International Journal of Metalcasting

, Volume 13, Issue 2, pp 463–472 | Cite as

Reducing Shrinkage Porosity in High-Performance Steel Castings: Case of an ASME B16.34 Gate Valve Body: Part 2—Simulation and Experimental Verification

  • Nawaz MahomedEmail author
  • Hendrik Andries Kleynhans


This study presents a systematic framework for reducing shrinkage porosity in high-performance steel castings, based on a simulation-driven optimisation process coupled to micro- and macrostructural evaluation of the castings. For the test case, the macro- and microstructural investigation of a Class 300 gate valve body, based on the ASME B16.34 standard and made from A216 WCB cast steel, using X-ray computed tomography and scanning electron microscopy, was presented in Part 1: Analysis, Techniques and Experimental Approach. This forms the basis for introducing appropriate design and process improvement measures to reduce shrinkage porosity severity levels, based on parameters that influence shrinkage porosity formation, particularly in terms of temperature gradient and solidification rate. Based on the improved design, and using a patternless sand mould manufacturing technology, a trial casting of the valve body was produced, showing a significant improvement in shrinkage porosity levels.


shrinkage porosity metal casting simulation X-ray radiography 


This paper should be read in conjunction with the first part,1 which expounds on the phenomena that give rise to shrinkage porosity defects in castings, its effect on part quality, productivity and competitiveness. Various parameters were noted, which include initial melt pouring temperature, heat dissipation through the mould (and hence the mould material characteristics), the solidification rate and the freezing range of the alloy, both of which influence the size of the mushy zone. All these parameters influence the liquid melt feeding of the mushy zone during solidification. Besides these design and process parameters, additional effects, such as the non-Newtonian behaviour of melt feeding in the mushy zone and the variation of permeability with volume fraction, need to be considered as part of an overall and systematic engineering approach for reducing shrinkage porosity.

At the same time, the casting process parameters that prevail during the solidification phase have a direct effect on mechanical properties, such as material strength and ductility (as a result of grain size), microsegregation and microstructural evolution, although some of these effects could be remedied through solution heat treatment. For example, lower solidification rates lead to coarser microstructure (i.e. larger grain size), and hence larger inter-dendritic regions and, therefore, increased shrinkage porosity. It, however, can improve material homogeneity (due to back-diffusion of solute), but will result in reduced ductility of the material (due to the coarser grain structure). Hence, the optimisation of casting and process parameters for reducing shrinkage porosity may need to be balanced with desired microstructural qualities, leading to multiple (and often conflicting) objectives during the optimisation process.

As also mentioned in Part 1, foundry engineers generally resort to the use of certain thermal criteria, such as the Niyama (Ny) criterion, to establish the potential for shrinkage porosity formation in castings, since shrinkage porosity is largely dependent on thermal gradients and heat dissipation rates during solidification (for a given alloy). Although this can be evaluated for a given casting design and process, there is a lack of a systematic improvement process that allows engineers to both evaluate and systematically reduce porosity levels in castings through design and process optimisation. This requires a full understanding of the various parameters that influence porosity, in terms of design, process as well as material, together with the modification and optimisation of these parameters.

Part 1 focused on the evaluation of shrinkage porosity in high-performance steel castings as part of an iterative improvement process for reducing shrinkage porosity in high-performance steel castings during the product development stage. As a test case, a gate valve body made from A216 WCB cast steel was used, and the evaluation process was embedded within the specific standard applicable to steel castings. Certain techniques were proposed to evaluate the severity levels of shrinkage porosity, namely (a) X-ray computed tomography (CT) for shrinkage microporosity (pore sizes ≥ 100 μm) as well as macroporosity (such as hot tears), and (b) scanning electronic microscopy (SEM) for shrinkage microporosity (pore sizes in the range 0.1–200μm). (See Part 1 for a discussion on the distinction between macro- and microporosity, and the practical limitations of certain techniques for high-density materials such as steels).

This paper focuses on the development of a quantitative and systematic approach for reducing porosity in castings, as depicted in Figure 1, building on the evaluation methodology established in Part 1. This is based on an iterative process in which porosity is minimised at the design stage using casting simulations, in which the component geometry and process parameters are optimised.
Figure 1

Systematic approach for reducing porosity in castings—integration of evaluation and simulation techniques.

Numerical Evaluation of Porosity

Modelling Porosity Formation in Castings

Models for predicting porosity formation in solidifying melts have been well established.2,3 These models, as intimated before, are highly complex, and simplifying assumptions in terms of the dependence and inter-dependence of density, volume fractions, melt viscosity and permeability, and temperature, as well as their spatial variations, have been suggested, together with spatially averaged parameters. In practice, models for porosity prediction are only based on experimentally verified quantitative criteria, most notable the Niyama criterion. The derivations of these models have been well established and will not be repeated here; however, certain principles are necessary to understand the causes of porosity, so as to propose a well-defined design approach to reduce porosity.

A microscale model of the solidifying melt region is shown in Figure 2, in which the mushy zone is treated as a porous medium with feeding flow \( \left\langle {\varvec{v}_{\text{l}} } \right\rangle \) averaged over the entire mushy zone. Mass conservation across a representative volume allows the modelling of density change due to solidification shrinkage and thermal contraction compensated by void growth, inward flow of the dendritic flow and compression of the solid phase, the latter due to external tensile loads during solidification, which can lead to hot tears.
Figure 2

Microscale model of solidifying melt region in a steady-state moving frame, showing the temperature and permeability variations in terms of the liquid fraction \( {\varvec{g}}_{\varvec{l}} \left( \varvec{x} \right) \), the temperature gradient G and the mushy zone feeding velocity \( \varvec{v}_{\varvec{l}} \).

Essentially, the inter-dendritic flow is modelled using Darcy’s Law for flow in porous media (ignoring external forces):
$$ \left\langle {\varvec{v}_{{l}} } \right\rangle = g_{l} \left\langle {\varvec{v}}\right\rangle_{{l}} = - \frac{K}{\mu }\left( {\nabla p_{{l}} } \right) $$
in which the averaged flow through the mushy zone, \( \left\langle {\varvec{v}_{{l}} } \right\rangle \), is replaced by the averaged localised or superficial flow \( \left\langle {\varvec{v}}\right\rangle_{{l}} \) multiplied by the liquid fraction \( g_{{l}} \), and is dependent on the pressure gradient in the liquid, \( \nabla p_{{l}} \), scaled by the permeability \( K \) of melt feeding flow in the mushy zone divided by the dynamic viscosity of the melt \( \mu \). Various models for viscosity have been suggested, as summarised by Cheng et al.4 Earlier research has shown that metal alloy melts exhibit Newtonian behaviour, similar to pure metals, with viscosity an inverse function of melt temperature across the alloy freezing zone. This is also supported by recent research.5 At the same time, some researchers have shown that metal melts exhibit non-Newtonian shear-thinning behaviour,6 suggesting models such as the power law model for shear rate-dependent viscosity of molten steel.

Currently, though, some commercial software systems simply use a constant viscosity (Newtonian behaviour) assumption, with viscosity measured at the liquidus temperature of the alloy. It is noted, though, that the high-temperature gradients \( G \) (i.e. lower temperatures) near the solidification front will lead to a higher viscosity in the high solid fraction part of the mushy zone, effectively inhibiting the feeding flow velocity. However, the higher solid fraction in this region will result in higher shear rates, which would (according to the shear-thinning model) reduce viscosity (more so for fine dendritic/grain structure) and aid the melt feeding process. Hence, a finer dendritic/grain structure (i.e. higher solidification rate \( \dot{T} \)) with a higher melt temperature (in the mushy zone) will result in reduced viscosity, better feeding flow and reduced porosity.

The permeability of the porous mushy zone is modelled using the Kozeny–Carman relation:
$$ K = \frac{1}{{c\left( {\varsigma_{V}^{\text{sl}} } \right)^{2} \bar{\tau }^{2} }}\frac{{g_{{l}}^{3} }}{{\left( {1 - g_{{l}} } \right)^{2} }} $$
where \( g_{\text{l}} \) is the liquid fraction, \( \bar{\tau } \) is the tortuity, c is a geometric constant, and \( \varsigma_{V}^{\text{sl}} = A_{\text{sl}} /V_{\text{s}} \). is the intrinsic specific solid–liquid surface.2 The latter indicates that coarse dendritic/grain structure (smaller \( \varsigma_{V}^{sl} \)) will increase the permeability K. Hence, a coarser dendritic/grain structure is preferred for higher permeability and improved feeding flow.7 Equation (2) also indicates that permeability is a function of liquid fraction, decreasing exponentially to zero at the solid–liquid interface, as shown in Figure 2. Hence, the narrower the mushy zone, the narrower the low permeability/high solid fraction region, resulting in improved feeding flow. However, a coarser dendritic/grain structure also means larger pools of entrapped liquid, which could result in inter-dendritic shrinkage microporosity during cooling.

Ultimately, inter-dendritic flow is caused by the pressure differential across the mushy zone. As the permeability increases deep into the mushy zone, the pressure drops below a critical value resulting in insufficient feeding flow and the onset of shrinkage porosity. Hence, it is important to establish how the temperature gradient \( G \) and the cooling rate \( \dot{T} \) scale the pressure gradient.

As mentioned before, in practice, shrinkage porosity prediction is based on a quantitative criterion, such as the Niyama criterion, Ny. Essentially, Ny is obtained by combining Darcy’s form of the momentum equation (1) with the mass conservation condition. The outcome of this analysis (see References 2 and 7 for details) is an expression for the pressure differential across two points a and b in the mushy zone, given in one-dimensional form as:
$$ \Delta p = \beta \mu \frac{{\dot{T}}}{{G^{2} }}\int \limits_{{\left( {g_{{l}} } \right)_{a} }}^{{\left( {g_{{l}} } \right)_{b} }} \frac{{g_{l} }}{K}\frac{{{\text{d}}T}}{{{\text{d}}g_{{l}} }}{\text{d}}g_{{l}} = \frac{\beta \mu }{{N_{y}^{2} }} \int \limits_{{\left( {g_{{l}} } \right)_{a} }}^{{\left( {g_{{l}} } \right)_{b} }} \frac{{g_{{l}} }}{K}\frac{{{\text{d}}T}}{{{\text{d}}g_{{l}} }}{\text{d}}g_{{l}} $$
where \( \beta = \left( {\rho_{\text{s}} - \rho_{{l}} } \right)/\rho_{{l}} \) is the solidification shrinkage. The region of interest is usually between the low permeability region (\( g_{{l}} = 0.5 \); \( g_{\text{s}} = 0.5 \)) and the solid–liquid interface where porosity is likely to occur (\( g_{{l}} = 0 \); \( g_{\text{s}} = 1 \)). The temperature variation with liquid fraction (\( {\text{d}}T/{\text{d}}g_{{l}} \)) can easily be estimated using a suitable microsegregation model such as the lever rule or the Gulliver–Scheil model.
It can then be shown that the parameter that scales the pressure gradient is given by the Niyama criterion, currently the most widely used criterion for porosity prediction in metal casting:
$$ N_{y} = \frac{G}{{\sqrt {\dot{T}} }} $$
where \( G \) is the temperature gradient at the solid–melt interface and \( \dot{T} \) is the cooling rate. Niyama et al.8 initially used this criterion to study porosity formation in steel castings and concluded that (macro) porosity occurs when \( N_{y} < 1 \), i.e. low-temperature gradient G and/or high cooling rate \( \dot{T} \). Carlson and Beckermann9 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 actual castings. They found that macroporosity, visible on radiographs, correlates to values of Niyama criterion \( N_{y} < 1 \), but also found that microporosity occurs at higher values of Niyama criterion \( N_{y} < 2 \) for the nickel based alloys used in their study. They concluded that critical areas in a casting should have values of Niyama criterion of at least \( N_{y} > 2 \) to be a sound casting. Hence, the Niyama criterion and other thermal criteria, such as that proposed by Lee et al.10 and Suri et al.,11 although quantitative indicators, are not used to directly quantify porosity, but to indirectly establish degrees of porosity based on experimental correlation.

Approach to Design and Process Improvement

The foregoing analysis has shown that porosity is not only a function of the thermal parameters \( (G\;{\text{and}}\;\dot{T}) \) as per the Niyama criterion, but also dependent on other parameters (viscosity \( \mu \) and permeability K). The dimensionless Niyama criterion proposed by Carlson et al.12 does capture the viscosity of the liquid metal; however, none of the criteria incorporate the permeability of the mushy zone [in terms of the Kozeny–Carman relation (2)].

However, the viscosity and permeability parameters can be related to the thermal parameters, and hence indirectly to the Niyama criterion. Hence, the desired casting conditions for reducing porosity formation established in the previous section, in terms of melt viscosity and mushy zone permeability, are summarised in Table 1. It is evident that the thermal parameters related to these conditions are consistent with the desired pressure scaling parameters given by the Niyama criterion, i.e. high-temperature gradient G and low heat dissipation/cooling rate \( \dot{T} \).
Table 1

Summary of Desired Conditions for Improved Feeding Flow/Reduced Porosity

Desired conditions

Mushy zone characteristics

Related thermal parameters

Low viscosity

High melt temperature in mushy zone

High \( G \)

Fine grain structurea

High \( \dot{T} \)

High permeability

Coarse grain structure

Low \( \dot{T} \)

Narrow mushy zone

High \( G \)

aSince the shear-thinning behaviour of a melt is known to occur at high shear rates, this desired condition will be ignored in the absence of actual shear rate data for mushy zone feeding flow

From a design perspective, high-temperature gradients and low cooling rates can be achieved through (a) increasing the pouring temperature and (b) using a mould material that provides better insulation, maximising heat transfer through the part (ultimately through the feeders/risers—see “Optimisation Procedure” section) instead of the mould. It is noted that lowering the cooling rate will lead to coarse microstructures, which are not always desirable due to loss in ductility (and fatigue strength). However, grain refinement can always be instated through solution heat treatment, which is usually necessary in any case for microstructure homogenisation.

A further important design consideration is that of flow geometry. Tapered flow geometry has been shown to increase the value of \( N_{y} \) and hence decrease the formation of shrinkage porosity.13,14 This is understood to be due to an increasing feeding velocity caused by the tapering geometry (particularly towards the core of the casting where porosity is likely to occur), leading to an increase in the thermal gradient.14

Numerical Simulations

Selection of Design and Process Parameters for Optimisation

Based on the foregoing discussion, various options for reducing porosity can be deduced, including material selection, melt temperature, mould material, cavity/part geometry, location of feeders, etc. For purposes of demonstrating the proposed approach for reducing porosity, the optimisation parameters have been limited to the initial melt (pouring) temperature and particular geometric features (Figure 3) in the regions of high porosity formation. The choice of the geometric parameters is based on creating tapered flow towards the porosity-prone regions, as discussed before.
Figure 3

The test case of a gate valve body: (a) generalised geometric parameters for optimisation; (b) layout of sandcasting mould, showing the introduction of tapered geometry.

The commercial casting simulation software used in this study does not use adaptive mesh refinement based on error estimation, and it is therefore necessary to establish mesh independence to ensure convergence of the error in the numerical scheme. Three different element sizes were tested (3 mm, 2.5 mm and 2.0 mm) and the calculated values of mean temperature history of the casting compared, confirming mesh independence. A constant kinematic viscosity of 1 mm2/s is used in the simulations, which is a good approximation for the temperature range close to the solidus temperature.5

The initial mould filling process, using a filling time of approximately 10 s, is shown in Figure 4.
Figure 4

Flow tracer for the mould filling process.

Optimisation Procedure

A multi-objective evolutionary algorithm (MOEA) is used for optimisation of the design space, details of which can be found in Reference 15. The use of such optimisation algorithms for reducing shrinkage porosity within a multi-objective design space has been well established—see Reference 16. The objective functions are based on (1) reducing the average shrinkage microporosity; and (2) reducing the maximum value of macroporosity in the casting (to minimise the risk of crack initiation due to stress concentrations in critical sections of the casting). The ranges of the parameters (causal parameters based on the discussion in “Selection of Design and Process Parameters for Optimisation” section) for the optimisation algorithm are shown in Table 2, as well as the step value for each parameter. The MOEA allows convergence to a particular set of design variables within the design space, as shown in Table 2.
Table 2

Parameters Used in Optimisation Algorithm, Indicating the Correlations Between the Process and Geometric Design Parameters and the Objective Functions of Reducing Average Microporosity and Max Macroporosity

Process/design parameter




Optimised set of values

Objective 1: reduce avg. microporosity

Objective 2: reduce max. macroporosity

Pouring temp (°C)



− 0.84

− 0.38


Machining thickness (MT) (mm)






Flow taper (SP) (mm)






Spindle (R) (mm)






The results revealed that the melt pouring temperature has a strong negative correlation on microporosity (i.e. increasing pouring temperature increases porosity). However, the effect on macroporosity is not so profound (i.e. increasing pouring temperatures marginally correlates to increasing macroporosity—due to already high values of \( N_{y} \) as a result of higher temperature gradients \( G \) at the solid–liquid interface.

Since the melt temperature has a strong negative correlation on microporosity, it may seem that the optimal pouring temperature is too high. However, this is to ensure that the melt temperature, as shown in Figure 5, remains above the equilibrium solidification temperature throughout the mould at the end of the filling stage.
Figure 5

Melt temperature distribution at the end of the filling stage.

The geometric parameters (MT, SP and R) have a moderate positive correlation with macroporosity (i.e. increasing the taper angles reduces porosity). The taper in the spindle section has a bigger effect on reducing the maximum macroporosity as compared to the taper in the flow section. These results are based on calculation of the Niyama criterion across the casting, as shown in Figure 6. The optimised casting still shows propensity for microporosity, for \( N_{y} < 2 \), in the critical areas of the casting, shown in Figure 7, which is unavoidable. However, the relatively high values of \( N_{y} \) show a very low potential for macroporosity in the critical areas of the casting, as indicated in the macroporosity distribution plots shown in Figure 8.
Figure 6

Distribution of Niyama criterion values for the optimised casting.

Figure 7

Microporosity predictions for the optimised casting.

Figure 8

Macroporosity predictions (\( {\varvec{N}}_{\varvec{y}} \,{\varvec{<}} \,{\varvec{1}} \)) for (a) initial design and (b) optimised design.

Solidification Contraction

Ensuring adequate feeding of the mushy zone during solidification contraction is a critical precondition for reducing shrinkage microporosity; otherwise, Eqn. (3) will be severely compromised. Premature solidification of feeders can also lead to hotspots giving rise to macroporosity in the form of hot tears. Foundries typically use the well-known Chvorinov rule for estimating the freezing time, and to ensure that the modulus of the feeder system (ratio of volume to surface area) is higher than that of the cavity. Design rules related to feeder locations and feeder efficiencies have been well established17 and will not be discussed in this paper. It is only noted here that solid fraction predictions for the optimised casting, as shown in Figure 9, indicate that the mould layout and component designs succeeded in ensuring that solidification proceeds from the component outward towards the feeders.
Figure 9

Solid fraction predictions for the optimised casting at times (a) 3 min 28 s and (b) 11 min 20 s.

Trial Sand Mould and Casting

Prototype mould production can easily be achieved using digital patternless sand mould machining (SMM) technology. This allows for the rapid production of highly accurate sand casting moulds using the mould geometry data produced in the design through simulation process. The prototype mould and resulting trial casting are shown in Figure 10.
Figure 10

Right: the prototype sand mould (drag and insert) produced using patternless sand mould machining technology. Left: prototype of the trial casting of the valve body.

Owing to the size of the casting (approximately 23 kg of steel), as well as the size and cost of the patternless sand mould, only a single trial casting was produced. The pouring rate through the sprue and runner system (see also Figure 3b) was measured as close as practically possible to the simulated pouring/filling time of 10 s.

Shrinkage Porosity Evaluation of Trial Casting

Radiographic inspection of the optimised trial casting (based on the optimised design and process parameters) was conducted in terms of the relevant ASTM standard (ASTM E446/ASTM E2868). The critical areas to be evaluated, as per the design standard (ASME B16.3418), are shown in Figure 11.
Figure 11

(a) Sections of casting for required radiographic examination (reprinted from ASME B16.34-2007,18 by permission from the American Society of Mechanical Engineers. All rights reserved). (b) Equivalent production radiograph numbers for the trial casting (radiographs 20 and 21 behind 18 and 23, respectively).

The radiographic inspection was conducted using standard 2D X-ray techniques. (The use of 3D X-ray computed tomography is possible with a suitable X-ray CT scanner that has the required penetration capacity, and then using the condensed CT radiograph for the radiographic inspection, as explained in Part 11). Evaluation of the production radiographs for the trial casting, given in Table 3, showed no visible shrinkage porosity on all the radiographs in the critical sections of the casting. A round flaw visible on one of the radiographs (see Figure 12) would be either due to a sand inclusion or due to entrapped gas.
Table 3

Evaluation of Production Radiographs for the Trial Casting

Radiograph number

Shrinkage porosity defect nature and quantity

Evaluated severity level (as per ASTM E2868)


None visible



None visible



None visible



None visible



None visible



None visible



A: round flaw 6 point



None visible


Figure 12

Radiographic test results for trial casting. The only defect (6 point round flaw) is visible on the radiograph number 23 (left). The other radiographs, such as radiograph number 24 (right), are defect free.


The study reiterates the importance of understanding the effect of solidification phenomena on porosity formation, particularly in terms of temperature gradient and solidification rate. A range of parameters are identified that influence the solidification phenomena, including design, material and process parameters. Understanding the influence of these parameters on porosity formation therefore becomes crucial in introducing appropriate design and process improvement measures to reduce porosity severity levels in castings through the use of simulation and optimisation tools.

The application of this approach to an ASME B16.34 class 300 gate valve body casting has been demonstrated. The test casting revealed areas of high porosity severity levels in the critical areas of the component (see Part 11). This warranted the need to optimise the design and process parameters. This study has shown how these parameters can be optimised using a multi-objective evolutionary algorithm based on parameters that influence porosity in castings, coupled to process simulation software.

The resulting optimised design of the casting showed a significant improvement in the porosity severity levels in the trial casting as compared to the that in the test casting, the latter evaluated in Part 1.1



This research was supported by a grant from the National Research Foundation (NRF; Grant No. 105910), South Africa.


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Copyright information

© American Foundry Society 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Mechatronic EngineeringStellenbosch UniversityStellenboschSouth Africa

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