lable at ScienceDirect

Acta Materialia 165 (2019) 177e182

Contents lists avai

Acta Materialia

journal homepage: www.elsevier .com/locate/actamat

Full length article

In situ x-ray diffraction analysis of 2D crack patterning in thin films

D. Faurie a, *, F. Zighem a, P. Godard b, G. Parry c, T. Sadat b, D. Thiaudi�ere d, P.-O. Renault b

a LSPM-CNRS UPR3407, Universit�e Paris 13, Sorbonne Paris Cit�e, 93430 Villetaneuse, Franceb Institut Pprime, CNRS - Universit�e de Poitiers - ENSMA, Bd Marie et Pierre Curie, 86962, Futuroscope Cedex, Francec SIMaP, Universit�e Grenoble-Alpes, BP 53, 38041, Grenoble Cedex 9, Franced Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin, BP 48, 91192, Gif-sur-Yvette Cedex, France

a r t i c l e i n f o

Article history:Received 5 October 2018Received in revised form15 November 2018Accepted 20 November 2018Available online 26 November 2018

Keywords:Flexible substratesMechanical propertiesCracksSynchrotron

* Corresponding author.E-mail address: faurie@univ-paris13.fr (D. Faurie).

https://doi.org/10.1016/j.actamat.2018.11.0401359-6454/© 2018 Acta Materialia Inc. Published by E

a b s t r a c t

In this work, the effect of the loading path on the multicracking of Nickel thin films on Kapton®

substrate was studied thanks to an experimental set-up combining controlled biaxial deformation,x-ray diffraction and digital image correlation. Samples were biaxially stretched up to 10% strainfollowing either a single equibiaxial path or a complex one consisting of loading successively alongeach of the axes of the cruciform specimen. While the first path leads to a mud-crack pattern(random), the second leads to a roman-bricks one (square). Moreover, the in situ x-ray diffractionexperiments show that the stress field developed in the thin film during the multicracking isclearly dependent on the loading path. By combining the study of stresses and x-ray diffractionpeaks linewidth, we evidenced mechanical domains related to initiation of cracks and theirmultiplication for each loading path. Moreover, stress evolution in the thin film during mud-crackpattern formation is significantly smoother than in the case of roman-bricks one as represented inthe plane stress space.

© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction

The field of stretchable and flexible electronics has beengrowing for many years [1e3]. The increasingly complex forms ofelectronic devices will benefit from the functionalities of thesesystems by their adaptability to non-planar surfaces (conform-ability) [4,5]. Other factors contributing to the growth of thismarket are the lightness and low cost of production compared torigid substrates. From a general point of view, themain limitation ofthese flexible/stretchable systems is their often too weak durability[6]. If the substrates generally made of polymers are adapted tolarge strains, the inorganic films that carry the functionality aremore prone to failure.

It has been known for a few decades that the cracking of thinfilms can lead to complex patterns that may be both harmful anduseful depending on the intended applications [7e10]. Thiscracking occurring for materials with significant mechanicalcontrast occurs both in nature at centimeter scale (deserts,crocodile skin [11]) or in the context of technological applicationsat micrometer scales [12]. In the latter case, uncontrolled

lsevier Ltd. All rights reserved.

cracking is generally an undesirable phenomenon that can leadto a modification or even a deterioration of the properties such aselectrical [13,14] or magnetic [15,16]. However, multicracking canalso be used to create patterns of material as can differentlithography techniques with the possibility of arriving at non-equilibrium geometries [17]. In addition, this may be useful forsubstrates used in stretchable or flexible electronics such aspolymers.

Regarding this last type of substrate, the most usual test is theuniaxial tensile test which induces a periodical array of cracks thatis more or less straight depending on the mechanical properties(fragile or ductile) and the thickness of thin films [18e21]. It is alsoknown that the equibiaxial test leads to a random structure ofcracks [22] as found in nature (sand or dried mud [23], animal skin[11]). Unlike rigid substrates that give way to very varied patterns,there are few alternatives to the straight cracks and mud-cracks.The formation of rectangular or square fragments is possible bycreating a cavity network before biasing the film in equibiaxialtraction [17,24], this of course requires a step upstream of micro-fabrication of the cavity network.

Among the works describing the multicracking of thin films onpolymer substrates, a few groups have described the mechanismsby in situ x-ray diffraction and uniaxial tests [18,21,25,26]. Indeed,

D. Faurie et al. / Acta Materialia 165 (2019) 177e182178

this technique allows measuring the residual stresses and thefollowing evolution of thin film stresses during macroscopicdeformation, which makes it unique. Hence, few researchers havefound a correlation between the crack multiplication and in-planestress relaxation after the initiation of cracks. However, this com-munity has poorly explored the biaxial loading effects on the stressevolution during development of more complex crack patterns.Until now, Djaziri et al. have studied the effect of loading ratioduring biaxial loading on the initiation of the cracking of W/Cu thinfilms [27], but without looking at the effect on resulting crackpatterns. Moreover, the effect of complex loading have not beenexplored.

In this paper, we show how two different mechanical biaxialloading paths of thin films on stretchable substrates can lead tocompletely different two-dimensional crack patterns, namelymud-cracks or roman-bricks. These are obtained using a biaxial machinethat is installed in a Synchrotron beamline (SOLEIL DiffAbs), whichallows controlling independently the applied load along each axe.Therefore, this set-up allows monitoring in situ the stresses in thethin film by x-ray diffraction (XRD) during the development ofthese patterns in order to find relationships between stresses andmulti-cracking micromechanisms.

2. Materials and experimental set-up

The Ni thin films were deposited onto 25-mm-thick polyimide(Kapton®) cruciform substrate and were produced at roomtemperature by physical vapor deposition (PVD) with an Arþ-ion-gun sputtering beam at 1.2 keV (Kaufman ion source) in a NOR-DIKO, Hampshire-3000 system. The base pressure of the depo-sition chamber was 7� 10�5 Pa while the working pressureduring films growth was approximately 1:4� 10�2 Pa. Nigrowing rates was previously calibrated by x-ray reflectivity andwas found to be 0.05 nm:s�1. The x-ray reflectivity was measuredusing a Seifert XRD 3003 diffractometer operating with a Cu x-ray source (linear focus, l¼ 0.15406 nm). The total Ni filmthickness of 50±0:5 nm was confirmed with visible light

Fig. 1. Schematic representation of the experimental setup at DiffAbs beamline(SOLEIL Synchrotron).

profilometry.A picture of the cruciform specimen mounted on the used

biaxial tensile tester is presented in Fig. 1. This tensile tester isavailable at the DiffAbs beamline of the synchrotron radiationfacility SOLEIL [27]. It comprises four independent motors andfour load sensors, that allow to perform tensile tests withdifferent (and not necessarily constant) load ratios. An opticalsetup is fixed underneath the testing machine (Fig. 1) to capturepictures of the back side surface of the specimens at each loadstep for the true strain measurement with Digital Image Corre-lation (DIC) analysis (q4-Correli software) [28,29]. The opticalmicroscope is composed of a telecentric lens (� 0.5 or� 1.0 fromEdmund Optics, York, UK) and a CCD camera (Pixelfly: from PCOAG, Kelheim, Germany, QE-12 bits dynamic range, horizon-tal� vertical: 1392� 1024 pixel resolution and a pixel size6.45� 6.45 mm2, black and white). In the present work the size ofthe region of interest at the sample surface is 9� 6.3 mm2 (� 1.0lenses). The grey levels are obtained by applying paint speckleson the rear surface of the substrate, and this paint containscrystallites of TiO2 in the rutile phase. With x-rays this givescontinuous Debye-Scherrer rings that allow a calibration of thediffraction parameters during the test. The in situ XRD mea-surements were performed at the DiffAbs beamline with a beamenergy of 16 keV. Images were recorded every 5 s with a two-dimensional detector, a Mar 165-SX lying 264mm from thesample [30]. The beam width was approximately 250� 300 mm2 ,vertical times horizontal, but the incident angle being 9�, thefootprint spreads to 1600� 300 mm2 insuring a high represen-tativity of these XRD results (mean grain diameter of Ni film is ofthe same order of magnitude as thickness, e.g. 50 nm).

As shown previously, the film/substrate adhesion ensures acomplete strain transfer at the interface [31]. Thus, the stressesmeasured by x-ray diffraction are indirectly applied via the appli-cation of themacroscopic strain to the substrate. In x-ray diffractionstress analysis, the strain in the crystal lattice is measured, and theapplied or residual stress associated to this strain is calculated usingthe elastic constants, assuming a linear elastic distortion of thecrystal lattice. This residual or applied stress can be called macro-scopic stress, or macrostress. The sin2j method was adopted todetermine the lattice strain evolution in the two principal in planedirections (thanks to the azimuthal rotation (angle f) of the tensilemachine). The Ni f111g diffraction peak recorded with the 2D de-tector was analyzed during single or complex loadings. It should benoted here that j angle depends on the orientation of the smallselected part of the Debye-Scherrer ring during post-treatment[32]. The macroscopic stress in Ni films have been calculated withthe x-ray elastic constant 1=2S1112 ¼ 5:2� 10�6 MPa�1. Thediffraction signals for 64 j angles (between 3� and 66�) were fittedby a home-made routine (using Pearson VII function) to determinethe position (2q) and the full width at half maximum (FWHM). TheFWHM is composed of the purely instrumental contribution andthe one related to the material. The first contribution does notchange during the test since the geometry of the problem remainsconstant. Thus the evolution of the FWHM is only related to themicrostructural evolution during the test. If the size of the coherentdomains of diffraction does not evolve (which must be our case oflimited plasticity), this evolution is related to the heterogeneities ofcrystal lattice strain in the probed volume. They can be linked to thenumerous cracks in the probed volume. Indeed cracks induce astrain (and stress) gradient in their immediate vicinity [33].Moreover, they can also be related to microstructure effects inde-pendently of the presence of cracks: grain-grain heterogeneities orin-grain ones.

Finally, optical images of the crack patterns were recorded exsitu thanks to a Keyence confocal microscope.

Fig. 3. Macroscopic curves for the complex loading: (a) applied load to the sample and(b) subsequent macroscopic strain along both axes as a function of time, (c) crackpattern observed after a simple uniaxial test at 8%, (d) crack pattern observed after thecomplex test.

D. Faurie et al. / Acta Materialia 165 (2019) 177e182 179

3. Experimental results and discussion

3.1. Loading effect on crack pattern

Two loading paths were adopted for this study: a first equi-biaxial loading (Fig. 2) and a second complex one consisting ofloading successively along each of the axis of the cruciform spec-imen (Fig. 3). Note that in the latter case, a slight transverse tensionforce has been applied in order to avoid the phenomenon ofbuckling of the thin film related to possible high compressivestresses [33]. The general goal is to achieve similar force valuesalong both axes through totally different loading paths. Note thatthe biaxial tester is here driven at constant displacement rate at theend of each jaw which does not ensure a constant force rate overtime given the viscoelastoplastic properties of the substrate.Moreover, even if the displacement rate at the end of the jaw isconstant, it is not necessarily the case for the macroscopic strainrate measured in the center. This is due to the probable strain non-uniformity along the cruciform Kapton® substrate which can varywith increasing load.

Fig. 2 shows the macroscopic curves for the equibiaxial loading.Fig. 2-a shows the evolution of the force applied along the two inplane axes as a function of the experiment time. It is clear that theforce along the axes evolve in a similar way while the macroscopicstrains (measured by DIC on the substrate surface) εxx and εyy areslightly dissimilar (see Fig. 2-b). The measured mechanical anisot-ropy is attributed to the fabrication process of Kapton® sheet.However, the measured deformations are close enough to create amud-crack pattern shown on Fig. 2-c, as other authors have beenable to highlight in more or less recent literature [11,22,23]. Indeed,in the case of macroscopic equibiaxial loading, the cracks can followa complex (not straight) trajectory because of local stress field atthe crack tips.

Fig. 3 shows the macroscopic curves for the complex loading,which is divided into two stages. It is clearly seen in Fig. 3-a that in afirst stage (noted 1 in the top insert) Fx increases about 3 timesmore than Fy. In a second stage (noted 2 on the lower insert) thisratio of forces is reversed in order to converge towards equivalentforces (around 80 N as for equibiaxial loading). This is reflected in

Fig. 2. Macroscopic curves for the equibiaxial loading: (a) applied load to the sampleand (b) subsequent macroscopic strain along both axes as a function of time, (c) crackpattern observed ex situ.

stage (1) by an increase in the εxx component associated with adecrease (due to the Poisson effect) and then stagnation of εyy after10min of loading in this test stage. The stagnation that is observedis undoubtedly due to the plasticity of the substrate. Indeed we seein Fig. 3-b that εxx is then greater than 5%which correspondswell tothe domain of plasticity of Kapton® [34]. We will see later that thisplays a role on the development of stresses in the thin film. Duringstage (2), εyy increases sharply with the rise in Fy which is accom-panied by a slight rise in εxx. Note that unlike Fx and Fy, εxx and εyy

do not have the same values (10.5% and 8% respectively). Asmentioned above, this is probably due to the anisotropy of thesubstrate and the plasticity of the latter in complex loading. Despitethese disparities, the complex path leads to a roman-brick struc-ture, which shows that the reached value of εyy is sufficient to attaina significant density of cracks. Firstly, during the stage (1), thestraight cracks perpendicular to the high tensile stress are created.This is commonly reported in the literature [18,21,33,34] andshown in Fig. 3-c. Moreover, the increase of Fy has prevented theformation of buckles, as shown on this figure. In the second stage,the displacement is mainly applied along the second axis of theplane of the sample. This results in the initiation of cracks insidepreviously created fragments. It may be noted that the cracks in afragment are not necessarily initiated at the same place as in theneighboring fragment, as already observed by Merabtine et al. [16].

3.2. In situ thin film stresses monitoring

From these ex situ observations at the surface of the thin films, itis interesting to follow the evolution of the stresses sxx and syy inthe thin films (measured by in situ XRD) during each test. If oneconsider first the case of equibiaxial loading (Fig. 4), the stress-timecurve shows three main mechanical domains: (i) a linear regimewhich corresponds to the elastic domain of the film, (ii) a cleardeviation to linearity which corresponds to the initiation of plas-ticity and/or first cracks in the film, (iii) a decrease of the stresswhen the multicracking phenomenon having a random pattern is

Fig. 4. XRD measurements for the equibiaxial loading: (a) stresses in Nickel thin filmand (b) FWHM as a function of time.

Fig. 5. XRD measurements for the complex loading: (a) stresses in Nickel thin film and(b) FWHM as a function of time.

D. Faurie et al. / Acta Materialia 165 (2019) 177e182180

engaged. Note that the deviation found for the domain (ii) can befound in the literature for ductile layers such as Ag [19] and forinherently brittle thin films such as Ta [21] or W/Cu multilayers[27,35], in the case of uniaxial tests. Therefore, this deviation can berelated either to microplasticity or to very first steps of crackinitiation, but this point was not clarified in the literature. As shownby modeling works of Qin et al. [11], after the initiation of firstcracks, the progressive decay of sxx and syy corresponds to thecreation of smaller and smaller sub-fragments within the primaryones until reaching a final pattern that would then correspond tovery small variation of stress (during the last part of the test, after13min). Note that the effect of Kapton® anisotropy is found in theslightly lower value of syy compared to sxx.

As far as the FWHM is concerned, it could only be measuredproperly for the low j angles because of the greater instrumentalcontribution at higher inclinations. Note that beyond the progres-sive noise of the curves, the trends found as a function of time andtherefore of the macroscopic strain are very similar for the differentj values. We show here the results for j ¼ 3�, i.e. scattering vectororiented almost normal to the film plane. In a perfect elastic regime,the FWHM should slightly increase because differently orientedgrains present different level of strain (due to elastic anisotropy). Inthe present case, in domain (i), the FWHM stagnates on the firstpoints then decreases significantly; this shows that the grain-to-grain heterogeneities are quickly counterbalanced by the in-grainones. In other words, microplasticity induces a mechanicalannealing, as has already been observed in sputtered Au films onKapton® [30]. A rise in the FWHM is then observed as soon as thedomain (ii) is engaged, which may also be expected since therelated phenomena (plasticity or possible first crack initiation)

must cause an increase in the strain heterogeneities in the thin film.Actually, there is no abrupt transition between the domains (ii) and(iii) but rather within the domain (ii) in Fig. 4 (shown by verticaldotted line). It is therefore allowed to hypothesize that initiation ofcracking (locally) must take place just before the global relaxationof the stress related to the phenomenon of crack multiplication, i.e.in domain (ii). Finally, the maximum value of the FWHM corre-sponds to the saturation of the number of cracks. The last part ofthe curve therefore corresponds to the widening of the cracks withthe external loading [11].

Fig. 5 shows the same curves for complex loading. During stage(1), the same domains (i), (ii) and (iii) can be shown as for equi-biaxial loading. A difference lies in the decrease of the stressesduring the multicracking which is much more important. This re-flects the fact that the multiplication of parallel cracks is charac-terized by a greater relaxation especially in the vicinity of cracks.The sharp decline is mainly at the early stage of multicracking,precisely where most cracks appear. Indeed the asymptoticbehavior appears at about 12min, i.e. for εxx ¼ 7%. Note that thesecond part of this domain is also characterized by a slight increasein syy . In several articles, this phenomenon is related to theappearance of blisters at the edge of cracks. However, in our case,the absolute value of syy (about 200MPa) is very low and especiallylower than the residual stress (about 400MPa). In addition, we didnot observe ex situ the appearance of blisters as said before. In ourcase, we interpret this result by the evolution of the substratemacroscopic strain εyy (Fig. 3-b) which does not evolve anymorefrom 10min of test. It consequently induces a positive slope for thestress syy in the thin film.

During stage (2) of the complex loading, one naturally observesan increase of the stress syy in the domains (i) and (ii), then a

Fig. 7. Von Mises applied stress in the thin films as function of Von Mises appliedstrain.

D. Faurie et al. / Acta Materialia 165 (2019) 177e182 181

substantial decrease that corresponds to the multicracking in thetransverse direction. It is interesting to note that this decrease is asimportant as in stage (1), which shows that the stress evolutionrelated to the multicracking phenomenon is similar during thesecond loading (stage (2)). On the other hand, it is noted that thestress sxx evolves very little during this domain because of thesaturation of the number of fragments along this direction alreadyreached in domain (1). In addition, the FWHM shows an evolutionclose to that encountered during stage (1). The main difference liesin its early decay during the transverse multicracking domain. Thisis still difficult to interpret, it is possible that the heterogeneitiescreated during the first stage are slightly balanced during thetransverse loading, but this remains speculative. Nevertheless, wehighlight again the net change in slope for the FWHM as a functionof time in each domain (ii) of each stage (vertical dotted lines). Thistherefore tends to show that the crack initiation must take place inthis domain, before the stress really relaxes. It means that justbefore the domain (iii) the adherent parts of the thin films aresufficiently strained to balance the local stress relaxations occur-ring around the cracks.

3.3. Loading path effect in plane stress space

In order to compare the two tests on a same graph we haverepresented the evolution of sxx and syy in the principal stressspace (Fig. 6). In the equibiaxial case, we have a very simplebehavior starting from the residual stress state until the end ofthe test. The lowering of the stresses during the multicracking isnot accompanied by a modification of the ratio sxx=syy in the thinfilm. This shows the planar isotropy of the phenomenon whencreating random patterns. On the contrary, the complex testleads to a much less direct path of stress, including within eachof the stages. The ratio is of course never the same and it evolvesdifferently in the same domain depending on whether one is inthe elastic loading, elastoplastic regime or during the multi-cracking. It can be seen that the difference in crack pattern isintimately related to a drastically different stress path, which isrelated to highly oriented mechanical phenomena in the plane ofthe sample during each domain (plasticity of the substrate, thinfilm multi-cracking).

To continue this comparison, we plotted the Von Misesapplied stress as a function of the Von Mises applied strain (seeFig. 7). In other words, the stresses used for the Von Misescalculation are applied x-ray macroscopic stress, and we did not

Fig. 6. Evolution of stresses (sxx and syy) in the thin films during equibiaxial andcomplex tests.

take into account the initial compressive residual stress state(hence applied stress and strain are obviously zero at thebeginning of loading). It should be noted here that these equiv-alent quantities are calculated from mean directional stresses(sxx and syy ) and strains ( εxx, εyy and εzz), thus by neglecting thestress and strain heterogeneities. Moreover, εzz has been deducedfrom εxx and εyy assuming a constant out-of-plane Poisson's ratioof the system (n ¼ 0:3). Although this last hypothesis is notperfectly verified during the whole of the test, this representa-tion allows us to give a comparison of the two tests by followingthe same hypothesis for both. It can be seen that for both tests,the elastic regime is perfectly superimposed. The first disparitiesappear as soon as the thin film enters its plastic domain, andthen when the multicracking is engaged. Interestingly, this cor-responds to the increase of FWHM which is related to the in-crease of stress and strain heterogeneities in the polycrystallinefilm (see Figs. 4 and 5). Thus the stress deviation obtained justbefore relaxation is probably a mechanical loading effect on thenature and intensity of heterogeneities.

The multicracking domain for the complex loading is charac-terized by three regimes already observed [21,36]. Let us denote s∞the reference value of the stress that would exist in an uncrackedfilm. One critical characteristics of multicracked systems is the“stress transfer length”, defined as the characteristic distance overwhich the stress s∞ is recovered inside the film starting from thefree surface (i.e. zero stress) induced by a crack [37,38]. The mul-ticracking domain for the complex loading is characterized by threeregimes already observed in the case of uniaxial tensile tests[21,33,36]. The first regime (for small applied strains) correspondsto a statistical regime with no obvious spatial organization of thecracks. Each new crack appears at random position mainly drivenby the presence of defects in the layer. The distribution of thestraight cracks are thus described by the distribution of filmstrength, for which the Weibull statistics have been found suitablefor modeling [22]. This initial fragmentation step is characterizedby a crack spacing significantly exceeding the stress transfer length.During this regime, the interaction between cracks is negligible;the rate of crack generation is governed solely by the mechanicalinhomogeneity of the thin film (related to structural defects). Thesecond fragmentation regime starts when the distance betweenmost of the neighboring cracks is smaller than the stress transferlength. As a result, the maximum stress in a fragment can not reachthe undisturbed far field level s∞, resulting in a marked reductionin the fragmentation rate with respect to applied strain. The stressprofile between two cracks is marked by a maximum value right inthe middle of the fragment. Hence, the next crack most likely

D. Faurie et al. / Acta Materialia 165 (2019) 177e182182

appears at this precise spot, making regime 2 deterministic, con-trary to regime 1. As can be observed in Fig. 7, in regime 2 the globalrelaxation of stress is progressing at a lower rate with respect toapplied strain (smaller slope). The third regime corresponds to thesaturation of the number of cracks (horizontal slope in Fig. 7). Itconfirms that the first stage of the complex loading have the samecharacteristics as uniaxial loading usually reported in the literature,except for the generation of buckles. It is worth noting that thesecond stage of the complex loading is very similar to the first one.Especially, the two first multicracking regimes are also identified inthis stage, the test being stopped probably just before the start ofthe third regime (the crack density along x and y direction havebeen found to be roughly the same (on ex situ optical images (seeFig. 3-d)).

The fragmentation for equibiaxial strain is more governed bybinary fragmentation: a fragment splits into two sub-fragments ofcomparable size, and therefore fragment breakup due to crackpropagation always generates two new fragments [39]. This can bealso accompanied at high strains by crack branching and fragmentshattering transition when viscoelastoplastic substrate is used,which can affect the stress transfer from substrate to the film. It hasbeen shown in Ref. [39] that for equibiaxial loading, the meanfragment size evolution with strain fits well with a decreasingpower-law behavior. This is consistent with our experimental re-sults (circle symbols in Fig. 7) and also with modeling results of Qinet al. [11] which shows a decreasing power-law for the fragmentsize as well as for the thin film stress as function of applied strain.This should explain why no particular regimes are observed for theequibiaxial loading.

4. Conclusion

We have biaxially tested Ni thin films (thickness of 50 nm) onKapton® cruciform substrates (thickness of 25 mm). Two mainloading paths were explored, which resulted in two differentcrack patterns, i.e. mud-cracks for equibiaxial path and roman-bricks for complex one (by successively loading along each ofthe axes of the sample). In situ x-ray diffraction experiments havebeen combined with digital image correlation measurements atSOLEIL Synchrotron DiffAbs beamline in order to probe the thinfilm stresses and macroscopic substrate strains, respectively. Wehave shown that the initiation of cracks for the two differentloading paths is related to a strong variation of full width at halfmaximum of x-ray diffraction peaks, which is a signature ofstrong strain and stress heterogeneities, that had not been pro-posed until now. In contrast the magnitude of stresses relaxationassociated to the crack multiplication is strongly dependent onthe loading path. Indeed, while it is smooth during the mud-crack pattern, this relaxation is characterized by three regimesas already observed by several groups in the case of uniaxialtensile tests. The strong differences in term of crack pattern de-velopments are introduced by fully different ways followed bythe in-plane thin film stresses. Thus, it is possible to vary thecrack patterns in thin films deposited on a polymer substrate bycontrolling the planar deformations and by varying the loadingpath. In the case of complex loading, one could for example varythe intensity of loading in one or other of the directions to createmore or less rectangular patterns. However, this kind of tech-nique, also known as crack lithography [24], involves importantstress fields in the thin film which must be given particularattention since they can strongly influence the functionalproperties.

Acknowledgments

This work has been partly supported by the Region Ile-de-France in the framework of DIM Nano-K. Authors would like tothank Philippe Gu�erin from the PPRIME institute for samplepreparation and acknowledge the support of the DiffAbs beam-line team for technical help during the experiments described inthis paper.

References

[1] M. Kaltenbrunner, M.S. White, E.D. Głowacki, T. Sekitani, T. Someya,N.S. Sariciftci, S. Bauer, Nat. Commun. 3 (2012) 770.

[2] S. Das, R. Gulotty, A.V. Sumant, A. Roelofs, Nano Lett. 14 (2014) 2861.[3] D. Makarov, M. Melzer, D. Karnaushenko, O.G. Schmidt, Appl. Phys. Rev. 3

(2016), 011101.[4] Q. Hua, J. Sun, H. Liu, R. Bao, R. Yu, J. Zhai, C. Pan, Z.L. Wang, Nat. Commun. 9

(2018) 244.[5] S. Wang, , et al.J.B.-H. Tok, Z. Bao, Nature 555 (2018) 83.[6] A. Kleinbichler, M. Bartosik, B. V€olker, M.J. Cordill, Adv. Eng. Mater. 19 (2016)

1.[7] J.L. Beuth Jr., Int. Jour. Sol. Struct. 29 (1992) 1657.[8] Z. Chen, B. Cotterell, W. Wang - Eng, Fract. Mech. 69 (2002) 597.[9] Z.C. Xia, J.W. Hutchinson - Journ, Mech. Phys. Sol. 48 (2000) 1107.

[10] J. Marthelot, B. Roman, J. Bico, J. Teisseire, D. Dalmas, F. Melo, Phys. Rev. Lett.113 (2014), 085502.

[11] Z. Qin, N.M. Pugno, M.J. Buehler, Sci. Rep. 4 (2014) 4966.[12] R. Seghir, S. Arscott, Sci. Rep. 5 (2015) 14787.[13] Z.Q. Liu, J.H. Liu, M.D. Biegalski, J.-M. Hu, S.L. Shang, Y. Ji, J.M. Wang, S.L. Hsu,

A.T. Wong, M.J. Cordill, B. Gludovatz, C. Marker, H. Yan, Z.X. Feng, L. You,M.W. Lin, T.Z. Ward, Z.K. Liu, C.B. Jiang, L.Q. Chen, R.O. Ritchie, H.M. Christen,R. Ramesh, Nat. Commun. 9 (2018) 41.

[14] B. Putz, B. V€olker, C. Semprimoschnig, M.J. Cordill, Microelectron. Eng. 167(2017) 17.

[15] S. Merabtine, F. Zighem, A. Garcia-Sanchez, V. Gunasekaran, M. Belmeguenai,X. Zhou, P. Lupo, A.O. Adeyeye, D. Faurie, Sci. Rep. 8 (2018) 13695.

[16] S. Merabtine, F. Zighem, D. Faurie, A. Garcia-Sanchez, P. Lupo, A.O. Adeyeye,Nano Lett. 18 (2018) 3199.

[17] M. Kim, D.-J. Kim, D. Ha, T. Kim, Nanoscale 8 (2016) 9461.[18] V.M. Marx, F. Toth, A. Wiesinger, J. Berger, C. Kirchlechner, M.J. Cordill,

F.D. Fischer, F.G. Rammerstorfer, G. Dehm, Acta Mater. 89 (2015) 278.[19] B. Putz, C. May-Miller, V. Matl, B. V€olker, D.M. T€obbens, C. Semprimoschnig,

M.J. Cordill, Scripta Mater. 145 (2018) 5.[20] K. Wu, J.Y. Zhang, J. Li, Y.Q. Wang, G. Liu, J. Sun, Acta Mater. 100 (2015) 344.[21] S. Frank, P.A. Gruber, U.A. Handge, R. Spolenak, Acta Mater. 59 (2011) 5881.[22] Y. Leterrier, D. Pellaton, D. Mendels, R. Glauser, J. Andersons, J.-A.E. Månson,

J. Mater. Sci. 36 (2001) 2213.[23] L. Goehring, R. Conroy, A. Akhter, W.J. Clegg, A.F. Routh, Soft Matter 6 (2010)

3562.[24] B.C. Kim, C. Moraes, J. Huang, T. Matsuoka, M.D. Thouless, S. Takayama, Small

10 (2014) 4020.[25] M.J. Cordill, O. Glushko, B. Putz, Front. Mater. 3 (2016) 11.[26] T. J€org, M.J. Cordill, R. Franz, C. Kirchlechner, D.M. T€obbens, J. Winkler,

C. Mitterer, Mater. Sci. Eng. 697 (2017) 17.[27] S. Djaziri, D. Faurie, P.-O. Renault, E. Le Bourhis, Ph Goudeau, G. Geandier,

D. Thiaudi�ere, Acta Mater. 61 (2013) 5067.[28] G. Besnard, F. Hild, S. Roux, Exp. Mech. 46 (2006) 789.[29] S. Djaziri, P.O. Renault, F. Hild, E.L. Bourhis, P. Goudeau, D. Thiaudi�ere,

D. Faurie, J. Appl. Crystallogr. 44 (2011) 1071.[30] P. Godard, P.-O. Renault, D. Faurie, D. Thiaudi�ere, Appl. Phys. Lett. 110 (2017)

211901.[31] P.O. Renault, T. Sadat, P. Godard, W. He, Ph Guerin, G. Geandier, N. Blanc,

N. Boudet, P. Goudeau, Surf. Coating. Technol. 332 (2017) 351.[32] D. Faurie, G. Geandier, P.-O. Renault, E. Le Bourhis, D. Thiaudi�ere, Thin Solid

Films 530 (2013) 25.[33] S. Frank, U.A. Handge, S. Olliges, R. Spolenak, Acta Mater. 57 (2009) 1442.[34] D. Faurie, F. Zighem, A. Garcia-Sanchez, P. Lupo, A.O. Adeyeye, Appl. Phys. Lett.

110 (2017), 091904.[35] S. Djaziri, D. Faurie, E. Le Bourhis, Ph Goudeau, P.-O. Renault, C. Mocuta,

D. Thiaudi�ere, F. Hild, Thin Solid Films 530 (2013) 30.[36] M. Heinrich, P. Gruber, S. Orso, U.A. Handge, R. Spolenak, Nano Lett. 6 (2006)

2026.[37] Y. Leterrier, L. Boogh, J. Andersons, J.A.E. Manson, J. Polym. Sci., Part B: Polym.

Phys. 35 (1997) 1449.[38] J. Marthelot, Doctoral thesis, Universit�e Pierre et Marie Curie, Paris vol. I

(2014).[39] J. Anderson, Y. Leterrier, Thin Solid Films 471 (2005) 209.