**3. Interdendritic feeding**

#### **3.1 Solidification Characterisation of Steels**

Before analysing interdendritic feeding, it is important to establish some important casting-related parameters of the steel during the solidification stage. These include the liquidus and solidus temperatures for the particular steel grade, so as to ascertain the superheat during pouring (i.e. the temperature difference between the pouring temperature (*Tp*) and the onset of solidification at the liquidus temperature (*Tl*)), and the freezing range (difference between the liquidus temperature (*Tl*) and solidus temperature (*Ts*Þ). In addition, the partition coefficient (*k*) and liquidus slope (*m*) are related to the evaluation of shrinkage porosity, as will be seen later.

Steels are generally alloyed, as well as post-cast heat-treated, to produce a desired microstructure (and hence specifically desired properties). Although the alloying levels (of chromium, nickel, etc.) may range from low (plain carbon steels) to high (stainless steels), the carbon composition plays a dominant role in determining dendrite size (and hence shrinkage porosity) of the solidifying melt [6, 7]. Of particular interest are low carbon steels, with carbon content in the range up to 0.3% wt. Such steels undergo a peritectic transformation during solidification at the peritectic temperature (*Tper*), at which δ-ferrite and liquid transforms into austenite. A number of empirical models can simply be used for determining the aforementioned temperatures for multi-component steels [8]. In this analysis, the binary (Fe-C) phase diagram of steel with C = 0.3%, as shown in **Table 1**, will be used to demonstrate these temperatures and their effect on shrinkage porosity<sup>1</sup> .

The Fe-C phase diagram shown in **Figure 7** was generated using Thermo-Calc. For a steel with C = 0.3%wt, solidification starts at the liquidus temperature *Tl* ¼ 1515°C with the nucleation of BCC δ-ferrite, and proceeds until the peritectic temperature, *Tper* ¼ 1495°C is reached. This is referred to as the *L* þ *δ* zone.

At this point, for the hyperperitectic (above C = 0.17%) steel, the phase fractions of value of δ-ferrite (of 0.10%C) can be calculated using the lever rule as follows:

$$\delta-ferrite: \mathbf{g}\_{\delta} = \frac{0.53 - 0.30}{0.53 - 0.10} = 0.53 \quad and \quad liquid: \mathbf{g}\_{l}^{per} = \mathbf{1} - \mathbf{g}\_{\delta}^{per} = \mathbf{0.47}$$

Now, for peritectic transformation to occur, using the lever rule at C = 0.17% (peritectic composition), the fractions of δ-ferrite (of 0.10% C) and liquid (of

*Phase diagram of Fe-C cast steel, showing the peritectic region enlarged (generated using Thermo-Calc).*

**C Mn P S Si Cu Ni Cr Mo V**

*Phase transformation of A216 WCB steel in the peritectic region (solidification zones), showing nucleation and growth of δ-ferrite and austenite at the respective transition zones across the freezing range from Tl* ¼ 1495°C *to*

*Shrinkage Porosity in Steel Sand Castings: Formation, Classification and Inspection*

*DOI: http://dx.doi.org/10.5772/intechopen.94392*

0.30 1.00 0.035 0.035 0.6 0.30 0.50 0.50 0.20 0.03

<sup>0</sup>*:*<sup>53</sup> � <sup>0</sup>*:*<sup>10</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>84</sup> *and liquid* : *<sup>g</sup>*

*per <sup>l</sup>* ¼ 1 � *g*

*per <sup>δ</sup>* ¼ 0*:*16

0.53% C) are given as:

**Figure 7.**

**139**

*δ* � *ferrite* : *g*

*per*

As per ASTM A216 Material Standard

*Chemical composition (% wt) of A216 WCB cast steel.*

*Ts* ¼ 1430°C *(freezing range* ¼ 65°C*), as well as solute rejection.*

**Table 1.**

**Figure 6.**

*<sup>δ</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>53</sup> � <sup>0</sup>*:*<sup>17</sup>

<sup>1</sup> For an actual steel grade, the phase diagram will be slightly different due to the influence of the alloying elements. See **Figure 6** for the case of A216 WCB steel, showing an additional *L* þ *δ* þ *γ*.

#### **Figure 6.**

The effect of the modulus ratio *m <sup>f</sup> =mc* on shrinkage porosity is quite significant – with no feeding (i.e. modulus ratio = 0), shrinkage porosity as high as 7% can result. However, whilst modulus ratios higher than 1.2 can significantly reduce shrinkage porosity, it will not be entirely eliminated due to interdendritic phenomena. That is, the inclusion of oversized feeders does not guarantee sufficient pressure differentials to feed the solidifying dendritic network. This will be the subject of further

Furthermore, the modulus ratio of 1.2 does not guarantee the formation of hotspots in the junction region between the part and the feeder, as shown in **Figure 5**. This can be resolved through increasing the modulus ratio, albeit at the cost of production. However, a better approach would be to use exothermic sleeves

Before analysing interdendritic feeding, it is important to establish some important casting-related parameters of the steel during the solidification stage. These include the liquidus and solidus temperatures for the particular steel grade, so as to ascertain the superheat during pouring (i.e. the temperature difference between the pouring temperature (*Tp*) and the onset of solidification at the liquidus temperature (*Tl*)), and the freezing range (difference between the liquidus temperature (*Tl*) and solidus temperature (*Ts*Þ). In addition, the partition coefficient (*k*) and liquidus slope (*m*) are related to the evaluation of shrinkage porosity, as will be seen later. Steels are generally alloyed, as well as post-cast heat-treated, to produce a desired microstructure (and hence specifically desired properties). Although the alloying levels (of chromium, nickel, etc.) may range from low (plain carbon steels) to high (stainless steels), the carbon composition plays a dominant role in determining dendrite size (and hence shrinkage porosity) of the solidifying melt [6, 7]. Of particular interest are low carbon steels, with carbon content in the range up to 0.3% wt. Such steels undergo a peritectic transformation during solidification at the peritectic temperature (*Tper*), at which δ-ferrite and liquid transforms into austenite. A number of empirical models can simply be used for determining the aforementioned temperatures for multi-component steels [8]. In this analysis, the binary (Fe-C) phase diagram of steel with C = 0.3%, as shown in **Table 1**, will be used to

demonstrate these temperatures and their effect on shrinkage porosity<sup>1</sup>

The Fe-C phase diagram shown in **Figure 7** was generated using Thermo-Calc. For a steel with C = 0.3%wt, solidification starts at the liquidus temperature *Tl* ¼ 1515°C with the nucleation of BCC δ-ferrite, and proceeds until the peritectic temperature, *Tper* ¼ 1495°C is reached. This is referred to as the *L* þ *δ* zone. At this point, for the hyperperitectic (above C = 0.17%) steel, the phase fractions of value of δ-ferrite (of 0.10%C) can be calculated using the lever rule as

<sup>0</sup>*:*<sup>53</sup> � <sup>0</sup>*:*<sup>10</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>53</sup> *and liquid* : *<sup>g</sup>*

<sup>1</sup> For an actual steel grade, the phase diagram will be slightly different due to the influence of the alloying elements. See **Figure 6** for the case of A216 WCB steel, showing an additional *L* þ *δ* þ *γ*.

.

*per <sup>δ</sup>* ¼ 0*:*47

*per <sup>l</sup>* ¼ 1 � *g*

investigation in the next section.

**3. Interdendritic feeding**

follows:

**138**

*<sup>δ</sup>* � *ferrite* : *<sup>g</sup><sup>δ</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>53</sup> � <sup>0</sup>*:*<sup>30</sup>

around the feeders, as can be seen in **Figure 4**.

*Casting Processes and Modelling of Metallic Materials*

**3.1 Solidification Characterisation of Steels**

*Phase transformation of A216 WCB steel in the peritectic region (solidification zones), showing nucleation and growth of δ-ferrite and austenite at the respective transition zones across the freezing range from Tl* ¼ 1495°C *to Ts* ¼ 1430°C *(freezing range* ¼ 65°C*), as well as solute rejection.*


#### **Table 1.**

*Chemical composition (% wt) of A216 WCB cast steel.*

#### **Figure 7.**

*Phase diagram of Fe-C cast steel, showing the peritectic region enlarged (generated using Thermo-Calc).*

Now, for peritectic transformation to occur, using the lever rule at C = 0.17% (peritectic composition), the fractions of δ-ferrite (of 0.10% C) and liquid (of 0.53% C) are given as:

$$\text{1.6} - \text{ferrite} : \text{g}^{\text{per}}\_{\delta} = \frac{0.53 - 0.17}{0.53 - 0.10} = 0.84 \quad \text{and} \quad \text{liquid} : \text{g}^{\text{per}}\_{l} = \mathbf{1} - \mathbf{g}^{\text{per}}\_{\delta} = 0.16$$

Hence, in our case of a hyperperitectic steel (C = 0.3%), there is a shortage of δferrite to react with the amount of liquid fraction for a full peritectic transformation to austenite. The amount of liquid fraction that is transformed with the δ-ferrite fraction of 0.53 into austenite at the peritectic temperature is only 0*:*53*=*0*:*84 � 0*:*16 ¼ 0*:*10. The resulting fractions of liquid and austenite just below the peritectic temperature are therefore given as:

to distinguish between actual phases formed and porosity on a micrograph, since *g<sup>α</sup>* þ *gpearlite* þ *gpores* ¼ 1. This effectively means that the density of the steel will be lower than its theoretical density, due to the formation of shrinkage pores.

*Shrinkage Porosity in Steel Sand Castings: Formation, Classification and Inspection*

ture parameters during the solidification stage.

*DOI: http://dx.doi.org/10.5772/intechopen.94392*

where *C*<sup>∗</sup>

**3.2 Mushy zone feeding**

velocity becomes *v<sup>l</sup>* ¼ �*βvT*.

**141**

The melt pouring temperature (*Tp*) is often chosen without a clear understanding of its effect on macro and microstructural defects. Knowing the liquidus temperature (*Tl*) allows a better choice of *Tp*. It is known that higher values of *Tp* increases the amount of porosity in castings [10], and increases hot tear susceptibility (HTS). The former is due to the increased possibility of hotspots, and the latter due to high thermally-induced stresses in the solidifying melt. Lower pouring temperatures are therefore preferred. **Figure 2** summarises the important tempera-

As a final word in this Section, the liquidus slope *m* and partition coefficient *k* can

*and k<sup>γ</sup>*

partition coefficient indicates the extent of solute rejection during the solidification process. Low values of *k* implies high levels of solute rejection. This can lead to high levels of microsegregation and, hence, inhomogeneity in microstructure – this is beyond the scope of this Chapter. As regards shrinkage porosity, the rejection of solute from the solidifying phase into the liquid melt contributes to the remelting of smaller dendrite arms and, subsequently, coarsening of larger dendrite arms. This is related to the difference in curvatures between the larger and smaller dendrite arms. A more detailed examination of dendritic coarsening can be found in [11]. The liquidus slopes and partition coefficients are important parameters for determining the evolution of solid fraction *gs* as a function of temperature through the mushy zone, in the solution

The nucleation and growth of the solid phase in the mushy zone involves highly complex phenomena, not all of which can be adequately dealt with in this Chapter. The aim here will be limited to discussing the mushy zone solidification in the context of shrinkage porosity formation. **Figure 9** depicts a typical equiaxed growth of a solid dendrite in a liquid melt, depicting the growth of secondary dendrite arms with spacing *λ*2, and the velocity of the interdendritic feeding flow *vl*. The velocity of the solidifying

(known as the solidification shrinkage factor), where *ρ<sup>s</sup>* and *ρ<sup>l</sup>* are the solid and liquid densities respectively. Hence, it can be shown that the (localised) feeding

*β* ¼ *ρ<sup>s</sup>* � *ρ<sup>l</sup>* ð Þ*=ρ<sup>l</sup>* (8)

front is shown as *vT*. The accompanying solidification contracts by a factor of:

*<sup>s</sup>*,*<sup>C</sup>* refers to the solute composition of carbon (subscript "*C*") in the solid

*<sup>C</sup>* <sup>¼</sup> *<sup>C</sup>*<sup>∗</sup> *s*,*C C*∗ *l*,*C*

(7)

*<sup>l</sup>*,*<sup>C</sup>* is similarly defined. The

likewise be determined from the phase diagram of the steel alloy. An in-depth discussion on these parameters is beyond the scope of this Chapter, except to note that these parameters affect the spacing between secondary dendrite arms (as will be shown in Section 3.2), and hence the level of interdendritic shrinkage porosity. In peritectic steels, the liquidus slopes (temperature versus solute composition gradients) are given as *<sup>m</sup><sup>δ</sup>* and *<sup>m</sup><sup>γ</sup>* for the *<sup>L</sup>* <sup>þ</sup> *<sup>δ</sup>* and*<sup>L</sup>* <sup>þ</sup> *<sup>γ</sup>* zones respectively. Similarly, the

partition coefficients for the solute in δ-ferrite and austenite are given by:

*kδ <sup>C</sup>* <sup>¼</sup> *<sup>C</sup>*<sup>∗</sup> *s*,*C C*∗ *l*,*C*

(subscript *s*) within the multicomponent steel alloy, and *C*<sup>∗</sup>

of shrinkage porosity formation, as will be shown in the next Section.

$$\text{liquid}: \text{g}\_l = 0.47 - 0.10 = 0.37 \quad \text{and} \quad \text{autenite}: \text{g}\_\gamma = 1 - \text{g}\_l = 0.63$$

The remaining liquid now transforms fully into austenite as the solid–liquid mixture cools down to the solidus temperature *Ts* ¼ 1470°C. This is referred to as the *L* þ *γ* zone. (See [9] for an in-situ account of the solidification phase transformation of a peritectic steel). The freezing range ΔT*<sup>f</sup>* is given as:

*freezing range* ΔT*<sup>f</sup>* ¼ *Tl* � *Ts* ¼ 1515°C � 1470°C ¼ 45°C

It can be seen that hyperperitectic steels have longer freezing ranges compared to hypoperitectic steels, and high carbon steels (C > 0.53%) have even longer freezing ranges. In the latter, however, solidification starts with nucleation of FCC austenite instead of BCC δ-ferrite.

Further cooling of the solidified steel down to 800°C results in the transformation of austenite into α-ferrite (either allotriomorphic ferrite nucleating at the austenite grain boundaries or idiomorphic ferrite nucleating inside the austenite grains), until the eutectoid temperature of 740° C is reached. The remaining austenite in this hypoeutectoid steel then transforms into pearlite, a cooperative growth of α-ferrite and cementite (Fe3C), hence showing up as a lamellae microstructure.

In the case of the 0.30% C steel, the volume fractions of α-ferrite and pearlite (α-ferrite + cementite) can similarly be determined using the lever rule:

$$a - \text{ferrite}: \mathbf{g}\_a = \frac{\mathbf{0}.77 - \mathbf{0}.30}{0.77 - \mathbf{0}.02} = \mathbf{0}.63 \quad \text{and} \quad \text{pearrite}: \mathbf{g}\_{\text{parlitte}} = \mathbf{1} - \mathbf{g}\_a = \mathbf{0}.37$$

These volume fractions would be the case if no micro-porosity was present during the solidification stage, which is not exactly possible, even under highly efficient feeding of the mushy zone. Entrapped interdendritic liquid is bound to occur, even at high levels of solid fraction coherency. Porosity shows up as black (almost zero density) areas on a micrograph, which may sometimes be confused for the lower density phase (α-ferrite), as shown on the micrographs in **Figure 8**. Hence, it is important to establish the phase fractions as above, and use this data

#### **Figure 8.** *Optical Micrograph of an A216 WCB cast steel sample (left) and the contrasted image showing the porosity (right).*

*Shrinkage Porosity in Steel Sand Castings: Formation, Classification and Inspection DOI: http://dx.doi.org/10.5772/intechopen.94392*

to distinguish between actual phases formed and porosity on a micrograph, since *g<sup>α</sup>* þ *gpearlite* þ *gpores* ¼ 1. This effectively means that the density of the steel will be lower than its theoretical density, due to the formation of shrinkage pores.

The melt pouring temperature (*Tp*) is often chosen without a clear understanding of its effect on macro and microstructural defects. Knowing the liquidus temperature (*Tl*) allows a better choice of *Tp*. It is known that higher values of *Tp* increases the amount of porosity in castings [10], and increases hot tear susceptibility (HTS). The former is due to the increased possibility of hotspots, and the latter due to high thermally-induced stresses in the solidifying melt. Lower pouring temperatures are therefore preferred. **Figure 2** summarises the important temperature parameters during the solidification stage.

As a final word in this Section, the liquidus slope *m* and partition coefficient *k* can likewise be determined from the phase diagram of the steel alloy. An in-depth discussion on these parameters is beyond the scope of this Chapter, except to note that these parameters affect the spacing between secondary dendrite arms (as will be shown in Section 3.2), and hence the level of interdendritic shrinkage porosity. In peritectic steels, the liquidus slopes (temperature versus solute composition gradients) are given as *<sup>m</sup><sup>δ</sup>* and *<sup>m</sup><sup>γ</sup>* for the *<sup>L</sup>* <sup>þ</sup> *<sup>δ</sup>* and*<sup>L</sup>* <sup>þ</sup> *<sup>γ</sup>* zones respectively. Similarly, the partition coefficients for the solute in δ-ferrite and austenite are given by:

$$k\_C^\delta = \frac{\mathbf{C}\_{s,\mathbf{C}}^\*}{\mathbf{C}\_{l,\mathbf{C}}^\*} \quad and \quad k\_\mathbf{C}^\tau = \frac{\mathbf{C}\_{s,\mathbf{C}}^\*}{\mathbf{C}\_{l,\mathbf{C}}^\*} \tag{7}$$

where *C*<sup>∗</sup> *<sup>s</sup>*,*<sup>C</sup>* refers to the solute composition of carbon (subscript "*C*") in the solid (subscript *s*) within the multicomponent steel alloy, and *C*<sup>∗</sup> *<sup>l</sup>*,*<sup>C</sup>* is similarly defined. The partition coefficient indicates the extent of solute rejection during the solidification process. Low values of *k* implies high levels of solute rejection. This can lead to high levels of microsegregation and, hence, inhomogeneity in microstructure – this is beyond the scope of this Chapter. As regards shrinkage porosity, the rejection of solute from the solidifying phase into the liquid melt contributes to the remelting of smaller dendrite arms and, subsequently, coarsening of larger dendrite arms. This is related to the difference in curvatures between the larger and smaller dendrite arms. A more detailed examination of dendritic coarsening can be found in [11]. The liquidus slopes and partition coefficients are important parameters for determining the evolution of solid fraction *gs* as a function of temperature through the mushy zone, in the solution of shrinkage porosity formation, as will be shown in the next Section.

#### **3.2 Mushy zone feeding**

The nucleation and growth of the solid phase in the mushy zone involves highly complex phenomena, not all of which can be adequately dealt with in this Chapter. The aim here will be limited to discussing the mushy zone solidification in the context of shrinkage porosity formation. **Figure 9** depicts a typical equiaxed growth of a solid dendrite in a liquid melt, depicting the growth of secondary dendrite arms with spacing *λ*2, and the velocity of the interdendritic feeding flow *vl*. The velocity of the solidifying front is shown as *vT*. The accompanying solidification contracts by a factor of:

$$
\beta = (\rho\_s - \rho\_l) / \rho\_l \tag{8}
$$

(known as the solidification shrinkage factor), where *ρ<sup>s</sup>* and *ρ<sup>l</sup>* are the solid and liquid densities respectively. Hence, it can be shown that the (localised) feeding velocity becomes *v<sup>l</sup>* ¼ �*βvT*.

Hence, in our case of a hyperperitectic steel (C = 0.3%), there is a shortage of δferrite to react with the amount of liquid fraction for a full peritectic transformation to austenite. The amount of liquid fraction that is transformed with the δ-ferrite fraction of 0.53 into austenite at the peritectic temperature is only 0*:*53*=*0*:*84 � 0*:*16 ¼ 0*:*10. The resulting fractions of liquid and austenite just below the peritectic

*liquid* : *gl* ¼ 0*:*47 � 0*:*10 ¼ 0*:*37 *and austenite* : *g<sup>γ</sup>* ¼ 1 � *gl* ¼ 0*:*63

The remaining liquid now transforms fully into austenite as the solid–liquid mixture cools down to the solidus temperature *Ts* ¼ 1470°C. This is referred to as the *L* þ *γ* zone. (See [9] for an in-situ account of the solidification phase transfor-

*freezing range* ΔT*<sup>f</sup>* ¼ *Tl* � *Ts* ¼ 1515°C � 1470°C ¼ 45°C

It can be seen that hyperperitectic steels have longer freezing ranges compared

Further cooling of the solidified steel down to 800°C results in the transformation of austenite into α-ferrite (either allotriomorphic ferrite nucleating at the austenite grain boundaries or idiomorphic ferrite nucleating inside the austenite grains), until the eutectoid temperature of 740° C is reached. The remaining austenite in this hypoeutectoid steel then transforms into pearlite, a cooperative growth of α-ferrite

In the case of the 0.30% C steel, the volume fractions of α-ferrite and pearlite

These volume fractions would be the case if no micro-porosity was present during the solidification stage, which is not exactly possible, even under highly efficient feeding of the mushy zone. Entrapped interdendritic liquid is bound to occur, even at high levels of solid fraction coherency. Porosity shows up as black (almost zero density) areas on a micrograph, which may sometimes be confused for the lower density phase (α-ferrite), as shown on the micrographs in **Figure 8**. Hence, it is important to establish the phase fractions as above, and use this data

*Optical Micrograph of an A216 WCB cast steel sample (left) and the contrasted image showing the porosity (right).*

<sup>0</sup>*:*<sup>77</sup> � <sup>0</sup>*:*<sup>02</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>63</sup> *and pearlite* : *gpearlite* <sup>¼</sup> <sup>1</sup> � *<sup>g</sup><sup>α</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>37</sup>

to hypoperitectic steels, and high carbon steels (C > 0.53%) have even longer freezing ranges. In the latter, however, solidification starts with nucleation of FCC

and cementite (Fe3C), hence showing up as a lamellae microstructure.

(α-ferrite + cementite) can similarly be determined using the lever rule:

mation of a peritectic steel). The freezing range ΔT*<sup>f</sup>* is given as:

temperature are therefore given as:

*Casting Processes and Modelling of Metallic Materials*

austenite instead of BCC δ-ferrite.

*<sup>α</sup>* � *ferrite* : *<sup>g</sup><sup>α</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>77</sup> � <sup>0</sup>*:*<sup>30</sup>

**Figure 8.**

**140**

**Figure 9.** *Dendritic growth in a liquid melt.*

The densities of liquid steel (at *Tl*) and solid steel (at *Ts*Þ across the mushy zone freezing range depends on alloying composition and phase transformations. The metal's density increases as the temperature reduces from *Tl* to *Ts*, with further volumetric shrinkage to room temperature. Additionally, phase transformations (such as that at the eutectoid temperature from FCC austenite to α-ferrite + cementite) change the degree of volumetric shrinkage. Refer to [12] for a more detailed discussion. The densities for different steel grades as a function of temperature can be determined using Thermo-Calc. In the case of A21 WCB steel, the value of *β* ¼ 0*:*033 was established in **Figure 1**.

As the mushy zone solidifies, the liquid fraction (*gl* ) decreases at the expense of increasing liquid fraction (*gs* ), assuming that no pore fraction (*gp*) forms (*gl* þ *gs* þ *gp* ¼ 1) as shown in **Figure 10**. This means that, at any time, the average localised feeding velocity across the mushy zone becomes *gl v<sup>l</sup>* . This feeding velocity is dependent on the existence of a pressure gradient across the mushy zone, scaled by the permeability *K* of the mush zone and the dynamic viscosity of the liquid *μ* – related by the well-known Darcy equation (derived from conservation of momentum in a porous medium):

$$\mathbf{g}\_l \mathbf{\bar{\nu}}\_l = -\frac{K}{\mu} \left( \nabla \mathbf{p}\_l - \rho\_l \mathbf{g} \right) \tag{9}$$

local solidification time, this *coarsening* process is further compounded by what is referred to as the *remelting* of adjacent smaller dendrite arms, due to phenomena related to curvature differences and solute diffusion. A detailed analysis can be found in [11], except to mention that the SDAS can be determined anywhere in the mushy

*Two-dimensional view of a typical equiaxed mushy zone: solid fraction, permeability and temperature*

*Shrinkage Porosity in Steel Sand Castings: Formation, Classification and Inspection*

*DOI: http://dx.doi.org/10.5772/intechopen.94392*

<sup>¼</sup> *Kt <sup>f</sup> tf*

where *Kt <sup>f</sup>* is a coarsening parameter derived experimentally. More complex models, based on solute diffusion, solidification phase transformation and the Gibbs–Thomson coefficient for the material, can be found [11]. Perhaps a more

*<sup>λ</sup>*<sup>2</sup> *<sup>T</sup>*\_ <sup>¼</sup> *KT*\_ *<sup>T</sup>*\_ �<sup>1</sup>

<sup>1</sup>

<sup>3</sup> (11)

<sup>3</sup> (12)

*λ*<sup>2</sup> *tf*

practical approach is to write Eq. (11) in terms of cooling rate *T*\_ [14]:

zone using a coarsening law:

**Figure 10.**

*variation.*

**143**

where p*<sup>l</sup>* is the liquid pressure and *g* is the gravitational acceleration.

The permeability of the porous mushy zone is modelled using the Kozeny-Carmen relation:

$$K(\mathbf{g}\_s(\mathbf{t}\_f), \lambda\_2(\mathbf{t}\_f)) = \frac{\lambda\_2^2(\mathbf{t}\_f)}{180} \frac{\left(\mathbf{1} - \mathbf{g}\_s(\mathbf{t}\_f)\right)^3}{\mathbf{g}\_s^2(\mathbf{t}\_f)} \tag{10}$$

where *λ*<sup>2</sup> is the secondary dendrite arm spacing (SDAS), dependent on the local solidification time *tf* (the time for a point in the mushy zone to cool from the liquidus temperature *Tl* to the solidus temperature *Ts*). Eq. (10) indicates that coarser grain structures (larger *λ*2) will increase the permeability *K*. Hence, coarser grain structure is preferred for higher permeability and improved feeding flow2 [13]. In addition to

<sup>2</sup> It is noted that coarser grain structure can compromise the mechanical properties of a material, and it may be necessary to balance grain size for improved interdendritic flow and lower shrinkage porosity with mechanical properties, through controlling the solidification rate – see later.

**Figure 10.**

The densities of liquid steel (at *Tl*) and solid steel (at *Ts*Þ across the mushy zone freezing range depends on alloying composition and phase transformations. The metal's density increases as the temperature reduces from *Tl* to *Ts*, with further volumetric shrinkage to room temperature. Additionally, phase transformations (such as that at the eutectoid temperature from FCC austenite to α-ferrite + cementite) change the degree of volumetric shrinkage. Refer to [12] for a more detailed discussion. The densities for different steel grades as a function of temperature can be determined using Thermo-Calc. In the case of A21 WCB steel, the

(*gl* þ *gs* þ *gp* ¼ 1) as shown in **Figure 10**. This means that, at any time, the average

is dependent on the existence of a pressure gradient across the mushy zone, scaled by the permeability *K* of the mush zone and the dynamic viscosity of the liquid *μ* – related by the well-known Darcy equation (derived from conservation of momen-

), assuming that no pore fraction (*gp*) forms

) decreases at the expense of

**<sup>∇</sup>**p*<sup>l</sup>* � *<sup>ρ</sup>l<sup>g</sup>* (9)

(10)

*v<sup>l</sup>* . This feeding velocity

value of *β* ¼ 0*:*033 was established in **Figure 1**.

*Casting Processes and Modelling of Metallic Materials*

increasing liquid fraction (*gs*

*Dendritic growth in a liquid melt.*

**Figure 9.**

tum in a porous medium):

Carmen relation:

**142**

As the mushy zone solidifies, the liquid fraction (*gl*

localised feeding velocity across the mushy zone becomes *gl*

*gl*

 , *λ*<sup>2</sup> *tf* <sup>¼</sup> *<sup>λ</sup>*<sup>2</sup>

with mechanical properties, through controlling the solidification rate – see later.

*K gs tf*

*<sup>v</sup><sup>l</sup>* ¼ � *<sup>K</sup> μ*

where p*<sup>l</sup>* is the liquid pressure and *g* is the gravitational acceleration. The permeability of the porous mushy zone is modelled using the Kozeny-

> <sup>2</sup> *tf* 180

where *λ*<sup>2</sup> is the secondary dendrite arm spacing (SDAS), dependent on the local solidification time *tf* (the time for a point in the mushy zone to cool from the liquidus temperature *Tl* to the solidus temperature *Ts*). Eq. (10) indicates that coarser grain structures (larger *λ*2) will increase the permeability *K*. Hence, coarser grain structure is preferred for higher permeability and improved feeding flow2 [13]. In addition to

<sup>2</sup> It is noted that coarser grain structure can compromise the mechanical properties of a material, and it may be necessary to balance grain size for improved interdendritic flow and lower shrinkage porosity

1 � *gs tf* <sup>3</sup> *g*2 *<sup>s</sup> tf*

*Two-dimensional view of a typical equiaxed mushy zone: solid fraction, permeability and temperature variation.*

local solidification time, this *coarsening* process is further compounded by what is referred to as the *remelting* of adjacent smaller dendrite arms, due to phenomena related to curvature differences and solute diffusion. A detailed analysis can be found in [11], except to mention that the SDAS can be determined anywhere in the mushy zone using a coarsening law:

$$
\lambda\_2(\mathbf{t}\_f) = \mathbf{K}\_{\mathbf{t}\_f} \left(\mathbf{t}\_f\right)^{\frac{1}{5}} \tag{11}
$$

where *Kt <sup>f</sup>* is a coarsening parameter derived experimentally. More complex models, based on solute diffusion, solidification phase transformation and the Gibbs–Thomson coefficient for the material, can be found [11]. Perhaps a more practical approach is to write Eq. (11) in terms of cooling rate *T*\_ [14]:

$$
\lambda\_2(\dot{T}) = K\_{\dot{T}} \dot{T}^{-\frac{1}{3}} \tag{12}
$$

Ultimately, the interdendritic feeding velocity deep into the mushy zone drops rapidly (due to rapidly decreasing permeability), resulting in insufficient feeding flow and, hence, the onset of shrinkage porosity. Applying the conservation of mass (*∂ρ=<sup>∂</sup> <sup>t</sup>* <sup>þ</sup> <sup>∇</sup> � ð Þ¼ *<sup>ρ</sup><sup>v</sup>* 0) to the liquid domain:

$$\frac{\partial}{\partial t} \left( \rho\_s \mathbf{g}\_s + \rho\_l \mathbf{g}\_l \right) + \nabla \cdot \left( \rho\_l \mathbf{g}\_l \mathbf{\nu}\_l \right) = \mathbf{0} \tag{13}$$

and substituting the Darcy Eq. (9), assuming that the gravitational pressure head in a sandcast is the actual pressure gradient, gives:

$$\underbrace{\left(\rho\_s-\rho\_l\right)\frac{\partial\mathbf{g}\_s}{\partial t}+\frac{\partial\rho\_l}{\partial t}\left(\mathbf{1}-\mathbf{g}\_s-\mathbf{g}\_p\right)+\mathbf{g}\_s}\_{\text{pure information}}+\underbrace{\frac{\partial\rho\_s}{\partial t}-\rho\_l\frac{\partial\mathbf{g}\_p}{\partial t}}\_{\text{solidification shrinkage}}=\nabla\cdot\left(\rho\_l\frac{K}{\mu}\left(\nabla\mathbf{p}\_l\right)\right)\tag{14}$$

where *gl* þ *gs* þ *gp* ¼ 1 has been used to introduce the pore fraction in place of the liquid fraction. This form of the conservation equations gives a sense of the terms responsible for capturing (a) the shrinkage porosity compensated by feeding flow (positive) and (b) the pore formation due to a lack of feeding flow (negative). Eq. (14) can be reformulated by introducing the Kozeny-Carmen relation (Eq. (10)) and assuming that the liquid and solid densities variations (*∂ρl=∂ t* and *∂ρs=∂t*) are minimal across the freezing temperature range:

$$(\rho\_s - \rho\_l)\frac{\partial \mathbf{g}\_s}{\partial t} - \rho\_l \frac{\partial \mathbf{g}\_p}{\partial t} = \nabla \cdot \left(\rho\_l \frac{\mathbf{1}}{\mu} \frac{K\_T^2 \dot{T}^{-\frac{2}{3}}}{\mathbf{1} \mathbf{8} \mathbf{0}} \frac{\left(\mathbf{1} - \mathbf{g}\_s\right)^3}{\mathbf{g}\_s^2} \left(\nabla \mathbf{p}\_l\right)\right).$$

and introducing *β* from Eq. (8), a concise mathematical form for shrinkage pore formation in the mushy zone can be established:

$$
\beta \frac{\partial \mathbf{g}\_s}{\partial t} - \frac{\partial \mathbf{g}\_p}{\partial t} = \nabla \cdot \left( \frac{\mathbf{1} K\_T^2 \dot{T}^{-\frac{2}{3}}}{\mu} \frac{\left(\mathbf{1} - \mathbf{g}\_s\right)^3}{\mathbf{g}\_s^2} \left(\nabla \mathbf{p}\_l\right)\right) \tag{15}
$$

In practice, though, shrinkage porosity prediction is often based on a quantitative criterion, based on the scaling of the pressure gradient given in Eq. (15). By substituting for solid fraction *gs* as a function of temperature (see **Figure 10**), using a microsegregation model (such as the lever rule or the Gulliver-Scheil model), it is possible to integrate Eq. (15) to obtain such a scaling parameter, and use this as a *criterion* for shrinkage pore formation. The scaling parameter, known as the Niyama criterion, given by:

$$N\_{\mathcal{Y}} = \frac{G}{\sqrt{\dot{T}}} \tag{16}$$

actual castings. They found that macroporosity (visible on radiographs) correlated to values of Niyama criterion *Ny <*1, but also found that microporosity occurs at higher values of Niyama criterion *Ny <*2 for nickel based alloys. Hence, critical areas in a steel casting should have values of Niyama criterion of at least *Ny >*2 to be a

*Distribution of Niyama criterion values for a steel casting, showing macroporosity (Ny* <1*) and microporosity*

*Shrinkage Porosity in Steel Sand Castings: Formation, Classification and Inspection*

*DOI: http://dx.doi.org/10.5772/intechopen.94392*

Although the Niyama criterion, and other similar thermal criteria, such as that proposed by Lee et al [17] and Suri et al [18], are only quantitative indicators, it allows process control interventions to reduce shrinkage porosity formation. From the Niyama criterion (Eq. 16), it is clear that reducing the cooling rate (*T*\_ ) will result in higher values of *Ny* and, hence, lower levels of shrinkage porosity - as mentioned before, this is due to coarser grain structures with higher permeability (i.e. improved feeding flow). Practically, this may involve preheating the mould,

Furthermore, high thermal gradients (*G*), will also lead to higher values of *Ny*. From **Figure 10**, it is clear that lower freezing range allows (i.e. narrower mushy zones) will provide higher values of *G*, resulting in more columnar dendritic growth with higher permeability, as opposed to equiaxed growth with lower permeability.

In the previous sections, the mechanisms for shrinkage porosity formation were discussed, from a thermal perspective – that is, during solidification contraction of the mushy zone. In this section, the various types of shrinkage porosity, based on morphology, will be classified. In doing so,, it is important to understand their likely causes, at least from a foundry perspective. A useful approach is to look at these causes in terms of design (both part and mould design), process and material

At the outset, it is important to distinguish between micro and macro shrinkage

porosity. A common misconception is to make this distinction purely based on

or/and using silica sand with lower thermal conductivity.

**4. Classification of Shrinkage Porosity Types**

sound casting (**Figure 11**).

**Figure 11.**

*(Ny* <1*) in critical areas.*

factors.

**145**

where *G* is the temperature gradient at the solid-melt interface and *T*\_ is the cooling rate, is currently the most widely used criterion for porosity prediction in metal casting. Niyama et al. [15] initially used this criterion to study porosity formation in steel castings, and concluded that (macro) porosity occurs when *Ny <*1, i.e. low temperature gradient *G* and/or high cooling rate *T*\_ . Carlson and Beckermann [16] investigated the use of the Niyama criterion for shrinkage porosity in nickel alloy castings by simulating the filling and solidification and correlating the Niyama criterion with (micro- and macro-) porosity-containing areas in the

*Shrinkage Porosity in Steel Sand Castings: Formation, Classification and Inspection DOI: http://dx.doi.org/10.5772/intechopen.94392*

#### **Figure 11.**

Ultimately, the interdendritic feeding velocity deep into the mushy zone drops rapidly (due to rapidly decreasing permeability), resulting in insufficient feeding flow and, hence, the onset of shrinkage porosity. Applying the conservation of mass

and substituting the Darcy Eq. (9), assuming that the gravitational pressure head

*∂ρs <sup>∂</sup><sup>t</sup>* � *<sup>ρ</sup><sup>l</sup>*

where *gl* þ *gs* þ *gp* ¼ 1 has been used to introduce the pore fraction in place of the liquid fraction. This form of the conservation equations gives a sense of the terms responsible for capturing (a) the shrinkage porosity compensated by feeding flow (positive) and (b) the pore formation due to a lack of feeding flow (negative).

> 1 *μ K*2 *<sup>T</sup>*\_ *<sup>T</sup>*\_ �<sup>2</sup> 3

and introducing *β* from Eq. (8), a concise mathematical form for shrinkage pore

180

In practice, though, shrinkage porosity prediction is often based on a quantitative criterion, based on the scaling of the pressure gradient given in Eq. (15). By substituting for solid fraction *gs* as a function of temperature (see **Figure 10**), using a microsegregation model (such as the lever rule or the Gulliver-Scheil model), it is possible to integrate Eq. (15) to obtain such a scaling parameter, and use this as a *criterion* for shrinkage pore formation. The scaling parameter, known as the Niyama

*Ny* <sup>¼</sup> *<sup>G</sup>*

where *G* is the temperature gradient at the solid-melt interface and *T*\_ is the cooling rate, is currently the most widely used criterion for porosity prediction in metal casting. Niyama et al. [15] initially used this criterion to study porosity formation in steel castings, and concluded that (macro) porosity occurs when *Ny <*1, i.e. low temperature gradient *G* and/or high cooling rate *T*\_ . Carlson and Beckermann [16] investigated the use of the Niyama criterion for shrinkage porosity in nickel alloy castings by simulating the filling and solidification and correlating the Niyama criterion with (micro- and macro-) porosity-containing areas in the

ffiffiffi

0 @

180

1 � *gs* � �<sup>3</sup> *g*2 *s*

1 � *gs* � �<sup>3</sup> *g*2 *s*

> ∇p*<sup>l</sup>* � �

1

*<sup>T</sup>*\_ <sup>p</sup> (16)

*vl*

*∂gp ∂t* |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} solidification shrinkage

� � <sup>¼</sup> <sup>0</sup> (13)

*K μ* ∇p*<sup>l</sup>* � � � �

(14)


> ∇p*<sup>l</sup>* � �

1 A

A (15)

¼ ∇ � *ρ<sup>l</sup>*

� � <sup>þ</sup> <sup>∇</sup> � *<sup>ρ</sup><sup>l</sup> gl*

þ *gs*

Eq. (14) can be reformulated by introducing the Kozeny-Carmen relation (Eq. (10)) and assuming that the liquid and solid densities variations (*∂ρl=∂ t* and

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> <sup>∇</sup> � *<sup>ρ</sup><sup>l</sup>*

*μ K*2 *<sup>T</sup>*\_ *<sup>T</sup>*\_ �<sup>2</sup> 3

0 @

(*∂ρ=<sup>∂</sup> <sup>t</sup>* <sup>þ</sup> <sup>∇</sup> � ð Þ¼ *<sup>ρ</sup><sup>v</sup>* 0) to the liquid domain:

*Casting Processes and Modelling of Metallic Materials*


*<sup>ρ</sup><sup>s</sup>* � *<sup>ρ</sup><sup>l</sup>* ð Þ *<sup>∂</sup>gs*

*β ∂gs <sup>∂</sup><sup>t</sup>* � *<sup>∂</sup>gp*

criterion, given by:

**144**

*<sup>ρ</sup><sup>s</sup>* � *<sup>ρ</sup><sup>l</sup>* ð Þ *<sup>∂</sup>gs*

*∂t* þ *∂ρl ∂t*

*∂*

in a sandcast is the actual pressure gradient, gives:

1 � *gs* � *gp* � �

*∂ρs=∂t*) are minimal across the freezing temperature range:

*∂gp*

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> <sup>∇</sup> � <sup>1</sup>

*<sup>∂</sup><sup>t</sup>* � *<sup>ρ</sup><sup>l</sup>*

formation in the mushy zone can be established:

*<sup>∂</sup><sup>t</sup> <sup>ρ</sup>sgs* <sup>þ</sup> *<sup>ρ</sup>lgl*

*Distribution of Niyama criterion values for a steel casting, showing macroporosity (Ny* <1*) and microporosity (Ny* <1*) in critical areas.*

actual castings. They found that macroporosity (visible on radiographs) correlated to values of Niyama criterion *Ny <*1, but also found that microporosity occurs at higher values of Niyama criterion *Ny <*2 for nickel based alloys. Hence, critical areas in a steel casting should have values of Niyama criterion of at least *Ny >*2 to be a sound casting (**Figure 11**).

Although the Niyama criterion, and other similar thermal criteria, such as that proposed by Lee et al [17] and Suri et al [18], are only quantitative indicators, it allows process control interventions to reduce shrinkage porosity formation. From the Niyama criterion (Eq. 16), it is clear that reducing the cooling rate (*T*\_ ) will result in higher values of *Ny* and, hence, lower levels of shrinkage porosity - as mentioned before, this is due to coarser grain structures with higher permeability (i.e. improved feeding flow). Practically, this may involve preheating the mould, or/and using silica sand with lower thermal conductivity.

Furthermore, high thermal gradients (*G*), will also lead to higher values of *Ny*. From **Figure 10**, it is clear that lower freezing range allows (i.e. narrower mushy zones) will provide higher values of *G*, resulting in more columnar dendritic growth with higher permeability, as opposed to equiaxed growth with lower permeability.
