Fatigue behaviour of 10% wt. short glass fibre reinforced recycled Polypropylene with mineral filler in presence of notches

An experimental investigation of the fatigue behaviour of plain and notched specimens made of 10% wt. short glass fibre reinforced partially recycled Polypropylene filled with mineral filler is presented. To this end, plain and V-notched specimens (with notch radius ranging from 0.07 mm to 10 mm) were produced by injection moulding and tested under tension-tension fatigue. During the fatigue test, the damage evolution was monitored using a traveling microscope to define the number of cycles spent for the fatigue crack initiation. The fracture surfaces were analysed at microscopic level in order to investigate the fatigue damage mechanisms of plain and notched specimens. The fatigue tests were first analysed in terms of net stress amplitude to define the stress-life curves. Then, an energy-based approach was proposed to reduce the scatter of the fatigue data of plain and notched specimens. Starting from the damage evolution observed during the fatigue tests, the model relies on the strain energy density numerically evaluated in the matrix and averaged on a structural volume embracing the notch tip.


Introduction
Due to its mechanical properties-to-density ratio the industry has extensively relied on Polypropylene (PP) making it a prime choice for various structural applications.However, the increasing demand for PP has raised significant environmental concerns, necessitating the adoption of recycled PP (rPP) to minimize waste in line with sustainability and circular economy principles [1,2].Although recycling processes for PP have been well-assessed [3], a critical obstacle limiting the widespread adoption of rPP lies in the lack of comprehensive data regarding its mechanical properties [4].This knowledge gap restricts the confidence in using rPP in critical applications and limits its potential as a sustainable alternative to virgin PP (vPP).To address this challenge, the integration of short glass fibres and mineral fillers have emerged as a promising industrial solution to enhance the mechanical properties of rPP.While a relatively large database there exists in literature regarding the mechanical characterization of short fibre reinforced vPP, [5][6][7][8][9][10], for recycled PP few papers are available investigating the notch effect [5] and the fibre fraction influence [6] on the fatigue behaviour of partially or completely recycled short glass fibre reinforced rPP.Therefore, the aim of the present work was to provide new experimental data regarding the tension-tension fatigue behaviour of partially recycled matrix short fibre reinforced thermoplastic composites (SFRTCs) in presence of notches.Then, given the actual damage evolution observed during the tests, an energy-based approach is presented and used to rationalise the fatigue life spent for crack initiation by means of the strain energy density evaluated in the matrix and averaged on a structural volume embracing the notch tip.

Material and methods
The material investigated was a partially recycled (84 % wt.) Polypropylene reinforced with 10 % wt.short glass fibres and 25 % wt.mineral filler.Net-shape plain and V-notched moulded-in planar fatigue specimens with a nominal thickness of 1.8 mm were produced by means of a Battenfeld HM 110/525H/210S injection moulding machine.Process conditions are reported in table 1. Fatigue tests were carried out at room temperature under tension-tension fatigue (load ratio R = 0.05) using a servopneumatic EnginLAB ASM testing machine having a 3kN load cell, closed loop and LiTeM RTC-9001 Real Time Controller.Load test frequency was set from 1 Hz to 10 Hz, depending on the applied load level and run-out specimens were assumed at 2 • 10 cycles.During the tests the damage evolution was monitored at regular intervals using a traveling microscope Dino-Lite Edge3.0AM73915MZT to define the number of cycles spent for the nucleation of a crack equal to 0.4 mm.By doing this, the typical Stress-Life curves were obtained both at crack initiation and failure.Damage analysis was carried out on a subset of specimens by means of a ZEISS MA10 Scanning Electron Microscope (SEM), in order to evaluate the damage mechanisms at microscopic level.
Figure 1 shows the plain and notched specimen geometries used for fatigue testing along with their Kt,n values referred to the net section, numerically evaluated taking into account the fibre orientation as described in section 6.The V-notch depth and opening angle 2α were maintained constant and equal to 10 mm and 90°, respectively, while the notch root radius ρ ranged from 0.07 mm to 10 mm.In addition, specimens with lateral symmetrical semi-circular (namely: s-c) notches with ρ=10 mm were tested.Machine grip Y X t = 1.80 mm K t,n =14.20 K t,n =4.20 K t,n =1.61 K t,n =1.62

Experimental results
Table 2 reports the mean value of the first detected crack length during the fatigue tests for each notched geometry, while for the plain specimens the number of cycles to crack initiation (Ni) was considered equal to the number of cycles to failure (Nf), according to [7].In table 2 it can be seen that the scatter of the results, expressed by means of the standard deviation reported between brackets, remains nearly constant and that is primarily attributable to the accuracy adopted measurement system.Figure 2 and figure 3 show the fatigue tests results reanalysed in terms of net-stress amplitude versus the number of cycles to crack initiation and failure, respectively.Here, the fatigue curves are obtained using equations 1 and 2 and their inverse slope, k, is reported along with the relative stress-based scatter index, Tσ (calculated as the stress ratio between the 10% and 90% survival probability curves, with a confidence index of 95%).2).However, this value reduced from 2.86 to 1.61 when examining the fatigue tests result of the same investigated geometries at failure (10.6 6.6 ⁄ 1.61 as reported in figure 3).Further, it can be seen that the inverse slope k of the plain geometry was higher than the notched ones both at crack initiation and failure.

Damage analysis
After the fatigue failure, a subset of fracture surfaces was observed by means of a SEM in order to investigate the effects of load levels and stress concentrations on the damage mechanisms at microscopic scale.Figure 4 reports the fracture surface of a plain specimen close to the area of nucleation of one or multiple cracks and characterised by stable crack propagation.In figure 4 the observed damage mechanisms were accumulation of plastic matrix deformation, which was responsible of the matrix roughness, and matrix-filler debonding.Further, as experienced also in [9], it was found that many of the visible fibres (i.e., 79% on 209 analysed fibres coming from 5 SEM images magnified 500X) were covered by a thin matrix layer. of magnification, it was found that fibre failure damage mechanism was limited and concerned only the 5.4% of a total of 56 analysed fibres: in these cases, indeed, a portion of a fibre was found, in the same location, on both Surface 1 and 2. Figure 5 reports an example of the above-mentioned analysis, where 12 (highlighted by the arrowed numbers) out of the 56 identified fibres location in Surface 1 and 2 are reported.In light of this, it can be assumed that fatigue cracks propagated mainly in the matrix following the fibre avoidance mode of crack propagation presented in [10] and experienced also in [11].

Fatigue crack nucleation criterion based on a Strain Energy Density-based approach
Since the fatigue crack nucleated and propagated mainly in the matrix, in this paper the Strain Energy Density (SED) approach, proposed in [12] for linear elastic isotropic materials and applied to blunt notched in [13], was extended considering as damage parameter the SED averaged over a control volume of matrix Vc,m, surrounding the notch tip.When equation ( 3) is satisfied, the damage accumulated at microscopic scale causes the initiation of a crack at the notch tip. where: In case of plain specimens and linear elastic context, it can be written [7,12]: In this work, the size of the control volume of matrix Vc,m was numerically calculated according to equation ( 3) by equating !" # evaluated at NA=2•10 6 of the notched specimen with the smallest radius (ρ = 0.07 mm) and the plain specimen [14], as summarised in figure 6.

Numerical simulations
Geometrical features in the injection moulding are known for affecting the fibres orientation in critical areas where stress concentrations may rise, therefore influencing the mechanical properties of the resultant components.In order to predict these effects, linear elastic Finite Element Analyses (FEA) coupled with simulations of the injection moulding process were conducted to implement the energybased criterion introduced in Section 5 as well as to obtain the Kt,n values (reported in figure 1).In more detail, the Multi-Continuum Theory, MCT [15], was adopted to calculate the matrix strain energy density for each structural finite element, which was finally averaged in the structural volume.In this work, Autodesk Moldflow Insight/Sinergy 2019 has been used for IM simulations, Ansys 19 for structural analysis, Autodesk Helius Advanced Material Exchange 2019 for the application of the MCT and Matlab R2022a to average Wm in the structural volume.Finally, the Kt,n values reported in figure 1 were calculated by analysing the stress fields along the notch bisector in the weak core-layer of the specimens, where fibres are mainly oriented transversally to the loading direction.a) b)

Fatigue crack assessment using SEDm Criterion
First, the size of Rc was numerically evaluated according to equation ( 3) and ( 4), finding Rc=0.40 mm.Then all fatigue data to crack initiation were reanalysed in terms of the range of !" # according to equation (8), as reported in figure 7a.Here, it can be seen that by reanalysing all the crack initiation data in a single population the scatter 5 ∆7 + = 2.47 8!5 ∆7 + # . ,⁄ 1.57:, calculated as the ∆ ratio between the 10% and 90% survival probability curves, was significantly reduced in respect to that obtained in figure 7b where the fatigue data are reported in terms of a,n.Further, the square root of 5 ∆7 + was found to be only 21% higher than the intrinsic scatter index Tσ=1.30obtained normalising the applied net-stress amplitude with the relevant σA,n,50%.In light of this, it can be concluded that the proposed criterion successfully rationalized the fatigue life spent for crack initiation.∆ • ; (8)

Conclusions
In this work the effect of geometrical notches (notch radius ranging from 0.07mm to 10mm) and fibre orientation on the damage mechanisms and on the tension-tension fatigue behaviour of partially recycled (84 % wt.) Polypropylene reinforced with 10 % wt.short glass fibres and filled with a mineral filler produced by injection moulding was investigated.The obtained results are summarised as follows:  The presence of notches influenced the fatigue strength of material.In particular, the fatigue strength decreased as the notch radius decreased.More precisely, the fatigue strength at crack initiation evaluated at 2 • 10 cycles was found 2.86 times higher when considering the plain geometry in respect to the ρ=0.07 mm V-notched one. The fatigue cracks nucleated and propagated mainly in the matrix: the main damage mechanisms were matrix plastic deformation and matrix-filler debonding. The Strain Energy Density evaluated in the matrix and averaged in a structural volume was proposed as fatigue criterion and it was able to strongly reduce the scatter of the fatigue data at crack initiation of plain and notched specimens with notch radii ranging from 0.07 mm to 10 mm. The radius of such a structural volume was found equal to Rc=0.40 mm;

Table 1 .Figure 1 .
Figure 1.Geometry of plain and notched specimens for fatigue tests.

Figure 2 .
Figure 2. Net-stress amplitude-life experimental fatigue test results at crack initiation.

Figure 3 .
Figure 3. Net-stress amplitude-life experimental fatigue test results at failure.

Figure 6 :
Figure 6: a) scheme of the applied energy-based criterion and b) numerical evaluation of Rc

Figure 7 :
Figure 7: fatigue tests results reanalysed in terms of a) range of SEDm and b) applied net-stress amplitude.
of Engineering Against Failure Journal of Physics: Conference Series 2692 (2024) 012030 Referring to the 50% survival probability Stress-Life (S-N) curves reported in figure2, one can see that the notch root radius clearly affected the fatigue strength at 2 • 10 cycles evaluated according to ISO 12107 [8], , .Specifically, the , value at crack initiation was found 2.86 times higher when considering the plain geometry in respect of the ρ=0.07 mm ones (10.6 3.7 ⁄ 2.86 as reported in figure 4

Table 2
the elastic modulus of the matrix (intended as rPP + mineral filler), ( the matrix volume in which % &, is evaluated and &, the Beltrami equivalent matrix stress state, as equation (6):