of the tensile strength of ductile metals, . For FCC copper and BCC iron at room temperature, the available ranges are 1.2 MPa< <12.6 GPa and 45 MPa< <19.2 GPa, respectively. The contingent limit of homogeneous brittle fracture. For materials that cleave, as BCC metals, brittle fracture can establish a strength limit at stresses smaller than the ideal stress for dislocation-less plastic flow4,7,9. For such materials, a critical ductile-brittle transition temperature, DBTT, can be defined as the temperature for which the tensile stress normal to the weakest crystallographic direction for homogeneous cleavage (<001> for BCC materials), sicl , is smaller than the ideal tensile plastic flow stress in the same crystallographic direction Eq. (2) For BCC metals, σicl ≅ 0.08E<001>, where E<001> is the elastic modulus in the direction normal to the cleavage plane7,9. For iron at room temperature, this ideal fracture stress is 10.8 GPa, smaller than its ideal tensile plastic flow stress in <001> direction, 15.7 GPa ( ). In an iron polycrystal a grain with the weakest orientation for cleavage will constitute the weakest-link for brittle failure under tensile stress; consequently, the available strength range for iron at room temperature is 45 MPa< <10.8 GPa and the upper bound strength would be limited by brittle fracture. 60 | WIRE JOURNAL INTERNATIONAL The limit strength of disordered metallic lattices. Now, a word concerning another structural state limit of a solid metallic material: the total absence of long-range order, i.e., the metallic glass state below the glass-transition temperature. Metallic glass alloys (MG) can today be made in bulk form (BMG) and BMG wire drawing has been performed10,11. At low temperature and high stress, plastic deformation of MG occurs by superposition of the shear of localized groups of atoms, known as “shear transformation zones.” Plasticity of MG is confined to a small number of very thin shear bands where the local strain and strain rate are very high12-14. The ideal shear strength of a MG for shear nucleation without recourse to any geometrical defect or compositional heterogeneity is only accessible to atomistic calculations. The conditions of incipient plastic shear under the contact surface of a MG with a blunt nanoindenter approximately reproduce experimentally the ideal shear strength scenario. Results for several Zr- and Fe-based MG15 indicate that (τi )MG ≤ 7 -10-2GMG, a value smaller than the ideal shear strength for the crystalline state. On account of its isotropy, the maximum MG tensile plastic flow strength would be twice such value, Eq. (4) The subscript of the modulus is meant to indicate that it is the modulus of the glassy metal, slightly smaller than the isotropic average modulus of the polycrystalline metal, G. The ideal tensile strength for homogeneous cleavage of the metallic glass, assuming the relationship valid for crystals also to hold for MG, would be σicl ≅ 0.08EMG ≅ 0.2GMG. Consequently, in tension, MG alloys would fail after plastic shear instead of by brittle fracture from the elastic state, as confirmed by tensile experiments of small and smooth (near “perfect”) MG samples, e.g., ref.11. A reinterpretation of the experimental nanoindentation results leading to the upper-bound (4) and new theoretical estimates of the ideal shear strength of MG16,17 both lead to (τi) MG = 2.7.10-2GMG, a value about three times smaller than the upper-bound. The current estimate of the tensile flow strength of MG is thus Eq. (5) The predicted values for, respectively, copper and iron are 2.48 GPa and 4.48 GPa (using here their respective isotropic polycrystalline shear elastic modulus G for the