Flow stress

Whereas a linear relation between flow stress and lattice-parameter change is obeyed for any single solute element in nickel, the change in yield stress for various solutes in nickel is not a single-valued function of the lattice parameter, but depends directly on the position of the solute in the Periodic Table... 

Metals Successful applications of metals in high-temperature process service depend on an appreciation of certain engineering factors. The important alloys for service up to I,I00°C (2,000°F) are shown in Table 28-35. Among the most important properties are creep, rupture, and short-time strengths (see Figs. 28-23 and 28-24). Creep relates initially applied stress to rate of plastic flow. Stress... 

Figure 6.1. Stress-strain behavior of shock-loaded copper compared to the annealed starting condition illustrating an enhanced flow stress following shock-wave deformation compared to quasi-static deformation (based on an equivalent strain basis).

Bai [48] presents a linear stability analysis of plastic shear deformation. This involves the relationship between competing effects of work hardening, thermal softening, and thermal conduction. If the flow stress is given by Tq, and work hardening and thermal softening in the initial state are represented... 

The evolution of T, is just an exercise in mesoscale thermodynamics [13]. These expressions, in combination with (7.54), incorporate concepts of heterogeneous deformation into a eonsistent mierostruetural model. Aspects of local material response under extremely rapid heating and cooling rates are still open to question. An important contribution to the micromechanical basis for heterogeneous deformation would certainly be to establish appropriate laws of flow-stress evolution due to rapid thermal cycling that would provide a physical basis for (7.54). 

In (8.35) Y is the flow stress in simple tension (and may itself be a function of the temperature and strain rate) and is the critical volumetric strain at void coalescence (calculated within the model to equal 0.15 independent of material). Note that the ductile fragmentation energy depends directly on the fragment size s. With (8.35), (8.30) through (8.32) become, for ideal ductile spall fragmentation,... 

In the numerical calculations, an elastic-perfectly-plastic ductile rod stretching at a uniform strain rate of e = lO s was treated. A flow stress of 100 MPa and a density of 2700 kg/m were assumed. A one-millimeter square cross section and a fracture energy of = 0.02 J were used. These properties are consistent with the measured behavior of soft aluminim in experimental expanding ring studies of Grady and Benson (1983). Incipient fractures were introduced into the rod randomly in both position and time. Fractures grow... 

Mott played a major part, with his collaborator Frank Nabarro (b. 1917) and in consultation with Orowan, in working out the dynamics of dislocations in stressed crystals. A particularly important early paper was by Mott and Nabarro (1941), on the flow stress of a crystal hardened by solid solution or a coherent precipitate, followed by other key papers by Koehler (1941) and by Seitz and Read (1941). Nabarro has published a lively sequential account of their collaboration in the early days (Nabarro 1980). Nabarro originated many of the important concepts in dislocation theory, such as the idea that the contribution of grain boundaries to the flow stress is inversely proportional to the square root of the grain diameter, which was later experimentally confirmed by Norman Fetch and Eric Hall. 

Figure 9.6. (a) The temperature dependence of the flow stress for a Ni-Cr-AI superalloy containing different volume fractions of y (after Beardmore et al. 1969). (b) Influence of lattice parameter mismatch, in kX (eflectively equivalent to A) on creep rupture life (after Mirkin and Kancheev... 

As for the compression test, the lowest stress amounted to 0.314 kp/mm at the lower deformation rate at 503K and to 0.535 kp/mm for the higher rate at the same temperature. For the lower deformation temperatures the values of the flow stress increased sharply and at 373K reached 2.3 and 4.5 kp/mm" for the lower and higher deformation rates, respectively At room temperature they were 9.0 kp/mm and 11.28 kp/mm . 

Fig.4. The dependence of flow stress on deformation temperature in tension test (left) and in compression test (right) of the A12n78 alloy after heat treatment.

Hydrogen effect on the mechanical properties results in markedly enhanced ductility and lowered flow stress of the alloys therefore they become workable at much lower temperatures. 

Figure 3. Flow stress of Ti-a H alloys on compression at several temperatures and the accumulated strain = 50%. Temperature are 300 (curve 1), 400 (2), 500 (3), 600 (4) and 700°C (5).

The hydrogen effect on ductility and the flow stress will be considered first on the example of non-alloyed titanium. The Ti - H phase diagram is given in Fig. 1, and Fig. 2 shows the temperature dependence of ductility of Ti-a H alloys, A , for several X values. Tensile tests were run at a rate e 10" s . Ductility of the commercial... 

Fig. 10 shows that the flow stress of the hydrogen-alloyed compacts is essentially less than that of the outgassed ones at all test temperatuics. The flow stress relation between the hydrogen-alloyed and outgassed compacts depended on the strain. At equal strains at test temperatures, this ratio could achieve 2 or more. Thus, the effect of hydrogen on the properties of compacted powders is much similar to that observed on bulk titanium. 

A corresponding pressure effect on the flow stress was observed on hydrostatic extrusion of conical specimens of the same alloy through a die of 5 mm dia at 220°C. The basic alloy was extruded at P = 12 kbar up to the area ratio equal to 4.1 while the alloy hydrogenated to a = 0.20 extruded to the area ratio of 7.6 even at a lower pressure, P = 11 kbax . Similar pressure/hydrogen effects on the flow stress were also observed on hydrostatic extrusion of ZrH,c, VH,c and Nb,c alloys with x = 0 and 0.1-0.2 wt.%. 

Hydrogen alloying decreases flow stress by 2 to 3 at optimum. 

Fig. 8.18 Effects of grain size on lower yield stress, 5% flow stress and stress-corrosion fracture stress for 0.08%C steel in 8 n Ca(N03)2 (after Henthorne and Parkins )...

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