In this study, I investigate the stress and deformation behavior of wax patterns during the entire full mold casting preparation route. Full mold casting is a near-net-shape manufacturing technology that can produce components with high dimensional accuracy, good surface quality, and complex geometry. In full mold casting, the wax pattern is the first physical copy of the final casting, so any dimensional error generated during wax injection molding is inherited by the shell, the molten metal, and finally the casting. I therefore treat wax injection molding not as an isolated filling event, but as a continuous full mold casting process consisting of filling and packing, in-mold cooling, demolding, and post-demold storage. This continuous view is essential because the viscoelastic nature of wax causes stress relaxation and creep even after the wax pattern has been removed from the die. The main objective of my work is to establish a numerical simulation framework for the full process of wax injection molding in full mold casting and to use that framework to reveal dimensional deformation laws and optimize injection parameters.
I begin from the observation that full mold casting dimensional errors accumulate along the process chain. The wax pattern preparation stage includes several physical events: the wax melt fills the cavity, packing pressure compensates volumetric shrinkage, the pattern cools inside the die, the pattern is ejected, and the pattern continues to deform outside the die. Each event contributes to the final pattern geometry. If only in-mold cooling or only demolding is considered, the predicted deformation cannot represent the real full mold casting pattern. I therefore constructed a joint simulation strategy that combines a mold-filling solver with a finite element solver. The mold-filling solver provides the initial temperature field, pressure history, frozen layer information, and residual stress state after packing. The finite element solver then calculates the thermomechanical response, stress relaxation, creep, and warpage during in-mold cooling, demolding, and storage.
For full mold casting wax materials, the rheological behavior during filling is strongly non-Newtonian. The viscosity depends on temperature, shear rate, and pressure. I adopted the Cross-WLF model because it is widely used for injection molding and provides a good representation of the viscosity curve over the temperature and shear-rate window of full mold casting wax injection. The Cross-WLF viscosity equation is
$$
\eta = \frac{\eta_0}{1+\left(\frac{\eta_0 \dot{\gamma}}{\tau^*}\right)^{1-n}}
$$
where \(\eta\) is the melt viscosity, \(\eta_0\) is the zero-shear viscosity, \(\dot{\gamma}\) is the shear rate, \(\tau^*\) is the critical stress at the transition to shear thinning, and \(n\) is the power-law index. The zero-shear viscosity is temperature and pressure dependent:
$$
\eta_0 = D_1 \exp\left[-\frac{A_1(T-T^*)}{A_2+(T-T^*)}\right]
$$
$$
T^* = D_2 + D_3 p
$$
$$
A_2 = \tilde{A}_2 + D_3 p
$$
Here \(T\) is temperature, \(p\) is pressure, \(T^*\) is the glass transition temperature under pressure, and \(D_1\), \(D_2\), \(D_3\), \(A_1\), \(\tilde{A}_2\) are fitting coefficients. I measured the viscosity of a K512-type wax at several temperatures and fitted the Cross-WLF parameters. The fitted values are summarized in Table 1. These parameters are used in the full mold casting filling simulation.
| Parameter | Value | Unit |
|---|---|---|
| \(n\) | 0.3691 | – |
| \(\tau^*\) | 0.427887 | Pa |
| \(D_1\) | \(2.18\times 10^{36}\) | Pa·s |
| \(D_2\) | 263.15 | K |
| \(D_3\) | 0 | K/Pa |
| \(A_1\) | 123.92 | – |
| \(A_2\) | 51.6 | K |
For the pressure-volume-temperature behavior of the wax in full mold casting, I used the modified dual-domain Tait equation. This equation is important because the volumetric shrinkage during packing and cooling controls a significant part of the final pattern dimension. The Tait equation is
$$
V(T,p)=V_0(T)\left[1-C\ln\left(1+\frac{p}{B(T)}\right)\right]+V_1(T,p)
$$
where \(V\) is the specific volume, \(C\) is a universal constant often taken as 0.0894, and \(V_0\) and \(B\) are functions of temperature. The dual-domain form uses different coefficients above and below the transition temperature. I fitted the Tait coefficients from PVT measurements at pressures of 4, 6, 8, and 10 MPa. The fitted coefficients are listed in Table 2. The coefficient of determination for both the solid and melt domains was above 0.99, which confirms that the modified dual-domain Tait equation is suitable for full mold casting wax injection modeling.
| Coefficient | Value | Unit |
|---|---|---|
| \(b_{1m}\) | 0.00114 | m³/kg |
| \(b_{2m}\) | \(1.372\times 10^{-6}\) | m³/(kg·K) |
| \(b_{3m}\) | \(6.4005\times 10^{7}\) | Pa |
| \(b_{4m}\) | 0.1685 | 1/K |
| \(b_{1s}\) | 0.001141 | m³/kg |
| \(b_{2s}\) | \(3.478\times 10^{-6}\) | m³/(kg·K) |
| \(b_{3s}\) | \(3.9838\times 10^{7}\) | Pa |
| \(b_{4s}\) | 0.0296 | 1/K |
| \(b_5\) | 324.15 | K |
| \(b_6\) | \(5\times 10^{-7}\) | K/Pa |
| \(b_7\) | 0 | m³/kg |
| \(b_8\) | 0 | 1/K |
| \(b_9\) | 0 | 1/Pa |
The thermal properties used in the full mold casting simulation include thermal conductivity, specific heat, and transition temperature. The thermal conductivity of wax is much lower than that of metal, so the wax pattern cools slowly and develops a non-uniform temperature field. I measured the thermal conductivity and specific heat over the relevant temperature range. The transition temperature was determined to be 49 °C. The Poisson ratio of the wax was measured as 0.47 at room temperature. These properties are used in the heat transfer and stress calculations for full mold casting.
Because wax is viscoelastic, I used the generalized Maxwell model to describe its time-dependent deformation. The generalized Maxwell model consists of one elastic spring and several Maxwell elements in parallel. The shear relaxation modulus is
$$
G(t)=G_\infty+\sum_{i=1}^{n} G_i e^{-t/\tau_i}
$$
where \(G_\infty\) is the fully relaxed shear modulus, \(G_i\) is the shear modulus of the \(i\)-th Maxwell element, and \(\tau_i\) is the corresponding relaxation time. Similarly, the bulk relaxation modulus can be written as
$$
K(t)=K_\infty+\sum_{i=1}^{n} K_i e^{-t/\tau_i}
$$
In my full mold casting wax model, I assumed that the bulk modulus remains approximately constant during relaxation. This is a common assumption for polymer-like materials and simplifies the three-dimensional viscoelastic formulation. The three-dimensional stress integral is
$$
\sigma_{ij}(t)=\int_{-\infty}^{t}G(\xi-\xi’)\frac{\partial e_{ij}(t)}{\partial t}dt
+\delta_{ij}\int_{-\infty}^{t}K(\xi-\xi’)\frac{\partial(\varepsilon_m(t)-\varepsilon_{th})}{\partial t}dt
$$
where \(e_{ij}\) is the deviatoric strain, \(\varepsilon_m\) is the mean strain, \(\varepsilon_{th}\) is the thermal strain, and \(\xi\) is the reduced time. The reduced time is defined through the time-temperature superposition principle:
$$
\xi=\int_{0}^{t}\frac{1}{a_T}d\lambda
$$
The time-temperature superposition principle is a key part of my full mold casting material model. It states that the viscoelastic modulus at one temperature can be shifted along the time axis to a reference temperature:
$$
E(t,T)=E(t/a_T,T_0)
$$
For temperatures above the glass transition but below the melting region, the Williams-Landel-Ferry equation is often used:
$$
\log a_T=-\frac{C_1(T-T_0)}{C_2+T-T_0}
$$
For the wax used in full mold casting, I found that the Arrhenius equation gave a better fit for the shift factor over the measured temperature range:
$$
\ln a_T=\frac{E_a}{R}\left(\frac{1}{T}-\frac{1}{T_0}\right)
$$
I measured the dynamic moduli of the wax at several temperatures and used 45 °C as the reference temperature. The storage modulus and loss modulus master curves were constructed by shifting the frequency sweep data. The relaxation time spectrum was then fitted with 15 Maxwell elements. The normalized spectrum is given in Table 3. The fit quality was high, with \(R^2\) close to 0.999 for the storage modulus master curve.
| No. | \(g_i\) | \(k_i\) | \(\tau_i\) |
|---|---|---|---|
| 1 | 0.249872 | 0 | \(3.05\times 10^{-6}\) |
| 2 | 0.108686 | 0 | \(4.17\times 10^{-5}\) |
| 3 | 0.100223 | 0 | \(4.26\times 10^{-5}\) |
| 4 | 0.075527 | 0 | 0.000302 |
| 5 | 0.048213 | 0 | 0.000635 |
| 6 | 0.043825 | 0 | 0.00132 |
| 7 | 0.070928 | 0 | 0.005115 |
| 8 | 0.04595 | 0 | 0.025809 |
| 9 | 0.033264 | 0 | 0.083786 |
| 10 | 0.037807 | 0 | 0.480111 |
| 11 | 0.004711 | 0 | 1.55232 |
| 12 | 0.003099 | 0 | 2.2558 |
| 13 | 0.037882 | 0 | 25.5829 |
| 14 | 0.04011 | 0 | 10176.7 |
| 15 | 0.000997 | 0 | 277165 |
After establishing the material models, I designed the full mold casting wax injection simulation workflow. The workflow has four stages. In the first stage, I use a mold-filling simulation to calculate the filling and packing process. The inputs are the wax viscosity model, the PVT model, the thermal properties, the mold temperature, the wax temperature, the filling time, the packing pressure, and the packing time. The outputs are the temperature field, pressure field, shear rate field, frozen layer fraction, and residual stress distribution after packing. In the second stage, I import the packing-end state into a finite element solver to calculate in-mold cooling. The wax pattern is constrained by the die cavity or core, so the displacement is not free. In the third stage, I simulate demolding by releasing the die constraints. The residual stress redistributes rapidly, and the pattern warps. In the fourth stage, I simulate storage outside the die. The pattern continues to cool to room temperature and then continues to relax and creep at room temperature. This four-stage sequence is the core of my full mold casting wax injection model.
I selected a three-way pipe wax pattern as the validation geometry. The mold was designed with a central or off-center injection gate depending on the experiment. The process parameters for the baseline case are given in Table 4. The wax temperature was 55 °C, the mold temperature was 22 °C, the filling time was 5.5 s, the packing pressure was 1.5 MPa, the packing time was 40 s, and the in-mold cooling time after packing was 300 s.
| Parameter | Value | Unit |
|---|---|---|
| Wax temperature | 55 | °C |
| Mold temperature | 22 | °C |
| Filling time | 5.5 | s |
| Packing pressure | 1.5 | MPa |
| Packing time | 40 | s |
| In-mold cooling time | 300 | s |
In the filling simulation for full mold casting, I observed a stable flow front. Because the wax viscosity is high, the melt fills the three-way pipe in a laminar manner. The fountain effect appears near the flow front, and the race-track effect appears in the thicker sections. The flow front temperature was almost uniform, changing by only about 0.65 °C. The pressure at the velocity-to-pressure switch was low, and the maximum pressure was about 0.0545 MPa. To validate the flow pattern, I performed an off-center injection experiment. The experimental flow front shapes at several filling times were compared with the simulated filling patterns. The simulated flow front and the experimental flow front were consistent, which supports the use of the Cross-WLF model for full mold casting wax filling.
After filling and packing, I calculated in-mold cooling with both an elastic model and a viscoelastic model. The elastic model overestimates the residual stress because it ignores stress relaxation. The viscoelastic model allows the stress to relax during cooling. The stress at two representative points decreased by about 30 % during in-mold cooling. This stress relaxation is a key reason why the full mold casting wax pattern does not behave like a purely elastic solid. The viscoelastic stress field is therefore more realistic for full mold casting.
During demolding, the die constraints are removed. I treated demolding as a rapid stress-release step. The residual stress and displacement fields redistribute almost immediately. I compared the warpage of the elastic model and the viscoelastic model after demolding. The elastic model predicted a maximum deformation of 1.527 mm, while the viscoelastic model predicted 1.279 mm. The elastic model therefore overestimated the demolding warpage by about 19 %. This difference shows that stress relaxation must be included in full mold casting wax injection analysis. If the material is treated as elastic, the full mold casting pattern deformation will be overpredicted.
After demolding, I simulated storage outside the die. The wax pattern was placed horizontally, and it was allowed to deform for 24 h. The pattern continued to cool to room temperature and then continued to relax and creep. The stress and strain at two representative points showed that the pattern had not reached equilibrium immediately after cooling. The storage stage caused additional viscoelastic deformation. The deformation was concentrated in the first several hours. More than 98 % of the total deformation occurred within the first 9 h after demolding. The approximate contribution of each stage to the total deformation was 35 % for in-mold cooling, 40 % for demolding, and 25 % for storage. This stage-wise distribution is one of the main findings of my full mold casting wax injection study.
To verify the numerical results, I measured several key dimensions of the three-way pipe wax pattern. The mold dimensions, measured dimensions, and simulated dimensions are listed in Table 5. The deviations between measurement and simulation were less than 0.3 mm for all key dimensions. This agreement demonstrates that the joint simulation strategy is reliable for full mold casting wax pattern deformation prediction.
| Feature | Mold dimension / mm | Measured / mm | Simulated / mm | Deviation / mm |
|---|---|---|---|---|
| \(X_{AE1}\) | 170.5 | 168.62 | 168.50 | 0.12 |
| \(X_{AE2}\) | 170.5 | 168.25 | 168.15 | 0.10 |
| \(Y_{A12}\) | 117 | 115.53 | 115.29 | 0.24 |
| \(Z_{B12}\) | 117 | 115.28 | 114.98 | 0.30 |
| \(X_{C12}\) | 95 | 93.65 | 93.49 | 0.16 |
| \(Z_{D12}\) | 95 | 93.67 | 93.54 | 0.13 |
I also analyzed the evolution of a warpage indicator during the full mold casting wax preparation route. The indicator \(X_A\) was defined as the difference in X-direction displacement between two points on opposite sides of the long pipe. In the die, the pattern is constrained, so \(X_A\) starts near zero or slightly negative. During demolding, \(X_A\) increases rapidly because the residual stress is released. During storage, \(X_A\) continues to increase and then stabilizes. This means the wax pattern continues to warp after demolding. The warpage is not finished when the pattern leaves the die. In full mold casting, therefore, the storage stage must be considered as part of the dimensional control strategy.
After establishing the full mold casting wax injection model, I studied how injection process parameters affect pattern shrinkage and deformation. The selected parameters were mold temperature \(A\), packing pressure \(B\), filling time \(C\), wax temperature \(D\), and packing time \(E\). The parameter ranges are listed in Table 6. The ranges were chosen from practical full mold casting experience. The mold temperature range was 19–25 °C, the packing pressure range was 1.5–3.5 MPa, the filling time range was 4–7 s, the wax temperature range was 55–65 °C, and the packing time range was 20–60 s.
| Parameter | Symbol | Range | Unit |
|---|---|---|---|
| Mold temperature | \(A\) | 19–25 | °C |
| Packing pressure | \(B\) | 1.5–3.5 | MPa |
| Filling time | \(C\) | 4–7 | s |
| Wax temperature | \(D\) | 55–65 | °C |
| Packing time | \(E\) | 20–60 | s |
I first used the Taguchi method to screen the significance of the process parameters. The factors and levels are given in Table 7. Each factor was set at two levels. The experimental plan and the corresponding simulation results are shown in Table 8. The quality characteristics were the average volumetric shrinkage and the maximum deformation of the wax pattern after demolding. Both were treated as smaller-is-better responses. The signal-to-noise ratio was calculated as
$$
S/N=-10\log\left(\frac{1}{n}\sum_{i=1}^{n}y_i^2\right)
$$
where \(y_i\) is the response and \(n\) is the number of repetitions.
| Level | \(A\) / °C | \(B\) / MPa | \(C\) / s | \(D\) / °C | \(E\) / s |
|---|---|---|---|---|---|
| 1 | 19 | 1.5 | 4 | 55 | 20 |
| 2 | 25 | 3.5 | 7 | 65 | 40 |
| Run | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | Shrinkage / % | Deformation / mm |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 6.5056 | 1.2923 |
| 2 | 1 | 1 | 1 | 2 | 2 | 7.2122 | 1.3189 |
| 3 | 1 | 2 | 2 | 1 | 1 | 6.2556 | 1.2522 |
| 4 | 1 | 2 | 2 | 2 | 2 | 6.6905 | 1.2833 |
| 5 | 2 | 1 | 2 | 1 | 2 | 7.0792 | 1.2970 |
| 6 | 2 | 1 | 2 | 2 | 1 | 8.2306 | 1.3483 |
| 7 | 2 | 2 | 1 | 1 | 2 | 6.9728 | 1.2569 |
| 8 | 2 | 2 | 1 | 2 | 1 | 8.2096 | 1.3509 |
From the Taguchi analysis, I found that the ranking of factors was different for shrinkage and deformation. For volumetric shrinkage, the importance order was mold temperature, wax temperature, packing time, packing pressure, and filling time. For deformation, the importance order was wax temperature, packing pressure, mold temperature, packing time, and filling time. The filling time had the smallest effect on both responses. This result is important for full mold casting because it means that, within the studied window, changing the filling time alone does not strongly control the final wax pattern shrinkage and warpage.
Because filling time had the smallest effect, I performed an additional study to confirm its role in full mold casting wax injection. I varied the filling time from 2 s to 9 s while keeping the other parameters fixed. The results are shown in Table 9. The maximum clamping force, sink mark depth, volumetric shrinkage, and maximum warpage were used as quality indicators. The sink mark depth first decreased and then increased. The volumetric shrinkage also showed a non-monotonic trend. The warpage was not strongly correlated with filling time. The clamping force generally increased as the filling time increased. Based on this additional study, I fixed the filling time at 6 s for the subsequent response surface optimization. This choice balances filling stability with a reasonable cycle time in full mold casting.
| Filling time / s | Clamping force / t | Sink depth / mm | Shrinkage / % | Deformation / mm |
|---|---|---|---|---|
| 2 | 2.36 | 0.7374 | 6.7426 | 1.2936 |
| 3 | 4.89 | 0.7702 | 6.9522 | 1.2975 |
| 4 | 2.61 | 0.7433 | 6.7334 | 1.2955 |
| 5 | 3.40 | 0.7379 | 6.6977 | 1.2973 |
| 6 | 4.84 | 0.7592 | 6.8992 | 1.2979 |
| 7 | 5.98 | 0.7651 | 6.8919 | 1.2966 |
| 8 | 7.68 | 0.8203 | 6.9193 | 1.2973 |
| 9 | 7.69 | 0.7940 | 6.9158 | 1.2966 |
I then used response surface methodology to optimize the remaining four parameters: mold temperature \(A\), packing pressure \(B\), wax temperature \(C\), and packing time \(D\). The central composite face-centered design was used. The factor levels are listed in Table 10. The design matrix and simulation results are listed in Table 11. The objective responses were again the volumetric shrinkage \(\phi\) and the deformation \(\delta\).
| Level | \(A\) / °C | \(B\) / MPa | \(C\) / °C | \(D\) / s |
|---|---|---|---|---|
| -1 | 19 | 1.5 | 55 | 20 |
| 0 | 22 | 2.5 | 60 | 40 |
| 1 | 25 | 3.5 | 65 | 60 |
| Run | \(A\) | \(B\) | \(C\) | \(D\) | Shrinkage / % | Deformation / mm |
|---|---|---|---|---|---|---|
| 1 | -1 | -1 | -1 | -1 | 6.4082 | 1.2919 |
| 2 | 1 | -1 | -1 | -1 | 7.1877 | 1.2980 |
| 3 | -1 | 1 | -1 | -1 | 6.1319 | 1.2472 |
| 4 | 1 | 1 | -1 | -1 | 7.0338 | 1.2574 |
| 5 | -1 | -1 | 1 | -1 | 7.6278 | 1.3364 |
| 6 | 1 | -1 | 1 | -1 | 8.2349 | 1.3483 |
| 7 | -1 | 1 | 1 | -1 | 7.6117 | 1.3245 |
| 8 | 1 | 1 | 1 | -1 | 8.2136 | 1.3483 |
| 9 | -1 | -1 | -1 | 1 | 6.4074 | 1.2919 |
| 10 | 1 | -1 | -1 | 1 | 7.1381 | 1.2976 |
| 11 | -1 | 1 | -1 | 1 | 6.1110 | 1.2468 |
| 12 | 1 | 1 | -1 | 1 | 7.0124 | 1.2561 |
| 13 | -1 | -1 | 1 | 1 | 7.1599 | 1.3183 |
| 14 | 1 | -1 | 1 | 1 | 7.7783 | 1.3208 |
| 15 | -1 | 1 | 1 | 1 | 6.8674 | 1.2866 |
| 16 | 1 | 1 | 1 | 1 | 7.3914 | 1.2889 |
| 17 | -1 | 0 | 0 | 0 | 6.7102 | 1.2870 |
| 18 | 1 | 0 | 0 | 0 | 7.3259 | 1.2906 |
| 19 | 0 | -1 | 0 | 0 | 7.1100 | 1.3063 |
| 20 | 0 | 1 | 0 | 0 | 6.7923 | 1.2681 |
| 21 | 0 | 0 | -1 | 0 | 6.8632 | 1.2804 |
| 22 | 0 | 0 | 1 | 0 | 7.3625 | 1.3052 |
| 23 | 0 | 0 | 0 | -1 | 7.4542 | 1.3030 |
| 24 | 0 | 0 | 0 | 1 | 6.9991 | 1.2885 |
| 25 | 0 | 0 | 0 | 0 | 6.9991 | 1.2885 |
From the response surface analysis, I fitted a full quadratic model for shrinkage. The significant terms were the linear effects of mold temperature, packing pressure, wax temperature, and packing time, as well as the quadratic effect of packing time and the interaction between wax temperature and packing time. The analysis of variance showed that the model was significant. After removing insignificant terms, the final shrinkage response equation was
$$
\phi = -3.314 + 0.11631A – 0.1048B + 0.1483C + 0.0554D + 0.000326D^2 – 0.001499CD
$$
For deformation, the significant terms were the linear effects of all four factors, the interaction between packing pressure and wax temperature, and the interaction between wax temperature and packing time. After removing insignificant terms, the final deformation response equation was
$$
\delta = 1.0185 + 0.001394A – 0.0883B + 0.00505C + 0.00484D + 0.001207BC – 0.000088CD
$$
The response surface results show that lowering the mold temperature and the wax temperature reduces both shrinkage and deformation. Increasing the packing pressure also reduces shrinkage and deformation. Increasing the packing time helps initially because more material is packed into the cavity, but after the gate freezes, further packing time has little effect. The interaction between wax temperature and packing time is significant because a higher wax temperature delays gate freezing and allows packing pressure to act for a longer time. The interaction between packing pressure and wax temperature is also significant for deformation. These interactions are important for full mold casting process design because they mean that the optimal packing pressure and packing time depend on the selected wax temperature.
I used the NSGA-II multi-objective genetic algorithm to find the Pareto front for the two responses. The optimization problem can be written as
$$
\begin{aligned}
\min \quad & F(A,B,C,D) = [\phi(A,B,C,D), \delta(A,B,C,D)] \\
\text{subject to} \quad & 19 \le A \le 25 \\
& 1.5 \le B \le 3.5 \\
& 55 \le C \le 65 \\
& 20 \le D \le 60
\end{aligned}
$$
The Pareto front showed that shrinkage and deformation are in conflict. A solution with very low shrinkage may have slightly higher deformation, and a solution with very low deformation may have slightly higher shrinkage. In the computed Pareto set, the deformation changed only slightly among many solutions, while the shrinkage changed more noticeably. I therefore selected the point with the lowest shrinkage among the solutions with nearly minimum deformation. The selected optimum was mold temperature 19 °C, packing pressure 3.5 MPa, wax temperature 55 °C, and packing time 41.5 s. The predicted shrinkage was 6.1248 %, and the predicted deformation was 1.246 mm. I then ran a direct numerical simulation with these parameters. The simulated shrinkage was 6.1661 %, and the simulated deformation was 1.264 mm. The relative errors were 1.33 % and 1.42 %, respectively. The comparison is shown in Table 12.
| Response | Numerical simulation | Genetic algorithm | Relative error |
|---|---|---|---|
| Volumetric shrinkage \(\phi\) / % | 6.1661 | 6.1248 | 1.33 % |
| Deformation \(\delta\) / mm | 1.264 | 1.246 | 1.42 % |
The results of this study lead to several conclusions for full mold casting wax injection. First, the wax pattern deformation in full mold casting is a full-process phenomenon. It begins during filling and packing, continues during in-mold cooling, increases sharply during demolding, and continues during storage. Ignoring the storage stage underestimates the final deformation. Second, the viscoelastic behavior of wax is essential. Stress relaxation reduces the residual stress before demolding, and creep continues to change the pattern after demolding. An elastic model overestimates demolding warpage and cannot capture the time-dependent dimensional evolution. Third, the mold temperature and wax temperature are the most influential parameters for volumetric shrinkage. The wax temperature and packing pressure are the most influential parameters for deformation. The filling time has the smallest effect among the studied parameters. Fourth, response surface methodology and genetic algorithms can be combined to optimize full mold casting wax injection. The optimized parameters reduce both shrinkage and deformation while maintaining a feasible filling and packing window.
For practical full mold casting production, I recommend that the wax injection process be designed with a full-process simulation rather than a single-stage simulation. The material database should include the Cross-WLF viscosity parameters, the modified dual-domain Tait PVT parameters, thermal conductivity, specific heat, Poisson ratio, and the generalized Maxwell relaxation spectrum. The simulation should include the die constraint during in-mold cooling, the stress release during demolding, and the viscoelastic storage deformation. The storage stage should be controlled by a fixture or support when the pattern is flexible, because the pattern can continue to warp for several hours after demolding. In full mold casting, dimensional accuracy is not only a mold design problem; it is also a time-dependent material problem.
I also note that the full mold casting wax injection process is sensitive to the thermal history. A lower mold temperature and a lower wax temperature reduce shrinkage and deformation, but they also increase the melt viscosity and may reduce filling ability. Therefore, optimization must respect the filling window. In my study, the response surface model captured this trade-off. The genetic algorithm found a balanced solution at the lower temperature and higher packing pressure side of the design space. This solution is consistent with the physical understanding that reducing the thermal load decreases shrinkage, while increasing packing pressure compensates for volumetric contraction and reduces deformation.
In summary, I developed a numerical simulation framework for the entire full mold casting wax injection molding process. The framework combines a Cross-WLF viscosity model, a modified dual-domain Tait PVT model, a generalized Maxwell viscoelastic model, time-temperature superposition, and a four-stage stress-deformation calculation. I validated the flow model with off-center injection experiments and validated the deformation model with measured wax pattern dimensions. I then used Taguchi screening, response surface modeling, and NSGA-II optimization to identify the significant full mold casting process parameters and to find an optimized parameter set. The optimized parameters were mold temperature 19 °C, packing pressure 3.5 MPa, wax temperature 55 °C, and packing time 41.5 s. The predicted and simulated responses agreed within about 1.5 %. This work provides a quantitative basis for controlling dimensional deformation in full mold casting wax injection and for reducing trial-and-error mold correction in full mold casting production.