The in-situ micro-damage mechanisms in semicrystalline PolyAmide 6 are examined in 3D by Xray imaging for crack initiation and propagation in a large flat specimen. The characteristic sizes of the damage features are quantified. Distinct damage zones are found well distributed ahead of the initial notch, and characterized as a function of stress states. The formation of tunnel cracks during crack propagation and the effect of notch defect are discussed.
Supplementary Information 3D damage micromechanisms in polyamide 6 ahead of a severe notch studied by in situ synchrotron laminography Yin Cheng,1,2,3∗ Lucien Laiarinandrasana,1 Lukas Helfen,2,3,4 Henry Proudhon,1 Olga Klinkova,1 Tilo Baumbach,2,3 and Thilo F. Morgeneyer1,∗ 1
Centre des Matriaux, MINES ParisTech, PSL Research University, CNRS UMR 7633, BP 87 Evry Cedex, France. Tel: +33 160 763061; E-mail:
[email protected];
[email protected] 2 ANKA/Institute for Photon Science and Synchrotron Radiation (IPS), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen, Germany. 3 Laboratory for Applications of Synchrotron Radiation (LAS), Karlsruhe Institute of Technology (KIT), D-76049 Karlsruhe, Germany. 4 European Synchrotron Radiation Facility (ESRF), F-38043 Grenoble, France.
S1 Semicrystalline polymer PA6 The PA6 material of interest was provided by Angst & Pfister as 610 mm × 1230 mm flow moulded plates with 10 mm in thickness. 1 The main physical-chemical properties of this PA6 material are as follows: the glass transition temperature Tg = 53◦ C, the melting point TF = 219◦ C and crystallinity index z = 43% were obtained with the help of modulated differential scanning calorimeter (MDSC). The Young’s modulus at room temperature E = 2850 MPa was estimated with the initial slope of the stress-strain curve. The density of the material ρ ≈ 1.15 g/cm3 . All the tensile tests were carried out at room temperature (23 ◦ C) and 50% relative humidity (RH). In order to reveal the expected spherulitic microstructure, samples were examined by scanning electron microscopy (SEM) after chemical etching. The spherulite mean size is about 5 µm. Table S1 Physicochemical characteristic of the polyamide 6 under study. 2
53 ◦ C 43% 5 µm
glass transition temperature, Tg degree of crystallinity spherulite mean diameter
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S2 Anti-buckling device and sample frame The loading was achieved via a 2-screw displacement controlled wedging rig, that imposes the specimen crack mouth opening displacement (CMOD) without measuring the load level. The rate of the stepwise increase was 1-2 second per quarter screw turn. The magnitude was 0.7 mm per turn for ANKA and 1 mm per turn for ESRF, respectively. An anti-buckling device was used in order to prevent the thin sample sheet from significant buckling and out-of-plane motion during tensile tests (Figure S1(a)). Then the entire in situ tensile device (contains of the specimen, the 2-screw loading rig and the anti-buckling frame) was mounted onto a rectangular sample holder. Finally, the whole sample frame was mounted onto the laminography rotary stage by magnets and it allows for the positioning and searching the ROI of the specimen around the rotation axis on the rotary stage (i.e., Figure S1(b)).
Figure S1 (a) A photograph of the loading rig, anti-buckling device as well as the notched sheet specimen mounted on the sample frame/holder. (b) A wide view shows the entire in situ machine mounted onto the rotary stage of the laminography instrument at ANKA.
S3 Experiment S3.1
A concise comparison of synchrotron computed tomography (CT) and laminography (CL)
Computed tomography (CT) is a three-dimensional (3D) imaging method well established at large synchrotron facilities. 3 For compact or prolate specimens (i.e. long objects, Figure S2(a)) extending more or less isotropically along the rotation axis, CT is competent to yield artifactfree reconstructed cross-sections. However, laterally extended (i. e. flat, plate-like) specimens are much less amenable to CT since reliable projection data are difficult to be acquired from angles where the plate is oriented parallel to the X-ray irradiation direction (due to little or no transmission at all). Computed laminography (CL) (Figure S2(b)) therefore was introduced at synchrotron imaging beamlines 4 to overcome this limitation of CT concerning the specimen geometry. The 2
Figure S2 Principles of parallel-beam synchrotron radiation (a) computed tomography (CT), in comparison with (b) computed laminography (CL).
efficiency of synchrotron radiation CL as a method for non-destructive 3D imaging of flat, laterally extended specimens has already been demonstrated in a variety of scientific areas covering microsystem technology, 5–7 cultural heritage investigations, 8 paleontology 9 and fracture mechanisms in engineering aluminum alloys. 10–12 S3.2
Experimental apparatus at the TopoTomo beamline, ANKA
Figure S3(a) shows the micro-laminography instrument at ANKA. The entire sample frame is attached to a sample plate Sxy by magnetic force, allowing for translations on the plate in order to search for the ROI. The sample frame also rotates in accordance with the laminography rotary stage ω . The goniometer system allows for the inclination of the rotary geometry so as to achieve the laminography geometry (Figure S2(b)).
Figure S3 Photographs show the synchrotron radiation µ-laminography instrument at ANKA.
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S4 Results of the defect-free (smooth) notched specimen Figure S4 illustrates how the initial notch was missed in the field of view after CMOD = 6 mm (Figure S4a) during our X-ray imaging experiment. As one can see at CMOD = 9.5 mm in Figure S4(b), we only captured the tip of the propagating main crack but lost the original notch tip in our FOV. One can compare this image to Figure 6(j-l), where both the notch tip and the initiated and propagation main crack tip are kept in the FOV. A possible solution in the future which may avoid this mistake is addressed in the Section S6.
Figure S4 2D L-P cross-sections at midplane of the defect-free notched specimen. (a) CMOD = 6.0 mm (the same image as Figure 3d); (b) CMOD = 9.5 mm. One can find the initial notch tip was missed in the FOV so that we could not correlate the location of the main crack with respect to the notch tip in the former loading step.
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S4.1
Through-thickness (L-S) plane
Figure S5 2D L-S cross-sections at distance ∼ 13 µm ahead of the notch tip at different CMODs showing the damage initiation and evolution in the defect-free notched specimen. (a) CMOD = 2.5 mm; (b) CMOD = 4.5 mm; (c) CMOD = 6.0 mm.
Figure S5 shows the through-thickness (L-S) cross-section at distance ∼ 13 µm ahead of the notch tip of the defect-free notched specimen. This straight cross-sectional plane roughly intersects with the three distinct damage zones from top to bottom (referring to the L-P cross-section in Figure 3 in the main article). Zones ii, i and 0 are well distributed from the up/bottom margin to the center of the image (Figure S5(c)), which is consistent with the L-P plane distributions.
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S4.2
3D views of damage evolution
Figure S6 pictures the 3D damage evolution in the defect-free notched specimen at the crack initiation stage. The well distributed damage zones are clearly visualized.
Figure S6 3D renderings (337.5 µm thick volume) around the defect-free notched specimen’s midplane at different CMODs. (a) CMOD = 0 mm; (b) CMOD = 2.5 mm; (c) CMOD = 4.5 mm; (d) CMOD = 6.0 mm. The notch is in black, the polymer matrix is shown in gray and the damages are shown varying from light to deep golden dependent on the cavitation density of a specific area.
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S5 Results of through-thickness (L-S) plane of the defective notch specimen S5.1
Distance ∼ 13 µm
Figure S7 2D L-S cross-section of the as-received material (CMOD = 0) at a net distance ∼ 13 µm ahead of the notch tip. The bulk material seems very homogeneous without any pre-existing damage.
Figure S7 shows the through-thickness (L-S) cross-section of the as-received material (CMOD = 0) at distance ∼ 13 µm ahead of the notch tip. Two regions are labeled as “Region 1” (blue box) and “Region 2” (green box) respectively, which will be presented individually in the following sections. Figure S8 shows the damage evolution in Region 1 at different CMODs. At CMOD = 0.525 mm (b), crazes that elongated along the S direction, perpendicular to the loading direction are observed. At CMOD = 0.7 mm (c), shear bands are observed between multiple crazes. At CMOD = 1.05 mm (d); shear banding is more pronounced leading to a zig-zag cracking path. At CMOD = 1.4 mm (e), crazes expanded in height (L direction) and the specimen boundary started shrinking. At CMOD = 2.1 mm (f), a shear induced coalescence between two parallel crazes is clearly seen compared to the former loading step (e). From CMOD = 2.8 mm (g) to CMOD = 3.5 mm (h), the damage in Region 1 did not develop considerably. In fact this is due to the stress concentration in the upper Region 2 because of the initial defect, which will be shown later in Figure S9. Void columns found in Figure S8(h) imply the moderate stress level in Region 1 at this moment. From CMOD = 4.2 mm (i) to CMOD = 5.25 mm (k), stress gradually released in Region 1 owing to the main crack initiation and propagation in the upper area Region 2. Figure S9 follows the damage evolution in Region 2 at different CMODs. The damage start to set in at CMOD = 1.4 mm. From this moment on, the stress gradually accumulated and concentrated in this region due to the initial notch defect, and giving rise to rapid growth of 7
Figure S8 2D L-S cross-sections in Region 1 at different CMODs showing the damage initiation and evolution. (a) As-received material; (b) CMOD = 0.525 mm; (c) CMOD = 0.7 mm; (d) CMOD = 1.05 mm; (e) CMOD = 1.4 mm. (f) CMOD = 2.1 mm; (g) CMOD = 2.8 mm; (h) CMOD = 3.5 mm; (i) CMOD = 4.2 mm; (j) CMOD = 4.9 mm; (k) CMOD = 5.25 mm.
crazes/cracks. Away from this region, stress gradually dropped off and these regions are mainly arrested by void column like damage features.
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Figure S9 2D L-S cross-sections at different CMODs showing the damage initiation and evolution in Region 2. (a) CMOD = 1.4 mm; (b) CMOD = 2.1 mm; (c) CMOD = 2.8 mm; (d) CMOD = 3.5 mm; (e) CMOD = 4.2 mm. (f) CMOD = 4.9 mm; (g) CMOD = 5.25 mm.
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S5.2
Distance ∼ 200 µm
Figure S10 2D L-S cross-sections at a distance ∼ 200 µm ahead of the notch tip at different CMODs showing the damage initiation and evolution. (a) CMOD = 2.8 mm; (b) CMOD = 3.5 mm; (c) CMOD = 4.2 mm; the inset is a zoom-in image of the red dashed box and the scale bar is 50 µm. (d) CMOD = 4.9 mm.
Figure S10 shows 2D cross-section in the through-thickness plane at a distance ∼ 200 µm ahead of the notch tip at different CMODs. From CMOD = 2.8 mm (a) to 3.5 mm (b), stress is gradually concentrated in the upper part of notch causing damage intensification. The void columns in zone i are also re-orientated from vertically towards the stress concentration point. At CMOD = 4.2 mm, the ligament between multiple long crazes at the maximum stress region starts to be teared and transformed to the micro-fibrillar structure. And at CMOD = 4.9 mm, the micro-fibrils are fractured and the main crack reached this position. S5.3
The CTOD and CTOA
The crack tip opening displacement (CTOD) was determined to evolve from Figure 7(c) 146.3 µ m to Figure 7(d) 191.4 µ m, and the crack tip opening angle (CTOA) 13,14 developed from 10
Table S2 The evolution of CTOD during crack propagation.
Applied CMOD 3.5 mm 4.2 mm 4.9 mm 5.25 mm
Local CTOD 47.3 µm 146.3 µm 167.2 µm 191.4 µm
87.1◦ to 93.4◦ , respectively. In addition, the CTOA profile was descending from the midplane to the surface of the specimen as can be discerned in Figure 9(b)). S5.4
3D magnified views of a small volume during crack propagation
A small volume of size (100 µm)3 was chosen (as indicated in Figure 6(i), red dashed box) around the specimen’s core in order to highlight the damage evolution in more detail. Only voids/cracks were picked out for 3D rendering. One can clearly resolve the microstructure evolution in front of the main crack tip during its propagation. It evolved from zone iii (voids) to zone i (polar fan cracks) to zone ii (tunnel cracks, coalescence), and finally leading to the merger with the main crack tip - crack propagation mechanism follows such scenario.
Figure S11 3D volumes of (100 µm)3 around the specimens midplane at the same region in the path of crack propagation reveal in situ voids/cracks evolution in PA6 (defective notch) during deformation. (a1-b1) CMOD = 2.8 mm; (a2-b2) CMOD = 3.5 mm; (a3-b3) CMOD = 4.2 mm; (a4-b4) CMOD = 4.9 mm.
S6 Perspectives Indeed, finding the ROI to be observed is more difficult in laminography than in tomography as the specimen is wider than the detector’s FOV. In addition, local laminography has been 11
applied in the ESRF experiment. This means that the thickness of the sample was larger than the detector height, which makes finding the ROI even more difficult. This may lead to the situation that the sample is in the X-ray beam but not actually in the intersection of the rotation axis and the beam. To avoid this drawback, an online reconstruction scheme is forseen. That is to reconstruct a selectable 3D volume with ultrahigh speed right after the scan (on the fly). Such online reconstruction scheme will require a specially designed efficient algorithm coupling to a powerful computing hardware (i.e. parallel GPUs). In fact the online reconstruction system is currently under development among several institutions because it is highly demanding in various fields such as imaging of fast dynamical processes.
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