Steady state creep in metals

Dislocations are known to be responsible for die short-term plastic (nonelastic) properties of substances, which represents departure from die elastic behaviour described by Hooke s law. Their concentration determines, in part, not only dris immediate transport of planes of atoms drrough die solid at moderate temperatures, but also plays a decisive role in die behaviour of metals under long-term stress. In processes which occur slowly over a long period of time such as secondaiy creep, die dislocation distribution cannot be considered geometrically fixed widrin a solid because of die applied suess. 

An account of the mechanism for creep in solids placed under a compressive hydrostatic suess which involves atom-vacancy diffusion only is considered in Nabano and Hemirg s (1950) volume diffusion model. The counter-movement of atoms and vacancies tends to relieve the effects of applied pressure, causing extension normal to the applied sU ess, and sluinkage in the direction of the applied sU ess, as might be anticipated from Le Chatelier s principle. The opposite movement occurs in the case of a tensile sU ess. The analysis yields the relationship 

In many of the transition metals, such as titanium, vanadium and molybdenum, carbon, nitrogen and oxygen atoms can fit into octahedral holes, and hydrogen into the teualredral holes. The fit here is estimated by assuming the atoms all have incompressible radii, and die contact must be such tlrat tire interstitial atoms do not rattle around in the holes. 

In the face-centred cubic structure tirere are four atoms per unit cell, 8x1/8 cube corners and 6x1/2 face centres. There are also four octahedral holes, one body centre and 12 x 1 /4 on each cube edge. When all of the holes are filled the overall composition is thus 1 1, metal to interstitial. In the same metal structure there are eight cube corners where tetrahedral sites occur at the 1/4, 1/4, 1/4 positions. When these are all filled there is a 1 2 metal to interstititial ratio. The transition metals can therefore form monocarbides, niU ides and oxides with the octahedrally coordinated interstitial atoms, and dihydrides with the tetrahedral coordination of the hydrogen atoms. 

According to the transition state theoty, the diffusion process can be described by the equation 

Although the face-centred cubic structure of metals is close packed, it is still possible for atoms which are much smaller than the host metal atoms to fit into interstitial sites inside the structure, while maintaining the essential properties of metals such as electrical conductivity and heat transport. These interstitial sites are of two kinds. The octahedral interstitial sites have six metal atoms at equal distances from the site, and therefore at the apices of a regular octahedron. The tetrahedral interstitial sites have four nearest neighbour metal atoms at the apices of a regular tetrahedron. A smaller atom can just fit into the octahedral site if the radius ratio is 

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Because of the relatively high temperatures that are required to establish steady-state creep in metals and alloys, diffusion-controlled mechanisms typically underlie the resulting deformation. Those mechanisms include the simple... 

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