This article is the second part of an article on the application example of a multipole connector (Multipoint Connector, Figure 1) from Robert Bosch. It shows how a short-fiber-reinforced component can be simulated using FEM with reasonable effort and by using "on-board tools".

PART 1 described how the component stiffness can be determined in a simplified manner without taking anisotropy into account. The second part now explains how a strength assessment can be carried out. Again, a procedure based on isotropic standard material properties and reduction factors is presented (Figure 2, top). To evaluate the results, component tests and the results obtained using a more complex anisotropic holistic simulation (Fig. 2, bottom) are discussed.

**Global and local component properties**

Unlike component stiffness, which is a global property, component strength is a local property. What does this mean? Global properties are integral and result from the consideration of the entire component or a larger component area. For example, the component mass is a global property that results from the component volume and material density. The same applies to component stiffness, which in the case of a short-fiber-reinforced plastic component results from the orientation of the fibers and the main direction of stress within the component area under consideration as well as the material stiffness. Regarding the fiber orientation, it is the statistical distribution that is important and not the orientation of a single or a few fibers. The situation is completely different for strength. The failure of the component is determined by the spot in the component at which the ultimate breaking strength of the material is exceeded, assuming a rather brittle behavior (failure due to fracture), as can usually be expected with short-fiber-reinforced materials. The failure is therefore local, comparable to a chain in which the overall strength of the chain is determined by the strength of each individual chain link.

**Nominal properties from databases overestimate the strength**

The material properties available in databases are usually determined on injection-molded, longitudinally injection-molded tensile bars. This means that the properties are determined in the direction of the main fiber orientation; these are the properties with the highest stiffness and strength. In the component, however, most of the fibers are not aligned in the direction of the main stress direction as in the tensile test but deviate from it at an angle. Figure 3 shows examples of stiffness and strength for tensile bars taken from an injection molded test plate parallel and perpendicular to the main fiber direction. The differences are considerable.

**Micromechanical behavior is crucial**

The strength-determining processes at the micromechanical level are shown in Figure 4. Fibers can be pulled out of the matrix or can break in the fiber direction, while fibers can detach from the matrix, matrix breakage or generally mixed forms of these phenomena can occur transverse to the fiber direction. The significantly reduced strength of a short-fiber-reinforced material transverse to the fiber direction is therefore understandable, as the strength here is limited by the strength of the matrix material or the adhesive strength of the fiber to the matrix. There is no reinforcing effect from the fiber here.

In addition to anisotropy, the fiber volume fraction causes other effects that reduce strength. Figure 5 shows the stress distribution in fibers and matrix for a microscopic section of a short fiber-reinforced material (a so-called representative volume element RVE). Due to the fiber volume fraction, the matrix is constrained with regard to its deformation capability. This leads to stress peaks primarily at the fiber ends as well as stress hot spots in the matrix areas between the fibers, as can be seen in Figure 5. This can lead to the strength of the reinforced material transverse to the main fiber orientation being even lower than the strength of the pure matrix material.

**Keep it simple but not too simple**

The above phenomena are all of a local nature and can only be resolved in the simulation using more complex multiscale simulations and are only used here as a reference for evaluating simpler procedures. Part 1 of the article already presented a simple procedure for determining the component stiffness using a reduction factor for the stiffness. In particular, with a reduction factor of 0.55 in relation to the original modulus, the measured component stiffness based on an isotropic analysis was well met (Figure 6, purple curve). One could now assume in a first approach that the component strength can also be determined just as well with the stress-strain curve reduced in this way. However, this is not the case. If the fracture stress of the material, also reduced by 0.55, is used as the evaluation criterion for reaching the strength limit, the result is a failure force that is clearly (69 %) too low (Figure 6, purple dot). If the isotropic FEM simulation were carried out with the non-reduced stress-strain curve (Fig. 6, yellow curve), the failure force of the component would be significantly too high (120 %) (Fig. 6, yellow dot).

A different approach is proposed by Oberbach [1]. Here, an isotropic analysis is carried out with the non-reduced nominal stress-strain curve and then the strength is reduced in the stress direction according to the load type (single, repeated, long-term, alternating) and material type (semi-crystalline unreinforced, amorphous unreinforced, fiber-reinforced) according to the diagram shown in Figure 7 to evaluate the stresses obtained from the FEM. The stress-strain curve as such is not reduced. The method also includes other variants. It is shown in detail in [1]. In [2], the method was extended to the effect that the local stress state (degree of multiaxiality) is considered to determine the exact value of the reduction factor within the proposed reduction factor ranges (Figure 7).

The result of an analysis of the component using the method according to [2] is also shown in Figure 6 (blue dot on yellow curve). Although the failure force is still slightly underestimated (93 %), it is closer to the actual value. The method is simple, and its use is particularly useful in early product development phases, where often only feasibility analyses are required. Likewise, the required fiber orientations from an injection molding simulation for a more complex anisotropic simulation are often not yet available in early phases. However, the correct failure force (as well as component stiffness, see Part 1) can only be determined with an anisotropic analysis (Figure 6, green dot). Figure 8 summarizes the results obtained with the described procedures in standardized form.

**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 analyses can be carried out as part of optimization or concept studies based on simple FEM simulations with an isotropic material model. In addition to a contour plot of the degree of utilization, S-Life Plastics also provides a comprehensive assessment report for each FE node (Fig. 9).

MatScape can also be used to generate anisotropic material cards for more precise analyses (Figure 10), to carry out a holistic simulation with consideration of the fiber orientations.

The software thus offers an easy-to-use approach for the simulation of short-fiber-reinforced plastic components that meets the different requirements in terms of effort and benefits in the various product development phases. Converse and S-Life Plastics can be obtained either directly from PART Engineering or via the Altair Partner Alliance.

[1] Karl Oberbach, „Reprint Allowable Strength Limits Plastics-Oberbach“, translated from *Tagungsband Konstruieren mit Kunststoffen, 11. Konstruktions-Symposium der DECHEMA*, Frankfurt/Main, 1981, S. 181–196. [Online]. Available here

[2] M. Stommel, M. Stojek, und W. Korte, *FEM zur Berechnung von Kunststoff- und Elastomerbauteilen*, 2. Aufl. München: Carl Hanser Verlag, 2018. Available here

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

Co-Authors: Marta Kuczynska und Natalja Schafet, Robert Bosch GmbH, Stuttgart, Germany