A common casting structural design question falls along the lines of this: We are aware of safety-critical, long strain life castings in challenging structural applications. Yet, castings have surface defects and solidification defects in their microstructure. How is such durability possible?

When safety is critical, many designers default to a forging, although this process is a lot farther from net shape, with considerably more machining to reach the net shape. Plus, forging tooling cost doesn’t always amortize well based on component volume requirements.  If designers had more confidence in the structural integrity, they would design components to be cast instead of forged to save mass and cost.
The fact is, casting structural designs are powerful when integrated with four critical elements:  (1) structural geometry, overlaid upon (2) “castability geometry,” (3) advances in mold cavity-making processes, and (4) advances in the metallurgical engineering of alloys for better mechanical properties.

Huge advances have been made in recent years in the surface and internal integrity capability of mold cavity-making processes—especially those applicable to the light metals. Metallurgical advances have been significant in alloy development, cleaner melting and pouring technologies; inoculation, modification and treatment technologies all have resulted in stronger microstructures across all alloy families.
That said, the most powerful parameter in safety-critical casting performance in any alloy, made from any metalcasting process, is the structural geometry itself.

Geometry alone controls the stress in a structure. Uniquely, castings can form any geometry, making control of stress very local, very specific and very powerful.

Stress is defined cross-section-by-cross-section in a structure. The cross-section type that is unique to controlling bending and torsional stress is Area Moment of Inertia (Area MOI), and it is the bending and torsional stress that always result from complex load cases.
How much stress that can be tolerated is an alloy’s mechanical properties capability, but it is far easier to use geometry to lower stress with a casting’s minimal mass addition than it is to raise allowable stress metallurgically in the alloy’s microstructure.  

The reason Area MOI can efficiently lower bending and torsional stress is the stiffness that its geometry creates. That stiffness is another great attribute for light metal castings because Area MOI’s stiffness augments their low modulus of elasticity (material stiffness.)  Aluminum and magnesium alloys are one-third to one-fifth as stiff as steel alloys, but the stiffness of Area MOI has enabled safety-critical aluminum and magnesium castings to perform as if they were stiff.

Figure 1, illustrating Area MOI in an I-beam geometry to resist bending and a torque tube geometry to resist twist (torsion), shows in a glance why Area MOI is so effective in casting structural design. The formula for Area MOI is an integral, but the concept is easy to grasp. The distance from the center of bending or the center of torsion is squared (Y2 or R2), so any increase in cross-sectional area should be far away from the center. This is why I-beam flanges are wide and torque tubes are hollow.

Two other important casting design attributes of the I-beam and torque tube are:  (1) low mass compared to a simple, cross-sectional area, and (2) large perimeter and relatively thin walls for rapid cooling—assisting solidification integrity.

Figure 2 illustrates the form of stress that causes structural failure. The stresses measured in mechanical property testing are nearly universally known as simply “stress.”  Specifically, they are ultimate tensile “stress” and yield “stress.” However, those “stresses” are actually transformed stress, the stress that causes failure, and the stress that causes tensile test coupons to stretch plastically and break. In Figure 2, that transformed stress—maximum Shear stress in this case—causes the test bars to fracture straight across, but with 45-degree peaks and valleys across the fracture face.

That transformed stress is what is calculated by stress analysis software. Figure 3 explains why a casting designer needs to know how to anticipate transformed stress and adjust casting geometry with Area MOI to reduce it with the least mass using improved heat transfer strategies for better interior mold cavity solidification integrity.

Transformed stress analysis software is convenient and powerful, for any kind of structural component—metal, nonmetal, casting or not, and throwing together a solid model quickly so the high transformed stress regions can be identified and minimized with quick geometry changes is tempting. On its face, that approach doesn’t make good engineering sense if the designer could anticipate the high transformed stress regions and design a more structurally robust geometry in the first place. For designs intended to be castings, the first quick solid model attempts are usually too much like a fabrication, formed in building-block shapes that are too orthogonal for what a casting could/should be. With a fabrication-like initial shape, it may be difficult to back up to revise the model’s basic shape to be more casting-like and lighter, while tweaking local features to reduce stress.  

Figure 3 shows that fabrication-style thinking in an initial welded steel solid model that could have been initially sketched much more effectively as a ductile iron casting. The ductile iron casting, which is actually lower in transformed stress than the welded wrought steel, uses the Area MOI of an I-beam, tapered to match the shape of the bending moment patterns from the center rotating support to the load-supporting ends. Then a much better initial solid model can be built from such a sketch.

Another issue with the convenience and power of transformed stress analysis software is choosing and inputting a value for allowable transformed Stress. The transformed stress values come from complex algorithms based on the physics of strain energy. The colors displayed on the solid model surfaces are just the consequence of someone’s choice—or the software’s default—for an allowable transformed stress. Figure 4 shows the complexity of making an allowable transformed stress choice for a ductile iron casting. So, before making judgments about the colors displayed from transformed stress analysis of a solid model, the input number for casting allowable transformed stress needs to be thought about carefully. “Compared to what?” is the question.

Figure 4 is a Goodman Diagram, useful for comparing fatigue life data for the same alloy and heat treatment, if applicable, tested for the same number of fatigue cycles. Given those consistencies, significant differences in the microstructure and surface finish can be compared for allowable transformed stress. Also, significantly, different R ratios for the load case can be translated into different allowable transformed stress.

Allowable transformed stress is expressed as a fraction of the alloy’s ultimate tensile (transformed) stress. In Figure 4, the calculation for the beam in Figure 3 is in the green box.

Now, let’s integrate these principles of casting structural design in an actual casting.  The component is a bracket mounted on a roll bar to a commercial-size mowing/utility tractor. This low alloy steel casting conversion has been used to illustrate the types of interior junction geometry that causes solidification integrity problems in casting design. Carbon and low alloy steels, as a family, are among the metalcasting alloys with a “bad attitude” about the mold cavity geometry when it doesn’t fit their optimal conditions.  So, interior junctions with large mass are a solidification integrity problem.

This casting can also be used to illustrate how Area MOI mitigates some of the heat transfer constraints caused by interior geometry junctions.  We will also see how Area MOI can lower transformed stress in specific local areas of a casting while reducing mass and improving local solidification integrity.

Figure 5a is the original 1045 wrought steel, welded fabrication.  Figure 5b is the much lower mass 8630 low alloy steel casting conversion. Figure 5c is a solidification simulation showing regions where interior casting junctions cause the low alloy steel to remain mushy late in the solidification process, isolated, and difficult to feed, illustrating that “bad attitude” toward interior mold cavity junctions.Figure 6a shows the load case for a roll-over incident. The fastener bosses have as-cast holes that improve the solidification gradients of the casting’s interior junction geometry. Depending on the metalcasting process, the as-cast holes can either meet size and position tolerance requirements without machining or can be bored to final size and position.  In a roll-over incident, some of the fastener bosses experience torsional stress, and according to the mathematics of polar moment of inertia, the holes do not diminish the stress resistance of the bosses significantly. And, as-cast holes can have fillets on their top and bottom edges, which reduces stress concentration.

Figure 6b shows the remaining late-solidifying, mushy zones in the casting before gating and risering geometry is attached. Circled in green is an area that would be better hollowed out with the benefits of Area MOI for an omega cross-section. Solidification gradients would be improved, and resistance to tensile bending stress should remain high.

Circled in orange is an area that could be cooled faster with a narrow “radiator” fin that also would serve the function of the top flange of an I-beam, resisting bending stress. Figure 7a shows local changes in Area MOI based on the green and orange circle areas in Figure 6b. The purpose of these geometry changes is to improve the solidification mass and temperature gradients at these two local areas. The expected risering scheme to provide a sound casting would benefit from these two circled areas cooling quicker, one with less mass and more surface area and the other with a “radiator” fin. The green area has structural stiffness added from an “omega” Area MOI shape and the orange area has added stiffness from an “I-beam flange.”  

Figure 7b shows the benefit of the Area MOI changes to the geometry in a simulation of solidification macroshrinkage in the low alloy steel. Cleaning up the solidification macroshrinkage in these two local areas helps the efficiency of the risering design for the rest of the casting’s overall solidification integrity.

Figure 8a is the transformed maximum shear stress (Von Mises Stress) plot of the bracket before Area MOI modifications were made to the two circled areas. The transformed stress is low in the green circle, and we want to remove mass, yet use small, local Area MOI to keep the transformed stress low.  

The transformed stress is high in the orange circle, and we want to use small, local Area MOI to reduce that stress. Figure 8b shows that both were accomplished.

Here is one other nuance in the recommended methodology of sketching isometric views of a casting design before getting “trapped” in an initial solid model that is too orthogonal, too “fabrication-like.” After that sketch is converted to a solid model, having anticipated what the transformed stress might look like and using Area MOI to counteract transformed stresses, small tweaks to the casting structural geometry can be made. Bigger adjustments are done with Area MOI, as we saw with the “omega-like” dimple and “I-Beam-like” cooling fin. Smaller tweaks are done with simple cross-sectional area.

Here’s why: The form of transformed stress for all casting alloys (except the most brittle cast irons) is maximum shear stress, identified as Von Mises stress in stress analysis software. Unlike bending and torsion, shear stress is controlled by simple cross-sectional area. So, tweaking small, high-stress local areas can be done with small, simple shapes. For really fine-tuned tweaks to achieve least mass, maximum shear stress can be calculated from Mohr’s Circle. With that calculation comes the angle on which maximum shear stress acts, and knowing that angle enables those little, simple tweaks to be even more mass efficient.     CS

Click here to view the article in the January/February 2021 digital edition.