Numerical and Experimental Results on Charpy Tests for Blends Polypropylene + Polyamide + Ethylene Propylene Diene Monomer (PP+PA+EDPM)

This paper presents results from numerical and experimental investigation on Charpy tests in order to point out failure mechanisms and to evaluate new polymeric blends PP+PA6+EPDM. Charpy tests were done for initial velocity of the impactor of 0.96 m/s and its mass of 3.219 kg and these data were also introduced in the finite element model. The proposed model take into account the system of four balls, including support and the ring of fixing the three balls and it has a finer discretization of the impact area to highlight the mechanisms of failure and their development in time. The constitutive models for four materials (polypropylene with 1% Kritilen, two blends PP+PA6+EPDM and a blend PA6+EPDM) were derived from tensile tests. Running simulations for each constitutive model of material makes possible to differentiate the destruction mechanisms according to the material introduced in the simulation, including the initiation and the development of the crack(s), based on equivalent plastic strain at break (EPS) for each material. The validation of the model and the simulation results was done qualitatively, analysing the shape of broken surfaces and comparing them to SEM images and quantitatively by comparing the impact duration, energy absorbed by the sample, the value of maximum force during impact. The duration of the destruction of the specimen is longer than the actual one, explainable by the fact that the material model does not take into account the influence of the material deformation speed in Charpy test, the model being designed with the help of tests done at 0.016 m/s (1000 mm/min) (maximum strain rate for the tensile tests). Experimental results are encouraging for recommending the blends 20% PP+42% PA6+28% EPDM and 60% PA6+ 40%EPDM as materials for impact protection at low velocity (1m/s). Simulation results are closer to the experimental ones for the more brittle tested materials (with less content of PA6 and EPDM) and more distanced for the more ductile materials (with higher content of PA6 and EPDM).

move only in the vertical direction, impactor velocity being as the initial condition. Johnson-Cook failure criterion was applied only to a narrow region including the notch, along the specimen height. The constants of constitutive and failure model were deduced from tensile tests. This simulation used explicit time integration and was run for a total time of 2x10 -3 s. The simulation results are validated by experimental ones. those being in reasonable agreement.
Recent tests provided complex data on the behavior of polymeric materials, with increasingly complex constitutive models, which take into account several factors (temperature, deformation rate, structure, stress). The importance of modeling the behavior of the material, regardless of its nature, is emphasized by valuable works [23], [34][35][36]. Recent studies, experimental and obtained by simulation, have emphasized the importance of modeling the material at high deformation rate, [22], [37][38][39][40]. But most studies refer to metal alloys, used in aero, space and military applications. Equipment for testing materials at high deformation rates does not reproduce the conditions encountered in practice and the obtained results, although realistic, cannot be extrapolated to actual applications without accepting a higher degree of risk than in the case of low deformation rates. Hence, the usefulness of numerical simulations, along with experiments, because it presents an alternative for studying of damage processes.
As the temperature increases, yielding may occur and its limits decreases with increasing temperature. The deformation at break, increases with increasing temperature, the polymer becoming a brittle material at low temperature, but a ductile material at higher temperature. The effect of the loading rate on the stress-strain curve is opposite to that caused by temperature. At low loading rates, the polymer may behave ductile, with a more pronounced hardening but at high loading rates, the same polymer behaves as a more brittle material.
For polymeric materials, simulation of Charpy tests are few, but the interest in using them as shock absorbers and protective materials makes this subject to be the treated in this study.

Materials and Constitutive Models
Samples were obtained by injection molding at Monofil Savinesti SA, Romania, the compositions being given in Table 1 [41], [42]. Details of the laboratory scale process for obtaining them are given in] [27].
Based on the documentation [43][44][45][46], the authors modeled the four materials with the help of multilinear elasto-plastic curves.
The results reported in the literature show that polymers also have a stress-strain curve dependent on the strain rate (if other test parameters are kept constant) [24], [47]. The tested polymeric blends are based on polyamide 6 (PA6), polypropylene (PP) and EPDM (ethylene propylene diene monomer rubber), polybond 3000 și kritilen, the blend concentration being given in Table 1.
The material model was obtained based on experimental data obtained at traction for the highest speed (v=1000 mm/min) [27] because it was estimated that for these materials the influence of the test rate, except for the lowest test strain rate (v=10 mm/min), is very low for the shape of the stress-strain curve and the characteristic values obtained from the tensile tests [Musteata, PhD 2020] For instance, Musteata [42] reported small differences in strain-stress curves obtained in tensile tests for PA6 and PP, under test rate of 250...1000 mm/min (aprox. 35x10 -3 s -1 ...150x10 -3 s -1 ), but different shape and characteristic values at the lowest test rate of 10 mm/min (approx. 10 -3 s -1 ). Charpy test with 1 m/s could have 10...25 s -1 (taking into account the possible span between anvils). Figure 1 presents the results from tensile tests (first column of plots), the selected curve for introducing as constitutive model (second column) and the ten-point true stress-true strain curve used as constitutive model for each material. From these experimental results, the four materials have different values for EPS (echivalent plastic strain at break) ( Table 2).

The Model
For this model, the impactor an the anvils were considered as rigid bodies as the differences in material properties between those and tested materials is more than one order of magnitude (around 60, considering the tensile strength limit). Analyzing the fracture in this model, for all materials, one may notice that, even if, at crack initiation, a symmetry of the stress & strain fields is visible, this is disturbed by the occurring of high stress and strain. To use the whole sample volume in the simulation seems to be more reasonable for having a more realistic model. The issue of the mesh network for the Charpy model is the big difference between the dimensions of the specimen and the dimensions of the notch. Chosing a uniform mesh network would increase the time required for the simulation, without bringing significant improvements in the results of interest (stress and strain distributions etc.). In [16], [18][19][20][21], there are given several solutions of mesh networks for modeling and simulating the Charpy test.
The mesh network was selected to simulate the Charpy test as presented in Fig. 2. The size of the sides of the elements is between 0.25 mm and 0.75 mm. Growth ratio between elements 1.2, relatively lower than in the discretisations of other works [Haušild, 2005]. In addition, the model was formed entirely, because in the first simulations with a coarser mesh, it was observed that, although the application of the load and the geometry of the model are symmetrical to a vertical plane, stress distributions and the tendency to zigzag under the notch appeared, a fact also observed on the surfaces of broken specimens..  The assumptions considered in these models are as follows.
-The supports and the impactor are considered rigid, given the difference in properties; impactor and rigid supports were also considered in the works [16], [ 18], [19], [48] but in the work of Sainte Catherine [21] the impactor and supports they were considered perfectly elastic, given the testing of steel specimens.
-The initial velocity (just before impact) is v0=0.96 m/s (impact velocity, with which the actual tests were performed). performed).

PA6m
-Boundary conditions: friction between specimen and supports, friction between specimen and impactor (COF=0.3) for all analyzed cases; Poussard et al. [19], Haušild [17] and Sainte Catherine [21] did not consider friction, but the friction between impactor and sample and sample and supports was taken into account in the models from [42].
-Failure criterion was selected for equivalent plastic strain at break (EPS): when the critical value of EPS (at break) is reached in the model, the crack is initiated.
From the experimental results, it was found that the four materials for which the impact behavior was simulated with an impactor having linear trajectory, have different values for EPS at break, as calculated from the diagram true stress -true strain ( Table 2).   Table 3 Body The size of the elements varies between a minimum of 0.25 mm and 0.75 mm and the number of nodes and elements for each part of the test system is given in Table 3 Hypotheses are the followings: -the supports for the sample and the impactor are considered perfectly rigid, this hypothesis being reasonable if the large differences in material properties are considered (sample are made of polymeric blends that have tensile limit even 10 times and more lower than that of the impactor and supports), -initial velocity (just before the impact) v0=0,96 m/s (it is the same value as that used for the experimental work), -boundary conditions include: contact with friction between sample and support and between sample and impactor, the friction coefficient being constant for all cases (COF=0.3), -the equivalent plastic strain at break was the failure criterion selected in this work (see values for ecah material in the last line of Table 2).

Experimental Results of Charpy Tests
In this paper, the tests were performed on the CEAST 9340 impact test machine within the materials strength laboratory at "Politechnica" University of Bucharest. The tests were performed with a hemispherical impactor, with a speed of 0.96 m/s and the mass of the impactor 3.219 kg. The specimen has the drawing shown in Fig. 3, and Fig. 4 shows the geometry of the impactor.
According to the SR ISO 179 standard, ten tests were chosen for each material considered to be typical for the respective material (the tests that gave results far from the typical values were eliminated). For the material PPm (Fig. 5b, the force-time curves have large oscillations especially in the first part of the destruction process, the oscillations being of 30-60 N, which means a mixed structure of amorphous and crystalline volumes. The breaking time for the most of the specimens is up to 1x10-3s except for test eleven, for which the specimen broke at t=0.9x10 -3 s. On absorbed energy-time zones, two zones can be distinguished: the first up to 0.07 J which has a very large curvature followed by a linear zone except for test 11, the result falling in a very narrow band of 0.025 J. The very short time to failure shows the more fragile nature of PP. The addition of Kritilen in PP does not introduce noticeable changes in the form of force-time curves, but in the case of PPm several specimens "crowd" the breaking to higher values of moments (considered for F=0). If one compares the values of some parameters from the Charpy test for PP and PPm, it is observed that PPm has slightly higher values, both for Fmax and for the energy absorbed on impact ( Table 5). The time to failure (F=0) is approximately the same for PP and PPm (0.85...1.4 ms). It turns out that the addition of this agent Kritilen PP940 has improved the behavior of PP on impact, even if its concentration is only 1%, and it also improved the shape quality of the samples when they were extracted from the mold. One may compare the curves in Fig. 5a (for the neat polypropylene) to those in Fig. 5b (for PP+1% kritilen).
The behavior of material H in the Charpy test is similar to that of the PPm material ( Fig. 6), but the time to failure (considered at F=0) is close, the specimens having the time to failure from 0.9x10 -3 s to 1.29x10 -3 s. The oscillations of the force-time curve show the presence of two polymeric structures, one more tenacious and the other weaker. The oscillations of the force-time curve show that in the breaking section the material is composed of an alternating succession of more resistant micro-volumes and weaker materials from a mechanical point of view, but also amorphous and crystalline micro-volumes of the two constituent polymers (PP and PA6, see Fig. 5f).
Material G (Fig. 7b) has much smaller amplitude of force oscillations. The oscillations start with values between 30-60 N, after which the amplitude of the oscillations does not exceed ~ 20 N. The maximum values of the force are concentrated between 150-180 N, which reflects that the specimens are more similar in terms of response to the request, that is, the quality of the injection process is more controllable for this material. The energy-time curves are very close and very similar. The scattering band of the curves is narrower up to 0.5 J (up to 1 ms) and then on the linear area it is slightly more scattered. The value of the moment of completed failure (F = 0) is in the range of t=2.16x10 -3 s to t=3.77x10 -3 s. If G is compared with the other materials (Table 5), it is observed that the maximum value of time to failure has the value of t=3.77x10 -3 s, the highest of all materials of the second family. If the materials are ordered in descending order of the greatest value of time to failure (F=0), this is G, PA6m, PA6, PP and very close to each other, PPm and H. For Fmax the highest value is for PA6, followed by that for PA6m.
The SEM images (Fig. 6) shows that the introduction of PA6 in higher concentration changed the morphology of the blend. Material H has a PP matrix with PA6 droplets and pores of the order of a few microns. The droplets located right on the breaking zone are very deformed, elongated and the matrix breaks as a more brittle polymer, with linear micro-flows, probably as a result of a lower crystallinity of PP. Material G has the inverted phases, as it resulted from the EDX analysis. The PP droplets are larger and do not have cohesion on the whole surface with the matrix, which seems to be a homogeneous blend of PA6 and EPDM. But the most important feature, the energy absorbed during impact, has the highest value for PA6m (0.305...0.389 J).  The addition of EPDM in PA6m has a force-time diagram similar to that of simple polyamide, but the failure occurs after a slightly longer time interval. At t=2.59x10 -3 s, for PA6, all the specimens were already broken, whereas for PA6m the damage of the specimens (with incomplete failure), is achieved between t=3.34x10 -3 s and t=3.59x10 -3 s. In other words, the addition of EPDM increases the time to failure (even partially, in the case of PA6m material). The evolution over time of the destructive energy has similar forms only that most of the PA6m specimens break partially after storing an energy between 0.305 J and 0.389 J, while PA6 reaches only 0.279 J at the complete failure of the specimens.

PP
The energy at break plot for PA6m is characterized by two zones: a curved line in which the energy increases after a curve up to 0.15 J, after which the evolution of the energy stored in the test tube is linear. Comparing the four materials (PPm, H, G and PA6m), the value of the maximum force was obtained for PA6m. The material for which the following maximum force value was obtained is G, with 170.7 N, only 6.46% lower than the PA6m material. PPm has the maximum force about half of G, and for H the lowest value was obtained, in other words, H is the weakest material in terms of the maximum force required for damage.   Studying these images, it is not possible to specify whether the failure advanced only from the notch or occurred in the impact area of the impactor, also. The aspects of breaking material H are similar to PPm. Material G has a different appearance from the materials discussed above: the breaking surface is much rougher and it is likely that the tear was initiated first near the notch but then under the impactor. The very uneven area is very likely to have yielded more abruptly than the material under the notch and under the impactor, some dispersed droplets are partially detached from the matrix, but others, usually smaller, are trapped in the matrix. The most interesting SEM images were obtained for PA6m (Fig. 9d). An area parallel to the breaking surface of the crack is  For materials G and PA6m, the results are very good, in the sense that PA6m exceeds PA6, and G also exceeds the energy at break on impact of polyamide.  The impact strength of the specimen was calculated with the formula where E  is the energy absorbed up to F=0 and 0 specimen notch

Time [ms]
PPm H G PA6m PA6 Stress concentrators are created at the edges of the theoretical impact line due to the fact that large deformations appear as an edge effect at the ends of the impact line (Fig. 12).

Analysis of Simulations for Each Material
At time t=3.0x10 -3 s (Fig. 11b) At t=3.5x10 -3 s (Fig. 11c), the crack is already propagated over almost half the distance between the tip of the notch and the impacted surface. Next, the highest equivalent stress is observed under the impactor ech=38 MPa.
At time t=4.0x10 -3 s, the initiation and propagation of the second crack is observed from the impacted part of the specimen to its center. The maximum equivalent stress is visible only at the tip of one of the cracks, at that one initiated from the tip of the notch. On the height of the specimen, the still undetached area appears to be 2 mm. At this moment, the material left between the two cracks has only a small area, with low stresses of 7 MPa.
At time t=4.5x10 -3 s (Fig. 11d), the sample has two broken areas, the one propagated from the notch, but also a smaller one under the impactor. A maximum equivalent stress of 32 MPa is observed, in a narrow ribbon remained between the tips of the two cracks. Although at the beginning, the impact had symmetrical characteristics as compared to the initial plane passing through the tip of the notch, it is observed that, later, the stress distribution within the material becomes slightly asymmetric. This phenomenon can occur due to the automatic discretization of the model, although a fine mesh was used, but also to the elasto-plastic behavior of the material. The failure has a zig-zag character, which is also visible on the SEM images (Fig. 9a) and on a macrophoto (Fig. 21a).
At time t=5.0x10 -3 s, the still unbroken material has a size of less 1 mm, this decreasing at time t=5.5x10 -3 s, leading to the growth of the two cracks, the crack starting from the tip of the notch being longer in length than that started from the impacted surface; linkages (small bridges) between the two fragments of the specimen distributed unevenly across the width of the specimen can be observed. At moment t=6.0x10 -3 s, the specimen fragments are already separated. If high equivalent stresses occur at later times, they are due to the pushing of the fragments into each other until the impactor separates them.
At t=6.0x10 -3 s, the maximum equivalent stress moved to the tip of the crack started under the impactor and has a value of 33 MPa. The moment t=6.5x10 -3 s is characterized by ech max lower than the previous one, meaning that the failure process (also described by stress distributions) alternates with a process of relaxation of the material (ech decreases), which is specific to plastics. At t=7.0x10 -3 s, ech= 33.29 MPa, that may be seen in the virtual cross section of the specimen, which means that there are still small areas unbroken (unsepareted), local bridges between the two already detached fragments of the specimen. At time t=7.5x10 -3 s, only the crack under the impactor, may be stressed due to compression, due to the opening of the specimen. Starting from t=7.5x10 -3 s till t=1.0x10 -2 s, the equivalent stress drops to 20 MPa. These stress values, without reaching the stress at break, are due to the collision of the two fragments of the specimen.
t=2.5x10 -3 s t=3.0x10 -3 s t=3.5x10 -3 s t=4.5x10 -3 s The smooth surfaces that appear from the moment t=7,5x10 -3 s, indicate the areas where the upper crack is closed due to the rapid movement of the fragmented gates of the specimen.
The conclusion drawn from the above comment is that the impact does not generate high stress in all the volume of the impacted specimen, but determines volumes of stress concentrators where the crack starts. Figure 12 shows the breaking surface for the material PPm, its appearance being similar to that obtained in the simulation, but the crack under the impactor is less developed on actual specimen and a superficial crushing destruction is observed which could not be highlighted by modeling. The cracking occurred on a short length and from the impactor.  Fig. 14a is virtually resulted by sectioning with the imaginary plane. It is observed how the crack advances from one moment to another and the area where the last strip of material is lasting (t=3.25x10 -3 s) before the total fragmentation of the specimen.
If a qualitative comparison is made with SEM images of the H material, they are close enough in appearance. In Fig. 15, one may notice that the material H has a fragile failure and the initiation of the crack is made first from the tip of the notch, but there is a second crack, initiated from under the impactor, which joins the first at almost 1/4 of the height of the specimen. The actual appearance of the broken surface (Fig. 15) resembles the appearance of the failure at the end of the simulation. a) t=2.0x10 -3 s b) t=2.25x10 -3 s c) t=2.5x10 -3 s   Figure 16 shows the evolution of the crack generated from the tip of the notch. Figure 16a presents the initiation of the crack at the notch tip, the zig-zag development of the crack from the notch tip (Fig. 16 b, c and d), the generation of the second crack under the impactor, starting from both edges of the specimen (Fig. 16e) and a moment when a small material bridge is remained between the two fragments (Fig. 16f), until the complete separation of the fragments of the specimen (see moments in Fig. 17). Comparing the images in the simulation from one moment to the next allows for establishing the start points of the cracks and how they develop.  unbroken (a and b). At t=1.5x10 -2 s, the resulted fragments are completely separated (Fig. 17c). The opening of the crack and the change of the angle between the still undetached fragments of the specimen concentrate more the area with high stress.
Images from Figures 16 and 17 are taken from different angles, for pointing out important moments in the failure process. This is one of the advantages of simulation that destruction mechanisms can be studied and viewed from angles favorable to their explanation.
At the beginning of the impact (t=7.5x10 -4 s), it is observed the formation of two zones of stress concentration on the width of the specimen, along the tip of the notch and under the impactor, but the crack is not yet initiated. For material G, the failure occurs between moments t=3x10 -3 s and t=3.75x10 -3 s, and the crack begins in the middle of the notch tip width. At time t=4.5x10 -3 s, the crack is propagated over the entire width of the specimen and has already advanced by almost 1.5 mm (Fig. 16b). The crack advances towards the other surface of the specimen and the von Mises stress distribution has high values on the impacted surface as well ( Fig. 16c and d).
At time t=6x10 -3 s, the specimen is not yet completely broken, leaving a band of ~2 mm still uncracked. Another step in the crack development is shown in Fig. 16f, showing a moment of crack converging for material G.
Comparing the image in Fig. 18d with SEM image (Fig. 9c), one may noticed that: -the aspect of failure is rough, both in the model and on the actual specimen, the actual uneven aspect of the specimen surface being probably caused by the inhomogeneity of the material; -a very thin compressed strip is observed on the specimen side the impactor stroke. keeping high values on the impacted side (Fig. 18 c and d, but also Fig. 19 a and b).
Changing the angle of observing the specimen failure, the development of the first crack and the initiation of the second one, under the impactor are visible at time t=1.25x10 -2 s (Fig. 19c), there is a crack of much smaller depth than the one started from the tip of the notch. The images from the following moments show that the material left in common, between the two fragments decreases from time t=1.125x10 -2 s (Fig. 19c) till t=2.0x10 -2 s (Fig. 19e), leaving only a thin band that connects the two fragments. At the last moment of the simulation (t=2.5x10 -2 s, Fig. 19f), there is a remaining common material band and a decrease of the equivalent stress values with only a high spot generated by bending the non-detached fragments.
From the sequence of moments in failure process in Fig. 19, it can be seen that: -the specimen did not detach completely (both experimentally and in simulation), -the running time is the longest for this material, as compared to the other modeled materials, -for PA6m material, the EPS at break has the biggest value. Analyzing the actual aspect after specimens had been tested (Fig. 21b), it was observed that there was a very narrow band of material that did not break, as noticed in the simulation. The PA6m material is more prone to local deformation, the area under the impactor was strongly deformed, observing the developing trapezoidal shape with the larger side under the impactor (Fig. 20).
A virtual cross section of the specimen reveal how the cracks are generated and the shape change of the specimen (Fig. 20). The crack initiates between t=6.25...7.5x10 -3 s (a and b), being located in the middle of the notch tip. This advances quite quickly with larger stress concentration zones in front of the crack tip and on the impacted side (Fig. 20c). At this time t=1.125x10 -2 s, a crack initiated in the area where the impactor strikes is visible.
The cracks advance intermittently (one is developing faster, the other is waiting to act and ten the roles are changed).
The breaking process is continued in Figs Qualitative validation of the crack propagation mode in the PA6m material may be argued by comparing the actual shape of the cracks (Fig. 21b) with the simulated shape (Fig. 19f).

Conclusions from Comparing Simulation and Experimental Results
The review of available and recent impact modeling documentation in the Charpy test highlighted mesh pattern too coarse or too fine, disregard for friction in the vast majority of works, simplified modeling of the specimen material, with only a quarter or a half of the test system (specimen, impactor and supports) and simplifying hypotheses that may alter the virtual behavior of the specimen. Comparison between the stress distributions at the same time moments of the simulation, for different materials, is useful because the degree of damage of the specimen could be different (Table   6). Moments when the crack initiation is visible on the simulation are presented in Figure 22.   -qualitative: the shape of the broken surfaces by comparing to SEM images, -quantitatively by comparing the impact duration: the duration of the destruction of the specimen is longer than the real one, explainable by the fact that the material model does not take into account the influence of the material deformation speed in the Charpy test, the model being introduced with a 0.016 m/s (1000 mm/min) (maximum strain rate for tensile tests). It is very likely that the appearance of the stress-strain curve will change for 1m/s in the sense of increasing the yield limit and decreasing the EPS.
The higher the value of EPS and the higher the yield point, the wider the distribution of high stresses (red) (in a larger volume). and/or hits of the fragments with strong local compression. For G and PA6m materials, these curves reflect a much more ductile behavior. If it is analyzed the time until the breaking of the Charpy specimen, it is observed that the breaking time increases from material H, PPm, G to PA6m, for which the breaking is not with the total detachment of specimen fragments (t=2.5x10 -2 s). In reality, the time of destruction of Charpy specimens is ranked in the same way as in simulations.  (Table 8). Small differences in energy at break and residual velocity were obtained between the model and actual material parameters for materials PPm, H and G (Fig. 26c). The best concordance for these two parameters was obtained for material H, followed by G and PPm.