Evolution of grain structure in deformed metal-polymer laminates

E. T. Faber • W.-P. Velinga • J. Th. M. De Hosson

Received: 14 April 2014 / Accepted: 7 August 2014 / Published online: 19 August 2014

� Springer Science+Business Media New York 2014

Abstract The paper examines the roughening along a

metal-polymer interface, to find out whether the relevant

length scale is on a sub-grain level or on 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 com-

ponents of the local orientation gradient tensor as well as

the local Schmid factor for deformation along [100] and

[001] 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 con-

cluded that roughening at a sub-grain length scale along the

interface is due to plasticity in the interior of the grains.

Introduction

Upon deformation metallic surfaces become rough affect-

ing surface properties such as friction, wear and adhesion.

In particular rough surfaces facilitate sites for crack

nucleation, which may seriously deteriorate the mechanical

performance. 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 [1–6], embracing 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 [7–10]

but some authors report deviations from the linear behav-

ior, especially at higher strains [10, 11]. In a number of

studies, texture was found to have a significant influence on

the roughness [12–17]. Most of these studies are aimed at

understanding the development of a typical roping or

ridging roughness. Differences in crystallographic orien-

tation, 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 [12, 14].

In earlier work [18] 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 circle of ductile metal sheet is stamped into a

cylinder shaped 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. Com-

monly a can formed this way is still too wide so the step is

repeated with increasingly small dies yielding a thinner

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).

We investigated [18] in particular how roughening

appears to affect the adhesion, identifying that delamina-

tion (cracks between the ECCS and PET) occurs primarily

at overhanging features on the micrometer scale and

smaller. There was a clear correlation between the rough-

ening of the interface, and observed de-adhesion

E. T. Faber � W.-P. Velinga � J. Th. M. De Hosson (&)

Department of Applied Physics, Materials Innovation Institute

M2i, University of Groningen, Nijenborgh 4,

9747 AG Groningen, The Netherlands

e-mail: j.t.m.de.hosson@rug.nl

123

J Mater Sci (2014) 49:8335–8342

DOI 10.1007/s10853-014-8542-3

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 localized shear in the polymer

in order to cause this de-adhesion. However it is not known

which deformation mechanisms [6] and at what underpin-

ning length scales are the relevant mechanisms creating

these particular surface features. The current paper goes a

step further and concentrates on the mechanisms which

determine the interface roughening behavior, rather than

the stability of the interface. 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 terephthal-

ate (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.

Experiments

In this work we examine laminates of 15–30 lm polyeth-

ylene terephthalate (PET) on sheets of electrolytically

chrome coated steel (ECCS, 200 lm sheet, 10 nm Cr

adhesion layer) with a large DRD strain. The strains and

directions used in this paper are indicated schematically in

Fig. 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; and 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 [18].

SEM images of the cross-sectioned interface were taken

using a FEG Philips XL30 s. Orientation maps were

obtained from each of these sample cross-sections using

TSC OIM data collection software. A square grid with

100 9 100 nm pixels and 0.1 s acquisition time per pixel

was used. The resulting data was cleaned using grain

confidence index standardization and grain dilation steps

once each.

Results and discussion

Figure 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 h111i texture in the normal direction (ND). The DRD

strain introduced in sample B changes the texture in two

ways. Firstly, the orientations are less defined (concen-

trated) by the ND and more focused in the RD and the TD.

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 h111i texture emerges in the RD;

and a h101i 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

(Fig. 3).

However, this texture data explains very little of what

happens locally. Figure 2 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—

EBSD measurementcoordinates

DRD strains applied compressivetensile

(no DRD strain)

RD

TD

NDRD

TDND

PET

PET

ECCS

Fig. 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 lm, coated on both sides with an adhesive

thin chromium and chromium oxide multilayer, and with a 15–30 lm

thick PET layer. Dimensions and strain are shown on the sheet (left)

and with the strains on the can wall (right)

8336 J Mater Sci (2014) 49:8335–8342

123

the orientation of the steel is collected on a very local level,

with very little noise due to the presence of the non-con-

ducting interface. From this local orientation data we cal-

culate 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 as a starting point,

si ¼ r � cos uið Þ � cos kið Þ ¼ r �Mi ð1Þ

where si is the resolved shear stress, r is the applied stress

and Mi 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 h111i 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 M ¼ Ri cos /ið Þ � cos kið Þ for each system in each

point.

The results are plotted in Figs. 4 and 5. In Fig. 4 we

observe that there are large differences among the vari-

ous grains. Since the Schmid factor predicts the highest

critical resolved shear stress, we expect that a volume

with a higher Schmid factor responds more easily to

plasticity. This plays a major role in the roughening of

the sample [10], so it could well explain or even predict

the roughness profile observed on the grain scale. Indeed

also some local differences can be observed within

grains.

TD

RD

ND

ND TD

RD

sample coordinate

system

(a) (b) (c)

PF

A

B

C

Sheet

Orientation distribution (normalized to random

texture) [-]

Fig. 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 h111ioriented grains with low

anisotropy, which evolves to

approximately h112i oriented

grains in ND with strong

anisotropy in sample C

001 101

111

40 µmSample normal (ND)

ND IPF

(a)

(b)

PET coatingSteel substrate

Fig. 3 A view of the cross-sectioned PET/ECCS interface of sample

C as measured by SEM to reveal the geometry of the interface (a) and

by EBSD to show the grain orientations below this interface (b). The

EBSD data is shown as a normal direction (ND) Inverse Pole Figure

(IPF) map. In image (a) he two materials contrast strongly, showing

PET in black and ECCS in light shades of gray. In image (b) it can be

seen that the ECCS is well-indexed even close to the interface. The

PET is shown in black because it is amorphous, and no Kikuchi

pattern was observed from it

J Mater Sci (2014) 49:8335–8342 8337

123

Rough features at the interfaces are of particular interest.

In Fig. 6 several rough regions are plotted, and large local

differences in deformability can be observed. Roughening

and even cracking at the surface appears to be caused by a

large difference in the deformability of surface grains.

The distributions of Taylor factors are plotted for vari-

ous strain directions and slip systems in Fig. 5. These

graphs indicate that the resolved shear stress is more uni-

form for {112} systems than for {101} systems. After

significant strain and work hardening, the texture (shown in

Fig. 2) can be described as grains in a few particular ori-

entations, with some misorientations in the grains

depending on the strain. These final orientations are a result

of grain rotation [19] 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 contrib-

uting most to plastic deformation.

The displacement fields in the crystal can be measured

by EBSD. The observed strain/stress field is the result of

many dislocations grouped together. Certain deformation

mechanisms [6] 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

(a)40 µm

(b)

(c)

(d)

(e)

Taylorfactor

[-]

Fig. 4 PET/ECCS interface

and Taylor factor, calculated for

various slip systems 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

2.0 2.5 3.0 3.5

Taylor sum of Schmid factors

Taylor sum distribution

2.0 2.5 3.0 3.5

Taylor sum of Schmid factors

Taylor sum distribution

2.0 2.5 3.0 3.50

1

2

3

4

Taylor sum of Schmid factors

Taylor sum distribution

prob

abili

ty d

ensi

ty

2.0 2.5 3.0 3.50

1

2

3

4

Taylor sum of Schmid factors

prob

abili

ty d

ensi

ty

Taylor sum distribution

(4c)(4b)

(4d) (4e)

Fig. 5 The same Taylor factors

shown in Fig. 4, plotted as

distribution functions. 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 II for the {112} slip

responding to stress applied in

the TD. Presumably this slip

system is most active and

contributes strongly to hardness

8338 J Mater Sci (2014) 49:8335–8342

123

grain boundaries, the strain fields of which can be grouped

as disclinations (although topological different from GB

dislocations). While disclinations may be important for the

properties of severely plastically deformed materials [20],

they are more commonly studied in liquid crystals [21].

The way to obtain information about the group of dis-

locations, that we summarize as defects constituting sub-

grain boundaries, from EBSD is described by Pantleon

[22]. It compares orientations obtained from two mea-

surement points separated by a distance dx or dy to cal-

culate a partial gradient tensor jlatticeij in that region.

Another elegant but time-consuming method, described by

Wilkinson et al. requires the acquisition of a higher quality

pattern for each measurement point [23].

Several regions of the Kikuchi pattern itself are then

examined and compared to a strain-free reference pattern to

obtain information (including some strain and rotation

components) for that point. In this paper the method pro-

posed by Pantleon is applied. Orientations mapped by

EBSD are commonly expressed in Euler angle rotation

terms, but for this type of analysis it is more practical to

express them in axis/angle terms and perform relevant

calculations using a quaternion description:

qpassivei ¼ cos u1=2ð Þ; 0; 0; sin u1=2ð Þf g cos U=2ð Þ;f

sin U=2ð Þ; 0; 0g cos u2=2ð Þ; 0; 0; sin u2=2ð Þf gð2Þ

where u1;U;u2 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:

qmis;BAB ¼ q

passiveB q

passive;inverseA Sj ð3Þ

where Sj is the symmetry operator. For ferrite (bcc) there

are 24 symmetry operators in total. Each measurement

point has its own frame of reference, and for a meaningful

comparison a single frame of reference should be used. It is

therefore practical to express the obtained quaternion in the

laboratory (or sample) frame shown in Fig. 1 rather than in

the frame of the local lattice:

qmis;labAB ¼ q

passive;inverseB q

passiveB q

passive;inverseA Sj

� �q

passiveB

¼ qpassive;inverseA Sjq

passiveB ð4Þ

and from there the misorientation angle and axis can be

retrieved:

qmis;labAB ¼ cos h=2ð Þ; a1 sin h=2ð Þ; a2 sin h=2ð Þ; a3 sin h=2ð Þf g

ð5Þ

where a1; a2; a3½ � is the unit vector determining the axis and

h is the angle in an axis/angle description of rotation. Of

the 24 solutions, the solution with the lowest angle is

selected. That particular misorientation is used to calculate

the orientation gradients:

jlattice1;3 ¼ a3;Dx � hDx

Dxð6aÞ

jlattice2;3 ¼ a3;Dy � hDy

Dyð6bÞ

Such a calculation is performed for each point pair at {x,

y} and {x ? Dx, y} (for jlattice1;3 ) as well as each pair {x, y}

and {x, y ? Dy} (for jlattice2;3 ). The resulting orientation

gradient maps are plotted in Figs. 7 and 8. The denomi-

nators 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 sub-grain-boundaries show up as lines

perpendicular to the compressive stress. These are

observed throughout the sample, with a spacing of 1.0 lm,

10 µm

Taylor factor [-]

(a)

(b)

Fig. 6 Zoom of the data shown in Fig. 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

J Mater Sci (2014) 49:8335–8342 8339

123

apparently independent of grain size. Such lines are visible

in many grains, but not in all. Especially in Fig. 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 Figs. 6 and 8

shows us that the most compliant grains also have more

sub-grain boundaries and they are more pronounced. These

more compliant grains are oriented the same as the main

texture components, as opposed to the less compliant

grains which are oriented differently from the main texture

components.

We have observed more sub-grain boundaries in com-

pliant regions, as 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 and more stiff grains would remain rigid

bodies until they have rotated 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 and GNDs 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.

While the roughness on the length scale of grains is

usually a function of the resolved shear stress, there are

three main candidates for roughness on the sub-grain scale

[6]: 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

40 µm(a)

(b)

(c)

Fig. 7 SEM image of interface with lattice curvature maps for j31

and j32 according to Eq. 6, showing local orientation differences in

the ferritic steel. a the interface viewed by SEM, to reveal the

interface geometry; b the orientation gradient in the transverse

direction j31, which shows many small vertical lines. These are low-

angle grain boundaries, or sub-grain boundaries. The measured

misorientations are less than 1� between nearest neighbors. c the

orientation gradient in the normal direction j32, which looks more

homogeneous. Local differences and the effect of texture are

examined in Fig. 8

31κ

32κ

texture selection 20 µmFig. 8 Orientation tolerance

map, compared with curvature

maps. 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

j31 and j32 is shown for

comparison. The vertical lines

observed in Fig. 7 are found in

the selected grains, and rarely in

grains with an orientation which

is different from the main

texture

8340 J Mater Sci (2014) 49:8335–8342

123

twinning and transformation phenomena have not occur-

red, but glide traces are visible. To determine the extent to

which the surface roughness is the result of dislocations we

will employ the elegant description by Nye [24]: a bending

strain on the crystal (such as in the glide traces) though the

bulk of the material, including the surface, bends to the

same degree. Conversely, dislocation slip creates

roughness.

In other words, we can calculate the interface curvature

of our 2D interface in terms jinterfaceij , and we state that this

is the sum of a term jlatticeij and an unknown roughness

caused by slip. The ECCS interface was obtained from

SEM images using a standard Canny edge detection [25] 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 smooth interface was interpolated by

a 3rd degree spline fit. The curvature of this interface line

L is the term jinterfaceL;3 , (a rotation around the RD with

increasing L) and was calculated from this spline fit.

For the same curvature analysis two orientation mea-

surements (LA and LB) close to the interface line L are

selected, and a misorientation calculation is performed

between each such point pair:

jlatticeL;i � ai;L � hL

dL

ð7Þ

where dL is the distance between the locations ofLA and LB.

The term jlatticeL;3 was compared to the interface curvature

jinterfaceL;3 , but we observed there is no clear relation, and the

correlation is a negligible 0.024. The aforementioned

interface smoothening 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.

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 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 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 our earlier work [18] are in fact glide

steps, which which appear as overhang in 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 Fig. 9. This will

be the subject of a future study.

Summary and conclusions

We have measured the local lattice orientation in heavily

strained ferrite steel using EBSD, and from the data we

have calculated 6 of the 9 components of the local orien-

tation gradient tensor as well as the local Schmid 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 tensile strain along the RD. The texture of the

material evolves throughout the entire process, and grains

are reoriented as the applied strain subtly changes.

The strain caused by stress fields resulting from groups

of dislocations can be measured. We observe sub-grain-

boundaries, i.e. vertical bands running through one or

several grains in our gradient maps. Such lines occur in

approximately 50 % of the material, and the spacing

between the sub-grain-boundaries is 1.0 ± 0.2 lm, inde-

pendent of grain size.

We have observed that these sub-grain boundaries are

most commonly found in grains with preferred orienta-

tions. 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, pro-

vided there are surface grains with a high resolved shear

stress. 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.

Slip plane

PET

ECCS

PET Stress release

Delamination

Fig. 9 Schematic representation of suspected delamination mecha-

nism. Initial delamination may be caused by overhanging feature on

the sub-micrometer scale such as a slip plane, and stress in the

polymer may cause pockets at the delaminated interface to grow to

larger size

J Mater Sci (2014) 49:8335–8342 8341

123

Acknowledgements The financial support of Materials innovation

institute (M2i), Delft, the Netherlands, under the project number

M63.7.09343b is gratefully acknowledged.

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