**3.7 The temperature gradient (G) and rate of cooling (R) ratio (G/R)**

In a foundry the various local factors like the extent of superheat, the extent of heterogeneous nucleation, the mould characteristics, etc. decide the variations in the thermal gradient (G) and the rate of cooling (R). Needless to say, the ratio G/R forms an important parameter to decide the mode of growth and the consequence of structure development.

**Figure 14** illustrates that as the G/R ratio progressively changes from a high to a low volume the effect of undercooling becomes more and more pronounced. Columnar, plane-front growth gradually gives way to independent nucleation.

During freezing the thermal conditions prevailing in the melt continuously change. Thus separate structural zones as shown in **Figure 15** are encountered in the solidifying melt.

These zones are consequences of the continuously changing G/R ratio in the melt. Assuming of a lower value of the G/R ratio with the lapse of time results in the increasing extents of undercooling which are instrumental in the separable structural zones as preserved in **Figure 15**. The above can be made more clear with the aid of **Figures 16** and **17**.

Both **Figures 16** and **17** provide for an explanation of the mixed structure in a solidifying casting on the basis of the prevailing thermal conditions. To start with, as presented in **Figure 16**, the temperature gradient is stiff. Solidification initially occurs under this marked thermal gradient. This is often sufficient to cause

**Figure 13.**

*Change in equilibrium temperature profile as a consequence of solute concentration crystal variation.*

**Figure 14.**

**Figure 15.**

*Schematic presentation of critical changes in the G/R ratio during freezing and its influences on the different structural zones.*

**Figure 16.**

*Variation of undercooling with alteration in the thermal gradient showing different grain morphology.*

**33**

**Figure 18.**

*Solidification of Metals and Alloys*

**Figure 17.**

*DOI: http://dx.doi.org/10.5772/intechopen.94393*

columnar dendritic growth in the outermost region and adjacent to the mould wall as shown in **Figure 16** in this central zone (in some cases, throughout the entire

*Variation of undercooling with alternation in the thermal gradient showing different grain morphology.*

This shallow gradient generates excessive undercooling. Here solidification proceeds by widespread nucleation, the rate of nucleation being very high. Independent nucleation occurs in the interior of the melt. These nuclei, without any barrier for growth across their periphery, grow into equiaxed grains. To be more specific, initially the temperature gradient is stiff. The rate of cooling is low, G/R assume high values. Initial solidification, thus, occur under a marked temperature gradient which is sufficient to cause columnar dendritic growth in the outermost layer. Gradually 'G' decreases, i.e., the temperature gradient becomes shallow and 'R' the rate of cooling increases as a consequence of increasing extents of undercooling. The shallow temperature gradient in the casting and the increasing extents of undercooling in the melt give rise to the formation of independent nucleation in the melt interior form-

Schematically the practical, ideal cast structure can be presented as in **Figure 18**. Although, the above refers to alloys forming solid solutions, analogous changes occur in alloys subject to eutectic freezing. The **Figure 18** shows small dendrites (equiaxed) in the outermost surface because of chilling effects at the cold mould wall.

solidifying melt) the temperature gradient is shallow (**Figure 17**).

ing equiaxed grains, being free to grow on their unhindered periphery.

*Schematic presentation of a theoretical grain structure of the casting.*

*Casting Processes and Modelling of Metallic Materials*

*Schematic presentation of G/R ratio influencing the effect of undercooling and the resultant structure.*

*Variation of undercooling with alteration in the thermal gradient showing different grain morphology.*

*Schematic presentation of critical changes in the G/R ratio during freezing and its influences on the different* 

**32**

**Figure 16.**

**Figure 14.**

**Figure 15.**

*structural zones.*

**Figure 17.** *Variation of undercooling with alternation in the thermal gradient showing different grain morphology.*

columnar dendritic growth in the outermost region and adjacent to the mould wall as shown in **Figure 16** in this central zone (in some cases, throughout the entire solidifying melt) the temperature gradient is shallow (**Figure 17**).

This shallow gradient generates excessive undercooling. Here solidification proceeds by widespread nucleation, the rate of nucleation being very high. Independent nucleation occurs in the interior of the melt. These nuclei, without any barrier for growth across their periphery, grow into equiaxed grains. To be more specific, initially the temperature gradient is stiff. The rate of cooling is low, G/R assume high values. Initial solidification, thus, occur under a marked temperature gradient which is sufficient to cause columnar dendritic growth in the outermost layer. Gradually 'G' decreases, i.e., the temperature gradient becomes shallow and 'R' the rate of cooling increases as a consequence of increasing extents of undercooling. The shallow temperature gradient in the casting and the increasing extents of undercooling in the melt give rise to the formation of independent nucleation in the melt interior forming equiaxed grains, being free to grow on their unhindered periphery.

Schematically the practical, ideal cast structure can be presented as in **Figure 18**.

Although, the above refers to alloys forming solid solutions, analogous changes occur in alloys subject to eutectic freezing. The **Figure 18** shows small dendrites (equiaxed) in the outermost surface because of chilling effects at the cold mould wall.

**Figure 18.** *Schematic presentation of a theoretical grain structure of the casting.*
