Thermal Stress Evolution
The thermal stress evolution (TSE) model in FLOW-3D CAST extends the range of casting processes that can be modeled. The FSI/TSE model describes fully-coupled interactions between fluid and solid using a finite element approach to model stresses and deformations in solid and solidified components in response to pressure forces from the surrounding fluid, thermal gradients, and specified constraints. Thermal stresses develop during the solidification process which are caused by non-uniform cooling. These stresses are influenced by shrinkage at mold walls and irregularities in the casting’s shape.
The simulation above shows the Von Mises stresses in a solidified aluminum V6 engine block. The block is composed of an Aluminum A380 alloy that was cast within a steel die. The pour temperature of the aluminum was 527°C and the initial die temperature was 125°C. The part was cooled within the die for 60s, after which the die was opened and the part continued to cool for 9 minutes in ambient conditions (125°C), totaling 10 minutes of simulation time. The von Mises stress shown is a measure of the magnitude of shear stresses within the part, thus showing regions where tearing is most like to occur. Stresses can be simultaneously computed in the mold and in the solidifying metal. Meshing can be done automatically using FLOW-3D‘s structured mesh as the initial template. Users can control the local resolution of the mesh by creating nested or linked mesh blocks, and with V11.0’s new conforming mesh feature. Alternatively, users have the option of importing Finite Element meshes from third-party mesh generation software in Exodus-II format.
Simulating Thermal Stress
Shown below is an aluminum cover, also composed of Aluminum A380 alloy cast within a steel die. The pour temperature was 654°C and the initial die temperature was 240°C. The part was cooled within the die for 6s at which point the part was completely solidified (except for the runner system). The die was then opened and the part was allowed to cool a further 10s in ambient conditions (25°C). The runner system was then removed, after which a further 10s of cooling in ambient conditions occurred. The normal displacement shown here indicates the motion of the surface of the part, magnified 30 times to highlight the greatest regions of deformation.
Component Coupling within the Fluid-Structure Interaction and Thermal Stress Evolution Models
A new feature in FLOW-3D v11 is an upgrade to the existing finite-element solid mechanics solver that allows the elastic stresses between neighboring Fluid-Structure Interaction (FSI) components and/or the Thermal Stress Evolution (TSE) solidified fluid region to be coupled. This new capability opens the door to a wealth of modeling possibilities, including simulating thermal stresses and deformations in complex, deforming, multi-material parts (e.g., a metal casting solidifying in a mold, or bimetallic gauges), and simulating forces on connected hydraulic structures, like radial gates and pipeline support systems.
There are several different options in the model that allow for efficient computation of complex processes:
This option represents the simplified case where neighboring FSI components do not exchange stresses. It is computationally efficient and is suitable for scenarios where the interaction of the stresses between components is not significant.
The full coupling option is for modeling neighboring FSI components that are fused together but have differing material properties. The two components cannot pull apart or slide past one another, but the stresses at the interface are transferred between the components. This is ideal for modeling bonded structures, like a bimetallic strip.
The partial coupling option is for modeling general problems where neighboring FSI components interact through frictional and normal forces but can pull apart. This option can be used to couple FSI components and the TSE solidified fluid region, making it ideal for investigating the effects of thermal stresses on a cast part and the die as the part cools in the die.
Two simulations are presented to demonstrate the new features of the model in more detail. The first situation uses the full coupling option to model a bimetallic strip bending in response to a time varying temperature, while the second example shows the use of the partial coupling model to look at thermal stresses during the solidification of a V6 engine block in a die.
Full Coupling Example: Bimetallic Strip
One of the simplest examples of the full coupling option is the motion of a bimetallic strip in response to temperature gradients. Such strips are commonly used in thermal switches and bend because the two metals do not expand at the same rate in response to changes in temperature. The bimetallic strip modeled in the simulation is a cantilever beam consisting of a 15cm long, 0.5cm thick steel strip bonded to a copper strip of same dimensions, as shown in Figure 1.
The strip was then placed in an environment where the temperature was uniformly varied over 70 seconds. Figure 2 shows the deflection of the tip of the strip for the simulation and an analytical solution at various temperatures over time. The results show some interesting features, including a slight delay between when the temperature changed and the response of the strip due to the thermal inertia of the strip. This delay also influences the difference in timing between the computed and analytical deflections because the analytical solution assumed instantaneous changes in temperature. The differences in amplitude of the displacement can be attributed to the assumption of an infinitely thin strip in the analytical result. The thickness in the computational model adds additional stresses at the mounting point which leads to an increased deflection.
Partial Coupling Example: Metal Casting within a Deformable Die
The second example simulation uses the partial coupling model to show the stress development in a metal casting within a deformable steel die. The two halves of the die and the solidified fluid are partially coupled to one another, meaning that they interact through normal stresses and friction. The simulation shows the thermal stress evolution in the die and the cast part as they cool from just below the solidus temperature at 770K to the surrounding temperature of 293K. The cast part is composed of A380 aluminum alloy while the die halves are composed of H-13 steel.
The finite element mesh of the cast part and of the surrounding die is composed of 3,665,533 elements and 3,862,378 nodes, as shown in Figure 3. Also shown are the meshes, which are separate for each die half and the TSE solidified fluid region. The red circles on the front face are due to the support pistons, which are not shown.
The stresses at the interface between the mold and solidified fluid surfaces are partially coupled, and the constrained shrinkage can be seen. Figure 4 shows the resulting deformation in the cast part and one half of the die partway through the simulation. The die halves and the casting shrink at different rates as the temperature decreases, resulting in large stresses in the interfering regions and indicating potential problem areas. Computing the coupled stresses in the die and in the part allows users to better predict the stresses developing within each component and give insight into how to improve part quality and extend tool life.
The interaction of different solid objects is an important part of modern design and engineering. The addition of the new coupling options between FSI components and TSE solidified fluid regions to FLOW-3D provides a useful tool for evaluating the complex geometries regularly encountered by today’s engineers.