CHAPTER 5. RESULTS

5.1 Density

Table 5-1 displays the density values of SLS PA-12 at 0° and 90° orientations and of IM PA-12. The density of IM PA-12 is higher than that of SLS PA-12, with no differences between 0° and 90° orientations.

These results are lower than the density of neat PA-12, which is 1.02 g/cm³ [137]. Nevertheless, the IM PA-12 material is almost full dense, with only a porosity percentage of 0.19% versus 3.7% and 3.4% for SLS PA-12 at 0° and 90° orientations, respectively. In addition, it is also higher than the theoretical sintered density value of 0.93 g/cm³ provided by the manufacturer [28] (Table 4.3).

5.2 Surface roughness

Table 5-2 shows the surface roughness results for the three materials. While there is no difference in both R_a and R_z parameters between SLS orientations, a clear difference is distinguished between SLS and IM materials.

The roughness average, R_a, of SLS PA-12 are more than one order of magnitude larger than that of IM PA-12 and lightly smaller than the values obtained by Guo et al. [160] and Xu et al. [161]. In case of the average maximum height of the profile, R_z, the values of SLS PA-12 are 20 times higher than those of IM PA-12.

5.3 Microstructural analysis

Figure 5-1 shows the characteristic microstructure of the specimens analysed: SLS at 0° (Figure 5-1.a) and at 90°orientations (Figure 5-1.b) and IM PA-12 (Figure 5-1.c). These images show the spherulites of the crystalline phase, which are usually distributed as spherical crystal colonies with a typical Maltese-Cross pattern, resulting from the birrefrigence of highly ordered lamellae within the spherulites oriented randomly [141], [162]. The spherulites that were fully discernible correspond to those cut in half during the slicing process with the microtome.

Figure 5-2 represents the diameter distribution versus the occurrence probability. The probability density was calculated using a normal distribution as the Kurtosis for all the materials reached values between 0.2 and 0.5, whereas the perfect Gaussian distribution takes values of 0 [163].

Table 5-3 collects the average spherulite diameter, $\overline{D}$, and the standard deviation, s, obtained from the measurements. No differences in average size and distribution are observed between SLS orientations, obtaining a mean spherulite size around 50 ± 10 μm. This is partly due to the fact that the average size of the spherulites depends upon the cooling conditions and the density of potential nucleating sites for crystallisation, being maintained in the SLS process for both orientations.

It is also worth mentioning that the average values of spherulites are quite large and this can be explained by slower crystallisation kinetics during the SLS process and a lower nucleation density [142]. The spherulite size of the IM PA-12 is much finer, with average size of 13 ± 3 μm, four times lower than that of SLS PA-12. The differences in the spherulite size between the SLS and IM materials is caused by the thermal history during the manufacturing process. The IM material is fully molten before ejection and then cooled rapidly after injection. This rapid cooling allows less crystallisation growth. SLS material is also fully molten during laser sintering but the cooling rate is much lower allowing a much-developed transformation of the crystalline structure [164].

Moreover, in case of IM PA-12, a skin-core morphology was clearly observable in the cross-sectional samples (Figure 5-3), with a skin layer size around 14% of the total sample thickness. The spherulites were measurable in the core as they were not discernible in the surface layer, even with the inspection at the highest magnification of the optical microscope (x1482). The high level of molecular orientation together with the injection speed and the rapid cooling occurring during injection moulding may make difficult the crystallisation process in the skin. However, a micro-spherulitic structure in the core was observable (but always smaller than in SLS), due to a different temperature profile in the cooling stage to that undergone in the skin.

5.4 Thermal characterisation

The Differential Scanning Calorimetry (DSC) tests performed allow to obtain the thermograms shown in Figure 5-4. The crystallinity characteristics, the crystallization temperature, T_c, the melting temperature, T_m, and when observable, the glass transition temperature, T_g, can be computed from them and are collected in Table 5-4.

The thermal properties of SLS PA-12 at 0° and 90° orientations are almost identical, indicating that specimens at both orientations must have cooled at similar rates to give such consistent levels of crystallinity and temperatures. However, some differences were observed when comparing with IM PA-12. Specifically, IM specimens showed lower T_g, T_m and crystalline degrees, χ_c and χ_m, but higher T_c than SLS specimens. Once again, these differences are to do with the thermal history during the manufacturing process [165].

Dynamic Mechanical Analysis (DMA) gave information about the loss modulus, the storage modulus and the loss factor (tanδ). Figure 5-5 shows the evolution of these parameters from -110 °C to 170 °C for SLS PA-12 at 0° orientation in Figure 5-5.a, for SLS PA-12 at 90° orientation in Figure 5-5.b and for IM PA-12 in Figure 5-5.c. The storage modulus plot gives a full picture of the load-bearing characteristics of the material as a function of changes in temperatures, while tanδ curves identify the regions where relatively large changes in properties occur over relatively narrow bands of temperatures and, consequently, related with material transition stages. Two obvious transitions at the ranges between 50 °C and 60 °C and between -60 °C and -70 °C are found independently of the processing technique in Figure 5-5. They are defined as the α and β relaxations, respectively.

As known, the α-relaxation corresponds to the glass transition temperature, T_g, and displays the peak of greatest magnitude. The α-relaxation results from the rupture of hydrogen bonds between polymeric chains, which gives rise to the motion of long-chain segments in the amorphous region [165], [166]. On the other hand, the β-relaxation reflects the mobility of local hydrogen-bonded amide groups in the amorphous region and its appearance indicates that the material has good low temperature flexibility and cold endurance [165], [167]. Table 5-5 collects the glass transition temperature and the β-transition temperature determined from the peaks of the tan δ curves. Firstly, these transitions are similar for both orientations in SLS specimens, confirming the no dependency with the manufacturing orientation. Nevertheless, both the glass transition temperature and the β-transition temperature in IM specimens shift to lower temperatures. This also occurred in DSC measurements (Table 5-4). The reason might be the faster crystallisation in the IM process, causing an amorphous phase with more irregularly arranged molecular chain and better mobility, thus implying lower values of T_a and T_β [168].

Table 5-5 also shows the storage modulus at room temperature. As in other properties, there is no influence of the orientation on the storage modulus in SLS PA-12, but the value of the IM PA-12 specimens was almost 40% lower than the values of the SLS PA-12 samples. It is well settled that the Young’s moduli increase with the crystallinity degree [169], but the opposed behaviour observed in this case may be due to the presence of a no negligible skin layer of amorphous material together with a much smaller spherulitic structure.

5.5 Mechanical properties

Figure 5-6 and Figure 5-7 show characteristic engineering stress-strain curves of SLS PA-12 at 0° and 90° orientations, respectively, obtained from tensile tests at -50 °C, 23 °C and 50 °C. As expected, the mechanical response is strongly influenced by the temperature. At -50 °C, above T_β, SLS at 0° and 90° orientation presented semi-brittle behaviour due to the activation of mobility of side groups of the chain. For temperatures above T_g, that is, at 23 °C and 50 °C, the material displayed a ductile behaviour. As usually, the ductility decreased but the stiffness and the strength increased as the temperature reduced.

Figure 5-8 analyses the effect of orientation and manufacturing process on the tensile behaviour, showing clear differences. Firstly, SLS PA-12 presented higher strength and stiffness but lower ductility than IM PA-12. In addition, it is easily observed that in SLS material, the mechanical response at both orientations is similar except for the ductility.

Figure 5-9, Figure 5-10, Figure 5-11 and Figure 5-12 show the evolution of Young’s modulus, tensile strength, elongation at break and Poisson’s ratio with temperature, orientation and manufacturing process, respectively. Regarding Young’s modulus (Figure 5-9), the values decrease with the temperature increase, being this reduction more accentuated at 50 °C, due to the nearness to T_g (Table 5-4).

For SLS PA-12, there were hardly differences in the Young’s modulus with the orientation for the same temperature. On the other hand, IM PA-12 exhibited the lowest Young’s modulus at room temperature, being 20% lower than the larger one corresponding with SLS PA-12 at 0° orientation.

The tensile strength followed the same trend as the Young’s modulus (Figure 5-10): the higher the temperature, the lower the tensile strength at both orientations in SLS PA-12, and the lowest value at room temperature was obtained for IM PA-12. Concerning the orientation, SLS PA-12 at 0° orientation showed higher values than at 90° orientation, but the differences reduced as the temperature rose till reaching similar values at 50 °C.

When analysing the influence of the temperature on the elongation at break (Figure 5-11) in SLS PA-12, the values of this parameter increases with temperature rising independently of the orientation. Nevertheless, the elongation at break at 0° orientation was more elevated than at 90° orientation at any temperature, registering the higher difference at 50 °C, with values at 0° orientation 3 times larger than those at 90° orientation. The proximity of 50 °C to the T_g of the material was the reason of this significant increase because the mobility of large scale coordinated motions of the polymer chains occurs, resulting in a massive relaxation of the material. At room temperature, the elongation at break of IM PA-12 is more than twice the value measured in SLS PA-12 at 0° orientation.

Regarding the Poisson’s ratio, Figure 5-12 shows increments with temperature, having the 0° orientation the largest value for SLS PA-12 at the three tested temperatures but being overtaken by the value of IM PA-12 at room temperature.

These results match with the existing bibliography (section 2.2.1, Table 2-1). Firstly, the Young’s modulus and the tensile strength of IM PA-12 were smaller than those of SLS PA-12 despite the higher crystallinity degree of the former (Table 5-4). Crist et al. [141], [169] stated the opposite trend, the higher the crystallinity degree the higher the elastic modulus and the tensile strength. Nevertheless, the presence of an amorphous skin layer with significant dimensions in the IM PA-12 is an important factor to have in mind. Also, a different spherulite size between SLS PA-12 and IM PA-12 seems to affect the elongation at break [170]. Results obtained in SLS specimens at 23°C are analogous to those of Seltzer et al. [31], Caulfied et al. [33], Stichel et al. [34], Munguia et al. [118], [119], Xu et al.[161], Mousa [171] and Hao et al. [172]. Finally, the results obtained in IM PA-12 are comparable to those reported by Hooreweder et al. [30].

5.5.1 Tensile tests fractographies

SEM fractographies were taken from the fracture surfaces of the tensile test specimens to study the effect of temperature, orientations and manufacturing processes, identifying the micromechanisms of deformation and fracture.

Figure 5-13 and Figure 5-14 show the fracture surfaces at -50 °C, 23 °C and 50 °C of SLS PA-12 at 0° and 90° orientations, respectively. The common trend observed in both orientations was an increment in the surface smoothness with lower temperatures. However, there are several differences between the SLS orientations.

There is no influence of the orientation on the morphology of the fracture surfaces at -50 °C (Figure 5-13.a and Figure 5-14.a). The morphology was irregular, identical to those observed by other authors [173]. The similarity of the fracture morphology is consistent with the values of the tensile parameters, specially the elongation at break (Figure 5-11), which were identical at this low temperature for both orientations.

At 23 °C (Figure 5-13.b and Figure 5-14.b), the fracture surface at 0° orientation is much rougher than those resulting from tests at -50 °C, being characterized by the presence of voids surrounded by amorphous filaments of PA-12, which had been stretched and finally broken along the crack growth direction. These features are associated with the nucleation, growth and coalescence of crazes, which is a phenomenon commonly observed in thermoplastic polymer fractures [174].

The nucleation site could be at defects as pores or interspherulitic areas. The stretched filaments surrounding voids are displayed in Figure 5-15. On the other hand, the 90° orientation exhibits a plain surface with no evidence of plastic deformation of filaments but where pores and unmolten particles are discernible. This distinct morphologies at different loading directions are in accordance with the elongation at break values (Figure 5-11), specifically the increase in surface roughness goes hand in hand with the increase in the elongation at break.

Finally, the fractographies of specimens tested at 50 °C (Figure 5-13.c and Figure 5-14.c) show a much higher ductile deformation of the amorphous filaments than at 23 °C, and when comparing the orientations, the specimens tested at 0° orientation presented more tearing than at 90° orientation. In this case, the ductile behaviour is enhanced with the closeness to the material T_g (Table 5-4). The high mobility of the molecular boosts the ductile tearing along the load direction at both orientations. Once again, this fractographic morphologies agree with the elongation at break results (Figure 5-11), which are the highest of all the tested temperatures and with values at 0° orientation more than twice those measured at 90° orientation.

To determine the effect of the processing technique, Figure 5-16 shows the fracture surface of IM PA-12. The panoramic view (Figure 5-16.a) evidences that the failure starts at a surface defect (outlined in black dashed line) followed by macroscopic plastic deformation of the gage length with the formation of a necking zone which propagates along the specimen. The high level of plastic deformation undergone by the amorphous filaments is in agreement with the high values of elongation at break (Figure 5-11). The detailed view (Figure 5-16.b) clearly denotes the stretched gage length broken after ductile tearing.

Moreover, there is complete lack of defects in form of pores or unmolten particles. Therefore, the crazing mechanism together with the presence of internal defects may be the reason why the ductility at failure of the SLS PA-12 is much lower than that of IM PA-12 [168].

5.6 Fracture behaviour

For the determination of the fracture parameters, different approaches were applied depending on the mechanical response of the material at each experimental condition as described in the section 4.6.2.

Figure 5-17 shows the representative load-displacement records obtained from fracture tests at -50 °C of SLS PA-12 at 0° and 90° orientations. Despite the semi-brittle behaviour, all the requirements of the LEFM approach were fulfilled, so the recommendations of ISO 13856 standard [149] were followed to determine the critical stress intensity factor, K_IC, and the critical energy release rate, G_IC.

Figure 5-18 displays the representative load-displacement records obtained from fracture tests at 23 °C of IM PA-12 and of SLS PA-12 at 0° and 90° orientations.

The difference in stiffness is mainly due to the different initial crack lengths. The behaviour of IM PA-12 specimens and both orientations of SLS PA-12 samples was also semi-brittle but, at this temperature, not all the tests verified the linearity criterion, because there were some tests which deviated from the linearity, as the $\frac{P_{max}}{P_Q}$ ratio exceeded narrowly 10%. Therefore, the two approaches, LEFM and NLFM, were applied at 23 °C despite most of the tests complied with the LEFM requirements. The normalization method described in ASTM E1820 standard [150] was followed to determine the J-R curve and the energy at crack growth initiation, J_IC, and the G_IC values provided by LEFM were also calculated.

Finally, Figure 5-19 includes the representative load-displacement records of the fracture test at 50 °C of SLS PA-12 at 0° and 90° orientations. The nonlinearity was so high that the application of NLFM approach was undoubtful and the normalization method was used to determine the J-R curve and J_IC values.

Figure 5-20 shows the evolution of the fracture toughness in terms of the stress intensity factor, K_IC, when computable, with the temperature, the load orientation for SLS PA-12 and the manufacturing technique. Firstly, all the values were in plane strain conditions. As expected, K_IC values decrease as the temperature increases in SLS PA-12. Regarding the effect of the orientation, the values of K_IC obtained at 90° orientation were lower than at 0° orientation. The values of K_IC at 23 °C computed in this investigation were comparable to those obtained by Seltzer et al. [31] and by Salazar et al. [39], but higher than those obtained by Linul et al. [46]. The discrepancy in this case has to do with the low density of the parts measured by the latter, correlated with the values of the manufacturing parameters employed.

Attending to the effect of the manufacturing technique at 23 °C, no differences between IM PA-12 and SLS PA-12 results were found.

Within the computation of the fracture parameters under the NLFM approach, Figure 5-21 and Figure 5-22 show the J-R curves at 23 °C and 50 °C of SLS PA-12 at 0° and 90° orientations, respectively. Firstly, the J-R curves at 50 °C were all above those at 23 °C independently of the load direction with respect to the layered structure. Secondly, for the very same temperature, the J-R curves of SLS PA-12 at 0° orientation were above and steeper than those of SLS PA-12 at 90° orientation.

To investigate the effect of the manufacturing process, Figure 5-23 compares the J-R curves at 23 °C of SLS PA-12 at 0° and 90° orientations with those obtained from IM PA-12. Firstly, regarding SLS materials, the energy needed to produce the stable crack growth at 0° orientation is higher than that at 90° orientation, being the latter less resistant against crack growth. Secondly, the J-R curves of IM PA-12 presented a high dispersion but in average the behaviour was in between that of SLS PA-12 at 0° orientation and that of SLS PA-12 at 90° orientation.

Table 5-6 collects the quantification of all these differences, more specifically, the values of the exponent N_J and of the parameter C_J of the potential law with the form $J=C_J\mathrm{\Delta }{a}^{N_J}$ which has been used to fit the experimental values. Firstly, the exponent N_J and the parameter C_J increased when the temperature increased at both orientations of SLS PA-12. Secondly, at the same temperature, the higher values of the exponent N_J of SLS PA-12 at 0° orientation in comparison with those of SLS PA-12 at 90° orientation confirm the trend observed graphically.

Finally, although IM PA-12 exhibits an average behaviour between that of SLS PA-12 at 0° orientation and that of SLS PA-12 at 90° orientation, the curves were more like those of SLS PA-12 at 90° orientation, implying similar N_j coefficients.

Figure 5-24 shows the energy at crack growth initiation, J_IC and G_IC, as a function of temperature, orientation for SLS PA-12 and processing technique at 23 °C. Regarding the effect of the temperature in SLS PA-12, there is an important increment in the J_IC values obtained at 50 °C, which nearly doubled those at 23 °C.

This behaviour can be explained considering that 50 °C is close to the T_g of the material (Table 5-4), so the viscous state plays a notable role in the fracture behaviour, requiring more energy for crack growth initiation.

It can be remarkable the similarity of G_IC and J_IC obtained at 23 °C for SLS PA-12 at 0° and 90° orientations, without statistical differences between them. Meanwhile at -50 °C and at 50 °C, the fracture energy of SLS PA-12 at 0° orientation is higher than that of SLS PA-12 at 90° orientation.

Finally, the values of G_IC and J_IC of IM PA-12 were higher than those of SLS PA-12, showing the best crack growth initiation resistance.

5.6.1 Fractographic analysis of fracture tests

Figure 5-25 and Figure 5-26 display the fracture surfaces obtained from fracture tests carried out at -50 °C, 23 °C and 50 °C of SLS PA-12 at 0° and 90° orientations, respectively. It is important to mention that all SLS PA-12 fracture surfaces presented defects in form of pores or unmolten powder particles.

Independently of the orientation, the morphology of the fracture surfaces at -50 °C (Figure 5-25.a and Figure 5-26.a) and at 23 °C (Figure 5-25.b and Figure 5-26.b) presented small differences. The characteristic feature is a patchwork pattern with more evident deformed borders at 23 °C. However, at 50 °C the degree of plastic deformation is more pronounced with presence of voids

However, at 50 °C the degree of plastic deformation is more pronounced with presence of voids through the ductile tearing of the amorphous filaments along the crack propagation direction (Figure 5-25.c and Figure 5-26.c). This fractographic analysis agrees with the fracture toughness values collected in Figure 5-24.

No differences could be detected between the fracture surfaces of the SLS specimens tested at 0° and 90° orientations at all the testing temperatures. This fact matches with the indistinguishable values of the fracture energy at both orientations, except for those at 50 °C (Figure 5-24).

The dominant failure mechanism is crazing, characterized by the nucleation of microvoids followed by their growth (Figure 5-27) and final coalescence, leaving behind craters with more or less stretched amorphous filaments. The evolution of this damage mechanism during crack growth advancement leaves the patchwork pattern previously described. As the temperature rises, the dimples associated with crazing can be less visible due to the high elongation of surrounding filaments along the crack propagation direction.

Comparing this fractographic morphology with the analysis carried out by Karger-Kocsis and Friedrich in injection molded polyamide 6.6 [80], the nucleation sites of the craze micromechanism could be related with defects as pores or unmolten particles as well as the crystalline structure.

Figure 5-28 shows the fracture surface of IM PA-12. In this case, the patchwork pattern is much finer and more homogeneous than that observed in SLS PA-12 (Figure 5-25 and Figure 5-26), and what is more, the fracture surfaces were free of unmolten particles or defects.

The finer size of the patch in the IM samples could be related to the small size of the crystalline structure (Table 5-3), together with the lack of processing defects, providing higher values of the fracture toughness (Figure 5-24). As stated by Salazar et al. [175], the decrease of the crystalline size favors the number and flexibility of the molecular chains in charge of holding together the lamellae bundles and consequently, improves the fracture energy. The reason is that the fracture toughness is governed, among other factors, by the energy required for the deformation and break of these tie molecules. Therefore, the higher the number of tie molecules, the higher the fracture energy.

5.7 Fatigue crack growth behaviour

Figure 5-29 shows the fatigue crack growth curves as a function of the control parameter $\mathrm{\Delta }\sqrt{G}$ of SLS PA-12 at 0° orientation (Figure 5-29.a) and at 90° orientation (Figure 5-29.b), and of IM PA-12 (Figure 5-29.c). The log-log plots of $\frac{da}{dN}$ versus $\mathrm{\Delta }\sqrt{G}$ graphs displayed in Figure 5-29 only shows region II, a linear relationship between the crack growth rate and the control parameter described by the Paris law (or eq. (2-2)) and region III, dependent on the fracture toughness K_IC as the crack growth rates approach instability. The reason is that these curves were achieved from constant load amplitude tests or $\mathrm{\Delta }\sqrt{G}$-increasing tests.

The figures show the common scatter due to extrinsic factors like the experimental ones, such as material and geometry variability or variation in the testing conditions, and intrinsic factors as the probabilistic nature of the fatigue phenomenon itself [176]. For the characterization of region I and the determination of the control parameter threshold value, ${\left(\mathrm{\Delta }\sqrt{G}\right)}_{\mathrm{th}},\mathrm{\Delta }\sqrt{G}$-decreasing tests were performed starting at a specific AVG level to guarantee some data overlap and consequently, to confirm the fatigue crack growth behaviour.

The experimental curves were fitted to equation (2-2) and the average values are shown in Table 5-7.

From the $\mathrm{\Delta }\sqrt{\mathrm{G}}$-increasing tests, the maximum values of the control parameter of the last cycle before catastrophic failure, $(\sqrt{\mathrm{G}}{)}_{\mathit{\text{max}},c}$, their equivalent values max,c in term of the stress intensity factor, K_max,c, and the fracture toughness, K_IC, determined from fracture tests and contained in Figure 5-20, have been also included to facilitate the analysis. Furthermore, the threshold values of the crack driving force, $(\mathrm{\Delta }\sqrt{G}{)}_{th}$, obtained from $\mathrm{\Delta }\sqrt{G}$-decreasing tests are also displayed.

Moreover, to shed more light to the study, Figure 5-30 gathers in one single diagram the fatigue crack propagation behaviour of SLS PA-12 at 0° and at 90° orientations and of IM PA-12. The characteristic dispersion of each material and condition has been represented with an envelope.

All this information reveals that the fatigue crack growth behaviour is very similar independently of orientation and manufacturing technique but there are some point differences worth mentioning. The effect of the load direction with regard to the layered structure of SLS PA-12 on the fatigue crack growth behaviour is obvious as SLS PA-12 at 0° orientation shows higher threshold values and smaller values of the exponent of the Paris law than those of SLS PA-12 at 90° orientation. Therefore, it can be concluded that the fatigue crack growth resistance is worse when the load is applied along the building direction, that is, at 90° orientation.

When analysing the influence of the manufacturing process, the threshold values of IM PA-12 are the smallest, but the steepness of the Paris law curve is similar to that of SLS PA-12 at 0° orientation. So, the fatigue crack growth behaviour of IM PA-12 is in between those of SLS PA-12 at 0° and at 90° orientations.

The region III of the fatigue crack growth life is characterized by the maximum value of the control parameter of the last cycle before rupture. Independently of the material or testing condition, the values were around 10% higher than the fracture toughness measured via standard fracture tests.

There is scarce literature regarding this topic in the literature. In principle, the exponents of the Paris law of SLS PA-12 are smaller than those obtained by Salazar et al. [39]. Nevertheless, it is worth mentioning that these authors employed ΔK as the crack driving force and the starting PA-12 powder and manufacturing machine were different to those used for the processing of the materials under study. Although Blattmeier et al. [124] analysed the influence of the load direction with respect to the layered structure in SLS PA-12, they observed no differences in the fatigue crack propagation of specimens tested at 0° and 90° orientations. And their curves are difficult to compare to those in the present work because firstly, the control parameter is ΔK and there are no fitting values to a Paris-law equation and secondly, those curves were not obtained under constant load amplitude tests. Finally, the only works focused on the fatigue crack propagation of IM PA-12 are those of Blattmeier et al. [124] and Boukhili et al. [79]. The former obtained a fatigue crack growth behaviour of IM PA-12 clearly worse than that of SLS PA-12 and the latter realized that ΔK is not a valid crack driving force and also did not include the fitting values of the Paris-law equation.

5.7.1 Fractographic analysis from fatigue crack growth tests

The panoramic view of the fracture surfaces of SLS PA-12 at 0° and 90° orientations and of IM PA-12 are displayed in Figure 5-31.a, Figure 5-31 .b and Figure 5-31 .c, respectively. The arrow indicates the crack growth direction.

Firstly, the most characteristic feature of the fracture surfaces of SLS PA-12 is the high number of pores evenly distributed over the entire surface (Figure 5-31.a, Figure 5-31 .b). According to Caulfield et al. [33], these pores are the result of the lack of powder particles melting during sintering, producing a poor fusion in the surrounding area. Another important feature is the discernible horizontal lines with an equidistant separation of 200 pm observed in the low magnification analysis of the fracture surfaces of SLS PA-12 at 0° orientation (Figure 5-31.a). This distance matches with the manufacturing layer thickness (Table 4.2) so, the sintering among layers was defective as the fusion and sintering of one layer with the one underneath was not complete. Some authors have associated these lines with a low energy density supplied during the manufacturing process [33], [37].

Secondly, when comparing the 0° and 90° orientations, the fracture surfaces obtained at 90° orientation (Figure 5-31.b) was much smoother than that at 0° orientation (Figure 5-31.a). The crack tends to propagate along one single layer but when a coalescence of pores or defects occurs, this can lead to the jump of the crack to adjacent layers. This could explain the worse fatigue crack propagation at 90° orientation.

Thirdly, the panoramic view of the fracture surfaces of the IM PA-12 samples is completely smooth and plain, a striking contrast when compared to the morphology of SLS PA-12 (Figure 5-31.c).

In order to identify the deformation and fracture mechanisms, Figure 5-32.a , Figure 5-32.b and Figure 5-32.c show detailed fracture surfaces of SLS PA-12 at 0° and 90° orientations and of IM PA-12, respectively. Independently of the manufacturing technique or the orientation, the mechanism of deformation and failure is the formation, growth and coalescence of crazes, followed by a fibrillation of the amorphous phase till final rupture.

This type of damage progression leaves as marks the patchwork pattern displayed in Figure 5-33, being the only difference, the size of the craters and the more or less plastic deformation of the amorphous filaments surrounding them. In general, the stretched amorphous filaments are the most prominent in the SLS PA-12 at 0° orientation (Figure 5-33.a), less significant in the SLS PA-12 at 90° orientation (Figure 5-33.b) and not so remarkable in IM PA12 (Figure 5-33.c).

It is in these deformed amorphous filaments where fatigue striations were observed (Figure 5-34), being less numerous in the IM PA-12 (Figure 5-34.c) compared with SLS ones (Figure 5-34.a and Figure 5-34.b).

Therefore, the rough fracture surface (Figure 5-31.a, and Figure 5-32.a) together with the high deformed amorphous filaments in SLS PA-12 at 0° orientation (Figure 5-34.a) seems to be the reason of the best fatigue crack growth behaviour.

A more in-depth analysis of the nucleation and progression of the mechanism of failure during fatigue could be performed thanks to the fractographic analysis at high magnification shown in Figure 5-35.

In this patchy surface, pores and in most cases, some unmolten particles at the centre of the craters are observed and shown with white arrows pointing at the particles in Figure 5-33.b and Figure 5-33.c for SLS at 90° orientation and for IM PA-12, respectively, and in Figure 5-35. These defects act as nucleation sites during the crazes formation being not the only responsible of the failure initiation. The crystalline structure plays an important role in the initiation damage during cycling loading as pointed out by several authors [162], [177], [178].

During fatigue, the high deformation occurring at the crack tip is the origin of void nucleation between the crystalline lamellae within the spherulite, oriented perpendicularly or at angle of approximately 45° to the applied load direction [177]. This leads to an intra-spherulitic or trans-spherulitic failure in the equatorial plane, exposing in some occasions the nucleus of the spherulite, which has the appearance of an irregular rectangle (pointed out by a blue in Figure 5-33.b and Figure 5-35.b) or an ill-defined disc (pointed out by a blue arrow in IM PA-12 in Figure 5-33.c and in Figure 5-35.a).

Some authors have linked the dimensions of the patchwork patterns with the spherulite sizes. In this case, the crater size was around 50 pm for SLS PA-12 and 20-30 pm for IM PA-12 which is coincident with the spherulitic dimensions collected in Table 5-3. The bigger discrepancy was in IM PA-12. However, the fractographic analysis has shown that in IM PA-12, the damage was related with the spherulitic structure in a way that the micromechanism of failure is linked not only to individual spherulites but also to spherulite colonies when the former are extremely fine.

5.8 Fatigue life analysis

The results of the fatigue life tests carried out according to the ASTM D7791 standard recommendations are presented in the Figure 5-36. The tensile strength represented as the value at one cycle was also included, as well as the tests which reached 10⁶ cycles without failure (run-outs). A first look at the graph evidences not big differences between either distinct orientations or manufacturing processes. Nevertheless, some dissimilarities are important to highlight.

SLS PA-12 at 0° orientation exhibited better fatigue life resistance than at 90° orientation despite the similarity in the porosity percentage (Table 5-1) and in the surface roughness values (Table 5-2). The weak interlayer strength seems to be behind this behaviour, as the defective sintering among layers as well as its physical discontinuity has been observed in the fractographic analysis (Figure 5-31.a).

Attending to the manufacturing process, IM PA-12 presented a mixed behaviour, that is, showed a better fatigue resistance than SLS PA-12 at both orientations near 10⁶ cycles but a lower fatigue life resistance when the number of cycles to break was around 10⁵. At those number of cycles, the behaviour of SLS PA-12 at 0° orientation is above that of IM PA-12.

In order to fit these results to the Basquin’s equation, the average values of the number of cycles to failure for each load level were considered and represented in Figure 5-37. Attending to the values of the R² coefficient resulting from the fitting of the experimental values to the Basquin’s law (eq. (4-28)), the scatter for all materials and conditions was in general very high, especially for SLS PA-12 at 90° orientation.

Table 5-8 gathers the Basquin coefficients of SLS PA-12 at 0° and 90° orientations and of IM PA-12. While the exponents of m_b of SLS at both orientations were similar, there is a big difference with that of the IM PA-12 which was one half.

For the determination of the fatigue limit at 10⁶ cycles, Figure 5-38.a, Figure 5-38.b and Figure 5-38.c show the up-and-down fatigue test results of SLS PA- 12 at 0° orientation, SLS PA-12 at 90° orientation and IM PA-12, respectively. These graphs represent the run-out tests with a green circle and the failure tests with a red cross. In order to obtain more accurate results, in case of SLS PA-12 at 0° orientation, after 6 tests, the initial stress step between run-out and failure was reduced to one half of the initial value, followed by a second reduction of a 2.5 % of the initial value, analysing a total of 5 stress amplitudes. For SLS PA-12 at 90° orientation, only a first reduction of the step from 2.5%σ_T to 1.25%σ_T was implemented, with a total of 4 stress amplitudes. In case of IM PA-12, two step reductions were carried out, beginning with the first one of 11.5%σ_T and followed by a second one of 2.5%σ_T. The total number of stress amplitudes examined were 6.

Table 5-9 displays the fatigue lifetime results used in the estimation of the fatigue limit at 10⁶ cycles for both orientations of SLS PA-12 and of IM PA-12. It shows the number of failure tests, the number of “Run-outs” tests for each stress level, Δσ_i, and the fatigue limit at 10⁶ Cycles, Δσ_fl, resulting from the application of the maximum likelihood method assuming a normal distribution, as described in the previous chapter.

SLS PA-12 at 0° orientation had a statistical fatigue limit at 10⁶ cycles 13% higher than the one at 90° orientation. However, IM PA-12 had the highest fatigue limit, being 8% higher than the one of SLS PA-12 at 0° orientation.

5.8.1 Fractographic analysis of fatigue life tests

A panoramic view of the fracture surfaces of SLS PA-12 at 0° and 90° orientations and of IM PA-12 are shown in Figure 5-39.a, Figure 5-39.b and Figure 5-39.c, respectively. The white arrow indicates the crack growth direction on each specimen and, in all cases, the cracks propagated from the left side of the images to the right. It is obvious the influence of the manufacturing technique on the fractographic analysis of the broken specimens tested for the stress life fatigue curves characterization. While the fracture surfaces of SLS PA-12 maintained the initial cross-sectional dimensions, all the IM PA-12 fracture surfaces undergone a strong reduction of the initial cross section area despite the testing conditions were under High Cycle regime.

Moreover, while in all SLS PA-12 fracture surfaces three different areas were distinguishable and outlined by three different colours over the surfaces, in IM PA-12, only two zones were discernible. For all the cases, the zone delimited by the dashed green line is the subcritical crack growth area, which is followed by a transition region outlined in dashed blue line (only observed in SLS PA-12), and finally, the unstable crack growth region delineated in dashed red line.

For SLS PA-12, the subcritical area was characterized by a patchy irregular surface, unequivocal morphological sign of nucleation, growth and coalescence of crazes in both the early stages of formation of the macroscopic crack and subsequent propagation. The crater size of the marks left by this damage advancement was of around 50 μm, which matches with the spherulitic size determined in section 5.3 (Figure 5-40). This fact revealed a hampered crack growth due to the presence of spherulites in a trans-spherulitic growth mode. Therefore, the crack was nucleated at some point of the surface, favoured by the high roughness (Table 5-2), and once generated progressed through the spherulites and in many cases, going through their equatorial plane. This mechanism of failure was also observed in the fracture surfaces of SLS PA-12 obtained from tensile tests (section 5.5.1), from fracture toughness tests (section 5.6.1) and from fatigue crack growth tests (section 5.7).

The only difference between 0° and 90° orientations in SLS PA-12 was that this area seemed to be rougher in the samples tested at 0° orientation that in those tested at 90° orientation.

In case of IM PA-12, the crack also nucleated at some point at the surface, belonging to the skin layer due to the presence of small sink marks (Figure 5-39.c). The morphology of the subcritical crack growth area is completely different to that observed in SLS PA-12, characterized by fatigue striations bowed out in the direction of the crack propagation (Figure 5-41). The fatigue striations spacing became larger as moving away from the surface defect responsible of the crack nucleation.

In SLS PA-12, following the subcritical crack growth zone, a transition region, was observed and outlined in dashed blue line in Figure 5-39.a and Figure 5-39.b, and shown in detail in Figure 5-42. This region was characterised by a high ductile tearing of amorphous filaments around dimples, which in some cases could be hidden by the plastic deformation. The amorphous filaments were aligned along the crack propagation direction and fatigue striations were only observed on them (Figure 5-43). No differences were appreciated between SLS PA-12 at 0° and at 90° orientations. Moreover, the transition region was not observed in none of the fracture surfaces of IM PA-12.

In SLS PA-12, following the transition region, the unstable crack growth region, outlined in dotted red line in Figure 5-39.a and Figure 5-39.b was found. The border between these two regions was continuous (Figure 5-44.a) and the morphology was plain, with an irregular pattern and with no trace of distinguishable elongation of amorphous material (Figure 5-44.b). No differences in this zone were discernible between both orientations in SLS PA-12.

Finally, Figure 5-45 shows a detail of the unstable crack growth zone of IM PA- 12 outlined in dotted red line in Figure 5-39.c. The surface was smooth and plain with no characteristic feature except for some very fine river markings along the crack growth direction.

5.8.2 Application of the Fracture Mechanics approach to the fatigue life tests

The fractographic analysis of the broken specimens revealed a scheme of the damage progression till catastrophic failure occurring during the fatigue life tests. The nucleation of the crack occurred at some point at the surface, as a consequence of the high roughness in SLS PA-12 specimens or of the amorphous skin layer in IM PA-12 samples. The crack propagation occurred till reaching a critical value, coincident with the extension of the subcritical crack growth zone, a. At that moment, brittle failure occurred at the remnant ligament, giving rise a plastic deformation zone at the crack tip (transition region) followed by an undamaged polyamide (unstable crack growth zone) in SLS PA-12. However, in IM PA-12, only unstable crack growth area was observable but with evident plastic deformation along the gage length of the sample due to a pronounced reduction of the initial cross-sectional area. Just because the non-negligible plastic deformation along the gage length in IM PA- 12, damage modelling using the Fracture Mechanics approach was only applied to SLS PA-12 at 0° and 90° orientations.

From the sketch of the different zones delineated in Figure 5-39.a and Figure 5-39.b, the fatigue life specimens with the subcritical crack growth area could be fitted in with SENT configuration at the instant of failure. So, the results obtained from the application of the Fracture Mechanics approach using data from the last cycle are shown in Table 5-10 and Table 5-11 for SLS PA-12 at 0° and 90° orientations, respectively.

From the analysis of the results, several points are remarkable and worth discussing. Firstly, a common trend can be observed for both orientations, the length of the subcritical crack growth is lower as the applied stress level increases. Secondly, the estimated energy at crack growth initiation values are in accordance with those achieved in standardized fracture tests shown in section 5.6 for both orientations. Nevertheless, some deviations were obtained in SLS PA-12 at 0° orientation for the high stress levels of 0.8 and 0.85. For these testing conditions, the estimated values of Jc were extremely high and were not included in the computation of the average value displayed in bold in Table 5-10. To ascertain the possible reason of these overestimated values of Jc at those stress levels, the hysteresis loops of the last cycle before failure were examined. Figure 5-46 shows the hysteresis loops of the last cycle before failure of the fatigue life tests carried out at stress ratios of 0.7 and 0.85 of SLS PA-12 at 0° orientation. The main difference is that, while for the stress ratio of 0.7, the loading and unloading parts of the cyclic load-displacement record overlap, for the stress ratio of 0.85 an area within the loop is noticeable. This area represents dissipative energy per unit of volume due to viscoelasticity and/or plasticity, which can be the reason of the overestimation of the fracture parameters.

Another method to check the validity of the results is to determine the crack length from the unloading part of the load-displacement record of the last cycle using the following expression for SENT configuration [179]:

$$\begin{array}{rl}\frac{a}{W}=2.072& -16.411U+29.6U^2-211.67U^3\\ & +236.857U^4+27.371U^5-179.74U^6\\ & -86.28U^7+171.764U^8\end{array}$$

with U the normalized compliance obtained from the unloading part of the cyclic load-displacement record using equation (4-24). The calculations yield results which differed from the measured lengths of the subcritical crack growth zone in Table 5-10 utmost 20% for stress level lower than 0.8 and more than 90% for stress level higher than 0.80.

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