This article uses the application example of a multipoint connector (Fig. 1) from the automotive supplier Robert Bosch to show how a short-fiber-reinforced component can be simulated using FEM with reasonable effort and by using "on-board tools".

Simple procedures based on standard isotropic material properties and reduction factors are presented (Fig. 2, top). To evaluate the results, component tests and the results obtained using a more complex anisotropic holistic simulation (Fig. 2, bottom) are discussed. The article is divided into two parts. Part I focuses on component stiffness and Part II on component strength. Part II will be published in a subsequent blog article.

**All models are wrong, but some are useful**

This headline is a quote from the British statistician George E. P. Box and describes the situation quite well when it comes to the numerical simulation of technical plastic components. In many cases, such components are reinforced with short fibers. In practice, this regularly leads to the question of how to calculate such components. It is not necessarily appropriate to strive for what is technically feasible, but rather what is practical. This means that uncertainties in the results can be accepted if the simulation answers the question posed with sufficient accuracy. The Pareto principle applies.

What is to be understood by appropriate depends, among other things, on which product development phase you are in (Fig. 3). In early phases (conception), it is often sufficient to carry out an estimative analysis using simple means, e.g. as part of feasibility studies or design optimizations. It is often the case in early phases that many boundary conditions for more precise analysis are not yet fixed, e.g. injection points or material. Feasibility studies are also often not carried out by a specialist simulation department, but by a group responsible for the product during the design phase. More complex analyses are usually not feasible there.

If, on the other hand, the product is before release, more precise analysis is required to safeguard the tool design and subsequent application. These may then be carried out by a specialist simulation department. More complex modeling approaches are justified in this case.

**Multipoint connector under surface load**

The simplified procedure described above is described using a hypothetical load case for the multipoint connector in order to determine the component stiffness. The component, which easily withstands the required design load in the application, was intentionally loaded to failure to enable validation of the various simulation approaches. The component is manufactured using an injection molding process and consists of a polyamide 6.6 with a fiber content of 30% by weight. With two external bearing points and a surface load applied by a punch, the test setup is similar to a 3-point bending test (Fig. 4).

**Fiber-reinforced materials are "components"**

As with long and continuous fiber-reinforced materials, for short-fiber-reinforced plastics the mechanical properties cannot be considered as “material” properties in the true sense of the word. Rather, they are component properties, as the "material" is only created during the manufacturing of the component. The layered structure is characteristic of fiber-reinforced materials. While this is intentionally designed into the component in the case of continuous fiber-reinforced materials, it is created in the case of injection-molded short-fiber-reinforced materials as a result of the flow processes during mold filling. The mechanical properties of the "individual layers" superimposed over the component thickness then correspond to the material or component properties at this point.

**Simplified isotropic analysis with reduced modulus of elasticity**

From the above context and from practical experience, it is known that in relation to a basic component stiffness, the use of a modulus of elasticity measured in the flow direction of the melt, e.g. from a database, provides too high component stiffnesses for a simplified isotropic FEM analysis (Fig. 5, yellow curve). For this reason, an empirical reduction factor for the modulus of elasticity is often used in practice, with which the nominal modulus of elasticity from the data sheet is reduced to approx. 65-70%. It has been shown that for typical technical components (glass fiber weight content 20 - 50%, wall thickness 3 - 4 mm, mostly bending-dominated load) the basic component stiffness can be well represented in many cases. However, this only applies to the stiffness, not to the strength and only for components that do not show a predominant fiber orientation in the load direction.

Fig. 5 also shows the force-deflection curves for the reduction factors 70% (0.7) and 50% (0.5). A reduction factor of 0.7 is much closer to the test result but is still too stiff. In contrast, a reduction factor of 0.5 results in a component stiffness that is slightly too low. A reduction factor of 0.55 would have exactly matched the measured curve. This statement is pointless insofar as the force-deflection curve is not usually known, as this is what is to be determined. It is therefore not possible to determine a reduction factor a priori in such a way that an exact match with the real component stiffness is achieved.

**Short Fiber Calculator: Helpful tool for simple analyses**

However, the range of plausible reduction factors for a specific material can be estimated. The Short Fiber Calculator within MatScape can be used for this purpose. MatScape is the material modeling module within Converse and S-Life Plastics. This tool allows a quick analysis of the effect of different fiber orientation distributions on the anisotropic mechanical properties (Fig. 6). The overview table shows the nine stiffness parameters of the anisotropic material and the three coefficients of thermal expansion. These are calculated using the internal multiscale model for different values of the orientation tensor. The values of the orientation tensor can be freely entered as principal values (a_{1}|a_{2}|a_{3}) on the left (Fig. 6, red dashed line). The so-called "effective orientation" is of particular importance here. This refers to the constant orientation averaged over the wall thickness of a test bar, for example, which leads to identical stiffnesses (tensile moduli of elasticity) as the actual inhomogeneous distribution of the fiber orientation. The effective orientation can be set so that the value of E_{11} (modulus of elasticity in the fiber axis) corresponds approximately to the modulus of elasticity measured in tests or taken from a database in direction of flow (E_{11} = E_{0}, Fig. 6, red=green). In this case, the orientation found is a good estimate for the orientation state in the sample without the need for a CT measurement or injection molding simulation. Or vice versa, if the orientation tensor is known from a measurement or injection molding simulation, the anisotropic mechanical properties can be determined directly for this position in the component. Both procedures can be useful for plausibility checks in a simple way.

In the Short Fiber Calculator within MatScape, the associated mechanical properties are shown columnwise for particular orientation states. This is the fully oriented state (100|0|0) as an extreme state when all fibers lie exactly in one direction, which in fact never occurs with injection-molded short fiber-reinforced components. As well as the states of maximum random distribution in the plane (50|50|0) and in space (33|33|33). The random 2D state corresponds to a quasi-isotropy in the plane and the 3D state analogously in space, with identical properties in all directions. In a complex injection-molded component, the fibers can be described on a statistical average rather approximately via random 2D or 3D distributions.

The stiffnesses determined in the Short Fiber Calculator for the random 2D and random 3D state can now be used to determine a plausible range of the stiffness-related reduction factor. Fig. 6 (light blue) shows, for example, a modulus of elasticity E_{11} = 4312 MPa for the random 2D state and E_{11} = 2993 MPa for the random 3D state Fig. 6 (dark blue). A tensile modulus of elasticity E_{0} = 6210 MPa is taken from a database (Fig. 6, green). If the random values are now set in relation to the tensile modulus of elasticity E_{0}, this results in a range for the reduction factor of approx. 0.7 to 0.5 (see Fig. 5). This procedure often provides values with a surprisingly good agreement with the empirical reduction factor already mentioned in practice. Although there is still uncertainty with the range of reduction factors determined in this way, the choice of reduction factor is at least somewhat more reliable than simply using the known value of e.g. 0.65, which by the way lies within the estimated range.

Once you have decided on a reduction factor within the estimated range, one can use it to scale not only the modulus of elasticity (isotropic linear-elastic analysis), but also the entire stress-strain curve in the direction of stress (isotropic elastic-plastic analysis). This can also be carried out in MatScape using a stress scaling factor when defining isotropic material cards (Fig. 7).

Finally, the material cards with the scaled curve can be exported directly in the respective solver syntax. For first estimative analyses, this is an easy way to work with isotropic material models to perform comparative analyses without already having a fiber orientation distribution.

**There is no free lunch**

However, if a reliable assessment is required, there is ultimately no choice but to carry out an anisotropic analysis. The result of such an analysis is also shown in Fig. 5. The basic component stiffnesses are presented in Fig. 8. With the anisotropic analysis, the basic component stiffness is determined in good agreement with the test result. The failure point is also well met, as will be shown in more detail in Part II in a later blog article. The isotropic analyses with reduction factor are only a rough estimate in relation to a basic component stiffness; a strength assessment based on such a scaled curve should not be carried out. There are other simplified procedures for this, which are also discussed in Part II of the article.

**Conclusion**

The MatScape material modeling module integrated in Converse and S-Life Plastics makes it easy to perform both the simplified isotropic and more complex anisotropic analyses described in this article. For example, initial evaluations can be carried out as part of optimizations or concept studies based on simple FEM analyses with isotropic material models.

The software thus offers an easy-to-use approach for the simulation of short-fiber-reinforced plastic components. Converse and S-Life Plastics can be obtained either directly from PART Engineering or via the Altair Partner Alliance.

Authors: Dr. Wolfgang Korte and Sascha Pazour, PART Engineering GmbH, Bergisch Gladbach, Germany

Co-authors: Marta Kuczynska and Natalja Schafet, Robert Bosch GmbH, Stuttgart, Germany