This blog is translated from German with DeepL.
Martin Züger from our partner, pinPlus AG in Bern, has created a case study on the pinPlus AG and made it available to us for our experience letter.
The topic is stiffness calculations on short fiber reinforced plastic parts – in this example made of PBT with 30% glass fiber with consideration of the fiber orientation.
1 A preliminary look at fiber-reinforced plastics
Common thermoplastics can be reinforced with fibers, usually glass fibers:
For example, PP (polypropylene), PA (polyamide), PEEK (polyetheretherketone), PET (polyethylene terephthalate), etc. Fiber reinforcement is used when increased strength or stiffness is required.
The above thermoplastics are not exclusively processed by injection molding. Short glass fibers (length in the range of tenths of millimeters) or long glass fibers (1-2mm length typical for injection molding) are added to the granules of the base material (matrix). Depending on the requirements, the volume fraction can be specified lower or higher.
PA6GF30, for example, is a “normal” polyamide 6 with 30% glass fibers by volume. The main advantage of fiber reinforcement is that the positive aspects of injection molding (e.g. economical production of large quantities of parts with complex geometry) can be combined with the high stiffness of the glass fibers (Young’s modulus approx. 20-30 times higher than that of the matrix material, e.g. PA) and thus even highly stressed parts can be produced by injection molding. In the past, aluminum die casting, for example, often had to be used instead. The substitution of metal by plastic is thus made possible to some extent. This trend originated in the automotive industry, but is also affecting all other industrial sectors. Fiber-reinforced plastics are also being used more and more in aircraft construction and in lightweight construction in general, but in other processes.
The main advantage of producing a fiber reinforcement in the injection molding process also leads to the main disadvantages. It is difficult to influence the position of the fibers in the components; due to the flow processes, most of the fibers will be oriented in the direction of flow. This means that few fibers will lie transverse to the flow direction. This means that the composite is not mechanically isotropic (= same stiffness properties in all spatial directions; see also next section), but anisotropic, i.e. it has different stiffness properties depending on the spatial direction. In addition, the “mixture” of materials is also important for the failure behavior.
Fiber fractures, matrix fractures and fiber detachments (the fibers slip out of the matrix) are then possible – and this from the combination of load application direction and actual locally existing material properties of the fiber-matrix composite.
The increased complexity of the material also increases the complexity in the calculation.
2 Explanation Isotropy
The dependencies of material properties taking into account the fiber structure or fiber orientation.
Measured values on data sheets are recorded on injected test specimens. Due to the geometry of the test specimens, the majority of the fibers lie in the tensile direction, so that the measured values (tensile strength, Young’s modulus, etc.) correspond to a largely ideal condition, which is rarely or only occasionally encountered in real components.
The strength of PA6GF30 transverse to the fiber direction reaches values of just under 60% of the values in the fiber direction. With regard to stiffness, the differences are even greater.
This means that, when using the values from the tensile tests, one calculates with parameters which, at best, can be found in this quality at some points in a normal injection molded part, but which have much lower stiffnesses and strengths at other points in the force flow.
And now we come to the actual calculation and the software-supported possibilities.
The Digimat software makes it possible to take into account the fiber paths, or orientations, and the resulting flexibility or stiffness, as the case may be! Most FEM programs allow the definition of anisotropic material properties, which, in the case of controlled insertion of fabrics etc. in components to be produced (CFRP and GFRP structures in aircraft and vehicle construction), already allows a good simulation of the behavior, because the fiber orientation in the component is reasonably clear from the production process. As mentioned, in an injection molded part, it is not known how the fibers are oriented. And if one has knowledge (e.g., from CT scans or flow simulations) of the local fiber orientations, it is very costly “tinkering” to manually incorporate these orientations into an FE model. In addition, the error rate is very high with this approach. Digimat allows the “mapping” of the fiber orientation from the injection molding simulation with Moldflow, Moldex, Cadmould or comparable simulation tools to FE solvers such as MSC.Marc, MSC.Nastran, LS-Dyna or ABAQUS. The calculation does not take into account each individual fiber (as is also the case with injection molding simulation), but works with so-called homogenized material data, which can represent the equivalent stiffness for a given location with sufficient accuracy.
Digimat thus serves as a link between the injection molding simulation, with which the fiber orientation is determined computationally, and the FE simulation, in which, thanks to the use of Digimat, the local, anisotropic component stiffnesses as a result of the fiber direction can now be taken into account.
If components are developed only according to the material properties data sheet, experience shows that the desired result is not satisfactory – how much closer to the desired result can one get if (an)isotropy is taken into account and included in the calculations?
Experience shows that deformations are strongly underestimated computationally with isotropic simulation. 50% -100% deviation to the unsafe side is typical. The change in stiffness also changes the locations where the largest strains occur and thus also the location of the max. stresses. This means that the results may not only be quantitatively inaccurate, but also qualitatively simply wrong, because the stress distribution cannot be correctly reproduced.
The approaches used so far have been cumbersome, costly, and not necessarily effective: It is possible to reduce the Young’s modulus by a certain factor in an isotropic calculation. However, this does not allow a binding verification calculation to be made, since a “fancy factor” can never be proven experimentally. In the case of unambiguous fiber layers, one can try something with anisotropic material models in combination with the manual definition of fiber orientations. In addition, component measurements can be used to “tune” the simulation model afterwards, but this “back-of-the-envelope” calculation is seldom expedient, since many things will be different again in the next project and the empirical values are therefore not as valuable.
As a conclusion one can say that Digimat is a meaningful addition to the conventional developer software, which is worthwhile. The experience with Digimat shows that the prediction quality of the FE simulations increases considerably. Components with load-bearing functions can be calculated much more reliably by coupling injection molding simulation with FE simulation (Digimat is the link between the two), without a significant increase in calculation effort. It makes sense to purchase Digimat if you have a professional calculation infrastructure and corresponding experience in using standard FE programs. Digimat does not support FEM solutions directly integrated into the CAD systems, so it is advisable to work with a specialized calculation partner for these analyses.
5 About the case study
5.1 Initial situation, procedure
- Calculation of the component with isotropic data according to data sheet, linear elastic.
Determined deflections are too small compared to practical experience.
- Thanks to Moldflow simulations (Moldflow insight), fiber orientations are available.
mapped to the existing model with Digimat.
- The Digimat calculation for the component was performed on the complete assembly model, including pretensioned screws and O-ring.
The assembly model includes both halves of the housing, of which the upper part is critical. The whole is a housing under internal pressure. Additionally, preloaded bolts and an O-ring with hyperelastic, nonlinear material behavior are included in the simulation model. On first prototypes, the customer noticed a large deviation between the deflection of the upper part of the housing calculated with linear isotropic FEM and the deflection actually measured. A calculation with Digimat was then able to reproduce the measured values with good accuracy. Based on the calculation results, the component can now be optimally designed. The deviation between linear calculation (without Digimat) and simulation with Digimat is 60-90%. This means that the deformation is very strongly underestimated with the (still) commonly used tools. With the results from Digimat, the deformations measured on the component and its behavior during the simulation of a burst test up to the failure of the seal could be reproduced well.
Figure 1: Mapping of fiber orientation from Moldflow:
Mapped from Moldflow (right) to Marc (left). The part orientation from Moldflow (part coordinate system) to Marc model (assembly coordinate system) is adapted within Digimat.
Figure 2: Comparison of results isotropic calculation ↔ anisotropic Digimat calculation.
Z-displacement, nominal internal pressure (same scale), depending on position deflection +60% to +90% for anisotropic calculation
Figure 3: Comparison of results isotropic calculation ↔ anisotropic Digimat calculation
Figure 4: Comparison of results isotropic calculation ↔ anisotropic Digimat calculation
Figure 5: Comparison of results isotropic calculation ↔ anisotropic Digimat calculation
Figure 6: Comparison of results isotropic calculation ↔ anisotropic Digimat calculation
Martin Züger is responsible for product innovation and engineering at pinPlus AG in Bern. This report is based on the Digimat Case Study he conducted.
We would like to thank him for this contribution.