University of Groningen Nanotopography and morphology ... · 6 Evolution of grain structure in deformed metal-polymer laminates4 6.1 Abstract In this chapter the roughening along

University of Groningen

Nanotopography and morphology along metal-polymer interfacesFaber, Enne

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6 Evolution of grain structure in

deformed metal-polymer laminates4

6.1 Abstract In this chapter the roughening along a metal-polymer interface is examined, to find out which mechanism leads to roughening on a sub-grain level as opposed to the grain size level. This is relevant for understanding the possible delamination of a polymer coating on a metallic substrate. Therefore we have investigated the local lattice orientation in heavily strained ferritic steel using electron back-scatter diffraction. From that data we have calculated the components of the local orientation gradient tensor as well as the local Taylor factor for deformation along [100] and [001] directions on {101} and {112} slip systems. The curvature of the draw-and-redraw steel- polyethylene terephthalate (PET) laminate interface as well as the curvature of the underlying steel lattice was examined in detail. It is concluded that roughening at a sub-grain length scale along the interface is the result of dislocation slip, i.e. plasticity in the interior of the grains.

4 Adapted from: E. Faber, W.P. Vellinga, J.Th.M. De Hosson, Journal of Materials Science, Volume 49, Page 8335-8342, December 2014, DOI: 10.1007/s10853-014-8542-3

Chapter 6 – Evolution of grain structure in deformed metal-polymer laminates3F

104

6.2 Introduction Upon deformation metallic surfaces become rough affecting surface-related properties such as friction, wear and adhesion. In particular rough surfaces facilitate sites for crack nucleation, which may seriously deteriorate the mechanical performance of the adhesive interface. Adhesion at interfaces is of great interest, especially the effect of roughening on the interface between dissimilar materials like a metal and a polymer. Therefore roughening mechanisms and their consequence for the mechanical performance have been the subject of numerous investigations [24], [61], [85], [107]–[109], encompassing experiments and theoretical studies. The overarching outcome is that surface roughness depends on the strain, grain size and texture. The relationships between roughness and strain and between roughness and grain size are often found to be linear [25], [26], [110], [111] but some authors report deviations from linear behavior, especially at higher strains [25], [112]. In a number of studies, texture was found to have a significant influence on the roughness [111], [113]–[117]. Most of these studies are aimed at understanding the development of a typical “roping” or “ridging” roughness. Differences in crystallographic orientation, causing differences in strain incompatibilities between neighboring grains, lead to roughening at the grain scale level, which is observed as the typical ‘orange peel’ surface topography [113], [115].

In chapter 4 we have investigated the evolution of texture of draw-and-redraw (DRD) laminate consisting of electrolytically chrome coated steel (ECCS) coated on both sides with polyethylene terephthalate (PET). In such a process a disk of ductile metal sheet is stamped into a cylindrical die – this is called a draw step. The bi-axial strain that is applied to a sheet to form a can, is a tensile strain in the meridional direction of the can and a compressive strain in the circumferential direction. Commonly a can formed this way is still too wide so the step is repeated with increasingly small dies yielding a narrower can; this is called redrawing. During each step the material is pulled through a forming die, and the material undergoes repeated bending (over the edge of the die).

In the same chapter we investigated in particular how roughening appears to affect the adhesion, identifying that delamination (cracks between the ECCS and PET) occurs primarily at overhanging features on and below the micrometer. There was a clear correlation between the roughening of the interface and the observed de-adhesion phenomena. It is suspected that de-adhesion of the polymer occurs on a length scale smaller than the grain size, and that roughening of the steel surface (and the appearance of overhanging shapes) creates

Nanotopography and morphology along metal-polymer interfaces

105

localized shear in the polymer which causes this de-adhesion. However it is not known which deformation mechanisms [24] create these particular surface features. The current work further pursues this line of research, concentrating on the mechanisms which determine the interface roughening behavior. It focuses on the question: can roughening at the interface be described at the length scale of grains and grain boundaries, or is it necessary to include details from the interior of the grain?

In particular the study is aimed at giving insight in the deformation mechanisms of ferritic steel by measuring the interface geometry and lattice orientations in draw-and-redraw (DRD) deformed laminate of electrolytically chrome coated steel (ECCS) and polyethylene terephthalate (PET). Several parameters are calculated from scanning electron microscope (SEM) images and from electron backscatter diffraction (EBSD, also known as orientation imaging microscopy or OIM) maps. These parameters are meaningful for the deformation mechanisms and the scale at which they occur.

Figure 6.1: Schematic illustration of the material used and the directions involved in the measurements. The laminate consists of ferritic steel with a thickness of 200 μm, coated on both sides with an adhesive thin chromium and chromium oxide multilayer, and with a 15-30 μm thick PET layer. Dimensions and strain are shown on the sheet (left) and with the strains on the can wall (right).

6.3 Experiments In this work we examine laminates of 15-30 μm polyethylene terephthalate (PET) on sheets of electrolytically chrome coated steel (ECCS, 200 μm sheet, 10 nm Cr adhesion layer) with a large DRD strain. The strains and directions used in this

EBSD measurementcoordinates

DRD strains applied compressivetensile

(no DRD strain)

RD

TD

NDRD

TDND

PET

PETECCS


106

paper are indicated schematically in Figure 6.1. For the calculations later in the paper, the directions of the sample surface and strains are defined as follows:

• the Transverse Direction (TD) is aligned with the circumferential direction in samples from the can wall. It is left-to-right in the SEM and EBSD images of cross-sections.

• the sample Normal Direction (ND) is down-to-up in the SEM and EBSD images of cross-sections.

• For samples from the can wall, the Rolling Direction (RD) is aligned with the can’s meridional direction.

We made use of three samples with varying strain, A B and C. Sample A is blank sheet material (not strained by drawing). Sample B and C are can wall material with sample B having logarithmic strains −0.26 (compressive) along the TD and 0.26 along the RD; sample C is can wall material with logarithmic strains −0.70 (compressive) along the TD and 0.54 along the RD. Cross-sections of these samples were produced by a combination of grinding/polishing and Focused Ion Beam etching [88].

SEM images of the cross-sectioned interface were taken using a FEG Philips XL30s. Orientation maps were obtained from each of these sample cross-sections using TSC OIM data collection software. A square grid with 100x100nm pixels and 0.1s acquisition time per pixel was used. The resulting data was cleaned using grain confidence index standardization and grain dilation steps once each.

6.4 Results and discussion Figure 6.2 shows the evolving texture of samples A, B and C, obtained by EBSD measurements. As can be seen from the inverse pole figures, the texture in sample A is defined by a <111> texture in the normal direction (ND). The DRD strain introduced in sample B changes the texture in two ways. Firstly, the orientations are spread more in the ND plot and concentrated more in the RD and the TD plots. This is most likely because the preceding rolling step applied stress in the ND, while for the DRD deformation stress is applied in the RD and TD. Secondly, the actual orientations change – a <111> texture emerges in the RD; and a <101> texture can now be observed in the TD. The texture continues to evolve subtly but significantly between samples B and C, which may well be because of the increasing ratio of compressive TD to tensile RD strain.


107

Figure 6.2: 001 Pole Figure (PF) and Inverse Pole Figure texture plots for different degrees of deformation, ranging from A, a rolled sheet before DRD strain, to C, a heavily strained piece from the top of the can. The original texture in sample A is dominated by ND with <111> oriented grains with low anisotropy, which evolves to approximately <112> oriented grains in ND with strong anisotropy in sample C.

TD

RD

ND

ND TD

RD

sample coordinate

system

A B C

PF

A

B

C

Sheet

Orientation distribution (normalized to random

texture) [-]


108

Figure 6.3: A view

of the cross-sectioned PET/ECCS interface of sample C as m

easured by SEM to reveal the geom

etry of the interface (a) and by EBSD to show

the grain orientations below this interface (b). The EBSD data is show

n as a normal

direction (ND) Inverse Pole Figure (IPF) m

ap. In image (a) he tw

o materials contrast strongly, show

ing PET in black and ECCS in light shades of gray. In im

age (b) it can be seen that the ECCS is well-indexed even close to the interface. The PET

is shown in black.

001101

111

40 μmSam

ple normal (N

D)

ND IPF

ab

PET coatingSteel substrate


109

However, this texture data explains very little of what happens locally. Figure 6.3 shows the interface of sample C, as imaged by SEM and EBSD (ND inverse pole figure map, with grain boundaries of 5° or more indicated). Although the sample is heavily strained, the material is well-indexed by EBSD even close to the PET interface – the orientation of the steel is collected locally, with very little noise due to the presence of the non-conducting interface. The distance between orientation measurements was 100 nm.

The amorphous PET layer is easily filtered out, because from the PET no Kikuchi pattern is produced. The steel can be observed, and appears to be ferrite completely. There are large local variations in the orientation, but no twinning has been observed. The most common orientation observed in Figure 6.3 is around [112] just as may be observed in Figure 6.2c (ND plot).

From this local orientation data we calculate several interesting local quantities. To a first approximation the critical resolved shear stress can be predicted based on crystallography and direction of applied load, taking Schmid law:

𝜏𝑖 = 𝜎 ∙ cos(𝜑𝑖) ∙ cos(𝜆𝑖) = 𝜎 ∙ 𝑅𝑖 (6.1)

as a starting point, where 𝜏𝑖 is the resolved shear stress, 𝜎 is the applied stress and 𝑅𝑖 is the directional factor for a slip system 𝑖. We index the slip systems i.e. all pairs of {101} or {112} planes with a <111> slip vector. We assume that all slip systems can be activated under heavy deformation. Slip on {123} is not expected to be operative and contributions from {123} are ignored. Having measured the local lattice orientation, we calculate the Taylor factor 𝑅{ℎ𝑘𝑟} = ∑ cos(𝜑𝑖) ∙𝑖cos(𝜆𝑖) for each system in each point.

The results are plotted in Figure 6.4 and Figure 6.5. In Figure 6.4 we observe that there are large differences among the various grains. Since the Taylor factor predicts the highest critical resolved shear stress, a volume with a higher Taylor factor is expected to respond more easily to plasticity. This plays a major role in the roughening of the sample[25], so it could well explain or even predict the roughness profile observed on the grain scale. Due to local orientation differences, differences in the Taylor factor can also be observed within grain interiors.


110

Figure 6.4: PET/ECCS interface and Taylor factor, calculated for various slip system

s and directions. (a) Interface viewed

by SEM; (b) Taylor factor for stress in TD and {101} slip; (c) Taylor factor for stress in TD and {112} slip; (d) Taylor factor

for stress in RD and {101} slip; (e) Taylor factor for stress in RD and {112} slip system.

a40 μm

bcde

Taylorfactor

[-]


111

Figure 6.5: The same Taylor factors shown in Figure 6.4, plotted as distribution functions (with corresponding reference to Figure 6.4b, c, d and e). The sample is heavily strained, and significant work hardening has occurred. Because compliant grains in the material strain, rotate and harden preferentially, the hardness of the material may be expected to become more and more homogeneous with increasing strain. If the hardness is determined in large part by grain orientation, a peak might then be expected in the Taylor factor distribution. Such a peak can be seen especially in graph (4e), for the {112} slip responding to stress applied in the RD, and a similar peak with lower intensity can be observed in graph (4c) for the {112} slip responding to stress applied in the TD. Presumably this slip system is most active and contributes strongly to hardness.

Roughness features at the interfaces are of particular interest. In Figure 6.6 several rough regions are plotted, and in the same places large local differences in stress projection factor can be observed. Roughening and even cracking at the surface may be related to a large difference in the stress projection factor of surface grains.

2.0 2.5 3.0 3.50

1

2

3

4

Taylorsum of Schmid factors

prob

abilit

yden

sity

Taylor sum distribution

2.0 2.5 3.0 3.50

1

2

3

4


prob

abilit

yden

sity


2.0 2.5 3.0 3.50

1

2

3

4


prob

abilit

yden

sity


2.0 2.5 3.0 3.50

1

2

3

4


prob

abilit

yden

sity


4c4b

4d 4e


112

The distributions of Taylor factors are plotted for various strain directions and slip systems in Figure 6.5. These graphs indicate that the resolved shear stress is more uniform for {112} systems than for {101} systems. After significant strain and work hardening, the texture (shown in Figure 6.2) can be described as grains in a few particular orientations, with some misorientations in the grains depending on the strain. These final orientations are a result of grain rotation[118] which in turn depend on which slip systems are active. The most active slip system therefore determines the final value of the resolved shear stress. Because the resolved shear stress is clearly determined by the {112} system, we conclude this is the system contributing most to plastic deformation.

Figure 6.6: Plot of a subset of the data shown in Figure 4e, in a rough interface region. An SEM image of the interface (a) reveals the geometry of the PET/ECCS interface. Image (b) shows the Taylor factor plotted for {112} slip, and stress applied in RD. A high Taylor factor indicates a strong response to applied stress, which might be expected to increase roughness. However, higher Taylor factors do not appear to predict particularly rough features in our measurements. Instead, some rough features are located at the boundary between neighboring regions (grains) with dissimilar (high and low) Taylor factor.

EBSD can be used to quantify orientation locally, including local orientation differences. The observed orientation distribution is the result of many dislocations grouped together. Certain deformation mechanisms [24] introduce dislocations, the strain fields of which will not annihilate each other, and such mechanisms will introduce local orientation differences in the material lattice. Such differences can then be found in strained materials at geometrically necessary dislocations (GND’s) and at low energy dislocation structures such as low-angle grain boundaries, the strain fields of which can be grouped as disclinations (although topologically different from GB dislocations). While

a

b

10 μm

Taylor factor [-]


113

disclinations may be important for the properties of severely plastically deformed materials [119], they are more commonly studied in liquid crystals [120]. In this chapter we will summarize groups of dislocations contributing to local orientation differences as defects constituting grain boundaries.

The information on orientation gradients present in EBSD datasets can be quantified using a method due to Pantleon [121]. It compares orientations obtained from two measurement points separated by a distance 𝑑𝑥 or 𝑑𝑦 to calculate a component of the partial orientation gradient tensor 𝜅𝑖𝑗𝑟𝑟𝑡𝑡𝑖𝑓𝑟 in that region.

Orientations mapped by EBSD are commonly expressed in Euler angle rotation terms [122], but for this type of analysis we find it is more practical to express them in axis/angle terms and perform relevant calculations using a quaternion description:

𝑞𝑖𝑝𝑟𝑁𝑁𝑖𝑂𝑟 = �cos𝜑1

2, 0,0, sin𝜑1

2� �cos𝛷

2, sin𝛷

2, 0,0� �cos𝜑2

2, 0,0, sin𝜑2

2� (6.2)

where 𝜑1,𝛷,𝜑2 represent the passive Bunge (ZXZ) Euler angles. Quaternion calculations are non-commutative. The misorientation between two points A and B can then be expressed in the coordinate system of point B:

𝑞𝐴𝐵𝑛𝑖𝑁,𝐵 = 𝑞𝐵

𝑝𝑟𝑁𝑁𝑖𝑂𝑟𝑞𝐴𝑝𝑟𝑁𝑁𝑖𝑂𝑟,𝑖𝑛𝑂𝑅𝑗 (6.3)

where 𝑅𝑗 is the symmetry operator. The misorientation is the net rotation required to align the coordinate system of point A with that of point B. For ferrite (bcc) there are 24 symmetry operators in total. For a meaningful comparison of orientations a single coordinate system should be used. It is therefore practical to express the obtained quaternion in the laboratory (or sample) coordinate system shown in Figure 6.1 rather than in the frame of the local lattice:

𝑞𝐴𝐵𝑛𝑖𝑁,𝑟𝑟𝑏 = 𝑞𝐵

𝑝𝑟𝑁𝑁𝑖𝑂𝑟,𝑖𝑛𝑂�𝑞𝐵𝑝𝑟𝑁𝑁𝑖𝑂𝑟𝑞𝐴

𝑝𝑟𝑁𝑁𝑖𝑂𝑟,𝑖𝑛𝑂𝑅𝑗�𝑞𝐵𝑝𝑟𝑁𝑁𝑖𝑂𝑟 = 𝑞𝐴

𝑝𝑟𝑁𝑁𝑖𝑂𝑟,𝑖𝑛𝑂𝑅𝑗𝑞𝐵𝑝𝑟𝑁𝑁𝑖𝑂𝑟 (6.4)

and from there the misorientation angle and axis can be retrieved:

𝑞𝐴𝐵𝑛𝑖𝑁,𝑟𝑟𝑏 = �cos 𝜃

2, 𝑎1 sin 𝜃

2, 𝑎2 sin 𝜃

2, 𝑎3 sin 𝜃

2� (6.5)


114

Figure 6.7: SEM

image of interface w

ith lattice curvature maps for 𝜅

31 and 𝜅32 according to equation 6.6, show

ing local orientation differences in the ferritic steel. (a) the interface view

ed by SEM, to reveal the interface geom

etry; (b) the orientation gradient 𝜅

31 , which show

s many sm

all vertical lines. These are low-angle grain boundaries, or sub-grain

boundaries. The measured m

isorientations are less than 1° between nearest neighbors. (c) the orientation gradient 𝜅

32 , w

hich looks more hom

ogeneous. Local differences and the effect of texture are examined in Figure 6.8.

40 μmabc


115

where [𝑎1, 𝑎2, 𝑎3] is the unit vector determining the axis and 𝜃 is the angle in an axis/angle description of rotation. Of the 24 solutions, the solution with the smallest angle is selected. That particular misorientation is used to calculate the orientation gradients:

𝜅1,3𝑟𝑟𝑡𝑡𝑖𝑓𝑟 = 𝑟3,∆𝑥∙𝜃∆𝑥

∆𝑥 (6.6a)

𝜅2,3𝑟𝑟𝑡𝑡𝑖𝑓𝑟 = 𝑟3,∆𝑦∙𝜃∆𝑦

∆𝑦 (6.6b)

Such a calculation is performed for each pair of points at {𝑥,𝑦} and {𝑥 + 𝛥𝑥,𝑦} (for 𝜅1,3

𝑟𝑟𝑡𝑡𝑖𝑓𝑟) as well as for each pair of points {𝑥,𝑦} and {𝑥,𝑦 + 𝛥𝑦} (for 𝜅2,3𝑟𝑟𝑡𝑡𝑖𝑓𝑟). The resulting orientation gradient maps are plotted in Figure 6.7 and

Figure 6.8. The numbers 1, 2 and 3 refer to 𝑥, 𝑦 and 𝑧; which are the same as TD, ND and –RD respectively (as a consequence of the Cartesian coordinates definition).

We observe that some sub-grain-boundaries show up as lines perpendicular to the compressive stress. Such sub-grain-boundaries are observed throughout the sample, with a spacing of approximately 1.0 μm, apparently independent of grain size. They are visible in many grains, but not in all. Especially in Figure 6.8 we observe several (highlighted) regions with very pronounced sub-grain boundaries, as well as regions with few or no such boundaries at all. A comparison between Figure 6.6 and Figure 6.8 shows that the most compliant grains also have more and more pronounced sub-grain boundaries. The orientation of these compliant grains coincides with the main texture components, as opposed to the less compliant grains which are oriented different from the main texture components.

More sub-grain boundaries were observed in compliant regions. This is expected because the formation of such a boundary as a group of dislocations requires plasticity. While compliant grains deform and possibly strain harden, less compliant grains first need to rotate to a more favorable (higher compliance) orientation. Apparently not all grains form sub-grain-boundaries, so not all grains are rotated to a more favorable orientation. Sub-grain boundaries are formed mostly in the more compliant volumes in order to decrease local stresses (until the local stress is below the yield stress) in deforming grains or near rotating or moving grains.


116

Figure 6.8: Orientation tolerance map, compared with curvature maps. An orientation tolerance map shows the difference between selected orientations and the local orientation. In the white regions the local orientation is more than 10°. Measured points with orientation close to one of the two main texture orientations are selected and highlighted in the top plot . A zoom of the lattice curvature maps showing 𝜅31 and 𝜅32 is shown for comparison. The vertical lines observed in Figure 6.7 are found in the selected grains, and rarely in grains with an orientation which is different from the main texture.

The roughness on the length scale of grains might be considered a function of the local resolved shear stress [26], but there are three very different main candidates for roughness on the sub-grain scale [24]: dislocation slip steps; surface twins or transformation phenomena; and non-crystallographic glide traces caused by dislocation bands. It is clear from the EBSD data that twinning and transformation phenomena have not occurred. To determine the extent to which the surface roughness is the result of dislocations we will employ the elegant description by Nye [123]: a bending strain on the crystal (such as in the glide traces) though the bulk of the material, including the surface, results in that

31κ

32κ

texture selection 20 μm


117

surface bending to the same degree. Conversely, dislocation slip creates roughness without introducing such bending strain in the crystal.

Figure 6.9: Correlation plot of the lattice curvature 𝜅𝐿,3

𝑟𝑟𝑡𝑡𝑖𝑓𝑟 from equation 6.8 and the interface curvature 𝜅𝐿,3

𝑖𝑛𝑡𝑟𝑟𝑓𝑟𝑓𝑟. The correlation is 0.024, which can be considered insignificant.

In other words, we can calculate the interface curvature of our 2D interface in terms 𝜅𝑖𝑗

𝑖𝑛𝑡𝑟𝑟𝑓𝑟𝑓𝑟, and we state that this is the sum of a term 𝜅𝑖𝑗𝑟𝑟𝑡𝑡𝑖𝑓𝑟 and an unknown curvature caused by slip:

𝜅𝑖𝑗𝑖𝑛𝑡𝑟𝑟𝑓𝑟𝑓𝑟 = 𝜅𝑖𝑗𝑟𝑟𝑡𝑡𝑖𝑓𝑟 + 𝜅𝑖𝑗

𝑁𝑟𝑖𝑝 (6.7)

The geometry of the steel/PET interface was obtained from SEM images using a standard Canny edge detection [79] in the computer code Mathematica 9.0. The SEM images have a much higher resolution than EBSD measurements, and this was compensated by smoothing the interface: the interface pixel positions were convolved with a normalized Gaussian curve. This smoothened interface was interpolated by a 3rd degree spline fit. The curvature of this particular interface line 𝐿 is the term 𝜅𝐿,3

𝑖𝑛𝑡𝑟𝑟𝑓𝑟𝑓𝑟, (a rotation in the plane of the image with increasing 𝐿) and was calculated from this spline fit. This interface smoothening


118

was varied using Gaussians curve widths between 50 and 500 nm, in order to reduce the SEM measurement’s resolution to exactly that of the EBSD measurement.

Figure 6.10: Schematic representation of hypothetical delamination mechanism. Initial delamination may be caused by overhanging feature on the sub-micrometer scale such as a slip plane, and stress release in the polymer may cause pockets at the delaminated interface to grow to larger size.

For the same curvature analysis two orientation measurements (𝐿𝐴 and 𝐿𝐵) close to the interface line 𝐿 are selected, and a misorientation calculation is performed between each such point pair:

𝜅𝐿,𝑖𝑟𝑟𝑡𝑡𝑖𝑓𝑟 ≈ 𝑟𝑖,𝐿∙𝜃𝐿

𝑓𝐿 (6.8)

where 𝑑𝐿 is the distance between the locations of 𝐿𝐴 and 𝐿𝐵.

The term 𝜅𝐿,3𝑟𝑟𝑡𝑡𝑖𝑓𝑟 was compared point-by-point to the interface curvature

𝜅𝐿,3𝑖𝑛𝑡𝑟𝑟𝑓𝑟𝑓𝑟, but we observed that there is no clear relation, and the correlation is

a negligible 0.024.

Most probably the gradients observed in the lattice are due to sub-grain boundaries, low-angle grain boundaries etc. However the geometry and curvature of the interface may also be formed by other phenomena such as dislocation slip. It is likely that in an early stage of the deformation process, individual slip planes are already dominating the small-scale roughness profile. The roughness evolution would then be a combination of slip on the small scale

Slip plane

PET

ECCS

PET Stress release

Delamination


119

and grain orientations on the large scale. We conclude that the sub-grain scale roughness is primarily caused by dislocations.

Returning to the question of roughening behavior and adhesion, it is strongly suspected that the overhanging features observed in chapter 4 are in fact glide steps, which appear as overhang on interfaces deformed by compressive stress. It is possible that these glide steps create very high localized stress in the polymer, causing the interface to break locally as depicted schematically in Figure 6.10. This is the subject of chapter 5.

6.5 Summary and conclusions We have measured the local lattice orientation in heavily strained ferrite steel can wall using EBSD. From the data we have calculated 6 of the 9 components of the local orientation gradient tensor using a method due to Pantleon as well as the local Taylor factor for the TD and RD strains on {101} and {112} slip systems. In the specimens the resolved stress for {112} is very homogeneous throughout the material, and the applied strain is a biaxial strain along the RD and TD. However the last strain applied to the can wall in each draw or redraw step is a tensile strain in the RD.

We observe sub-grain-boundaries, i.e. bands approximately aligned with the ND through one or several grains. These sub-grain boundaries occur in approximately 50% of the material, and the spacing between the sub-grain-boundaries is 1.0 ± 0.2 μm, independent of grain size. We have observed that these sub-grain boundaries are most commonly found in where the orientation of the grain coincides with the main texture components. Some grains did not show rotations and they have no sub-grain boundaries. We find that at high strains such local details cannot be ignored.

Roughness appears at the PET-ECCS interface, provided there are surface grains with a high resolved shear stress (yielding glide steps) or differences in resolved shear stress between neighboring grains. The final texture of the material is determined by tensile strain in the RD (the meridional direction of the DRD can), working on {112} slip systems. The same compressive strain introduces sub-grain-boundaries in the compliant grains lowering the stress fields.

Roughening at a sub-grain length scale along the interface is dominated by dislocation plasticity.

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University of Groningen Nanotopography and morphology ... · 6 Evolution of grain structure in deformed metal-polymer laminates4 6.1 Abstract In this chapter the roughening along