Through-Thickness Stresses in Automotive Sheet Metal after Plane 

Strain Channel Draw 

Thomas Gnäupel-Herold1, a, Daniel E. Green2,b, Timothy Foecke3,c 

and Mark A. Iadicola3,d 

1NIST Center for Neutron Research, 100 Bureau Dr. M/S 6102 Gaithersburg, MD 20899-6102, 

USA 

2University of Windsor, Department of Mechanical, Automotive & Materials Engineering, Windsor, 

Ontario N9B 3P4, Canada 

3NIST Center for Automotive Lightweighting, 100 Bureau Drive, M/S 8553 

Gaithersburg, MD 20899-8553 

a

tg-h@nist.gov, bdgreen@uwindsor.ca, ctimothy.foecke@nist.gov, dmark.iadicola@nist.gov 

Keywords: Sheet Metal Stress; Plane Strain Stretch Bending; Diffraction; Springback; Forming. 

Abstract. A series of samples from four automotive materials - AKDQ, HSLA50, DP600, and 

AA6022-T43 - were deformed in a channel draw processes with different levels of draw bead 

penetration. As a result, varying magnitudes of deformations in plane strain mode and residual 

stresses were obtained. Through-thickness stress profiles were obtained non-destructively using a 

novel, high resolution X-ray diffraction technique. 

Introduction 

In automotive sheet metal forming the deployment of newer, high-strength materials for 

automotive applications is inextricably linked to the predictability of multi-axial forming behavior, 

particularly forming limits and final shape. The latter is a direct result of springback and therefore

the result of the residual stress profile that arises from inhomogeneous through-thickness plastic 

strains. Springback is known for the considerable cost it causes in the tryout phase for forming tool 

development. This problem is exacerbated through light-weighting constraints which force either 

thickness reduction with increased yield strength (steels) or altogether lighter materials (aluminum 

alloys) which typically have larger yield to elastic modulus ratios. All these effects increase the 

springback to varying degrees. Efforts for springback prediction generally focus on single number 

comparison, i.e. the comparison of a measured and predicted deflection angle or displacement. 

However, it is important to remember that springback is the result of balancing bending moments 

which are the result of residual stresses. Thus, the comparison of the through-thickness stress 

profiles from calculation and measurement can be a valuable tool in refining the underlying material 

model for the calculation. However, such a measurement represents an experimental challenge 

because of the minimum number of stress values necessary to describe the through-thickness 

profile. Typical sheet thicknesses are 1 mm or less and this places high demands on the spatial 

resolution of stress determination. Past efforts on select samples have focused on using neutron 

diffraction [1,2] and synchrotron X-ray diffraction [3,4] where spatial resolutions of 

≈0.1 mm..0.3 mm have been achieved. However, some measurements such as in [1] were fraught 

with problems stemming from insufficient spatial resolution and unsuitable measurement locations. 

For example, there were apparent stress balance violations and large uncertainties due to low 

neutron intensity. A recently developed X-ray method [5] provides easier access at resolutions 

similar to synchrotron X-ray diffraction, thus allowing the study of a larger number both of 

materials and forming parameters. The results presented here were obtained from X-ray 

measurements on samples of four different materials (AKDQ, HSLA50, DP600, and AA6022) 

deformed in a channel draw at different draw bead penetrations. 

Materials Science Forum Vols. 768-769 (2014) pp 433-440

Online available since 2013/Sep/23 at www.scientific.net

© (2014) Trans Tech Publications, Switzerland

doi:10.4028/www.scientific.net/MSF.768-769.433

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,

www.ttp.net. (ID: 129.6.225.69, National Institute of Standards and Technology, Gaithersburg, USA-22/01/15,22:32:18)
Experimental 

Material. The details and the purpose of the channel draw as well as materials property data for 

AKDQ, HSLA 50, DP 600, and AA6022-T43, were presented in earlier publications [1,6], thus 

only an outline is given. The channel draw investigated here produced samples deformed in the 

plane strain mode, i.e. samples were stretched in the sheet transverse direction (TD) only (from 

εTD≈0.05 at 25 % draw bead penetration up to εTD≈0.15 at 100 % penetration) with shrinkage strain 

only in the thickness (εND < 0; εRD ≈ 0). 

The forming geometry is shown in Fig. 1. A number of steps were necessary to produce samples 

suitable for X-ray diffraction. The side panels were trimmed, and smaller specimens (x=25 mm, 

y=12 mm, z≤1 mm) were removed at ≈15 mm distance from the rim by means of electro-discharge 

machining. The specimens were cast in a block of epoxy and their cross section surfaces polished to 

remove all influence of the EDM cutting (total removal ≈ 1 mm). The final polishing step was a 

0.05 μm SiC suspension intended to provide a surface undisturbed by mechanical damage other 

than the forming process. Fig. 2 shows the final assembly of samples for X-ray diffraction. The 

dimensions of the specimens were > 10 × thickness, and it is a reasonable assumption that the 

stresses were left undisturbed by the removal procedure. 

 

 

Figure 1. Top, left: setup of the channel draw process [1,6], sequences of bending and reverse 

bending (top, right). Bottom, left: final specimen with the X-ray sample cut-out (right, enlarged). 

 

Diffraction Measurements. Through-thickness stresses are not an obvious subject of X-ray 

(surface limited) stress measurements. The choice for measuring such sub-surface stresses is usually 

to use a bulk-penetrating neutron or synchrotron X-ray technique as discussed in [1-4]. However, if 

one assumes that the deformation is homogeneous along RD and TD, then the extraction of a 

smaller coupon (lateral dimensions 12× and 25× thickness) will preserve the stress fields of interest. 

Moreover, the same stresses are “visible” on the cross section surface as shown in Fig. 2, left. The 

associated strains can be measured using X-ray diffraction provided that diffracted intensity can be 

measured on a sufficiently small area commensurate with the required depth resolution. This was 

carried out using the technique described in [5] which is based on keeping a small (here: 0.05 mm x 

2.5 mm) X-ray beam both at a fixed sample location and a fixed beam spot orientation (Fig. 2). 

x

z

y

die

blank

holder

punch

draw

bead

draw bead at

100 % penetration

punch

sheet metal

+b-b+b-b

+b-b

+b +b-b+b

+b: bending

-b : reverse 

 bending

extrados

x-ray specimen

cut-out

Rpanel

intrados RD ND

measurement TD

area

25 mm

axial

12 mm

stress

434 International Conference on Residual Stresses 9 (ICRS 9)
Figure 2. Side surfaces of four stacked sheet metal samples (top and bottom are backing plates). The 

white rectangle is the area to which the X-ray beam is confined. The beam spot stays in the 

orientation shown (|| TD) through all rotations (φψ). The d-spacings at the next “depth” are 

measured by translating along ND with an effective resolution of 0.05 mm. 

Shown in Fig. 3, the central principle of this method is that the specimen rotations (φψ) cause a 

virtual rotation of the beam spot on the sample surface. In order to re-align the beam spot with a 

principal sample direction the specimen must be counter-rotated (angle δ) about the axis 

perpendicular to the sample surface (specimen: axis zs; diffractometer: axis φ|| zs). For symmetric 

diffraction (incident and diffracted beam have the same angle to the surface normal), the angle δ is 

( ) 















+ +

+

= ±

2 2

cos sin sin cos cot sin

sin sin cos cot sin

arccos

θ ψ θ ψ ψ θ

ψ θ ψ ψ θ

δ . (1) 

Here, θ is the Bragg angle, φ is the rotation about zs, and ψ is the tilt angle. 

 

Figure 3.Virtual rotation of the beam spot (line) on the sample with ψ. At ψ=0° the strain 

component parallel zs is measured while at φ=0, ψ=90° the strain component parallel to xs is 

measured. One has TD=xs (hoop), ND=ys (radial), and RD=zs (axial). 

In practice, each d-measurement is done at a different (φ,ψ) combination, i.e. even φ has a slight 

variation. Fig. 4. shows a more familiar plot as a sheet metal pole figure with the measurement 

angles denoted in the pole figure reference system.

primary 

beam

δ

y q s

xs

δ=0

ψ=0°

φ=0°

ψ=45°

φ=0°

zs

ys

xs

φ

q

ys xs

ψ=45°

φ=δ (10° )

,q

Ψ

zs

zs

Ψ

Pb-screen

t

t

ψ

counter-rotation about diffractometer 

axis || realigns beam spot with 

designated orientation

φ zs

ψ

δ

-tilt about causes virtual 

rotation of beam spot by 

ys

ψ-tilt plane

measurement areawith stress field

enlarged

tilt

correction

Materials Science Forum Vols. 768-769 435
Figure 4. Angular positions of measurements plotted on a HSLA 50 pole figure (25% penetration) 

of the (211) reflection. 

The boundary condition of a fixed orientation of the beam spot (line shape) on the sample surface 

requires both the Euler geometry of rotation and XYZ positioning of the sample. The equipment 

used is shown in Fig. 5. 

Figure 5. Euler geometry X-ray diffractometer used for the measurements discussed here. 

Intergranular Strains and Texture. Due to the large plastic strains in the channel draw both 

intergranular (IG) strains and elastic anisotropy of diffraction elastic constants are of concern. 

Texture was measured for each material at the 25 % penetration and 100 % penetration level, and 

the orientation distribution functions (ODF) were evaluated. ODFs at intermediate penetrations 

(75 % and 100 %) were obtained through linear interpolation between the ODF at 25 % and the 

ODF at 100 %. The ODFs were subsequently used for the calculation of the (hkl, φ,ψ) dependent 

diffraction elastic constants using IsoDEC [9]. 

Several steps were taken for suppressing the effect of IG strains on the stress evaluation: 1) at 

least two reflections (hkl) were measured and averaged (steel: (211) and (310); AA6022: (311), 

(331), (420)) stress balance and momentum balance were applied to the intermediate results of the 

stress evaluation (Fig. 6). More specifically, a constant is added such that stress balance 

( = 0 ∫∫ dydz σ xx) is obtained, and a depth-proportional stress is added to obtain balance of bending 

moments ( −y σ xxdy = 0

−t / 2

t / 2∫

). 

(211)

RD

TD

hoop stress measurement

axial stress measurement

ψ=0

φ=0

φ=90

436 International Conference on Residual Stresses 9 (ICRS 9)
Figure 6. Stresses determined from the as-measured strains for the (211) and (310) reflections of 

HSLA50, 25 % bead penetration. The label ‘balanced’ refers to the enforced conditions of stress 

and momentum balance. 

There are several potential problems in applying these corrections. While the applicability of both 

momentum balance and stress balance is without question, any non-linear (sin2ψ) through-thickness 

dependence of intergranular strains cannot be addressed this way. However, the compounded effect 

of intergranular strains is accessible through thickness-averaging, i.e. d-spacings for a given 

combination of (hkl, φ,ψ) are averaged over thickness (Fig. 7). 

Figure 7. Through-thickness average of ε((211), φ,ψ) which essentially represents the average 

intergranular strains. The conversion from d((211), φ,ψ) to ε was done using the global average of 

all measured d as reference. 

The slope of ε(sin2ψ) in Fig. 6 can be interpreted as the average intergranular stress. This average 

stress value is subtracted from the depth dependent stresses to obtain stress balance (see Fig. 6, the

(310) and (211) curves are shifted upwards by ≈80 MPa). For all materials and penetrations the 

momentum balance is consistently violated such that starting at intrados stresses are too far in the 

compressive region, thus giving all stresses (for all materials and penetrations) the characteristic 

tilted shape shown in Fig. 6 both for the (211) and (310) reflections. It can be surmised that this 

“compressive” contribution diminishes with increasing depth. In lack of other experimental data the 

intergranular stress contribution is therefore approximated through the aforementioned linear 

function. 

(310) (211) Balanced

-250

-200

-150

-100

-50

0

50

100

0 0.2 0.4 0.6 0.8

h

o

o

p

stre

s

s [M

P

a]

ys[mm]

HSLA - 25% bead penetration middle

-0.0004

-0.0003

-0.0002

-0.0001

0

0.0001

0.0002

0 0.1 0.2 0.3 0.4 0.5

strain

sin2ψ

strains after thickness-average

HSLA, 100 %

HSLA, 25 %

Materials Science Forum Vols. 768-769 437
Results and Discussion 

The stresses obtained by the procedures described above are summarily shown in Fig. 8. Due to the 

similarities in the forming processes, the qualitative distribution of stresses are similar as well. 

However, the principal shape of the stress distributions is determined less by the overall plastic 

strains (major strains between 0.05 and 0.2 in the extreme). The stretching produces plastic strain 

that is homogeneous through thickness, and it would not create residual stresses by itself. On the 

other hand, non-homogeneous through-thickness strain is produced by the sequence of bending and 

reversed bending as depicted schematically in Fig. 1. The bending sequence is the same for all 

samples, and it is responsible for the wave-like shape of the stresses vs. depth. Moreover, a survey 

of residual stresses from sheet metal forming operations reported in the literature shows the same 

wave-like distribution through thickness almost regardless of the combination of major strain and 

minor strain. For example, in the deep drawn cup / split-ring test [10] one has for the throughthickness average strains εaxial ≈ -εhoop (overall strains, overall > 0.2) while in pure bending one has 

εaxial ≈ εhoop ≈ 0 and yet the residual stresses are very similar. Both examples are shown in Fig. 9. 

Figure 8. Normalized through-thickness stresses in AA6022 (top left), AKDQ (top right), HSLA50 

(bottom left) and DP600 (bottom right). Increasing depth values go from intrados (ID) to extrados 

(Figure 1. 1). On average, one standard deviation for AA6022: 4 MPa; AKDQ: 8 MPa; HSLA: 10 

MPa; and DP600: 12 MPa. 

-40

-30

-20

-10

0

10

20

30

40

0 0.2 0.4 0.6 0.8 1

stress [Mpa]

normalized depth from ID

AA6022 R25

R50

R75

R100

-60

-40

-20

0

20

40

60

80

0 0.2 0.4 0.6 0.8 1

stress [MPa]

normalized depth from ID

AKDQ R25

R50

R75

R100

-120

-80

-40

0

40

80

120

0 0.2 0.4 0.6 0.8 1

stress [Mpa]

normalized depth from ID

HSLA R25

R50

R75

R100

-120

-80

-40

0

40

80

120

0 0.2 0.4 0.6 0.8 1

stress [Mpa]

normalized depth from ID

DP600

R25 R50 R75 R90

438 International Conference on Residual Stresses 9 (ICRS 9)
Figure 9. Through-thickness residual stresses from forming involving bending. Left: hoop stresses 

in split rings extracted from a deep drawn cup (AA6022: [4], AISI 1010 : [2]). Right: plane strain 

bending of HSLA 50 without stretching showing stresses in the bent and unloaded state. 

A closer comparison of the stresses in Fig. 8 shows that the lowest and highest stress values for 

each material increase with the respective yield strength (AA6022: 132MPa; AQDQ: 163 MPa; 

HSLA50: 406 MPa; DP600: 424 MPa). Furthermore, the relative depth at which stresses change the 

sign from compressive to tensile (and vice versa) increases with penetration depth of the draw bean. 

In other words, with increasing elongation (εmajor increases with penetration) the neutral plane is 

shifted more in the direction intrados ⇒ extrados). On the other hand, the shift of the neutral plane 

reduces springback and sidewall curl as reported in [1] (see Fig. 1). 

Summary 

The results of a study on through thickness residual stresses from a plane strain channel draw were 

presented. It was found that the general outline of the stress distributions is determined by the 

bending common to all samples. The effect of increasing draw bead penetrations is a shift of the 

entire stress distribution towards extrados. This finding was interpreted as the effect of the shift of 

the neutral plane. 

References 

[1] D.E. Green, T.B. Stoughton, T. Gnaeupel-Herold, M.A. Iadicola, T.Foecke, Influence of 

drawbeads in deep drawing of plane-strain channel sections, Proceedings of the IDDRG 2006 

Conference, Porto, Portugal (2006) 559-566 

[2] T. Gnaeupel-Herold, T.J. Foecke, H.J. Prask, R.J. Fields, An Investigation of Springback 

Stresses in an AISI-1010 Deep Drawn Cup, Mater. Sci. Eng. A399 (2005) 26-32 

[3] T. Gnaeupel-Herold, M.A. Iadicola, T. Foecke, Residual Stresses in Numisheet Benchmark 3 

Panels, Proc. of the International Deep-Drawing Research Group Annual Conference (2009) 7-16 

[4] T. Gnaeupel-Herold, H. J. Prask, R.J. Fields, T.J. Foecke, Z.C. Xia and U. Lienert, A 

Synchrotron Study of Residual Stresses in a Al6022 Deep Drawn Cup, Mater. Sci. Eng. A366 

(2004) 104-113. 

[5] T. Gnäupel-Herold, Formalism for the Determination of Intermediate Stress Gradients using Xray Diffraction, J. Appl. Cryst. 42 (2009) 192–197 

[6] M. A. Iadicola, T. Foecke, and T. B. Stoughton, Experimental Procedures and Results for 

Benchmark 3: Stage 2 Forming Process, Proceedings of Numisheet 2005, American Institute of 

Physics, CP778 Volume B (2005 905-915. 

-100

-50

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1

stress [MPa]

normalized depth 

hoop stresses in the split ring after drawing

Al-6022 AISI-1010

-300

-200

-100

0

100

200

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

stress [MPa]

depth from ID [mm]

HSLA 50, stresses in plane strain bending

unloaded, R=58 mm

bent, R=47 mm

Materials Science Forum Vols. 768-769 439
[7] M.C. Oliveira, A.J. Baptista, J.L. Alves, L.F. Menezes, D.E. Green, T. Gnaeupel-Herold, M.A. 

Iadicola, T. Foecke, T.B. Stoughton, Two Stage Forming: Experimental and FE Analysis, 

Proceedings of IDDRG, June 2006, Porto (Portugal) 279-286 

[8] T. Gnäupel-Herold, A.A. Creuziger, M.A. Iadicola, (2012), “A model for calculating 

diffraction elastic constants”, J. Appl. Cryst. 45 (2012) 197-206 

[9] T. Gnäupel-Herold, IsoDEC: A software for calculating diffraction elastic constants, J. Appl. 

Cryst. 45 (2012) 573-574 

[10] T. Foecke,T. Gnaupel-Herold, Robustness of the Sheet Metal Springback Cup Test, 

Metallurgical and Materials Transactions A 37 (2006) 3503-3510 

440 International Conference on Residual Stresses 9 (ICRS 9)
International Conference on Residual Stresses 9 (ICRS 9)

10.4028/www.scientific.net/MSF.768-769

Through-Thickness Stresses in Automotive Sheet Metal after Plane Strain Channel Draw

10.4028/www.scientific.net/MSF.768-769.433