# Research on Basic Properties of Polymers for Fused Deposition Modelling Technology
## 3 Results
### Numerical Simulations of Tensile Test  
The determination of Johnson-Cook (J-C) parameters through experimental testing and numerical simulation validation is a well-established methodology in materials research. It has been successfully applied across various material classes, ensuring that the mechanical behavior captured by the model is consistent with experimental observations. Studies such as those by [PERSON] et al. for Ti-6 Al-4V [42], [PERSON] and [PERSON] for Ti6 Al4V [43], and [PERSON] et al. using SHPB tests [44] demonstrate the robustness of this approach for metals and alloys. Similar methodologies have also been extended to thermoplastics, as shown in the work of [PERSON] et al. for thermoplastic composites [45] and [PERSON] et al. for structural steel [46]. However, while these methods are extensively applied to metals and conventionally processed materials, research addressing the determination of J-C parameters specifically for 3D-printed materials, such as PETG, PLA, PA+15 CF, or HIPS, remains sparse. This gap highlights the novelty of the current study, which applies tensile and flexural testing combined with numerical simulations to bridge this knowledge gap for additively manufactured thermoplastics. Below (Figure 28) are graphs comparing the experimental results from the strength tests of filament samples with the results of simulation tests in the Abaqus/Explicit computing environment. The results of the tensile test were compared after the application of previously developed parameters in the Johnson-Cook material model. Experimental studies and numerical simulations made it possible to assess the suitability of the Johnson-Cook model for future numerical analyses of components made  
Figure 27: General view of sample fracture surfaces of samples after the Rg bending strength test: (**a**) PETG Carbon, broken filler fibers stuck in the matrix are indicated by red arrows; (**b**) PA+15 CF Rosa 3D, the arrows indicate places in the matrix after pulling out the fibers. SEM analysis (BSE, accelerating voltage: 15 kV); 250\(\times\) magnification. from commercially available filaments, and indicated the possible parameters needed to use the model. In order to verify the compatibility of the curves obtained from numerical simulations and experimental studies, a method was used to compare the areas bounded by these curves in a designated area. The boundaries of the areas were determined at the points of intersection of the curves. Then, the obtained values of area differences for each area were summed, without considering the sign, and related to the area under the curve obtained experimentally. The results can be seen below (Figure 29). Figure 28: _Cont._  
The results show a high degree of agreement between the curves obtained via numerical analysis and those determined via experimental testing for materials such as FiberFlex 40D, PETG, HIPS, TPU, and PA+1 SCF Rosa 3D. Figure 29 illustrates that the maximum fitting error for the mentioned materials does not exceed the value of 2.6%. This state of affairs is due to the monotonic nature of the tested materials. In the case of each sample from the listed materials, the phenomenon of plastic strengthening was observed, which resulted in a powerfully increasing dependence of stress on strain. This behavior predisposes the use of the Johnson-Cook model due to the first term of the equation appearing in this model, which is also of a power-law nature. Minor deviations in the fit for the TPU filament in the yield region result from the difficulty of representing a smooth transition from elastic to plastic range. Therefore, an abrupt change in the angle of the curve from the numerical analyses is apparent in that area. For the HIPS material, it was impossible to map the characteristic willow, after which the polymer in the strain range of 0.025 to 0.070 underwent plastic softening and then, until rupture, manifested a perfectly plastic character.