Self-Organization at the Crack Tip of Fatigue-Resistant Thermoplastic Polyurethane Elastomers

Despite their technological relevance, the resistance of soft thermoplastic polyurethanes (TPU) to crack propagation in cyclic fatigue has never been investigated in detail. In particular a clear shortcoming in the literature for this class of materials is the lack of connection between the cyclic fatigue resistance and the large strain behavior that has a fundamental role in defining the material’s resistance to crack propagation . We demonstrate here for the first time that when the strain-induced stiffening mechanism of TPU (already observed for large deformation) is combined with the presence of the not-homogeneous strain, as in case of cyclic fatigue, it produces a selective reinforcement in the crack tip area which is the key to explain the remarkable cyclic fatigue resistance of TPU. Using commercial TPU with similar modulus (~8 MPa) but different large strain behavior we show that the described mechanism is intrinsically linked to the multi-phase nature of TPU and is not necessarily linked to a specific large strain property as the case of TPU which undergo strain-induced crystallization.


Introduction
Thermoplastic Polyurethanes (TPU) are segmented multiblock copolymers characterized by alternating blocks of soft segments (SS) and hard segments (HS). The former are composed of long and flexible polyester or polyether chains that ensure high deformability, while the latter consist of urethane-rich hard segments. The TPUs typically self-organize in hard-domains (HD) which are generated from the lateral stacking of HS through physical interactions and hydrogen bonding. They generally have dimensions of tens of nanometers 1,2 , comparable to that of common reinforcing fillers used in rubbers. TPUs can be produced in different grades with Young's moduli E ranging from some MPa to 1.000 MPa. Among those, soft TPUs (E<10 MPa), where the flexible chains represent the majority of the material and are physically crosslinked by the HD, generally show high elasticity and excellent abrasion resistance at ambient temperature. Despite their high price, soft TPUs have already found many applications in fields as sportswear and footwear and are gaining increasing industrial attention as recyclable alternative to replace classical filled and vulcanized rubber in structural applications such as cables, dampers and belts. One of the most desirable properties in this kind of structural applications is the ability to sustain a large number of cyclic loadings at low stress levels without hazardous rupture of the material. In other words, they must have an appreciable cyclic fatigue resistance.
In a previous paper 3 , we proposed a method to probe the cyclic fatigue resistance of soft TPU based on the classic fracture mechanics approach, originally developed for chemically crosslinked rubbers.
We highlighted that during cyclic deformation, TPU experience a shake down 4 and stabilization of the stress-stretch curve. Provided that the loading and unloading cycles are conveniently adapted to tackle the effects of plastic creep, the crack propagation process in standard notched pure shear samples can be robustly expressed as crack propagation per cycle dc/dn as function of applied energy release rate G. These preliminary results confirmed the very high resistance of soft TPU to crack propagation in cyclic fatigue conditions even for large applied strains. Up to now, a clear shortcoming in the literature for this class of materials comes from the lack of connection between the cyclic fatigue resistance and the large strain behavior that has a fundamental role in defining the material's resistance to crack propagation. Although the typical range of bulk strain used in fatigue experiments is generally considerably lower than the strain at break in uniaxial tests, the presence of the crack induces significantly larger local strains at the crack tip 5,6 . This strain concentration is particularly important for TPU since their structure, and hence the mechanical response, evolves with applied strain 1,[7][8][9][10][11] . However, previous studies on the structural evolution of hard domains with applied strain only focused on uniaxial tension samples and did not include the effect of local singularities generated by defects or notches as is the case for fatigue fracture. Indeed as proved by Mzabi et al. 5 in filled and crosslinked Styrene-Butadiene Rubber (SBR), the presence of a loaded crack generates a local strain gradient at the crack tip, the amplitude of which depends on external loading and on material's characteristics. To the best of our knowledge, a comprehensive characterization of the local morphology induced at the crack tip during a cyclic fatigue experiment, and the discussion of its effects on the crack propagation rate for soft TPU has never been carried out.
To understand the effect of a loaded crack on local structural modifications, it is useful to briefly recall some key results obtained in uniaxial extension of TPU 7,[9][10][11][12][13][14][15][16] . Bonart 1 was among the firsts to investigate the deformation behavior of TPU using small-and wide-angle X-Ray scattering, SAXS and WAXS respectively. He proposed that, for moderate levels of stretch (λ<3), the progressive alignment of the SS along the tensile direction exerts a torque on the HD. As a result, the HD tend to orient in a transversal direction relative to the applied load. In a TPU with a low percentage of HS, further elongation generally corresponds to a re-organization of HD and alignment along the loading direction. This process, defined as "restructuring of the cross-linking" by Ishihara 12 , consists in breaking and re-forming hydrogen bonds to realign the hard segments. An excellent summary on Xray investigations in deformed TPU with low HS content (weight percentage about 12%) was provided by Yeh and co-workers 7 .
In this work, we tested the cyclic fatigue resistance of two TPU which share very similar small strain properties but present completely different large strain behavior in uniaxial tension at ambient temperature: TPU_XTAL which displays a marked strain-hardening partially due to strain-induced crystallization (SIC) and TPU_SOFT which has higher extensibility and barely visible strainhardening before rupture. In addition to the fatigue experiments, expressed by dc/dn vs. G and uniaxial step-cycle tests, we used two additional techniques to characterize the differences between the bulk and at the crack tip as the sample is experiencing loading cycles in fatigue: digital image correlation (DIC) to characterize the strain field near the crack tip and spatially resolved in-situ X-Ray wide-and small-angle scattering analysis (WAXS, SAXS) to detect structural changes with number of cycles both in the bulk and near the tip.

Materials and methods: Materials
The used TPUs are commercial polyester-based polyurethane multiblock copolymers produced by BASF, Elastollan© series, with the trade names: 565A 12P and LP9277 10, respectively denoted as TPU_XTAL and TPU_SOFT based on their large strain behavior in uniaxial conditions. The  Figure S1 and Table   S1. The pure-shear geometry is generally used in cyclic fatigue experiments because the energy release rate G can be easily calculated and is independent of crack length 17 . All pure-shear samples were pre-notched using a fresh razor blade with a 20 mm cut. The chemical composition of both TPU is not available since they are commercial products. The number average Mn and weight average Mw molecular weight of TPU_XTAL after injection are 47 kg/mol and is 61 kg/mol respectively and were obtained by gel permeation chromatography (GPC). The values of absolute molecular weights were extracted from refractive index and light scattering signals, using a measure dn /dc value of 0.11 mL.g -1 for the TPU. Fourier-transform infrared spectroscopy (FTIR) was used for structural analysis of the polymers. Only in case of TPU_SOFT it revealed an absorbance peak around 1640 cm -1 which may be consistent with the presence of bidentate urea. The latter, is generally associated with stronger interactions than simple hydrogen bonding in HD 18 and may explain the poor solubility of TPU_SOFT suggesting a stronger inter-domain stability.
Step -strain cyclic tests   The dog-bone shaped samples were strongly fixed between mechanical clamps since TPU are very tough. An optical detection system was used to measure the local stretch in the gauge area of the sample and to check the absence of slippage from the clamps during the test. The samples were loaded in uniaxial conditions at the stretch rate of ̇ = 4s -1 . The loading was performed in a stepwise mode: 10 cycles were performed for each increasing value of maximum applied stretch for both TPU.
The stress was reduced to σ = 0 between two successive steps in order to prevent buckling. The mechanical quantities strain ε, stretch λ, Hencky strain h, nominal stress σ and true stress T are defined as below. Here, l0 and l indicate the initial length and instantaneous length respectively, A0 the initial cross section area and F the measured force.

WAXS and SAXS Characterization
In situ WAXS and SAXS experiments were carried out in two conditions: on relaxed samples (=1) and on strained samples (=2.5). The first set of experiments (=1) was carried out on a GANESHA  Table 1. The 2D scattering data were integrated using the software tool FIT-2D 19 . All data were corrected by subtracting background scattering. In situ WAXS and SAXS experiments were carried out for two sets of samples: samples that were pre-fatigued and pristine samples. All of them contained a notch.

WAXS analysis:
The 2D WAXS pattern was circularly integrated. Peaks in 2 range between 12° and 20° were deconvoluted using Gaussian/Lorentzian peak fitting routines. The crystalline fraction c was evaluated classically as the ratio between the total area of crystalline peaks and the total area (crystalline and amorphous: + ) underneath the diffraction profile as: = ∫ + 2 Azimuthal integration was performed on the most prominent peak as indicated in Figure 2  cycles. This effect is known as shake down 4 . We used the stress-stretch curve at 10,000 cycles to

Digital Image Correlation (DIC)
DIC is a technique which allows measuring displacement fields by matching a reference with a deformed image. Here, the Correli-LMT software 20 , which represents the displacement field by the same kind of mesh as in finite element methods, was used. The final displacement is evaluated using an algorithm that minimizes the difference in the gray levels between the matched images, while imposing some level of regularity to the solutions.
The objective adopted for this analysis corresponds to a pixel size of 7μm and the mesh size was x chosen as 16 pixels. In this condition the spatial resolution of the DIC analysis (minimum distance between two adjacent estimates of displacement) was 112 m. Since the datapoint associated by convention to a distance of 0 mm from the crack tip is indeed the closest available point, this spatial resolution should also be considered as an uncertainty on the distance of such point from the crack tip. The samples were uniformly backlit. A random speckle texture was obtained by black ink spraying, a method which provides a good contrast with the sample surface (either white or transparent). For each DIC characterization, a set of 40-60 images was acquired between = 0 and . In order to minimize the alteration of the gray levels by the large applied strains during DIC, the correlation procedure was first performed between each couple of subsequent images starting from the unloaded condition up to the maximum strain. Then the total displacement for each  was evaluated by progressively adding the differential displacement fields of each step. The total displacement field was then used to evaluate the local strain field following the same procedure as in Mzabi et al. 21 .  characterized by a high extensibility at failure (more than 1000%) and, after an initial linear elastic regime that only lasts a few percent strain, they soften as displayed in Figure 3(b). In the case of TPU_XTAL this is rapidly followed by a marked strain hardening, which is much less pronounced in TPU_SOFT. Table 2 reports the elastic moduli as well as the stress and stretch at break for both TPUs. Cyclic fatigue The threshold values Gt, indicated in the picture, are conventionally evaluated using the same procedure adopted in our previous paper 3 and correspond to the minimum value of G below which during a single fatigue experiment lasting 36,000 cycles and with the resolution of our optical system (38m), we could not detect any crack propagation. In this condition, the minimum detectable crack growth per cycle was equal to:  26 in an hydrogel material which, similarly to TPU, presents a multiphase morphology. They showed that highly fatigue resistance hydrogels containing a reinforcing hard phase at the 100 nm scale, much larger than the characteristic size of the polymer network defined as the characteristic distance between crosslinks (10 nm), can be deformed at  > 1 for thousands of cycles without initiating a catastrophic propagation of the crack. In those systems the maximum stretch is a critical parameter in determining the resistance of the material against fatigue.    tip. An additional remark must be made concerning the value of in fatigued samples. As shown in our previous work 3, 27 TPU generally present some residual strain when cyclically loaded in uniaxial tension. The latter implies that the actual length 0 of unloaded samples after fatigue is longer than the original in pristine sample 0 which we used to evaluate . Therefore, the real stretch experienced by the material is lower than  . This effect is visible in Figure 6 for both TPU where, for large distances from the crack tip, the value of 1 at the plateau (which corresponds to the macroscopic applied ) is slightly higher in pristine than in fatigued sample. This effect is however barely distinguishable and cannot explain the remarkable reduction of the strain singularity after fatigue. ii) The dissimilar morphology developed as the strain gradient increases is demonstrated by the different patterns observed in the bulk and in the crack tip region. In the 2D SAXS patterns corresponding to the crack tip area, the two meridional lobes are clearly less intense, while a new equatorial sharp streak appears. The appearance of the streak can be associated either to the presence of voids 30,31 or to a fibrillar morphology 32 and is frequently found in TPU deformed in large strains [7][8][9][10]14,29 . This feature stems from the destruction of HD in favor of rod-like soft domains composed of both elongated SS and HS in the most strained region at the crack tip. A similar behavior was also 19 observed in TPU_SOFT. The 1D WAXS integrated profiles for TPU_XTAL and TPU_SOFT are reported in Figure 8(b-c). In case of TPU_XTAL (Figure 8(b)), the 1D WAXS profile close to the crack tip shows the presence of two main crystalline peaks, absent in the bulk, indicating the presence of well oriented strain-induced crystallization (SIC) 29,33 in the higher stretched area (see DIC data in Figure 6). On the other hand, crystalline peaks are clearly detected in the bulk and still visible close to the crack tip for TPU_SOFT in the 1D WAXS profile of Figure 8(c). The position of these peaks corresponds to those of the crystallized butadiene terephthalate 29 (PBT) sequence probably present as a comonomer in TPU_SOFT. This is however a hard segment (crystalline in the absence of strain) and becoming less crystalline with strain. To evaluate how the effect of several cycles affects the local structure evolution in TPU, we now compare the X-Ray scattering results obtained at a similar distance from the crack tip for pristine and fatigued samples of TPU strained at max≈2.25. Consistent with the DIC results of Figure 6, we find that the level of orientation and crystallinity is lower for fatigued samples than for pristine ones.

Permanent modification of the microstructure induced by strain history
In the previous section we showed that loading cycles induce some re-organization of the original two-phase structure of TPU when stretched at the same value of  =2. 25. We now investigate whether the original morphology is completely recovered when the sample is unloaded. In order to understand which changes are permanent after the removal of the external load, we compare the scattering patterns of TPU in its relaxed state (=1) for pristine and fatigued sample with those obtained at  =2.25. Figure 10 shows 2D SAXS images and corresponding 1D scattering profiles for TPU_XTAL (a) and TPU_SOFT (b). In both cases the 1D scattering profile is shifted at higher q for the unloaded fatigued sample thereby, the interdomain distance L related to the periodicity of the hard and soft phases, reduces slightly for unloaded fatigued sample. The decrease of L can be interpreted as permanent fragmentation of HD in smaller units during the fatigue experiment 10 as shown in the schematic of Figure 10 (a) and (b) for TPU_XTAL and TPU_SOFT respectively. It is worthy to remark that the SAXS analysis for the unloaded sample was performed around 30 days after the sample was fatigued. This led us to believe that such fragmentation is not easy to recover at ambient temperature even for materials that present some relaxation effects as physical crosslinked TPU. The fragmentation of HD is not the only permanent effect induced by cyclic loading on TPU. In case of TPU_XTAL, the new crystalline phase formed near the crack tip during cycling, is partially retained after fatigue as shown by the DSC thermograms comparing pristine TPU_XTAL and a pureshear sample that was previously fatigued ( Figure 11). As also reported by other authors 35 , the endothermic peak (Tm_SIC) absent in the pristine sample, is associated to a new crystalline phase generated during loading which persists after the removal of the load (red bars in the schematic of Figure 11) .

Discussion
A model to explain the strain-induced reinforcement in TPU In strained TPU containing an initial crack the strain singularity along the crack direction X 2 , expressed as the stretch field  1 (X 2 ) evaluated at different distances X 2 ahead of the crack tip, is accompanied by a progressive change in the microstructure as proved by X-Ray analysis. The changes in local microstructure with applied uniaxial strain in TPU have been investigated in-depth in the past for homogeneously strained samples 7,10,11,13,14,29,33,36 . Different authors showed that some of those changes are permanent and that the unloaded material does not completely recover its original state 10,16,29 but, depending on the maximum experienced strain, the polymer retains a certain degree of anisotropy or strain-induced crystallites as shown by the DSC analysis of Figure 11. In particular, for TPU made from SS able to crystallize under strain, the formation of new crystalline domains, that are persistent after unloading, may be responsible for the strengthening of the material with increasing strain. In our case, the modulus of both TPU increases with applied strain, but X-rays analysis shows that only TPU_XTAL crystallizes under strain. This indicates that the strengthening effect induced by the strain is not uniquely related to the formation of a crystalline phase, but is a general property due to the self-organized structure of TPU in soft and hard domains. We believe that the permanent re-organization of the two-phase microstructure in TPU induces stiffening of the material through two main possible mechanisms which in some cases can act simultaneously:

The effects related to the presence of a crack in cyclic deformation
Previous investigations on the structural evolution of soft TPU with applied strain mainly focused on homogeneously strained materials, and sometimes discussed a remarkable strain-stiffening after elongation 10 . To the best of our knowledge, the effect of the presence of a crack and its associated strain localization has never been investigated in this context. In Figure 6 we have shown that the presence of a strain gradient at the crack tip causes a corresponding spatial gradient in the structural re-organization within the TPU, thus affecting the local mechanical response to the applied strain.
Intriguingly, we also observed that the repetition of several loading cycles (at the same bulk max) leads to a decrease of the strain-induced anisotropy and crystallinity fraction (in TPU_XTAL) in the crack tip region and in general to a decrease in the sharpness of the structural gradient. We infer that the less oriented structure created by cyclic fatigue at the crack tip, compared to their pristine counterpart, is associated with a reduction of the severity of the strain concentration at the crack tip with number of cycles. Obviously, in cyclic fatigue the strain experienced in the bulk is lower than that close to the crack tip, which in turn controls the crack propagation rate. This difference in strain generates a spatially heterogeneous structure consisting in the region far from the crack, which is deformed at below c (and similarly to classical elastomers has tangent modulus E lower than the pristine material, see Figure 5) and a stiffer core in the crack tip region where the strain eventually may become large enough to overcome the critical c generating an increase in E which locally becomes equal (TPU_SOFT) or higher (TPU_XTAL) than the pristine one. This difference in stiffness produced by the spatial dependent restructuration of hard domains can be consequently interpreted as a sort of protecting mechanism which, after a short transitory, shields the crack tip from achieving very large strain which may produce the rupture of material and therefore is correlated to crack propagation. Because of the stiffened core therefore, the material far from the crack in the fatigued TPU must deform more to reach the same local strain around the crack tip compared to the pristine sample and results in a decrease in the severity of the strain concentration at the crack tip as visible in Figure 6 and Figure 7. The proposed scenario is schematically showed in Figure 13 an is consistent with the lower crystallinity observed in TPU_XTAL after fatigue. Noteworthy, the equatorial streak that we observed in the SAXS 2D pattern for the area close to the crack tip ( Figure 8) above a characteristic stretch (max>) is characteristically seen by X-ray scattering in several TPUs 1,7,8,10 and was associated to the presence either fibrillar structures or voids which could be seen as signature of certain damage produced in the system. For moderate applied macroscopic strains this streak is only visible in the crack tip regime. However, when the whole sample is strained above this stretch threshold, some structural damage can take place in the bulk causing a ruin of the sample.  11 and was calculated from the data of Figure 7 . We used the 1 st and the 10 th cycle to evaluate ( ) (and therefore ) in pristine and fatigued sample respectively. The choice of using the 10 th cycle of the sample under uniaxial loading to evaluate for the fatigued sample is justified by the fact that the major changes in the cyclic stress-strain curve of the TPU take place at the beginning of the test. All the values are reported in Table 3. Noteworthy, in the case of the fatigued sample, provides only an upper bound value of the strain energy density experienced by the material at the crack tip. Indeed, as discussed in our previous paper, during cyclic loading the strain energy G reduces with number of cycles. The most dramatic drop in G vs. cycle occurs within the first cycles and then gradually achieves a steady-state after some thousands of cycles. For the same maximum applied strain, pristine TPU_SOFT, which has a lower fatigue resistance than TPU_XTAL, has higher values of . Moreover, the measured in fatigued samples is always lower than what is measured in the pristine counterpart and the drop is considerably more pronounced in TPU_XTAL (which presented the lowest values of 1 ( 2 ) measured in DIC after fatigue in all the area around the crack tip ( Figure 6). This result is in agreement with the suggestion of Mzabi et al.
that the crack propagation resistance does depend on the strain energy available within the highly strained region at the crack tip. In case of TPU_XTAL the ability of crystallization under strain and the corresponding remarkable increase in the modulus with applied stretch not only reduce the local strain but also the elastic energy available to propagate the crack compared to TPU_SOFT (where SIC is absent and the only strengthening mechanism at the crack tip is the fragmentation of HD).
Differently from SBR and other typical vulcanized elastomers, the peculiar feature of the TPU is their ability to maintain an excellent reversible elasticity in the bulk (necessary for applications), while retaining the ability to plastically deform at high strain to reduce the severity of the strain concentration at the crack tip. Similar mechanism has been recently shown for polyampholyte hydrogels where a strain dependent structural change is also active 26 .

Conclusion
The cyclic fatigue behavior and structural evolution of notched samples of two commercial soft TPU with nearly identical small strain moduli but different large strain behavior has been investigated at room temperature in the pure shear geometry 3 and reported as dc/dn vs. G. For both TPU the presence of a strain gradient in an area close to the loaded crack was shown to generate a self-strengthening non-uniform spatial organization of the TPU microstructure above a threshold value of strain. The more highly strained region at the crack tip becomes stiffer than the bulk reducing the intensity of the strain concentration and the elastic energy available at the crack tip. As a result of this weak strain concentration, the crack propagation resistance in TPU is markedly increased compared to classical However, when exceeds a critical value of stretch, the HD restructuration and some damage (suggested by the equatorial streak) starts to occur within the whole sample and no longer selectively at the crack tip. In those loading conditions the entire material would experience a strain-induced stiffening effect without the formation of a hard core protecting the crack tip leading to higher crack propagation rate.
Our study clearly shows that this self-strengthening mechanism due to localized crack tip plasticity is active in commercial TPU and is responsible for their remarkable enhanced fatigue resistance at high strains. Interestingly the value of such a localized stiffening mechanism may be more general and a similar localized strengthening has been observed for microphase separated polyampholyte hydrogels 26 .
Supporting Information: Additional details on the injection process and in-situ 2D X-Ray image of TPU_SOFT .