Predict Casting Defects at the Design Stage.

The foundation of any robust casting simulation lies in the spatial discretization of the continuous physical domain. PoligonSoft employs the Finite Element Method (FEM), specifically utilizing tetrahedral elements due to their superior capability to conform to the highly complex, arbitrary 3D geometries typical in modern casting designs. Unlike finite difference methods (FDM) which rely on orthogonal grids resulting in "stair-step" approximations of curved surfaces, the tetrahedral mesh ensures exact boundary representation. This is mathematically critical for accurately calculating boundary conditions, such as heat transfer coefficients at the intricate mold-metal interfaces.

The Mesh Generator module is designed to handle non-manifold geometries imported from standard CAD packages (STEP, IGES). It employs an advancing front algorithm or Delaunay triangulation techniques to generate high-quality meshes. Mesh quality is parameterized by the aspect ratio of the tetrahedrons; poorly shaped elements (slivers) can lead to ill-conditioned stiffness or conductivity matrices, resulting in divergent or inaccurate solutions. PoligonSoft automatically performs local mesh refinement in areas with high geometric curvature, steep thermal gradients, or thin-walled sections, ensuring computational resources are concentrated where physical phenomena vary most rapidly.

Furthermore, the software supports coincident meshing across assemblies. In a sand casting scenario involving the casting, multiple cores, chills, and the sand mold, the nodes at the interfaces are aligned. This allows for direct node-to-node heat flux calculations without the need for complex and computationally expensive interpolation schemes across non-conformal boundaries. The resulting global matrix equations, which represent the discretization of the governing partial differential equations (PDEs), are then solved using highly optimized iterative sparse matrix solvers, leveraging multi-core CPU architectures for rapid turnaround times at the design stage.

The Fourier module is responsible for solving the transient, non-linear heat conduction equation throughout the domain. The fundamental PDE is governed by Fourier's Law of Heat Conduction: ρ c_p (∂T / ∂t) = ∇ · (k ∇T) + q̇, where ρ is density, c_p is specific heat, k is thermal conductivity, T is temperature, and q̇ represents internal heat generation. In casting, this internal heat generation term is critically important as it accounts for the latent heat of fusion released during the liquid-to-solid phase transformation.

PoligonSoft employs the Enthalpy method to handle this phase change. Instead of tracking a distinct solid-liquid interface (which is highly complex for dendritic alloy solidification where a "mushy zone" exists), the solver relates temperature directly to enthalpy. The material properties database provides temperature-dependent thermo-physical data (conductivity, density, specific heat, and fraction solid) for specific alloys. Accurate latent heat release modeling is essential for predicting the exact position and evolution of thermal centers (hot spots) within the casting.

Predicting Shrinkage and Porosity: The primary goal of the Fourier solver is to identify areas prone to shrinkage cavities and micro-porosity. As the alloy solidifies and cools, it contracts. If a liquid metal feed path is cut off by surrounding solidified material (directional solidification fails), an internal cavity forms. PoligonSoft visualizes these isolated liquid pools. For micro-porosity prediction, the software often calculates the Niyama criterion (Ny = G / √Ṫ), where G is the local temperature gradient and Ṫ is the cooling rate at the end of solidification. A threshold Niyama value indicates areas where feeding is insufficient to compensate for solidification shrinkage, leading to dispersed micro-porosity defects.

The Euler module simulates the highly dynamic mold filling process. This involves solving the Navier-Stokes equations for incompressible fluid flow, coupled with the continuity equation to ensure mass conservation. The filling phase is critical because improper gating design can lead to excessive turbulence, air entrapment, mold erosion, and premature freezing (cold shuts).

The governing momentum equation is: ρ (∂v / ∂t + v · ∇v) = -∇P + μ ∇²v + ρ g, where v is the velocity vector, P is pressure, μ is dynamic viscosity, and g is gravity. PoligonSoft tracks the free surface of the molten metal as it flows through the complex sprue, runner, and gate geometries into the cavity. Techniques such as the Volume of Fluid (VOF) method are typically employed to track this liquid-gas interface accurately on the Eulerian grid.

During filling, the flow is strongly coupled with heat transfer. As the liquid metal contacts the relatively cold mold walls, it rapidly loses heat. The Euler solver calculates this convective and conductive heat loss simultaneously with the fluid flow. If the metal's temperature drops below the solidus temperature before two flow fronts merge, they will not fuse completely, resulting in a cold shut defect. Furthermore, by calculating local flow velocities, the solver can identify areas where the critical velocity is exceeded, indicating a high risk of turbulent flow which leads to the formation and entrainment of oxide bifilms, significantly degrading the mechanical properties of the final casting.

The Hooke solver addresses the complex mechanical interactions that occur during cooling and solidification. As the casting cools from the solidus temperature down to room temperature, it undergoes thermal contraction. However, this contraction is rarely uniform due to differing cooling rates in thick versus thin sections, and the casting is mechanically constrained by the rigid mold. This constraint and differential cooling generate thermal stresses within the part.

PoligonSoft calculates these stresses by solving the equations of equilibrium in solid mechanics, coupled with elasto-plastic constitutive models. In the high-temperature regime immediately following solidification, the alloy has very low yield strength and exhibits significant creep or viscoplastic behavior. The Hooke solver uses temperature-dependent mechanical properties (Young's modulus, Poisson's ratio, yield strength, hardening curves) to accurately model this deformation.

Hot Tears and Residual Stresses: A critical application of the Hooke solver is the prediction of hot tears. Hot tears occur when tensile stresses develop in the casting while it is still in the "mushy zone" (partially solid, partially liquid) or immediately after complete solidification when the ductility is minimal. If the accumulated mechanical strain exceeds the material's fracture limit at that specific high temperature, a crack initiates. Furthermore, the solver predicts final residual stresses and geometric distortion (warpage) at room temperature. This information is vital for determining if the part will meet dimensional tolerances after ejection from the mold and for designing appropriate subsequent heat treatment cycles to relieve these locked-in stresses.