## Weight and Interface Strength

This section defines and describes measurement techniques for several performance characteristics deemed appropriate for plastic products. While there are many subjective ways of classifying and quantifying a product's performance and quality, we will stick to only a few of the more well-defined aspects that can be physically measured. Certain characteristics that are important in plastic product design will be quantified and measured as performance aspects. For example, parameters such as weight and strength are both relevant and quantifiable, so they will be considered in this model.

For clarity, we will henceforth define a "performance aspect" (PA) as a measurable physical quality of a plastic product assembly that non-subjectively and non-arbitrarily quantifies its desirability. Therefore, each PA will have actual physical units (e.g. grams, millimeters, etc&) used to describe it. The following subsections will define the relevant PA's and describe how to measure and/or compute them.

### Performance Aspect 1: Weight

In most applications, weight reduction is an important goal. By minimizing the total weight of a product, significant performance increases (as well as cost reduction) can be achieved. In general, minimizing weight without sacrificing other performance aspects (e.g. strength) is a common goal for most products.

The computation of a product's total weight is simple. Although the actual weight of each shot can vary because the molded resin density varies throughout the part due to processing conditions, the nominal part weight can easily be calculated from its volume and the resin's average density. Hence, the nominal part weight will be used as PA 1. This value can be instantaneously and accurately be automatically calculated from the CAD file of the assembly. For MMM and SMM&A, the total product weight is the sum of both parts A and B, and any fasteners/adhesives. Most popular CAD systems will output the total weight of an assembly given the materials and/or densities of the components. We will use ounces as our measurement units for weight.

Weight is a valid PA because weight minimization is a common goal across all product classes. It is a proven performance measurement, and one that is calculated with relative ease.

### Performance Aspect 2: Interface Strength

The term "strength" can refer to a wide range of physical characteristics defining how well an object can sustain loads and moments. There are many material properties and corresponding physical tests that can be used to form some measure of the strength of a component or assembly.

#### Definition of Interface Strength

Here we will use the strength of the interface as our PA; that is, how hard it is to separate components A and B at their mutual interface. It should be noted that here, the definition of an interface will be loosened to include any section on the assembly where the separate materials meet, whether there is microscopic bonding or not. This way, articulated parts such as hinges or joints can have a strength PA associated with them.

Interface separation strength was chosen as a PA to represent strength since it is relatively straightforward and universal for the type of assemblies under analysis. This is because all two-material assemblies posses an interface, and separation is a defining and possible failure mode for two-material assemblies. While fracture of either or both materials is also a possible failure mode, interface separation is probably more likely (unless the interface is optimally designed) and is a defining characteristic of assemblies. Regardless, the strength test should allow for all possible failure modes. Furthermore, this PA was chosen to coincide with the physical tests commonly used in industry to characterize the strength of various material interfaces. Hence, interface strength will be defined as the force or moment required to produce one of the following three failure modes:

1) Complete separation of the components A and B along their common interface ("mode AB")

2) Fracture of component A ("mode A")

3) Fracture of component B ("mode B")

Although there are actually five possible types of failure mechanisms, only two mechanisms (embodied in the three failure modes listed above) are sufficient to characterize strength for the purposes of this model. This is based off observance of typical failed multi-material assembly specimens.

#### Types of Interface Strength Tests

Like all other measures of strength, interface strength could be characterized by a number of different attributes that define how well the interface performs under a particular loading scenario. Typically, the interface could is pulled apart (tension), or twisted apart (torsion). These two types of tests, among others, are valid strength attributes, but we will focus on only tensile and torsional forces here for the sake of brevity. This is because in industry tests, shear and normal strength are the most commonly-tested attributes. The model could quite easily be adapted to include other strength tests.

In addition to specifying the types of strength tests to use, the appropriate method of conducting such tests must also be defined. That is, the nature and directions of loadings and the type and location of restraints must be specified for each type of test. Unfortunately, it can be quite difficult to define a set of appropriate physical tests that can be universally applied to all types of assemblies, regardless of geometry or intended functionality. As with most physical tests or finite element simulations, the appropriate set of testing conditions should be chosen based on the product's structure as well as the expected conditions it will experience under normal use.

These conditions are typically chosen based on common sense and experience. For example, although a steel bolt could theoretically be loaded in an infinite number of arbitrary directions, tensile testing is usually conducted parallel to the bolt's axis, because this is the type of loading it would normally experience. Similar reasoning should be used to determine the appropriate loading conditions for plastic assemblies. For example, when tensile testing a hinge box, it seems reasonable to assume that the assembly would first break somewhere along the hinge. Therefore, a valid tensile test would attempt to pull the lid apart from the base by loading the lid parallel to its surface (and resultantly intersecting the hinge's center), as shown below in Figure 1.

It is highly recommended that each assembly be carefully analyzed and assigned an appropriate set of physical tests which are specifically catered to the form and function of the product. However, a set of universal physical tests will next be prescribed for the sake of consistency as well as the relative comparison purposes of this model.

Instead of assigning restraints (e.g. fixed surfaces or edges), the assemblies will be considered unrestrained with equal and opposite loadings. That is, the same forces will be applied in opposing directions on parts A and B to keep the entire assembly fixed in space.

Figure 2 shows two examples of choosing the proper loading direction based on the mold opening direction and insertion direction. It can be seen that the chosen loading directions are the most natural ones for the separation of the two parts. This is simply a result of the fact that they are put together along these same directions. While the figure only shows resultant tensile load pairs (equal and opposite), it should be noted that the loading would actually be manifested as a distributed loading over the entire exposed surfaces of the parts. These surface stresses are omitted from the figure for clarity.

The resultant load vector for a torsional force would look the same as that for the tensional loading. For the examples of Figure 2, the resultant moment vectors would also be vertical, and the resulting shear stress would tend to distort the part surfaces tangentially (in a horizontal circular path perpendicular to the page).

#### Conducting the Strength Tests

Actually conducting tensile and torsional tests on manufactured or prototyped assemblies would be physically difficult, cost prohibitive, and most importantly, it would negate the purpose of the model, which is to provide designers with performance estimates early on in the product development stages. Fortunately, computational mechanics allows designers to test their ideas before they are ever produced. Most CAD packages offer comprehensive finite element analysis (FEA) plug-ins that allow a range of physical testing on single parts or entire assemblies.

This model requires the use "virtual testing" through the use of such FEA packages to determine the tensile and torsional strength of the assemblies under comparison. It is actually a trivial matter to run the physical simulations on CAD files once the loads and restraints have been appropriately prescribed as discussed above. Unfortunately, most software has trouble accurately modeling either chemical bonds or adhesive bonding, the former of which is essential in most assemblies produced via MMM. This shortcoming makes it difficult to obtain accurate strength estimates for MM assemblies, which typically posses combination locking and chemical interfaces. Furthermore, it is possible to have purely chemical interfaces, which would result in meaningless strength values of zero from standard FEA simulations which only recognize mechanical locking.

In order to get around this difficulty, interface strength will be broken up into several independent subsidiary PA's rather than attempting to estimate the absolute interface strength. In stead of one load value representing total strength, we will split it into the following six independent PA's:

PA 2a: Tensile strength of the assembly's purely mechanically-locked interface (virtual testing of the actual un-bonded assembly)

PA 2b: Torsional strength of the assembly's purely mechanically-locked interface (virtual testing of the actual un-bonded assembly)

PA 2c: Relative shear strength of a test specimen with a purely chemically-bonded flat interface (physical testing on a representative specimen, value valid for MMM variant only)

PA 2d: Relative peeling strength of a test specimen with a purely chemically-bonded flat interface (physical testing on a representative specimen, value valid for MMM variant only)

PA 2e (optional): Relative tensile separation strength of a test specimen with a purely chemically-bonded flat interface (physical testing on a representative specimen, value valid for MMM variant only)

PA 2f (optional): Relative torsional separation strength of a test specimen with a purely chemically-bonded flat interface (physical testing on a representative specimen, value valid for MMM variant only)

Of the above six PA's, the first two are determined through FEA simulations, while the second two (and if necessary, the optional remaining two) are determined through actual physical testing on standardized specimens. Although physical testing on the actual assemblies is cost and time prohibitive, testving of standard specimens is straightforward as their molds should be readily available. All that is required is a quick molding run using the desired resin combinations on the existing MS molds for making the test specimens.

The first two PA's measure the specific mechanical strength of the interface, which depends solely on its geometry. The remaining four PA's measure the generic adhesion strength between the two materials. This strength is based solely on the polymers' chemical compatibility as well as the resin processing conditions used to mold both shots. While the actual chemical bond strength depends on many parameters such as the exact resin grade, the presence of fillers/colorants, and the specific processing conditions, several resin manufacturers have published independent results of material compatibility tests, such as the one shown in Figure 3.

Source: www.multishot.com

While charts such as the one above are useful as rough guides for determining the applicability of various resin combinations, it is strongly recommended that independent physical testing be conducted on potential resin combinations for the products under analysis. Simple test specimens should be molded under identical processing conditions as the intended product and physically tested to accurately determine the relative interface bonding strengths. Testing methods for PA's 2a through 2f are detailed below.
##### PA's 2a and 2b: Tensile/Torsional Mechanical Locking Interface Strengths
These two PA's represent the maximum tensional/torsional load the assembly could sustain before failure, assuming there is no chemical bonding along the interface. These force values are calculated using any 3D FEA package (e.g. Pro/Mechanica, ANYSYS, COSMOSWorks, etc&). The tensional and torsional strengths must be determined through separate simulations. The process is typically conducted as follows:

1) All of the materials are defined, including those of parts A and B and any fasteners.

2) No constraints should be set so that the assembly remains unfixed as described above.

3) The loading directions are prescribed as discussed above. The loads can be applied as distributed loadings (surface pressures) over all of the exposed surfaces of the assemblies, so that the resultant load is parallel to either the mold opening direction or the insertion direction (depending on the variant). An example of this type of loading is shown below in Figure 4.

4) Finally, the simulation is run to obtain either the tensional or torsional locking strength of the assembly [lbs] (PA's 2a and 2b, respectively).

It should be noted that currently, standard FEA packages are unable to accurately model bonded assemblies such as the MMM variants under consideration. Therefore, it must emphasized that the simulations suggested here are only used to indicate the relative locking strength of the assemblies. The actual bonded assemblies may perform quite differently in reality due to complex physical mechanisms such as bonded ligament failure [22].
##### PA's 2c and 2d: Shear/Peeling Chemical Interface Strengths
These two strength tests measure how well the chemical interfaces resist shear stresses and peeling, respectively. These are the most commonly-used PA's by the MSM industry. The physical tests are conducted on simple two-shot specimens, which are shown below in Figure 5:

The shear (lap-joint) test specimen (Figure 5a) is loaded with an increasing tensile force until a critical failure load, , at which the two materials separate along the flat interface. The peeling test specimen (Figure 5b) is loaded with a tensile force perpendicular to the flat interface until a critical failure load, , at which the materials begins to peel apart. This load is then increased until total separation of the interface. Both PA 2c and 2d can be uniquely defined by their corresponding failure loads, and [lbs], respectively. The actual dimensions of the test specimens is unimportant, as long as they are consistent throughout all tests and feasibly made using the same MS equipment that would produce the actual assemblies.
##### PA's 2e and 2f: Tensile/Torsional Chemical Interface Strengths
While some may argue that the two physical tests specimens discussed above are adequate to completely determine two materials' compatibility, an optional third type of test specimen is proposed in order to determine the purely tensional or torsional chemical interface strength. These optional tests are recommended in order to more closely match the loading conditions prescribed in the FEA simulations. The specimen geometry, as illustrated in Figure 6, consists of simple circular interfaces which will be pulled apart or twisted apart from pure tensional or torsional loads.

As with the previous two test specimens, the third test specimen can be used to determine measures for PA's 2e and 2f. These PA's are uniquely defined by the failure loads respectively.

#### Validity of Performance Aspect 2

The tests recommended above should yield valid measures of relative strength between assemblies as they are just expanded forms of tests proven in the MS industry. Both the FEA simulations and standardized tests are common methods of evaluating strength of plastic components used today.

The methodology for testing interface strength as well suggested optional tests comes directly from experimental results of interfacial strength testing [Bru04]. MMO's were molded with various interface geometries and bonding characteristics and then destroyed via tensile testing and analyzed using digital image correlation (DIC) in order to understand the fundamental physics behind MMO interface separation and/or component fracture.