I have investigated the formation of recrystallization defects in a second-generation nickel-based single-crystal superalloy turbine outer ring and developed a pre-heat-treatment electrolytic corrosion process to suppress them. The component is produced by the selector method in a directional solidification furnace and is intended for the hot section of an aero-engine combustion chamber. In my production data, casting defects such as stray grains and recrystallization were the dominant causes of single-crystal incompleteness. Recrystallization alone accounted for more than 75% of scrapped parts, and the overall recrystallization defect rate reached approximately 70%. My objective was to reduce this rate below 5% while preserving dimensional accuracy, surface quality, and single-crystal integrity. The work combines casting-defect analysis, thermal-stress reasoning, electrochemical removal modeling, systematic experiments, and process-window optimization. The resulting method provides a practical route for controlling casting defects in complex single-crystal turbine outer rings.
Background and motivation. Nickel-based single-crystal superalloys are widely used for turbine blades, vanes, combustor liners, and outer rings because they offer high-temperature strength, creep resistance, fatigue resistance, and oxidation resistance. As engine thrust and turbine inlet temperature increase, the hot-section components experience more severe thermal gradients, mechanical loads, and environmental attack. The turbine outer ring is a large, thin-walled, annular component with multiple bosses, windows, and geometric transitions. Its manufacture requires not only single-crystal solidification but also subsequent heat treatment and finishing. During these stages, casting defects can form or become visible. Among them, surface recrystallization is particularly damaging because it introduces random equiaxed grains into a material that is designed to have no grain boundaries. In single-crystal superalloys, grain-boundary strengthening elements are either absent or kept very low. Therefore, recrystallized grain boundaries provide weak paths for sliding, oxidation, and crack initiation. The presence of recrystallization can reduce creep life, fatigue life, and service reliability, and it can lead to premature fracture. Controlling casting defects such as recrystallization is thus essential for yield, cost, and safety.
Definition of recrystallization in the present context. Surface recrystallization refers to the formation and growth of new strain-free grains in a region that has experienced plastic deformation. The deformed region may arise from mold-shell contraction during directional solidification, core removal, grinding, machining, peening, handling, or minor impact. When the component is later exposed to high temperature during solution treatment or service, the stored deformation energy provides a driving force for recovery, nucleation, and grain-boundary migration. The original columnar or single-crystal orientation is locally replaced by randomly oriented equiaxed grains. Because the alloy lacks grain-boundary strengtheners, these new boundaries are weak. I therefore treat recrystallization as one of the most critical casting defects in single-crystal turbine outer rings.
Mechanistic framework. I describe the recrystallization driving force using stored energy from dislocation density and residual elastic strain. A simplified expression for the stored energy is
$$ E_s = \rho_d G b^2 + \frac{1}{2} E \varepsilon_p^2 $$
where \( \rho_d \) is the dislocation density, \( G \) is the shear modulus, \( b \) is the Burgers vector, \( E \) is Young’s modulus, and \( \varepsilon_p \) is the plastic strain. The first term represents dislocation storage, and the second term represents residual elastic strain energy. Nucleation occurs when the local stored energy exceeds the resistance from grain-boundary curvature and surface energy. The classical nucleation barrier can be written as
$$ \Delta G^* = \frac{16 \pi \gamma^3}{3 \Delta G_V^2} $$
where \( \gamma \) is the grain-boundary energy and \( \Delta G_V \) is the volumetric driving force. The nucleation rate is then
$$ \dot{N} = N_0 \exp\left(-\frac{\Delta G^*}{kT}\right) \exp\left(-\frac{Q_d}{kT}\right) $$
where \( N_0 \) is a pre-exponential factor, \( k \) is Boltzmann’s constant, \( T \) is absolute temperature, and \( Q_d \) is the activation energy for diffusion. Once nuclei form, the grain-boundary migration velocity is
$$ v_{gb} = M_{gb} P $$
where \( M_{gb} \) is the boundary mobility and \( P \) is the net driving pressure. The mobility often follows an Arrhenius form:
$$ M_{gb} = M_0 \exp\left(-\frac{Q_m}{RT}\right) $$
The overall recrystallized fraction can be approximated by the Johnson-Mehl-Avrami-Kolmogorov equation:
$$ X(t) = 1 – \exp\left[-\left(\frac{t}{\tau}\right)^n\right] $$
Here \( X(t) \) is the recrystallized volume fraction, \( t \) is time, \( \tau \) is a characteristic time, and \( n \) is the Avrami exponent. These equations explain why recrystallization is sensitive to temperature, time, and prior deformation. They also show why removing the deformed surface layer before high-temperature heat treatment is an effective strategy against casting defects such as recrystallization.
Role of component geometry. The turbine outer ring has large variations in wall thickness. The central window is deep, and there are multiple cross-sectional transitions. These features disturb the temperature field during solidification. The thermal stress generated in a constrained body can be estimated as
$$ \sigma_{\mathrm{th}} = \frac{E \alpha \Delta T}{1 – \nu} $$
where \( \alpha \) is the coefficient of thermal expansion, \( \Delta T \) is the temperature difference, and \( \nu \) is Poisson’s ratio. At geometric discontinuities such as small bosses and sharp fillets, the local stress is further amplified. A stress concentration factor can be approximated by
$$ K_t = 1 + q \left(\frac{r}{d}\right)^{-m} $$
where \( r \) is the fillet radius, \( d \) is a characteristic dimension, and \( q \) and \( m \) are empirical constants. The back-side bosses used for mechanical location are small and have a high height-to-diameter ratio. Their top transition radius is a severe stress concentration site. During solidification shrinkage and subsequent solution treatment, this region experiences rapid stress relaxation. The result is a high density of casting defects, especially surface recrystallization.
Casting defects and their consequences. I have classified the relevant casting defects in the turbine outer ring into several categories. The table below summarizes their origin, typical location, and impact on single-crystal integrity.
| Defect type | Typical origin | Common location | Impact on performance |
|---|---|---|---|
| Stray grains | Nucleation ahead of columnar front | Platform edges, thin walls | Loss of single-crystal orientation |
| Surface recrystallization | Plastic deformation plus high temperature | Boss fillets, machined surfaces | Weak grain boundaries, crack initiation |
| Porosity | Shrinkage or gas entrapment | Thick sections, hot spots | Stress concentration, fatigue debit |
| Hot tearing | Constrained solidification shrinkage | Thickness transitions | Crack-like defects, rejection |
| Surface contamination | Core residue or mold reaction | Internal passages, outer surfaces | Poor coating, oxidation, corrosion |
The image above illustrates typical casting defects that can appear in complex castings. In my work, I focus on recrystallization because it is the most frequent and most damaging casting defect for the turbine outer ring. The production statistics before my process change showed that recrystallization caused more than 75% of the scrap and that the defect rate was about 70%. This level of casting defects is unacceptable for batch production. It increases cost, extends lead time, and reduces confidence in single-crystal components.
Electrolytic corrosion as a stress-relief method. I proposed an electrolytic corrosion treatment before solution treatment. The purpose is to remove the surface layer that contains residual deformation, to round sharp corners, and to reduce stress concentration. The process is electrochemical rather than mechanical, so it can reach complex fillets and recessed regions. The fundamental removal law is Faraday’s law:
$$ m = \frac{M I t}{z F} $$
where \( m \) is the mass removed, \( M \) is the molar mass, \( I \) is the current, \( t \) is the time, \( z \) is the valence, and \( F \) is Faraday’s constant. If the exposed area is \( A \) and the density is \( \rho \), the theoretical removal thickness is
$$ h = \frac{M I t}{z F \rho A} $$
The current density is
$$ i = \frac{I}{A} $$
In practice, the current efficiency \( \eta \) is less than unity because of side reactions, gas evolution, and local passivation. The actual removal thickness is therefore
$$ h_{\mathrm{actual}} = \eta h_{\mathrm{theoretical}} $$
I used these equations to estimate the amount of material that must be removed to eliminate the deformed layer. If the deformed layer has a thickness \( \delta_d \), the condition for complete removal is
$$ h_{\mathrm{actual}} \geq \delta_d $$
At the same time, excessive removal can damage the component. A geometric constraint can be written as
$$ h_{\mathrm{actual}} \leq h_{\mathrm{max}} $$
where \( h_{\mathrm{max}} \) is the maximum allowable removal set by dimensional tolerance and surface-finish requirements. The optimum process window is therefore
$$ \delta_d \leq h_{\mathrm{actual}} \leq h_{\mathrm{max}} $$
This inequality guided my selection of electrolysis time. It also explains why the process must be controlled precisely. If removal is too small, recrystallization persists. If removal is too large, over-corrosion creates deep dendrite relief, poor surface quality, and dimensional loss. Both outcomes are undesirable casting defects or quality problems.
Electrolyte formulation. I prepared an electrolyte containing hydrochloric acid, water, ferric chloride, ethanol, citric acid, and dodecylbenzenesulfonic acid. The formulation is given in the table below. I selected this chemistry because it provides controlled attack on nickel-based superalloys, helps dissolve surface oxides, and promotes uniform current distribution. The organic additives improve wetting and reduce pitting.
| Component | Amount | Function |
|---|---|---|
| Hydrochloric acid | 950 mL | Provides chloride ions and acidic attack |
| Water | 800 mL | Solvent and conductivity medium |
| Ferric chloride | 550 g | Oxidizing agent and complexing species |
| Ethanol | 175 mL | Wetting and surface cleaning |
| Citric acid | 225 g | Complexing agent and pH buffer |
| Dodecylbenzenesulfonic acid | 22.5 g | Surfactant for uniform current |
Sample preparation and masking. I protected areas that were not intended for electrolysis with insulating tape. This masking step is important because uncontrolled removal on functional surfaces would create new casting defects or dimensional errors. The component was fixed to an electrode and immersed in the electrolyte. I set the power supply to a voltage of 1.5 V and a current of 4 A. The targeted region was the boss and fillet area, where recrystallization was most severe. I varied the electrolysis time to study the relationship between removal amount and recrystallization. The times were 3, 5, 8, 10, 13, and 15 minutes. The corresponding removal amounts were measured and are listed in the table below.
| Electrolysis time (min) | Removal amount (mm) | Nominal removal rate (mm/min) | Visual surface condition after electrolysis |
|---|---|---|---|
| 3 | 0.010 | 0.0033 | Bright |
| 5 | 0.020 | 0.0040 | Bright |
| 8 | 0.035 | 0.0044 | Bright |
| 10 | 0.040 | 0.0040 | Bright |
| 13 | 0.060 | 0.0046 | Dark, over-corroded |
| 15 | 0.080 | 0.0053 | Dark, over-corroded |
Heat treatment. After electrolysis, I rinsed and dried the castings thoroughly. Then I applied the standard solution and aging treatments. The heat treatment schedule is summarized below. The solution treatment temperature was selected in the range of 1295 to 1305 °C with a hold of 2 hours, followed by gas cooling to below 100 °C. The first aging treatment was at 1120 °C for 4 hours, and the second aging treatment was at 1080 °C for 4 hours. Both aging steps were followed by cooling to below 100 °C. This schedule is typical for second-generation nickel-based single-crystal superalloys, but it also provides the thermal exposure that can trigger recrystallization if a deformed layer remains.
| Process step | Temperature | Time | Cooling |
|---|---|---|---|
| Solution treatment | 1295–1305 °C | 2 h | Gas cooling to below 100 °C |
| First aging | 1120 °C | 4 h | Cooling to below 100 °C |
| Second aging | 1080 °C | 4 h | Cooling to below 100 °C |
Macro-etch inspection. After heat treatment, I macro-etched the castings to reveal grain structure and recrystallization. I examined the boss fillets and the surrounding surfaces. The results were grouped according to electrolysis time. The table below summarizes the observations. I counted recrystallized grains and noted whether they could be removed by subsequent polishing. I also recorded surface quality and dimensional appearance.
| Electrolysis time (min) | Removal (mm) | Recrystallization after heat treatment | Surface quality | Acceptance judgement |
|---|---|---|---|---|
| 3 | 0.010 | Many large grains | Bright, slight relief | Reject |
| 5 | 0.020 | Many large grains | Bright, slight relief | Reject |
| 8 | 0.035 | Few small recrystallized spots, fewer than 5 | Bright, acceptable relief | Acceptable after light polishing |
| 10 | 0.040 | Few small recrystallized spots, fewer than 5 | Bright, acceptable relief | Acceptable after light polishing |
| 13 | 0.060 | No recrystallization observed | Dark, deep dendrite relief | Reject due to over-corrosion |
| 15 | 0.080 | No recrystallization observed | Dark, severe dendrite relief | Reject due to over-corrosion |
Interpretation of results. The 3-minute and 5-minute treatments removed 0.010 mm and 0.020 mm, respectively. These removal amounts were insufficient to eliminate the deformed surface layer. After solution treatment, recrystallization still occurred extensively. The 8-minute and 10-minute treatments removed 0.035 mm and 0.040 mm. These conditions left only a few small recrystallized spots, fewer than five per inspected area. Those spots could be removed by subsequent polishing, so the castings were considered acceptable. The 13-minute and 15-minute treatments removed 0.060 mm and 0.080 mm. These conditions completely suppressed recrystallization, but they caused over-corrosion. The surface became dark and the dendrite pattern became deep. The dimensional accuracy and appearance were degraded, and finishing became difficult. Therefore, the optimum electrolysis window was 8 to 10 minutes, corresponding to a removal of 0.035 to 0.040 mm.
Mechanistic explanation. The success of the 8–10 minute treatment can be explained by three effects. First, the electrolytic removal eliminates the layer with the highest dislocation density and residual strain. This reduces the stored energy term in the recrystallization driving force. Second, the electrochemical attack preferentially rounds sharp edges and fillets. This reduces the stress concentration factor \( K_t \) and lowers the local thermal stress during solution treatment. Third, the removal of surface contaminants and damaged material creates a cleaner surface with fewer heterogeneous nucleation sites. As a result, the nucleation rate and growth rate of recrystallized grains are both reduced. The process directly addresses casting defects at their source rather than attempting to repair them after they form.
Residual stress relaxation model. I also considered the relaxation of residual stress during the pre-treatment and subsequent heating. A simple first-order relaxation model is
$$ \sigma(t) = \sigma_0 \exp\left(-\frac{t}{\tau_r}\right) $$
where \( \sigma_0 \) is the initial residual stress and \( \tau_r \) is a relaxation time that depends on temperature and microstructure. By removing the surface layer, the initial stress \( \sigma_0 \) is reduced. The stored elastic energy is approximately
$$ U = \frac{\sigma^2}{2E} V $$
where \( V \) is the affected volume. A reduction in \( \sigma \) lowers \( U \), which in turn lowers the driving force for recrystallization. This is consistent with my experimental observation that a moderate removal of 0.035–0.040 mm is sufficient to suppress most recrystallization, while a smaller removal is not.
Surface curvature and stress concentration. The electrolytic process increases the effective fillet radius. For a fillet subjected to a nominal stress \( \sigma_{\mathrm{nom}} \), the peak stress is
$$ \sigma_{\mathrm{peak}} = K_t \sigma_{\mathrm{nom}} $$
If \( K_t \) decreases from a sharp-edge value to a rounded-edge value, the peak stress drops. This reduces the local plastic deformation during solidification and heat treatment. In turn, the local stored energy for recrystallization is reduced. I observed that the boss fillets became visibly smoother after electrolysis. The macro-etched samples showed that recrystallization was concentrated at the original sharp transitions. After 8–10 minutes of electrolysis, these transitions were rounded and the recrystallization was largely eliminated.
Comparison with alternative methods. I compared the electrolytic process with mechanical polishing, abrasive flow, and chemical etching. The table below summarizes the advantages and limitations. Electrolytic corrosion was chosen because it can reach complex geometry, it does not introduce new mechanical deformation, and it can be controlled by current and time. Mechanical polishing can remove the deformed layer but may introduce new deformation and cannot easily access recessed fillets. Abrasive flow can reach internal passages but is less effective on external bosses. Chemical etching is simple but often less uniform and more difficult to control. The electrolytic method provides a better balance for the turbine outer ring.
| Method | Deformation introduced | Access to fillets | Uniformity | Dimensional control | Overall suitability |
|---|---|---|---|---|---|
| Mechanical polishing | Possible | Limited | Operator dependent | Moderate | Low for complex bosses |
| Abrasive flow | Low | Good for internal | Moderate | Moderate | Moderate |
| Chemical etching | None | Good | Low to moderate | Low | Moderate |
| Electrolytic corrosion | None | Excellent | High with masking | High with time control | High |
Process window and control strategy. Based on my experiments, I defined a process window for the electrolytic treatment. The key variables are electrolyte composition, temperature, voltage, current, time, and masking. In my setup, the voltage was fixed at 1.5 V and the current at 4 A. The critical control variable was time, because it directly determines removal thickness. The optimum window was 8–10 minutes, with a removal of 0.035–0.040 mm. I recommend monitoring the current density and electrolyte temperature continuously. If the current density drifts, the removal rate changes, and the process may move out of the window. I also recommend periodic measurement of removal on witness coupons. The table below lists the control parameters and their recommended ranges.
| Parameter | Recommended value or range | Reason |
|---|---|---|
| Voltage | 1.5 V | Stable dissolution, low gas evolution |
| Current | 4 A | Controlled removal rate |
| Electrolysis time | 8–10 min | Removes deformed layer without over-corrosion |
| Removal thickness | 0.035–0.040 mm | Optimum balance of stress relief and dimensional accuracy |
| Electrolyte temperature | Controlled near ambient | Prevents excessive attack and improves reproducibility |
| Masking | Insulating tape on non-target areas | Protects functional surfaces |
| Post-treatment cleaning | Thorough rinse and dry | Prevents salt residue and corrosion |
Effect on recrystallization defect rate. The most important industrial result is the reduction of the recrystallization defect rate. Before the electrolytic process, the defect rate was approximately 70%. After implementing the optimized 8–10 minute treatment, the defect rate fell below 5%. This is a dramatic improvement in single-crystal integrity and product yield. The table below compares the before and after conditions. I also include the scrap rate from recrystallization, which was above 75% before the change. After the change, the scrap rate due to recrystallization became a small fraction of the total.
| Metric | Before electrolytic treatment | After optimized electrolytic treatment |
|---|---|---|
| Recrystallization defect rate | About 70% | Below 5% |
| Scrap caused by recrystallization | More than 75% of rejected parts | Minor contribution |
| Single-crystal integrity | Frequently compromised | Significantly improved |
| Surface quality | Recrystallized grains and sharp fillets | Rounded fillets, acceptable surface |
| Dimensional accuracy | Acceptable but recrystallization-prone | Maintained within tolerance |
| Product yield | Low | High |
| Production cost | High due to scrap and rework | Reduced |
Statistical process control. For batch production, I recommend using statistical process control to maintain the electrolytic process. The removal thickness \( h \) should be measured on a sample basis. The process mean \( \bar{h} \) and standard deviation \( s \) can be tracked. A process capability index is
$$ C_p = \frac{\mathrm{USL} – \mathrm{LSL}}{6s} $$
where USL is the upper specification limit and LSL is the lower specification limit. For my process, the lower limit is the minimum removal needed to suppress recrystallization, approximately 0.030 mm, and the upper limit is the maximum removal allowed by dimensional tolerance, approximately 0.050 mm. The target is 0.035–0.040 mm. A capable process should have \( C_p > 1.33 \). I also monitor the recrystallization count per inspected area. The target is zero visible recrystallized grains after final polishing, with fewer than five small spots before polishing. The table below presents a recommended control plan.
| Control item | Frequency | Method | Action limit |
|---|---|---|---|
| Electrolyte composition | Daily | Titration or density check | Adjust if out of range |
| Electrolyte temperature | Continuous | Thermocouple | Keep near ambient |
| Current | Continuous | Power supply readout | 4 A ± 0.2 A |
| Voltage | Continuous | Power supply readout | 1.5 V ± 0.1 V |
| Removal thickness | Per batch | Witness coupon or micrometer | 0.035–0.040 mm |
| Recrystallization | Per batch | Macro-etch after heat treatment | Below 5% defect rate |
| Surface roughness | Per batch | Visual and profilometry | No deep dendrite relief |
Design optimization. The electrolytic process controls casting defects, but it does not eliminate the root cause of stress concentration. I therefore recommend design changes for future turbine outer rings. The boss height should be reduced moderately, and the transition radius should be increased. A larger radius reduces \( K_t \) and lowers the local stress. A lower boss reduces the thermal mass and the constraint during solidification. These changes reduce the driving force for recrystallization and make the electrolytic process more robust. The table below summarizes the recommended design modifications and their expected effects.
| Design feature | Current condition | Recommended change | Expected effect |
|---|---|---|---|
| Boss height | High height-to-diameter ratio | Reduce height moderately | Lower thermal stress and constraint |
| Transition radius | Sharp R corner | Increase radius | Lower stress concentration factor |
| Wall thickness transition | Abrupt changes | Gradual blending | More uniform temperature field |
| Window depth | Deep central window | Optimize depth and draft | Better mold filling and cooling |
| Machining allowance | Limited allowance | Provide controlled allowance | Allows stress-relief removal |
Thermal field considerations. The temperature field during directional solidification can be described by the heat conduction equation:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q $$
where \( \rho \) is density, \( c_p \) is specific heat, \( T \) is temperature, \( t \) is time, \( k \) is thermal conductivity, and \( Q \) is a source term. Complex geometry creates non-uniform \( \nabla T \), which leads to thermal stress and plastic deformation. The bosses and fillets are hot spots or cold spots depending on local section thickness. The resulting plastic strain provides the stored energy for recrystallization. By removing the surface layer and rounding the fillets, the electrolytic process mitigates the consequences of the non-uniform thermal field. In the future, I would combine the electrolytic process with thermal-field simulation to optimize both casting and finishing.
Microstructural evolution. During solution treatment, the deformed surface layer undergoes recovery and recrystallization. Recovery reduces dislocation density without forming new grains. Recrystallization forms new grains with low dislocation density. The driving force for recrystallization decreases as the stored energy is consumed. The kinetics can be described by the Avrami equation. My results show that when the deformed layer is removed, the Avrami curve shifts to longer times and lower fractions. In other words, the incubation time for recrystallization becomes longer than the heat-treatment time. This is why the 8–10 minute treatment is effective. The table below presents a qualitative kinetic comparison.
| Condition | Initial stored energy | Incubation time | Recrystallized fraction after solution treatment |
|---|---|---|---|
| No electrolysis | High | Short | Large |
| 3–5 min electrolysis | Moderate to high | Short to moderate | Still significant |
| 8–10 min electrolysis | Low | Longer than treatment | Very small |
| 13–15 min electrolysis | Very low | Very long | None, but over-corrosion |
Grain boundary effects. When recrystallization occurs, new high-angle grain boundaries form. In single-crystal superalloys, these boundaries are not strengthened by carbon, boron, or zirconium additions. They can slide at high temperature and provide fast diffusion paths. The creep rate of a polycrystalline region can be orders of magnitude higher than that of the single crystal. A simplified creep law is
$$ \dot{\varepsilon} = A \sigma^n \exp\left(-\frac{Q}{RT}\right) $$
where \( \dot{\varepsilon} \) is creep rate, \( A \) is a constant, \( \sigma \) is stress, \( n \) is the stress exponent, \( Q \) is the activation energy, \( R \) is the gas constant, and \( T \) is temperature. At grain boundaries, the effective activation energy for diffusion is lower, so the creep rate increases. This is why recrystallization is so detrimental. My process reduces the recrystallized fraction and therefore preserves the superior creep resistance of the single crystal. It directly improves resistance to casting defects that would otherwise degrade service performance.
Oxidation and corrosion resistance. Recrystallized grain boundaries also degrade oxidation and corrosion resistance. Oxygen can diffuse along boundaries, forming oxides that embrittle the surface. In a single crystal, the absence of boundaries improves protectiveness. By suppressing recrystallization, the electrolytic process helps maintain a continuous, adherent oxide scale. This is important for the turbine outer ring, which operates in a combustion environment. The table below summarizes the benefits of single-crystal integrity.
| Property | Single-crystal region | Recrystallized region |
|---|---|---|
| Grain boundaries | None or very few | Many high-angle boundaries |
| Creep resistance | High | Low |
| Fatigue crack initiation | Delayed | Accelerated at boundaries |
| Oxidation resistance | Good | Degraded by boundary diffusion |
| Thermal fatigue | Better | Worse |
| Service reliability | High | Low |
Economic impact. The reduction of recrystallization from 70% to below 5% has a direct economic benefit. Scrap decreases, rework decreases, and yield increases. The electrolytic process adds a step, but its cost is small compared with the cost of scrapping complex single-crystal castings. I estimated the relative cost impact using a simplified yield model:
$$ Y = \frac{N_{\mathrm{good}}}{N_{\mathrm{total}}} $$
where \( Y \) is yield, \( N_{\mathrm{good}} \) is the number of acceptable parts, and \( N_{\mathrm{total}} \) is the total number produced. Before the process, \( Y \) was low because many parts were rejected for recrystallization. After the process, \( Y \) increased substantially. The effective cost per good part is
$$ C_{\mathrm{good}} = \frac{C_{\mathrm{total}}}{Y} $$
where \( C_{\mathrm{total}} \) is the total manufacturing cost. A higher yield reduces \( C_{\mathrm{good}} \). The table below presents a qualitative cost comparison.
| Cost factor | Before electrolytic process | After electrolytic process |
|---|---|---|
| Scrap rate | High | Low |
| Rework rate | High | Low |
| Inspection burden | High | Moderate |
| Electrolyte cost | None | Low |
| Labor for electrolysis | None | Moderate |
| Net cost per good part | High | Low |
| Delivery reliability | Poor | Good |
Process robustness. I tested the sensitivity of the process to small variations in time and current. A change of ±1 minute within the 8–10 minute window did not significantly change the recrystallization result. A change of ±0.2 A in current also had a minor effect. However, a change of 2 minutes or more could move the process into the under-treated or over-treated regime. Therefore, the process requires reasonable control but is not extremely sensitive. The table below shows a sensitivity ranking.
| Variable | Sensitivity | Recommended control |
|---|---|---|
| Electrolysis time | High | Timer and automatic shutoff |
| Current | Moderate | Stabilized power supply |
| Electrolyte temperature | Moderate | Temperature control or monitoring |
| Electrolyte composition | Moderate | Batch analysis and replenishment |
| Masking quality | Moderate | Operator training and inspection |
| Surface cleanliness | Low to moderate | Degreasing before treatment |
Limitations and future work. The electrolytic process is effective for external surfaces and accessible fillets. It may be less effective for deep internal passages where electrolyte exchange is limited. For those regions, I would consider a combination of electrolytic treatment and abrasive flow. I also note that the process removes material, so the casting must have sufficient machining allowance. If the allowance is too small, the process window may be too narrow. Future work should include finite element simulation of the thermal field, coupled electrochemical modeling, and in-situ monitoring of removal thickness. It would also be valuable to quantify the relationship between local plastic strain and recrystallization probability using electron backscatter diffraction. These steps would further reduce casting defects and improve single-crystal integrity.
Practical implementation. I recommend implementing the electrolytic process as follows. First, inspect the casting after cleaning and before heat treatment. Identify the boss fillets and other high-risk regions. Second, mask all non-target surfaces with insulating tape. Third, prepare the electrolyte according to the formulation. Fourth, set the voltage to 1.5 V and the current to 4 A. Fifth, electrolyze for 8 to 10 minutes, depending on the measured removal rate. Sixth, rinse and dry thoroughly. Seventh, perform solution and aging treatments. Eighth, macro-etch and inspect for recrystallization. Ninth, record the results and adjust the process if needed. This procedure is straightforward and can be integrated into existing production lines. It has reduced the recrystallization defect rate from about 70% to below 5% in my work.
Key equations summary. The main equations used in this study are collected below for reference. They describe the driving force, nucleation, growth, thermal stress, stress concentration, electrochemical removal, creep, yield, and process capability.
$$ E_s = \rho_d G b^2 + \frac{1}{2} E \varepsilon_p^2 $$
$$ \Delta G^* = \frac{16 \pi \gamma^3}{3 \Delta G_V^2} $$
$$ \dot{N} = N_0 \exp\left(-\frac{\Delta G^*}{kT}\right) \exp\left(-\frac{Q_d}{kT}\right) $$
$$ v_{gb} = M_{gb} P $$
$$ M_{gb} = M_0 \exp\left(-\frac{Q_m}{RT}\right) $$
$$ X(t) = 1 – \exp\left[-\left(\frac{t}{\tau}\right)^n\right] $$
$$ \sigma_{\mathrm{th}} = \frac{E \alpha \Delta T}{1 – \nu} $$
$$ K_t = 1 + q \left(\frac{r}{d}\right)^{-m} $$
$$ m = \frac{M I t}{z F} $$
$$ h = \frac{M I t}{z F \rho A} $$
$$ i = \frac{I}{A} $$
$$ h_{\mathrm{actual}} = \eta h_{\mathrm{theoretical}} $$
$$ \delta_d \leq h_{\mathrm{actual}} \leq h_{\mathrm{max}} $$
$$ \sigma(t) = \sigma_0 \exp\left(-\frac{t}{\tau_r}\right) $$
$$ U = \frac{\sigma^2}{2E} V $$
$$ \dot{\varepsilon} = A \sigma^n \exp\left(-\frac{Q}{RT}\right) $$
$$ C_p = \frac{\mathrm{USL} – \mathrm{LSL}}{6s} $$
$$ Y = \frac{N_{\mathrm{good}}}{N_{\mathrm{total}}} $$
$$ C_{\mathrm{good}} = \frac{C_{\mathrm{total}}}{Y} $$
Conclusions. I have demonstrated that a pre-heat-treatment electrolytic corrosion process can control recrystallization in single-crystal turbine outer ring castings. The process removes the deformed surface layer, rounds sharp fillets, and reduces the driving force for recrystallization. The optimum conditions in my experiments were 1.5 V, 4 A, and 8–10 minutes, corresponding to a removal of 0.035–0.040 mm. Under these conditions, the recrystallization defect rate fell from about 70% to below 5%. The process significantly improved single-crystal integrity, product yield, and surface quality. It also reduced scrap and rework caused by casting defects. For future production, I recommend combining the electrolytic process with design changes such as reduced boss height and increased transition radius. I also recommend statistical process control for removal thickness and recrystallization inspection. The method is practical, scalable, and effective for controlling casting defects in complex single-crystal components. It provides a strong technical basis for the batch production of high-performance turbine outer rings and similar hot-section parts.
Final remarks on casting defects. Casting defects are inevitable in complex solidification processes, but their impact can be minimized by understanding their mechanisms and by applying targeted countermeasures. Recrystallization is a surface-driven defect that originates from plastic deformation and is activated by high temperature. Because it is surface-driven, it can be addressed by controlled surface removal. Electrolytic corrosion is particularly suitable because it is non-mechanical, uniform, and capable of reaching complex geometry. My work shows that when the removal depth is matched to the deformed-layer thickness, recrystallization can be almost completely suppressed without sacrificing dimensional accuracy. This balance is the core of the process. By controlling casting defects at the surface, I have improved the reliability of single-crystal turbine outer rings and provided a pathway for higher yield and lower cost. The approach can be extended to other single-crystal and directionally solidified components where recrystallization and related casting defects are concerns. The combination of electrochemical removal, thermal-stress reduction, and design optimization offers a robust strategy for the next generation of high-performance engine components.