Stephen P. Harston and Dr. Christopher A. Mattson, Mechanical Engineering
Introducing a novel product into the market place inevitably invites competitors to reverse engineer it; enabling them to determine proprietary trade secrets and decrease potential profits. Unfortunately, there are relatively few barriers to reverse engineering and the few that do exist are not easily implemented. We will show how a numerical optimization method was used to search for improved material properties in metals as obtainable by the rotation and lamination theory as defined below. These improved material properties are generally thought to be unobtainable in metals and results in unexpected (yet desirable) performance, thus a barrier to reverse engineering is built into the product.
Material properties in metals, such as Young’s modulus (flexibility of the material) and yield strength (how much the material can deform before failure), are typically not continuous variables in product design due to the complex nature of modifying them to a desired value. It is known that material properties may be modified by changing the material microstructure – sample composition including arrangement, size, orientation, and distribution density of grains. Recently, a theory was developed that enables one to obtain desired material properties by manipulating the microstructure with the use of multiple thin sheets being strategically oriented and welded together. This theory is known as the rotation and lamination theory.
As our overall goal is to prevent reverse engineering of metal parts by obtaining material properties that are difficult or impossible to obtain, it was important to know the range of material properties that are generally thought to be obtainable. Michael Ashby made a great contribution to materials science when he simply compiled data about material properties obtained from multiple suppliers of metal products. He then presented the data in charts, called Ashby charts, which relate the generally-thought-to-be-obtainable range of one material property to another as seen as the dashed line for commercially pure Nickel 201 in Figure 1.
With the common range of material properties defined in the Ashby charts, we proceeded to create and use an optimization algorithm. The objective of the optimization was to determine what material properties can be obtained with rotations and laminations that are significantly out of the typical range of material properties. Recalling that our goal is to prevent reverse engineering in metal parts, if we are able to consistently obtain a unique performance (which is directly correlated with unique material properties) that is difficult to mimic or reproduce, then we have effectively created a barrier to those who would reverse engineer the product.
The results of the optimization are best represented with a graph and may be seen in Figure 1. The horizontal axis represents yield strength for Nickel 201 while the vertical axis represents Young’s modulus. The dashed rectangular region represents the common range of two material properties (obtained from Ashby charts) and the solid curve (termed property closure) represents the range of material properties that are numerically obtainable from a single material microstructure. It is important to note that the initial material microstructure largely determines where the property closure will reside on the horizontal axis. A different microstructure will enable the property closure to reside further to the right or left of the current position on the graph. One can see that the range of Young’s modulus (vertical axis) obtainable with the rotation and lamination theory (solid curve) is significantly improved over the range of generally obtainable material properties.
With the numerical results of the optimization producing promising results in obtaining material properties that are significantly out of the typical range for Nickel 201, we wanted to conduct a simple case study to verify our numerical results and the rotation and lamination theory. This was done by obtaining a sample of Nickel 201, heavily rolling it (a common practice in industry to reduce the thickness of metals) to obtain a thin sheet (consequently obtaining material properties that are not the same in every direction) and cutting out rectangular test specimens at unique rotations. We then took the test specimens and secured them at one end in a cantilever fashion, then applied a prescribed deflection at each corner of the free end. While one might expect the beams to deflect straight down when the deflection is applied, the theory of rotations predicts that the beam will deflect and twist since the microstructure is not aligned with the geometry of the deflecting beam. The beam rotation was measured by applying the same deflection at each corner of the free end of the beam and measuring the force output. If the force output from the two corners is the same, the beam did not twist, if the force at each corner is significantly different, the beam has twisted during the deflection. The difference in force between the two corners was approximately 9.9% implying that there was a significant rotation of the beam as it underwent the prescribed deflection. This is the simplest application of the rotation and lamination theory since only a single layer was used, but the unique performance is apparent and may be difficult for one to reverse engineer the part. The degree of difficulty to reverse engineer the product increases as the number of layers increase, each layer set at a critical orientation to obtain the overall desired performance. This desired performance will be nearly impossible to obtain without the specific knowledge and proper equipment even if the geometry is exactly the same and the material is identical.