The mechanical performance of PA-12 processed by SLS has been evaluated mainly by tensile tests and fracture toughness tests. Table 2-1 collects the tensile properties such as the ultimate tensile strength, the elongation at break and the Young’s modulus of SLS PA-12 measured by different authors. The processing parameters, when provided by the authors, are also included, as the mechanical performance is strongly dependent on the resulting microstructure which is governed by the values of the fabrication parameters. The table also incorporates the values given by the two main manufactures of PA-12 for SLS as PA 2200 by EOS [28] and DuraForm PA [29], as well as those obtained from the conventional technique as injection moulding (IM). In general trends, the values of the tensile strength and the Young’s modulus of SLS PA-12 are very similar to those of IM PA-12, except for the elongation at break. In this case, the elongation at break of IM PA-12 is almost one order of magnitude higher than that of SLS PA-12. The main factors behind these differences are the processing parameters that control the SLS technique, the intrinsic anisotropy of the layer wise SLS manufacturing process or the hygroscopic nature of the polyamide.

Among the manufacturing parameters of the SLS technique, the supplied energy density (dependent on the laser power, laser scan spacing, laser beam displacement velocity and laser radius) has shown a great impact on the microstructure and crystalline features and consequently, on the mechanical performance of SLS PA-12. Dupin et al. [37] showed that the increase in the energy density decreases the porosity and nascent polyamide particles and increases the recrystallized fraction, implying higher mechanical properties. Similar results were obtained by Caulfield et al. [33] and by Stichel et al. [34].

The latter evaluated the tensile parameters of PA-12 sintered by different machines and then, different parameter sets optimum for the respective machine.

Another relevant factor is the intrinsic anisotropy induced by the stacking layer SLS process and there are many authors that have evaluated the mechanical response as a function of the applied load direction with respect to the layered structure. Hooreweder et al. [30] compared the tensile results of PA-12 manufactured by SLS obtained when the applied load was applied along the scanning direction and perpendicular to the scanning direction with the results obtained from IM PA-12. For SLS parts, the main difference between the two orientations was found in the elongation at break which was lower when the load was applied perpendicularly to the layered structure. Regarding the effect of the manufacturing technique, the SLS specimens showed a more brittle behaviour than IM but higher Young’s modulus. The same trend was obtained by Caulfield et al. [33], Stichel et al. [34] and Lammens et al. [36].The latter also analysed the effect of the different machine cross-head displacement rates (5, 50 and 500 mm/min) on the tensile properties, registering higher stiffness at higher displacement rates accompanied with lower elongation at break. On the other hand, the results obtained by Starr et al. [35], which tested six different orientations, revealed small differences in the mechanical properties among the distinct orientations, although the lower elongation at break was also found when the load was applied perpendicularly. In all the cases, the low elongation at break along the building direction was related to layer adhesion, very sensitive to process conditions. Some authors have analysed the effect of the hygroscopic nature of the SLS PA-12 on the mechanical performance. Seltzer et al. [31] studied the effect of humidity on SLS PA-12, obtaining an adverse effect of the hydrothermal aging on the mechanical properties, specifically, for water saturated specimens, with a reduction in strength, in the Young’s modulus, and in ductility. Similar results were obtained by Goodridge et al. [32] in their study comparing the effect of the storage conditions and length of time of SLS PA-12 and IM PA-12, except for the elongation at break which in water conditioned samples presented higher values than those of the dry specimens. In addition to the detrimental effect of humidity in PA-12, the SLS PA-12 showed better water resistance than IM PA-12. Besides, tensile testing at temperatures that ranged from -40 °C to 140 °C were performed on specimens with distinct humidity conditions and in all the cases, SLS samples held the strength better than IM specimens.

The research on the fracture behaviour of SLS PA-12 using the Fracture Mechanics approaches are not so prolific as those dealing with the tensile properties. Table 2-2 collects some of the most representative works found in the literature addressing the influence of different factors, such as the anisotropy due to the layered structure, the hygroscopic nature of polyamides or the processing parameters, on the fracture toughness of PA-12. Together with the values of the fracture parameters in terms of the mode I critical stress intensity factor, K_IC, or the energy at crack growth initiation, J_IC, the values of the manufacturing parameters are also included as their knowledge can shed more light on the results. Hitt et al. [38] compared the fracture behaviour of SLS and IM PA-12 parts as a function of the specimen thickness. The results were in contradiction in the sense that while for IM specimens, the energy at crack growth initiation decreased as the specimen thickness increased, the opposite trend occurred for SLS samples. The reason of this anomaly could be in the computation of the fracture parameters through the Linear Elastic Fracture Mechanics (LEFM) approach, despite the well-defined non-linear behaviour shown by the materials. Seltzer et al. [31] analysed the effect of water conditioning on the fracture behaviour of neat PA-12 and PA-12 composites reinforced with glass beads and short ceramic fibres. The reinforcement implied both a better fracture behaviour and a better water resistance. Salazar et al. [39], [40] investigated the effect of the temperature (23 °C and -50 °C) and the hygrothermal ageing on the fracture toughness of neat PA-12 and PA-12 filled with short ceramic fibres. In the case of the neat PA-12, the fracture toughness was not affected by the testing temperature but in case of the composite, the fracture toughness values at -50 °C were higher than at room temperature. In the specimens saturated in water, the fracture toughness showed an important impoverishment of up to 50%. Brugo et al. [41] evaluated the influence of the notch sharpening method and of the load direction with respect to the building direction. Regarding the notching technique, no differences on the fracture toughness values were obtained between the specimens notched by pressing a razor blade into the notch and those with a 0.3 mm in thickness notch generated during the SLS manufacturing process. Nevertheless, none of these techniques provided a sharp crack with no damage at the crack front which guaranteed quality fracture toughness values [42], [43]. In case of evaluating the orientation, the fracture toughness of the specimens loaded perpendicularly to the layers was lower than when the load was applied along the layers.

The effect of the load direction with respect to the layered structure on the fracture parameters of SLS PA-12 was also studied by Crespo et al [44], [45], Linul et al. [46], Schneider and Kumar [47] and Stoia et al. [48]. The former inferred the fracture toughness from the fracture of notched samples through the application of the theory of the critical distances. The fracture toughness of the specimens loaded parallel to the layered structure was also higher than for the specimens loaded perpendicularly. The same authors [44], [45] analysed the influence of the strain rate on the fracture toughness following the same methodology, carrying out tests that ranged from quasi-static conditions in electromechanical machines to very high strain rates attained by Hopkinson bar tests. On the other hand, Linul et al. [46] inspected the effect of the process energy density on the mode I and mode II fracture toughness evaluated on specimens loaded at different directions with respect to the layered structure. As expected, the fracture behaviour of the specimens processed with higher applied energy and loaded parallel to the layered structure was the best, unequivocal sign that the higher applied energy implied higher density and consequently, less defects. Moreover, the interlayer adhesion is still a limiting factor as the authors observed the crack growth tended to occur along the layer bonding interface. Schneider and Kumar [47] determined under plane stress conditions the fracture toughness as a function of the load direction with respect to the layered structure, finding no relevant differences between the parallel and perpendicular orientations. Finally, Stoia et al. [48] studied the effect of the geometrical defects introduced during sintering as well as the load direction on the fracture toughness. In case of defect-free specimens, there was an important anisotropy in the fracture toughness, with values of the specimens tested with the load applied perpendicular to the building direction more than twice those obtained from tests with the load applied along the building direction.

The fatigue performance of polymers due to cyclic mechanical loads is commonly characterized by the stress-life or the S-N curves [49]. The approaches established for metals have been used to define the mechanisms of fatigue initiation [50] and crack growth [51] in polymers. The reason is that the majority of fatigue data of stress-life curves and fatigue crack growth curves of polymeric materials appear significantly similar in shape to those found in metals, despite their different microstructure and chemical makeup. At present, there is no physical theory to explain the mechanical S-N behaviour of polymers. Notwithstanding, the S-N curves, where the cyclic stress amplitude is plotted versus the failure cycles, are fitted to Basquin’s empirical equation [52], useful for engineering practice although this empirical relationship does not represent well the entire fatigue data range.

Fatigue failure in polymers can occur by thermal fatigue or by mechanical fatigue [53]. In the former, failures occur by thermal softening and melting due to massive hysteretic heating while in the latter, fatigue crack initiation and stable crack propagation to fracture take place similarly to metals.

Thermal fatigue failure normally occurs due to extrinsic factors such as relatively high loading frequencies or strain rates, where thermal softening due to hysteretic heating arises from the viscoelasticity, high damping and low conductivity typical in polymers [54]–[56]. The hysteretic energy is dissipated as heat producing a rise in specimen temperature [57] and, consequently, loss of stiffness [58]–[60]. The temperature rise is very dependent on the frequency because the hysteresis arises from the phase lag between stresses and strains in the polymer, which is larger as the loading frequency is higher.

As a rule, the influence of test frequency on the fatigue response of polymers originates from the viscoelastic behaviour of polymers. An increase in frequency normally involves a greater energy dissipation and temperature rise. Nevertheless, in low frequency test conditions where thermal effects are not crucial, an increase in frequency leads to increase in modulus and strength due to increased strain rate, implying an increased fatigue life as observed in Polypropylene (PP) and Polypropylene reinforced with short glass fiber by Eftekhari and Fatemi [60] and in Polystyrene (PS), High Impact Polystyrene (HIPS) and Acrylonitrile Butadiene Styrene (ABS) by Sauer and Chen [61].

In fatigue crack growth behaviour of polymers, the thermal effects are localized at the crack tip, leading to crack tip blunting and consequently, increasing the fatigue resistance to crack growth. These effects were observed in PS [62], Polymethyl Methacrylate (PMMA) [63] and Polyvinyl Chloride (PVC) [64] but not in Nylon [65] and Polycarbonate (PC) [64] in which the crack growth curves were independent of frequency in studies performed in the range from 1 Hz to 100 Hz. Nevertheless, in these studies the crack growth behavior was correlated on the basis of Linear Elastic Fracture Mechanics (LEFM) approach, using as control parameter the stress intensity factor range, ΔK, even at frequency up to 100 Hz, doubtful parameter if excessive thermal softening occurs.

Regarding mechanical fatigue failure, Sauer and Richardson [51] stated that true mechanical fatigue failure, involving initiation and growth of fatigue crack under cyclic loading takes place in the range between one-fourth and one-half of the yield strength of the polymer. The macroscopic description of fatigue fracture in polymers is formed by the sequence of mechanical events similar to those in metals [49]–[51], [66], [67]. In glassy polymers, the initiation occurs by the development of a single craze at some surface location while in semicrystalline polymers, it takes place at spherulite boundaries after some fatigue cycles. Thereafter a fatigue crack is generated within the craze, by cyclic fracturing the fibrils farthest from the initial craze tip, and the advancement of the macroscopic crack growth, either continuously or discontinuously under cyclic loading, till the point of rupture is not any different in glassy or semicrystalline polymers. Purely mechanical fatigue failures normally occur in the absence of thermal effects, that is, at low frequency conditions.

Finally, fatigue behaviour of polymers is also influenced by the environmental temperature because some polymers undergo crystallization or brittle-ductile transition as the temperature is increased [49]-[51], [66], [67]. The fatigue resistance is reduced with increased temperature due to alteration of the crack tip deformation and fracture mechanisms [25], [68]-[70], the reduction of the tensile strength and the fatigue limit as the test temperature is increased [25], [60], [67], [71] or the temperature-dependent variation on the viscoelastic deformation of the polymer [25], [60], [72].

The proofs provided by the literature allows the use of the continuum fatigue behaviour tools of metals for describing the mechanical fatigue response of polymers. The S-N curves obtained under mechanical fatigue conditions usually exhibit the asymptotic approach toward the tensile strength at one fatigue cycle and the asymptotic flattening at the fatigue limit (the physical stress limit below which no fatigue failure occurs), as in the case of metals. Nevertheless, there are some gaps or difficulties in the fatigue characterization of polymers. In case of the stress-life, there is not an accepted physical theory capable of constructing the shape of the S-N curves. Some attempts were made by Baltenneck et al. [73], who derived a kinetic S-N curve based on the cumulative evolution of micro-defects till the point of fatigue rupture. The predicted curves agreed partly well with the experimental ones despite the physical basis assumed that the number of cycles to failure increased with initial defect concentration. Williams et al. [74] developed an equation for fatigue crack growth life considering a fatigue crack growing to reach the point of unstable failure. Although it predicted fatigue lives reasonably well, some parameters were chosen arbitrarily and was not applied to describe S-N curves of plain specimens. Shojaei and. Wedgewood [67] developed a model within the Continuum Damage Mechanics framework to enhance the life prediction capabilities of polymers. Considering that in the Low Cycle Fatigue regime, damage can be modelled by microvoid nucleation and propagation and that in High Cycle Fatigue regime, damage can be described by initiation and propagation of microcracks, plasticity and creep laws were coupled in fatigue Finite Element Analysis. Although the results were promising, the computation cost and the update of the damage fatigue history was an important difficulty. The most elaborate theory is that of Ravi Chandran [25] who, in the absence of thermal effects and starting from the macroscopic crack growth mechanisms, derived a continuum-based fatigue theory capable of predicting the effect of the mean stress and the temperature on the shape of S-N curves significantly well. He developed the constitutive equation for polymer fatigue assuming that the increase in stress in the uncracked ligament is responsible for the acceleration of the crack growth during fatigue, consistent with the experimental findings in metals of Frost, Dugdale and Weibull [75]-[77], whose works predate that of Paris [78]. However, more experiments with controlled changes in the structural and microstructural parameters as well as in the mechanical properties of polymers are needed to fully validate the proposed theory.

Regarding the fatigue crack growth behaviour of both glassy and semicrystalline polymers, LEFM approach has been mostly used to describe the crack growth rate as a function of the stress intensity factor range, ΔK = K_max − K_min [49], [79]-[86]. However, some works have questioned the validity of ΔK when dealing with the R-ratio effect [50], [87]-[94]. Rink et al. [92], Furmanski and Pruitt [93] and Boonyaookana et al. [94] observed that the crack growth propagation curves seemed to be unaffected by R-ratio when the crack growth rate was correlated with K_max. In contrast, Takemori [50] and Radon [89] showed an uncommon trend as the decrease in the crack growth rate, dadN, with the increase in the R-ratio when using either ΔK or K_max as crack driving parameters. This fact motivated the choice of energy release rate range, ΔG, [88], [95], [96] or the maximum energy release rate, G_max [97] as the crack driving force when brittle crack growth propagation was observed. Particularly, Sutton [88] employed ΔG in the analysis of fatigue crack growth propagation in epoxy polymers achieving the collapse onto one single master curve of the fatigue crack growing data obtained at different R-ratios. However, he also realized that this behaviour could not be extrapolated to all polymers.

The uncertainties on the predominant process involved at different R-ratios in polymers has driven to some researchers to consider two different crack driving forces to describe the fatigue crack growth rate as a function of the mean stress, applying the crack closure concept introduced by Elber [98] at low R-ratio and taking into account the creep process that seems to occur at high R-ratios [87], [89], [91], [93].

Cano et al. [99] proved the validity of ΔG=Gmax−Gmin with G_max as the maximum energy release rate and G_min as the minimum energy release rate, as a valid similitude parameter for describing the crack growth behaviour of glassy polymers, overhauling the gaps previously mentioned. ΔG relies on the same basis for similitude as ΔK, and is defined as:

where ΔP is the amplitude load of the cycle, B is the specimen’s thickness, C is the sample’s compliance and a is the crack length. Therefore, the crack growth rate, dadN, was correlated with this similitude parameter through a Paris-type relationship:

with N the number of elapsed cycles and A and n material’s constants.

ΔG parameter was proposed by Rans et al. [100] for adhesive joints and composites. The difficulty in the fatigue crack growth behaviour of these materials was that ΔK describes locally the stress field and this makes it unsuitable in fibre-reinforced polymer matrix composites and bonded joints. That was the reason of the widespread use of ΔG as crack driving force parameter [101]-[106].

However, the main concern of ΔG is that it could not be considered as a valid similitude parameter due to its dependence on the mean load of the cycle, P_med:

where P_max and P_min are the maximum and minimum loads of the cycle.

ΔG has been applied with more or less success in polymers, composites and adhesive joints as the R-ratio effect is still evident in many cases [99], [100], [107]–[111].

As previously mentioned, SLS PA-12 stands out for covering specific requirements for various applications in the automotive and aeronautical industries [26], [112]-[115]. In these applications, parts made of this material must have sufficient fatigue resistance to meet the in-service loading and operational performance as they are submitted to dynamic loading either applied directly or indirectly through the interaction of the entire structure with the surrounding environment [26], [114], [115].

Regarding the stress-life performance of SLS PA-12, Table 2-3 collects some of the most representative works in which the processing parameters (when provided), testing conditions and main results are summed up. Van Hooreweder et al al. [30], [116], [117] analysed the influence of the frequency (1 Hz and 3 Hz) and the building direction on the S-N curves at a stress ratio, R, of -1. They obtained that the building orientation had no influence on the fatigue properties and the thermal fatigue failure was attained at certain combination of high stress amplitude and test frequency. Besides, they also analysed the fatigue behaviour of notched samples and compared the results obtained from specimens processed via SLS and IM. Regarding the notch effect, the fatigue resistance of notched samples was better than that obtained from plain specimens, attributable to the reduced thermal load in the former. In case of the effect of the processing technique, no difference in the fatigue resistance was observed between the two manufacturing techniques [30]. Munguia and Dalgarno [118] obtained the SLS PA-12 fatigue behaviour in both reversed and rotating bending (R=-1), showing an isotropic response (no influence of the load direction with respect to the layered structure) in terms of the fatigue behaviour for both testing configurations. They also analysed the influence of the frequency (30 Hz and 50 Hz) in four point rotating bending fatigue tests, evidencing lower fatigue response at high frequency [119]. Moreover, they estimated a fatigue limit of 14 MPa, although no standard or recognized methodology was followed to attain this value. Amel et al. [120] investigated the effect of the geometry (thickness) on the fatigue behaviour explored through S-N curves obtained under displacement-controlled tension-tension (R>0) and force-controlled fully reverse fatigue loading (R=-1). The tests carried out in Low Cycle Fatigue regime evidenced creep as the main mechanism of failure. Schob et al. [121] followed the damage evolution through X-ray refraction, computed tomography and temperature rise under cyclic loading (fatigue tests at 3 Hz and R=-1) with the aim of finding the parameters of the Chaboche material model and the Gurson-Tvergarard-Needlemen damage model. Finally, Kim et al. [122] studied the effect of the shape and size of geometrical defects induced during sintering on the fatigue life. Evidently, the fatigue response impoverished with the increase in size of the defects and the authors applied the Castillo-Canteli-Siegele model [123] extended with the cyclic J-integral to predict the fatigue life of the specimens with induced geometrical defects.

Concerning the fatigue crack growth behaviour of SLS PA-12, Table 2-4 gathers the main results of the papers found in the literature dealing with this issue. Once more, for a proper comparison of the results in the literature, the processing parameters, when provided by the authors, are included. As observed, there is scarce literature in this topic. Salazar et al. analysed the effect of the temperature and the short glass fibre reinforcement and the hygrothermal ageing on the fatigue crack growth response of SLS PA-12 [39], and also determined the differences in the fatigue crack growth behaviour of petrol-based SLS PA-12 and bio-based SLS PA-11 [40]. The fatigue behaviour of the SLS PA-12 was similar at room temperature and at -50 °C but the reinforced material presented an improved fatigue crack growth behaviour at low temperature in comparison with the neat PA-12. The reason was the predominant crack tip bridging mechanism in the composite against the brittle intergranular fracture in the neat PA-12 [39]. On the other side, when comparing the fatigue performance of the bio-based PA-11 versus the petrol based PA-12 processed via SLS, the former presented better fatigue crack growth behaviour than the latter at both 23 °C and -50 °C. Once again, the reason was the fatigue failure, while in PA-11 the mechanism was ductile through cavitation, void growth and coalescence, in PA-12 the dominant mechanism was brittle crazing [40]. Under water conditions, the fatigue response worsened abruptly due to the reduction in crystallinity and molecular weight by hydrolysis, resulting in embrittlement [40]. Despite the inherent anisotropic nature of the stratified SLS process can suppose a major limitation, only Blattmeier et al. [124] have treated this issue, attaining no concluding results. Moreover, in this work the fatigue crack growth behaviour of SLS and IM processing techniques obtained through a load increase method is compared and the influence of the surface finishing is tackled. In case of the processing technique, there seemed to be a slight better performance on the fatigue response of the SLS specimens in comparison with the IM samples while the surface finishing seemed to have no significant influence. Finally, Boukhili et al. [79] studied the fatigue crack propagation behaviour of injection moulded PA-12 and the influence of the test frequency, load waveform, specimen configuration and thickness and the material orientation, that is, the material response depending if the load direction was applied parallel or perpendicularly to the injection flow direction. The most interesting result obtained by these authors was that ΔK was not an appropriate crack driving force to describe the fatigue crack propagation of polyamides. They also concluded that the fatigue crack growth behaviour was evidently dependant on the load wave form, the specimen configuration and thickness and above all, of the frequency.

Despite the theoretical densities provided by the manufacturers, the experimental ones were measured in the specimens produced. The density of the pieces was determined experimentally measuring 5 specimens of each geometry in a precision balance Mettler Toledo AX205 DeltaRange^®, which has a resolution of ± 0.00001 g. Following the Archimedes principle, each specimen was introduced in a beaker with a known immersion medium and measuring the amount of displace fluid. The density of the sample, ρ, is given by the following expression:

where W_air is the weight of sample in air, W_im is the weight of sample in the immersion medium, ρ₀ is the density of the immersion medium and ρ_L the density of air (0.0012 g/cm₃). Due to the nearness of the expected PA-12 density to that of distilled water, commonly used as immersion medium, which is ρ₀ = 0.99782 g/cm³, acetone was also employed as immersion medium in this case, with p₀ = 0.787 g/cm³. The closed porosity of each batch was calculated in reference to the theoretical bulk density value of 1.02 g/cm³ of the PA-12 [137]. Five replicas were measured for each material and condition.

Surface roughness was measured using a roughness tester Mitutoyo SJ-301 equipped with a detector whose tip had a radius of 60 μm and a tip angle of 60°. A total number of 62 tests were carried out in the dumbbell geometry of each material longitudinally and transversely. The profile roughness parameters obtained were the maximum peak to valley height of the profile, R_z, and the arithmetical mean value of the tested profile along a length l_r, R_a, given by:

Compact Tension (CT) configuration with the dimensions shown in Figure 4-6 was used for fracture and fatigue tests. The only difference between fracture and fatigue specimens was the initial notch length, which in the fatigue specimens was the half that in fracture ones in order to fulfil ASTM D5045 standard [145] in fracture and ASTM E647 standard [146] in fatigue characterisations.

The sharp crack in the fracture CT specimens was generated by tapping a razor blade with a thickness of 0.3 mm, previously frozen at liquid nitrogen temperature (-196 °C), on the root of the machined notch till attaining an initial natural crack length to width ratio, a₀/W, of 0.5. This ratio ensures a sharp crack length enough to avoid the influence of the manufactured notch on the results [43], [145].

In the fatigue CT specimens, the sharp crack was introduced by tapping in a similar way as in the fracture samples but, in this case the sharp crack lengths should be only larger than the notch height, of 2 mm, to avoid the notch effects [43], [146].

Small cracks were introduced in dumbbell specimens with lengths of 0.2 mm, 0.3 mm, 0.5 mm, 1 mm, 2 mm, 2.5 mm and 3 mm by pressing a microtome razor blade with a tip diameter of 5.3 μm (Figure 4-7). This tip diameter ensures a notch radius smaller than 10 μm, which is the estimated limit for considering the crack as a natural crack [147], [148]. These specimens were used for static and fatigue characterisations in the PSC regime (section 2.4)

After notch sharpening or small crack introduction, the crack front was inspected either visually or by optical means to guarantee no damage in form of microcracks or whitening. In case of presence of damage, the samples were discarded.

Tests were carried out in a universal servohydraulic testing machine MTS 810 Materials Testing, equipped with a load cell of ± 5 kN. The crosshead speed was 5 mm/min. A Crack Opening Displacement transductor (COD) MTS 632.02F-20 with a displacement range of + 3.9 mm/ -2 mm was also employed. The tests were performed in SLS specimens at 0° and 90° orientations, and in IM samples. To study the evolution of the fracture properties with the temperature, tests were undertaken at three different temperatures, -50 °C, 23 °C and 50 °C, completing three repetitions of each condition. For the -50 °C and 50 °C tests, an environmental chamber MTS 651.06E-03 was used, installing the load train, formed by the hinges, grips and the specimen with the COD transductor, inside it (Figure 4-8).

Similar procedure to that of the tensile tests was performed, maintaining a constant load of 50 N on the specimen during cooling and heating processes until the load frame finished of balancing the thermal contractions and, consequently, reaching a stationary state. When the required temperature was reached, conditioning was held 25 min more before starting the test to guarantee the thermal equilibrium.

Attending to the mechanical behaviour of each material and test condition, the results were analysed applying the Linear Elastic Fracture Mechanics (LEFM) or the Non-Linear Fracture Mechanics (NLFM) approach as appropriate. The ISO 13586 Standard was followed to determine the crack opening mode (mode I) fracture toughness in terms of the stress intensity factor, K_IC, and the energy release rate, G_IC, under LEFM approach [149].

From the load (P)-crack mouth opening displacement (v) record, the maximum load, P_max, and a conditional load, P_Q, are calculated. P_Q is used to determine a conditional stress intensity factor, K_Q, and a conditional energy release rate, G_Q.

Firstly, P_5% is computed as the intersection of the P-v record with a line having a 5% smaller stiffness than the initial one, S. If the maximum of the curve falls within the best straight line to determine S and the line with a 5% lower stiffness, then Pmax corresponds with the load at crack growth initiation, P_Q. If P_max falls outside these two lines, then P_Q is P_5%. If P_max/P_Q < 1.1 then P_Q is used for K_Q calculation, otherwise, the test is invalid. With this limitation, the critical stress intensity factor K_Q is obtained:

with B the specimen thickness, W the width and f(α) the geometry calibration factor depending on the crack length a given by:

being α=a/W.

In addition to the previous condition, the standard establishes that to guarantee the plane-strain state, it must be fulfilled:

with σ_y the yield stress of the material for the temperature and loading rate of the test and K_Q is K_IC in this case. The energy release rate, G_Q is G_IC and in principle it can be obtained from the following equation:

E is the Young’s modulus and v the Poisson’s ratio obtained at the same time and temperature conditions. Due to the many uncertainties introduced by this procedure, particularly, in the determination of the Young’s modulus, G_Q is computed from:

where U_Q is the energy obtained from the area under the P-v curve until the point P_Q and ϕ (a/W) is the energy calibration factor depending on the crack length given by this expression:

with

and

When the behaviour of the material deviates from LEFM, the J-integral vs. crack growth resistance (J-R) curves were obtained directly from the force displacement record according to ASTM E1820 standard using the normalization method [150]. The starting point of this procedure is the measurement, by optical means, of the initial crack length, a_o, and the final crack length, a_f, taken from the fracture surface. Then, each force value P_i is normalized up to but without including the maximum value P_max, following the expression:

where Ƞ_pl is the plastic constriction factor, which depends on the specimen geometry and is given by:

and a_bi is the crack growth applying the blunting correction:

where

with K_i the stress intensity factor obtained from eq. (4-4) and eq. (4-5) and J_pl,i the plastic component of the J-integral:

where U_i is the area under the curve until P_i.

The displacement corresponding with each force level P_i, δ_i, is also normalized to use a plastic normalized displacement, δ’_pli:

being C_i the specimen elastic load-line compliance using the crack length a_bi. The same procedure is employed to obtain the last point, at P_max, but using, the measured final crack length, a_f, instead of a_o, the P_Ni-δ’_pli values are fitted to the normalized function:

with a, b, c and d the fitting parameters. Once these parameters are determined, a_i values are calculated using an iterative method.

Finally, with the force, the displacement and the crack size estimated at each point, the J integral value for each i point was determined using:

With Ƞ = Ƞ_pl for the CT configuration and the crack extension, Δa, as:

The resulting J-crack growth resistance curve is fitted to a power law J = C_jΔa^N_J with N_J < 1. The crack initiation resistance, J_IC, is calculated as the minimum value between J_0.2, which defines crack resistance at 0.2 mm of the total crack growth, and J_BL, computed as the intersection between the crack growth resistance curve and the blunting line defined as:

The size requirements for plane strain J_IC is given by [151]:

The normalized method was applied using the MATLAB^® script included in the Annex A.1.

The fatigue tests were carried out under the recommendations of the ASTM E647 Standard [146] and ESIS TC4 protocol [152], which aim to obtain the crack propagation threshold value of the control parameter and the fatigue crack propagation curves.

A total number of eight samples of IM material and fourteen samples of each SLS orientation were tested at room temperature in a servo-hydraulic testing machine MTS 810 Materials Testing with a load cell of ± 5 kN and a crack opening displacement (COD) extensometer MTS 632.02 F-20 with a displacement range of +3.9 mm/-2 mm (Figure 4-9). The tests were carried out at room temperature (23°C), with a frequency of 1 Hz, load ratio R = P_min/P_max of 0.1 and imposing a sinusoidal load wave. Two test procedures were used according to ASTM E647.

To obtain the crack propagation behaviour until failure, five IM specimens and ten SLS specimens per orientation were tested in constant-force-amplitude configuration or increasing control parameter mode. On the other hand, to obtain the crack propagation threshold, three IM specimens and four SLS specimens per orientation were tested under the decreasing control parameter procedure. Beginning with a control parameter value under the critical value obtained from the fracture tests, tests with decreasing load amplitude were carried out with a step of decrease or normalized variation of the control parameter of -0.05 mm^-1. The threshold values were computed for crack growth rate downs to 3 • 10^-7 mm per cycle.

Two methods were used for obtaining the crack growth during the tests. In the first method, the crack growth was calculated by the compliance method from the flexibility of the specimen using expressions determined for metals but also validated for polymers [152]. The expressions that relate the crack length to width ratio, a/W, with the compliance in CT specimens are

where:

To validate the compliance method, an optical method was used. Images were captured during the test at a specific frequency allowing the tracking of the crack length with a millimetre scale stuck to the specimen’s surface. Moreover, the calculated final crack length was compared with the measured fatigue crack length on the fracture surface of each specimen.

The fatigue behaviour has been determined as the crack growth rate, da/dN, versus the Crack Driving Force, CDF, ΔG according to equation (2-2).

The crack growth rate at any average crack length a¯=ai+1−ai2 is obtained from the crack length versus elapsed cycle with the following expression:

The control parameter ∆G was obtained from equation (2-1) in which the value of dC/da is given by:

where g(α) is the non-dimensional load line compliance [26] and with dg/dα for CT specimens computed as:

Fatigue life tests were performed to obtain S-N curves for IM and SLS specimens at both orientations, according to ASTM D7791 Standard [153]. The specimens had the same geometry and dimensions as those utilized in tensile tests (Figure 4-2). A total number of 89 specimens were tested, of which 20 were used for the determination of IM PA-12, 32 for SLS PA-12 at 90° orientation and 37 for PA-12 at 0° orientation. Tests were performed at room temperature in a servo-hydraulic testing machine MTS 810 Materials Testing with a load cell of ± 5 kN. A contact extensometer MTS 634.31F-24 with a displacement range of +4 mm/-2 mm was employed to measure the axial strain.

The frequency was 1 Hz, using a sinusoidal load wave form at a constant load amplitude with a load ratio, R, of 0.1. Tests were done at 12 different stress levels, that is with the maximum stress of the cycle, σ_max, to the tensile strength ratio between 58.75% and 85%, to guarantee to be within the High Cycle Fatigue regime. At least, two repetitions for each stress level were carried out.

The tests at the lowest levels were finished at 10⁶ cycles due to their high timeconsuming aspect, establishing tests which reached this number of cycles without failure as run-outs. Each test was plotted as a single point of the stress range, Δσ, versus N representation, giving as result the Wöhler curve for each material.

The fatigue life curves were fitted to the Basquin equation:

The estimated value of the fatigue limit, Δσ_fl, at 10⁶ cycles were determined by the maximum likelihood method, following a test sequence based on the staircase method. In this method, fatigue tests were sequenced at different stress levels with a fixed difference in the applied stress range or initial step of 2.5% of the tensile strength. If a specimen failed before reaching the end of the test, the following test was carried out at a stress level one step lower. Otherwise, the stress level was increased one step in the following test. To obtain a more accurate value, the step was decreased after seven completed tests to 1.25% of the tensile strength. Although the change in the step removed the possibility of using the Staircase method equations developed for metals [154], the maximum likelihood method allowed to obtain an accurate estimation of Δσ_fl [155]–[157]. A total number of 17 for SLS PA-12 specimens at 0° orientation, 12 for PA-12 samples at the 90° orientation and 14 for IM material were tested to obtain Δσ_fl.

The maximum likelihood method was applied assuming that the stress levels of the run-out specimens follow a normal distribution [156], [158]. For a normal distribution with a mean value, μ, and a standard deviation value, s, the likelihood function, L, is given by:

where r_i are the number of run-outs and f_i are the number of failures at the i^th stress level, Δσ_i, n_T is the total number of stress amplitude levels and F is the cumulative probability of failure of the normal distribution.

This function depends on the stress at the i^th stress level, Aσ_i and the parameters of the normal distribution and is calculated with the following expression:

The maximum of the likelihood function was obtained using the MATLAB^® script proposed by Meizoso et al. [155] and included in the Annex A.2.

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].

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 PmaxPQ 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=CJΔaNJ 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.

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.

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.

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.

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]: aW=2.072−16.411U+29.6U2−211.67U3+236.857U4+27.371U5−179.74U6−86.28U7+171.764U8 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.