MEASUREMENT OF RESIDUAL STRESSES IN LARGE ENGINEERING
COMPONENTS
F Hosseinzadeh, DJ Smith and CE Truman
Solid Mechanics Group, Department of Mechanical Engineering
University of Bristol, UK, BS8 ITR
David.Smith@Bristol.ac.uk
ABSTRACT
Residual stresses may be introduced in components during manufacturing, heat or mechanical treatments and through
service. A variety of methods are available for residual stress measurements. However few of them are capable of measuring
through the thickness of large components. In this paper the deep hole drilling technique for residual stress measurement
through the thickness of large engineering components is described. Experiments are carried out on an industrial scale shrink
fitted assembly and a series of thick sleeves for vertical rolls used in steel rolling mills for long products. Residual stress
measurements were performed before and after machining the sleeves, and after assembly of a bearing into a sleeve. The
industrial scale component was examined after use in service. The contributions of the different operations and manufacturing
processes on the residual stress distributions are investigated.
Nomenclature
U rr (θ )
Normalized radial distortion of the reference hole
Δd (θ )
d (θ )
d ′(θ )
E
σ xx ,σ yy ,σ xy
Initial diameter of the reference hole as a function of θ
Deformed diameter of the reference hole as a function of θ
Young’s modulus
In-plane residual stresses
f (θ ), g (θ ), h(θ )
M
M∗
σˆ
Functions of angles
Compliance matrix
Pseudo-inverse of matrix M
Optimum stress vector
Change in radial displacement of the reference hole
Introduction
Residual stresses are invariably introduced in components during their manufacture. These stresses can then redistribute
because of subsequent heat or mechanical treatments, machining or service loading. A reliable assessment of the nature of
residual stress fields is essential if we wish to understand their influence, combined with operating stresses, on the component
life. Although analytical solutions and numerical analysis are being used increasingly to estimate the residual stresses in
materials, experimental measurements are essential, principally to validate the predictions. Residual stress measurement
methods are categorized generally as non-destructive, semi-destructive and destructive techniques as shown in figure 1. Nondestructive techniques allow several measurements at the same location. However in semi-destructive methods more
measurements can be made at different locations. Since the specimen is totally destroyed in destructive techniques no further
measurements can be gained.
Although there is a wide variety of measurement techniques only few of them are capable of measuring residual stresses
through the thickness of large components. Figure 1 represents the depth of penetration of various methods when applied to
steel. Non-destructive techniques such as X-ray [1] and magnetic [2] are restricted to surface measurements. Ultrasonic [3]
and centre hole drilling [4] are developed to determine near sub-surface residual stresses. The neutron diffraction [5] method
is also able to penetrate up to depth around 50 mm. Layering [6] or slotting [7] techniques which can measure residual
stresses through the thickness of the components, are destructive and entirely destroy specimens.
Logarithmic depth of measurement in steel, mm
0.001
NonDestructive
Conventional
0.01
0.1
1
Synchrotron X-ray
Magnetic
10
100
Neutrons
Ultrasonic
Centre-hole
SemiDestructive
Ring Coring
Deep-hole Drilling
Destructive
Layering
Slotting
Surface
Sub-Surface
Figure1. Residual stress measurement methods in steel.
The semi-destructive deep hole drilling method (DHD) has been developed extensively to measure variations in residual stress
at depth up to about 500 mm. Basically deep hole drilling relies on measurement of strain relaxation. First, a reference hole is
drilled through the specimen followed by trepanning a core containing the reference hole. The relative distortion of the hole at
different angles is used to determine the stress distribution through the thickness.
Since the early work by Zhdanov and Gonchar[8] and Beaney[9] a large number of studies have been carried out to improve
the technique. For example Smith and Bonner [10-12] showed that the accuracy of the method can be improved by increasing
the number of measurement angles from three to eight. Experimental validation of the technique was conducted by Leggatt et
al. [13]. The residual stresses through the depth of a precisely deformed steel bar was measured. Bouchard et al. [14]
measured residual stresses in thick section steel welds. Furthermore, experimental measurements by deep hole drilling can
be used to validate the numerical and analytical predictions, where the method has been applied in components with thickness
in the range of 35-108 mm [15]. Excellent agreement between predictions of residual stress from finite element analysis (FE)
and measurements confirmed that the deep hole drilling can be applied to components of complex shape. Moreover, it has
been shown that this technique is capable of measuring linear and non-linear stress distributions [16].
Therefore, the deep hole drilling technique has become a standard method for measuring residual stress fields in isotropic
materials. It has also been extended to permit measurement in orthotropic materials [17]. Recently the versatility of the DHD
method has been demonstrated by Smith et al. [18] where measurements were preformed on a variety of different
components of complex shape including very thick components (a forged roll), in sections with varying thickness (rail
sections), in components where access to the measurement location is very difficult such as mock-up submarine T specimen,
in a very large component like a full scale submarine structure and components requiring detailed near surface and interior
residual stress distributions (a punched aluminium plate).
Deep Hole Drilling Technique
Fundamentally the DHD technique relies on the theory of elasticity applied to an infinite plate containing a hole under uniaxial
loading. Residual stresses are related to displacement fields around the hole. The radial distortion at different angles around
the hole due to stress relaxation procedure is used to determine the stress fields. In order to measure the diametral strain
relaxation four procedures are required. These are:
1- Drilling a small reference hole.
2- Diametral measurement of the reference hole.
3- Trepanning a core coaxial to the reference hole.
4- Remeasurement of the reference hole after trepanning.
A schematic diagram illustrating these steps is shown in figure 2 applied to a ring. For convenience only one half of the ring is
shown. In the first step a small reference hole is drilled through the thickness of specimen at the location where the residual
stress fields should be measured. In thick components where the straightness of long holes is crucial a self-aligning gun-drill
is required.
It is assumed that drilling a reference hole does not introduce further residual stresses into the component. Furthermore in
order to obtain an accurate diameter measurement two bushes are also attached on the surface of the specimen. The front
bush is located at the start of the reference hole and the back bush at the end.
On completion of drilling diametral measurements of the reference hole are conducted. An air probe with acceptable accuracy
is performed for the diameter measurement. The diameter of the hole is measured as a function of different angles around the
hole and at equal intervals along the hole axis. Relaxation of the residual stresses is obtained by extracting a core coaxial to
the reference hole. In order to provide coaxiality of the reference hole and the core electro discharge machining is used for the
trepanning procedure. The final extracted core is considered to be stress free. Finally the air probe is used to re-measure the
diameter of the reference hole after trepanning at the same angles and intervals used prior to trepanning.
The changes in diameter of the hole before and after trepanning are used to determine radial distortion of the reference hole.
The DHD analysis assumes that the distortion of the reference hole diameter remains perpendicular to the reference hole axis.
Furthermore, the trepanned core can be considered as a series of independent plates containing a small hole subjected to a
uniform uniaxial stresses. Elastic analysis of an infinite plate with a hole [19] shows that normalized radial distortion around the
hole can be related to in-plane residual stresses, σ xx ,σ yy and σ xy .
The distortion is given by
U rr (θ ) =
Δd (θ )
1
= − ⎡⎣σ xx (1 + 2cos 2θ ) + σ yy (1 − 2cos 2θ ) + σ xy (4sin 2θ ) ⎤⎦
d (θ )
E
(1)
The normalized radial distortion is obtained from the difference in the reference hole diameters before and after trepanning.
Δd (θ ) = d ′(θ ) − d (θ )
Furthermore the distortion is linear with respect to the unknown in-plane stresses according to equation (1), so that
(2)
(a)Attach front and back bushes.
(b) Drill reference hole.
x
θ
y
(c) Diametral measurement of reference hole and local coordinate system of diameter measurement.
(d) trepanning.
(e) Re-measure reference hole
Figure2. Schematic diagram of procedures for DHD technique applied to a circular ring.
U rr (θ ) =
f (θ )σ xx + g (θ )σ yy + h(θ )σ xy
Δd (θ )
=−
d (θ )
E
(3)
Since the diametral measurements are carried out at m angular locations the above equation can be expressed in matrix form
as,
⎡
⎤
⎢
⎥
⎡ f (θ1 ) g (θ1 ) h(θ1 ) ⎤ ⎡ ⎤
U
(
θ
)
1
rr
⎢
⎥
⎢
⎥ σ xx
1
⎢U (θ ) ⎥ = − ⎢ f (θ 2 ) g (θ 2 ) h(θ 2 ) ⎥ ⎢σ ⎥
⎢ ⎥
⎢ rr 2 ⎥
#
# ⎥ ⎢ yy ⎥
E⎢ #
⎢ # ⎥
⎢
⎥ ⎣⎢σ xy ⎦⎥
⎢
⎥
⎣⎢ f (θ m ) g (θ m ) h(θ m ) ⎦⎥
⎣⎢U rr (θ m ) ⎦⎥
(4)
Consequently at a specified location along the axis of the reference hole equation (4) can be re-written as
U rr = −
1
Mσ
E
(5)
As proposed by Bonner [12] and Smith and Bonner [11] when measurements are obtained at m angles a least-squares fit to
the diametral strains can be used to determine the stresses and a pseudo-inverse matrix is used as follows
σˆ = − EM ∗ U rr
(6)
where
M ∗ = ( M T M −1 ) M T
(7)
is the pseudo-inverse of matrix M, M T is the transpose of matrix M and σˆ is the optimum stress vector that best fits the
measured diametral distortions.
Components, Measurements and Results
The deep hole drilling technique was performed to measure residual stress distributions on two series of components. The
results reveal the uniqueness of this technique to measure residual stress fields in large scale specimens. The effects of
manufacturing procedures, machining, assemblage and operational loadings were obtained through different sets of
measurements by DHD.
Schematic arrangements of the components are shown in Figure 3. The first experiment consisted of a spheroidal graphite
sleeve with diameter 845 mm that had been shrink fitted to a steel shaft as shown in figure 3 (a) and (b). The shaft and sleeve
was part of a horizontal roll assembly for a steel rolling mill and after shrink fitting had been used in rolling campaigns.
Consequently, DHD measurement on this assembly has been carried out after operation in service and several machining
procedures. The roll sleeve was supplied by CORUS and the chemical composition of the sleeve was 1.79% C, 0.99% Si,
0.82% Mn, 0.024% P, 0.008% S, 1.3% Cr, 1.48% Ni, and 0.17% Mo.
The second set of experiments was carried out on a series of sleeves at different stages of their manufacture: as-cast,
machined, and then with a bearing fitted. The sleeves are used in rolling steel mills as vertical rolls. The dimensions of the rolls
were approximately 622 mm outside diameter, sleeve thickness of 155 mm and depth of 222 mm as shown in Figure 3 (c) and
(d). These vertical sleeves were supplied by Akers via CORUS. The chemical composition was 3.25% C, 1.7% Si, 0.75% Mn,
0.03% P, 0.01%S, 0.1% Cr, 1.75Ni, 0.7% Mo, 0.08% Mg.
1300
φ
Axial
Hub diameter:845 mm
DHD Direction
DHD Direction
(a) Shrink fitted assembly (Side view)
(b) Shrink fitted assembly (Top view)
φ
DHD Direction
(c) Vertical roll (Side view)
(d) Vertical roll (Top view)
Figure 3. Schematic diagram of components and specified DHD direction, all dimensions in mm.
Experimental measurements were made using a gun-drill of 5 mm in diameter for drilling the reference hole. An air probe
calibrated for 5 mm hole diameter with 50 μ m resolution was used for diameter measurement. Subsequently a 15 mm
diameter core coaxial to the reference hole was trepanned using an electro-discharge machine. This was followed by remeasuring the hole diameter.
The radial distortion obtained from the change in diameter of the reference hole before and after trepanning the core was
subsequently used to determine two dimensional residual stresses using equations 1 to 7. As an example, the diametral
measurements of the reference hole in an unmachined sleeve are shown in figure 4. The measurement has been carried out
along a radial line through the thickness of the sleeve. Only the results for one measurement angle are shown.
4.992
Reference hole diameter (mm)
4.991
Before EDM
4.99
After EDM
4.989
4.988
4.987
4.986
4.985
10
30
50
70
90
110
130
150
170
Depth from outside surface(mm)
Figure 4. Typical results of the diameter measurement of a reference hole in an as-cast sleeve before and after trepanning.
Since the axial deformation of the reference hole was not measured, only the in-plane hoop, axial and shear stresses were
calculated. Results for the shrink fitted roll are shown in figure 5 with the measurements corresponding to a radial line through
the sleeve and shaft as shown in figure 3(a).
Hoop, axial and shear stresses were determined assuming Young’s Modulus E = 210GPa . The in-plane shear stresses were
essentially zero indicating that the hoop and axial stresses were the principal stresses.
250
200
axial stress
hoop stress
150
axial-hoop shear stress
Residual stress (MPa)
hoop stress-theory
100
50
0
0
50
100
150
200
250
300
350
400
450
-50
-100
-150
-200
-250
Radial distance from outer surface of hub to the shaft centre (mm)
Figure 5. Measured distribution of residual stresses through thickness of the shrink fitted assembly
The measured hoop stress variations from the second set of experiments are shown in figure 6. In the as-cast sleeve it is
evident that the outer surface of the sleeve was in compression at about -120 MPa. This compressive region was balanced by
tensile residual stresses reaching a peak value of about 40 MPa. After machining of the sleeve, to reduce the wall thickness
from 155 mm to about 110 mm the initial residual stress was redistributed raising the initial tensile residual stress from about
40 MPa to about 60 MPa. Finally, by fitting a bearing into the sleeve a further tensile residual stress of about 10 MPa was
introduced.
80
60
40
Hoop Stress (MPa)
20
0
0
20
40
60
80
100
120
140
160
-20
-40
-60
-80
As-cast
machined
machined-bearing fitted
-100
-120
-140
Radial distance from outer surface (mm)
Figure 6. Distribution of hoop stress in three of vertical sleeves: As-machined, Machined and machined specimen with a
bearing fitted.
Discussion
For the cast iron sleeve shrink fitted into a shaft we would expect a residual stress distribution that is determined from standard
Lame’ equations[19]. To allow comparison with the measurements shown in figure 5, it was assumed that the predicted peak
hoop stress matched the peak value obtained from the experiment. This is shown in figure 5. Comparison between the
predicted and measured hoop residual stress distributions reveals two features; 1) the near surface was in compression and 2)
there was not uniform compression in the shaft. The near surface compressive residual stresses are expected to arise from
the use of the sleeve in rolling campaigns to produce long products. The reason for the non-uniform compressive hoop stress
in the shaft is un-known and requires further work.
The residual stresses in the as-cast vertical sleeves principally arise from the manufacturing process and arise from differential
cooling after casting. Importantly subsequent machining of the castings did not lead to significant relaxation of the residual
stresses. There was, however, redistribution of the residual stress leading to higher tensile residual stresses than in the
original as-cast sleeves.
The use of DHD technique on such large components demonstrates that there is the potential to use the method on relatively
large components; and further work is being carried out to explore its application to even larger components.
Concluding Remarks
•
It is demonstrated that the deep hole drilling technique is a reliable method for measuring residual stress distributions
in large scale components.
•
The high levels of measured tensile hoop stresses near a shrink fitted shaft and sleeve interface are in general
agreement with theory.
•
Compressive hoop stress near the outer surface of the horizontal roll was expected to be due to the effects of service
loadings.
•
DHD residual measurements on as-cast sleeve revealed that subsequent machining redistributed and increased the
hoop stresses.
•
Fitting a bearing into a machined sleeve also marginally increased the hoop residual stresses.
Acknowledgments
The work was done as part of the RFCS EWRCOOL project. We are grateful to CORUS, in particular to Dr Steve Moir for
supplying the samples. We are also grateful to COSWIG for providing additional financial support.
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