Ductility is ability of material to plastically deform, this involves a role of dislocations.In elastic range only stretching of the bonds between the atoms plays a role while in plastic range dislocations already present or newly developed plays a role. how freely dislocations can move (breaking of the bonds between the atoms) defines the ductility of the material. Smaller the grain size the more is the grain boundary area unit volume where these dislocation are restricted and may pile up causing strengthening the material and hence reducing the ductility. on the other hand when the grain size is large the dislocation can more freely move hence causing higher ductility. Grain size at nano-level can have higher ductility due to grain boundary sliding. You can study this in any good metal strengthening text. and also the fractography of the ductile materials and its charters tics by microsopy
Is there any new discovery about grain size and ductility...
Reducing the GS does not decrease the ductility. Indeed, it is the one strengthening mechanisms that, if at all, it may actually increase it as explained above. Other strengthening mechanisms often decrease the ductility, although not always.
For example: cold deformation, via extrusion or rolling hardens the material at the expense of ductility. This happens because the strain hardening is exhausted during the extrusion/rolling, and that brings the onset of necking forward (see below).
Precipitation hardening may decrease the ductility too, depending on whether it occurs without increasing the strain hardening rate. Keep in mind that the Considere criterion states that necking starts when S= dS/de, where S is the true stress and e the true plastic strain. If S increases trough an additional strengthening necking will start earlier unless dS/de is increased in proportion. The latter is possible (i.e., preserving the ductility while making the alloy stronger) if the strengthening involves, for example, a mixture of coherent and non coherent particles. The former increase S and the latter increase dS/de via the Orowan mechanism.
1) Tensile ductility is generally controlled by parameters, viz. strain hardening (K and n in Hollomon equation) and strain rate sensitivity of flow stress, m. If Hollomon equation (connecting true stress and true plastic strain) is valid, then strain hardening parameters are strength co-efficient, K and strain hardening exponent, n. You may know that the true strain at necking is almost equal to n (εnecking = n). The onset of necking in tension is postponed/delayed thus improving ductility when m (strain rate sensitivity) and n (strain hardening exponent) are high. Please see Hart's instability criterion ("Theory of the tensile test", E. W. Hart, Acta Metall., 15,1967, pp. 351–355) and instability occurs when :- (n/ε) + m = 1. Otherwise, ε instability = n / (1 - m) and m = 0 gives you the Considere criterion.
2) One has to know how grain size will effect strain hardening and strain rate sensitivity, m. In other words, how ductility is influenced by grain size. It is generally known that n increases with increasing grain size (in certain range) and decreases with increasing volume fraction of second phase for a given particle size. It is the "mean free path" (MFP) of dislocations which is an important parameter that controls the strain hardening behavior and the n value.
3) You may please see the reference:- notes by Prof. Yngve Bergström on "The Hollomon n – value, and the strain to necking in steel"- for this, please see the link if you have access:- http://www.plastic-deformation.com/paper8.pdf
4) You may also see further references:- (i) "Strain hardening, strain rate sensitivity, and ductility of nanostructured metals", Y.M. Wang, E. Ma, Materials Science and Engineering A 375–377 (2004) 46–52. (ii) "The Relationship between the Strain-hardening Exponent n and the Microstructure of Metals", ZHANG FAN, HUANG MINGZHI and SHI DEKE, Materials Science and Engineering, A122 (1989) 211-213.
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