371
Residual Stres
15. Residual Stress
Yuri F. Kudryavtsev
15.1 Importance of Residual Stress ................
15.1.1 Definition of Residual Stresses .......
15.1.2 Origin of Residual Stresses .............
15.1.3 Residual Stress Management:
Measurement, Fatigue Analysis,
and Beneficial Redistribution ........
15.2 Residual Stress Measurement.................
15.2.1 Destructive Techniques
for Residual Stress Measurement ....
15.2.2 Nondestructive Techniques
for Residual Stress Measurement ....
15.2.3 Ultrasonic Method for Residual
Stress Measurement .....................
15.3 Residual Stress in Fatigue Analysis .........
15.4 Residual Stress Modification ..................
15.5 Summary .............................................
References ..................................................
371
372
372
373
373
373
375
377
381
383
386
386
residual stresses published by the Society of
Experimental Mechanics (SEM) in 1996 and 2005.
15.1 Importance of Residual Stress
Residual stress can significantly affect the engineering properties of materials and structural components,
notably fatigue life, distortion, dimensional stability,
corrosion resistance, and brittle fracture [15.1]. Such
effects usually lead to considerable expenditure in repairs and restoration of parts, equipment, and structures.
For this reason, residual stress analysis is a compulsory
stage in the design of parts and structural elements and
in the estimation of their reliability under real service
conditions.
Systematic studies had shown that, for instance,
welding residual stresses might lead to a drastic reduction in the fatigue strength of welded elements. In
multicycle fatigue (N > 106 cycles), the effect of residual stresses can be comparable to the effect of stress
concentration [15.2]. Even more significant are the ef-
fects of residual stresses on the fatigue life of welded
elements in the case of relieving harmful tensile residual
stresses and introducing beneficial compressive residual
stresses in the weld toe zones. The results of fatigue
testing of welded specimens in the as-welded condition
and after the application of ultrasonic peening shows
that, in the case of non-load-carrying fillet welded joint
in high-strength steel, redistribution of residual stresses
resulted in approximately twofold increase in the limit
stress range [15.1].
The residual stresses are therefore one of the main
factors determining the engineering properties of materials, parts, and welded elements, and should be
taken into account during the design and manufacturing of different products. Although certain progress has
been achieved in the development of techniques for re-
Part B 15
In many cases residual stresses are one of the main
factors determining the engineering properties of
parts and structural components. This factor plays
a significant role, for example, in fatigue of welded
elements. The influence of residual stresses on the
multicycle fatigue life of butt and fillet welds can be
compared with the effects of stress concentration.
The main stages of residual stress management
are considered in this chapter with the emphasis
on practical application of various destructive
and nondestructive techniques for residual stress
measurement in materials, parts, and welded
elements. Some results of testing showing the role
of residual stresses in fatigue processes as well as
aspects and examples of ultrasonic stress-relieving
are also considered in this chapter. The presented
data on residual stresses are complimentary to
the detailed review of various methods of residual
stress analysis considered in two handbooks on
372
Part B
Contact Methods
It is the first level or macroscopic (type I) residual stress
that is of interest to mechanical engineers and design
offices and that is considered in this paper.
σres (MPa)
300
12
15.1.2 Origin of Residual Stresses
x
200
12
100
0
–100
0
25
50
75
100
x (mm)
Part B 15.1
Fig. 15.1 Distribution of longitudinal (oriented along the
weld) residual stresses near the fillet weld in a bridge span.
x is the distance from the weld toe [15.3]
sidual stress management, considerable effort is still
required to develop efficient and cost-effective methods
of residual stress measurement and analysis as well as
technologies for the beneficial redistribution of residual
stresses.
15.1.1 Definition of Residual Stresses
Residual stresses (RS) can be defined as those stresses
that remain in a material or body after manufacture and
material processing in the absence of external forces or
thermal gradients. Residual stresses can also be produced by service loading, leading to inhomogeneous
plastic deformation in the part or specimen. Residual
stresses can be defined as either macro- or microstresses
and both may be present in a component at any one time.
Residual stresses can be classified as
Type I: Macro residual stresses that develop in the
body of a component on a scale larger than the
grain size of the material
Type II: Micro residual stresses that vary on the scale
of an individual grain
Type III: Micro residual stresses that exist within
a grain, essentially as a result of the presence
of dislocations and other crystalline defects
Residual stresses develop during most manufacturing processes involving material deformation, heat
treatment, machining or processing operations that
transform the shape or change the properties of a material. They arise from a number of sources and can
be present in the unprocessed raw material, introduced
during manufacturing or arise from in-service loading.
The origins of residual stresses in a component may be
classified as
•
•
•
differential plastic flow
differential cooling rates
phase transformations with volume changes etc.
For instance, the presence of tensile residual stresses
in a part or structural element are generally harmful
since they can contribute to, and are often the major
cause of, fatigue failure and stress-corrosion cracking. Compressive residual stresses induced by different
means in the (sub)surface layers of material are usually
beneficial since they prevent origination and propagation of fatigue cracks, and increase wear and corrosion
resistance.
Examples of operations that produce harmful tensile stresses are welding, machining, grinding, and rod
or wire drawing. Figure 15.1 shows a characteristic
residual stress profile resulting from welding. The residual stresses were measured by an ultrasonic method
in the main wall of a bridge span near the end of one
of the welded vertical attachments [15.3]. In the vicinity of the weld the measured levels of harmful tensile
residual stresses reached 240 MPa. Such high tensile
residual stresses are the result of thermoplastic deformations during the welding process and are one of the
main factors leading to the origination and propagation
of fatigue cracks in welded elements.
On the other hand, compressive residual stresses
usually lead to performance benefits and can be introduced, for instance, by peening processes such as shot
peening, hammer peening, laser peening, and ultrasonic
peening [15.1]. Figure 15.2 shows characteristic distributions of beneficial compressive residual stress in the
surface layers of material resulting from conventional
and ultrasonic shot peening processes [15.4].
Residual Stress
15.1.3 Residual Stress Management:
Measurement, Fatigue Analysis,
and Beneficial Redistribution
15.2 Residual Stress Measurement
373
σr (MPa)
200
100
It is very important to consider the problem of residual stress as a complex problem including, at least,
the stages of determination, analysis, and beneficial
redistribution of residual stresses. The combined consideration of these stages of the residual stress analysis
and modification gives rise to so-called the residual
stress management (RSM) concept approach [15.5].
The RSM concept includes the following main stages
0
–100
–200
–300
Stage 1. Residual stress determination:
•
•
Experimental studies
Computation
Stage 3. Residual stress modification (if required):
•
•
Changes in technology of manufacturing/assembly
Application of stress-relieving techniques
The main stages of residual stress management are considered in this chapter with the emphasis on examples
of practical application of various destructive and nondestructive techniques for residual stress measurement
in materials, parts, and welded elements. Some results
of testing showing the role of residual stresses in fatigue
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 0.9
Depth (mm)
Fig. 15.2 In-depth profile of residual stress in 2014-T6 aluminum
alloy produced by conventional (CS) and ultrasonic (US) shoot
peening [15.4]
processes as well as beneficial modification of residual
stresses directed mainly towards fatigue life improvement are also considered. New engineering tools such
as a computerized ultrasonic system for residual stress
measurement and a technology and corresponding compact system for ultrasonic hammer peening are also
introduced.
The data on residual stresses presented in this chapter are complimentary to the detailed consideration and
comparison of different methods of residual stress analysis considered in [15.6] and [15.1].
15.2 Residual Stress Measurement
Over the last few decades, various quantitative and qualitative methods for residual stress analysis have been
developed [15.6]. In general, a distinction is usually
made between destructive and nondestructive techniques for residual stress measurement.
15.2.1 Destructive Techniques
for Residual Stress Measurement
The first series of methods is based on destruction of the
state of equilibrium of the residual stress after sectioning of the specimen, machining, layer removal or hole
drilling. The redistribution of the internal forces leads
to local strains, which are measured to evaluate the residual stress field. The residual stress is deduced from
the measured strain using the elastic theory through the
use of an analytical approach or finite element calculations. The most usual destructive methods are:
•
•
•
•
the hole-drilling method
the ring core technique
the bending deflection method
the sectioning method
The application of these destructive, or so-called partially destructive, techniques is limited mostly to
laboratory samples.
Hole Drilling
The hole-drilling method requires drilling a small hole,
typically 1–4 mm in diameter, to a depth approximately
Part B 15.2
•
•
–500
Measurement: destructive, nondestructive
Computation
Stage 2. Analysis of the residual stress effects:
US
CS
– 400
374
Part B
Contact Methods
Strain gauge
rosette
Strain gauge
rosette
Residual stress (MPa)
100
0
–100
–500
Hole
Ring core
x-ray
method
Hole drilling
method
–1000
Fig. 15.3 Schematic illustrations of the application of
hole-drilling and ring core methods for residual stress
measurement (after [15.6])
Part B 15.2
equal to its diameter. A specialized three-element
rosette, such as that shown in Fig. 15.3, measures the
surface strain relief in the material around the outside of the hole. The ring core method is similar,
except that a ring hole, typically with an internal diameter of 15–150 mm, is drilled instead of a hole. The
measurements of relieved strain are then made on the
surface of the material remaining inside the ring, as
shown in Fig. 15.3. The typical depth of the ring core is
25–150% of its internal diameter. In both methods, residual stresses existing in the material before hole/ring
drilling can be calculated from the measured relieved
strains.
The ring core method is quite sensitive compared
with the hole-drilling method because it involves almost
complete relief of the surface strains. It is also insensitive to any minor diameter errors or eccentricity of the
annular hole with respect to the strain gages. However,
the size of the annular hole in relatively large, causing
much more damage than the hole-drilling method. Also,
the results are much less localized because the hole/ring
diameter defines the region of residual stress measurement. Another concern with the ring core method is the
need to disconnect the strain gage wires to allow ring
drilling to proceed. Also, any diameter errors or eccentricity of the hole with respect to the strain gages can
introduce significant errors in the residual stress calculation.
Despite some shortcomings, the hole-drilling technique remains a popular means of measuring residual
stress. Recent developments include the introduction
0
Phase γ (λKαMn)
Phase α (λKαMn)
Axial
Axial
Tangential
0.1 0.2 0.3 0.4 0.5 0.6
Depth (mm)
Fig. 15.4 Results of residual stress measurement by incremental hole-drilling and x-ray diffraction methods in steel
after shot peening (after [15.7])
of new rosette designs [15.8], the development of
laser speckle interferometry [15.9], moiré interferometry [15.10], and holography [15.11] for carrying out
the residual stress measurements.
One result of the application of the hole-drilling
technique is presented in Fig. 15.4. The residual stresses
in this case were measured by using the incremental
hole-drilling method in comparison with the application of x-ray diffraction method in a steel specimen
after shot peening [15.7]. As can be seen, good correlation of results of residual stress measurement by the
two different techniques was observed.
Curvature and Layer Removal
Layer-removal techniques are often used for measuring residual stress in samples with a simple geometry.
The methods are generally quick and require only simple calculations to relate the curvature to the residual
stresses. The curvature depends on the original stress
distribution present in the layer that has been removed
and on the elastic properties of the sample. By carrying
out a series of curvature measurements after successive
layer removals the distribution of stress in the original
plate can then be deduced.
Figure 15.5 presents the results of residual stress
measurement using the layer-removal technique in material after shot peening. It is shown that, after shot
peening, the magnitude and character of the distribution
of residual stresses depends on the mechanical properties of the material.
Residual Stress
100
100
0
0
–100
–100
–200
455 HV
–300
–300
–400
– 400
Shot peening condition:
Cast steel shot.dia. = 0.4 mm
Speed of turbine: 2500 tr/min
Time of treatment: 4 min
Thickness of sample: 20 mm
–600
–700
0.5
280 HV
365 HV
5454 aluminum alloy
AISI 304 grade steel
AISI 1070 grade steel
–500
620 HV
– 500
– 600
– 700
0.5
1
1
Depth (mm)
Depth (mm)
15.2.2 Nondestructive Techniques
for Residual Stress Measurement
The second set of methods for residual stress measurement are based on the relationship between physical
and crystallographic parameters and the residual stress
and do not requires the destruction of the part or structural element; they can therefore be used for field
measurements. The most well-developed nondestructive methods are:
Residual stress (MPa)
100
0
–100
–200
–300
x-direction
y-direction
–400
–500
0
0.2
0.4
0.6
0.8
1
1.2
Depth from surface (mm)
Fig. 15.6 Residual stress distribution in A572 Gr.50 steel
after shot peening measured by the x-ray diffraction
method combined with layer removal [15.12]
•
•
•
X-ray and neutron diffraction methods. These methods are based on the use of the lattice spacing as the
strain gauge. They allow study and separation of the
three kinds of residual stresses. Currently, the x-ray
method is the most widely used nondestructive technique for residual stress measurements.
Ultrasonic techniques. These techniques are based
on variations in the velocity of ultrasonic wave propagation in materials under the action of mechanical
stresses.
Magnetic methods. These methods rely on the interaction between magnetization and elastic strain
in ferromagnetic materials. Various magnetic properties can be studied, such as permeability, magnetostriction, hysteresis, and Barkhausen noise.
X-Ray Method
The x-ray method is a nondestructive technique for the
measurement of residual stresses on the surface of materials. It can also be combined with some form of
layer-removal technique so that a stress profile can be
generated, but then the method becomes destructive.
One of the major disadvantages of the x-ray method
is the limitation imposed on the sample geometry for
residual stress measurement. The geometry has to be
such that an x-ray can both hit the measurement area
and still be diffracted to the detector without hitting
any obstructions. Portable diffractometers that can be
taken out into the field for measurements of structures
Part B 15.2
Fig. 15.5 Results of residual stress measurement by the layer-removal method in shot-peened samples, illustrating the
effect of the mechanical properties of materials [15.6]
–600
375
Residual stress (MPa)
Residual stress (MPa)
–200
15.2 Residual Stress Measurement
376
Part B
Contact Methods
Part B 15.2
such as pipelines, welds, and bridges are now available [15.13].
The speed of measurement depends on a number of
factors, including the type of material being examined,
the x-ray source, and the degree of accuracy required.
With careful selection of the x-ray source and test
set-up speed of measurement can be minimized. New
detector technology has also greatly reduced the measurement time. x-ray diffraction has a spatial resolution
of 1–2 mm down to tens of microns and a penetration
depth of around 10–30 μm, depending on the material
and source.
Figure 15.6 shows the results of residual stress
measurement by the x-ray diffraction method combined
with layer removal in A572 Gr.50 steel after shoot
peening [15.12]. Measurements were made at the surface and at 11 nominal depths until the residual stress
decayed to zero. Stresses were obtained for both the
x- and y-directions. The maximum compressive stress
was −448 MPa in the x-direction and −514 in the ydirection. The depth of beneficial compressive residual
stresses in this case was approximately 0.8 mm.
As can be seen form Figs. 15.2 and 15.4–15.6, the
depth of the beneficial compressive residual stresses
after conventional and ultrasonic shoot peening is
typically 0.3–0.8 mm. Deeper beneficial compressive
residual stresses can be induced by using the ultrasonic
impact technique or ultrasonic hammer peening (UP).
The UP technique is based on the combined effect of
high-frequency impacts and the induction of ultrasonic
energy in the treated material [15.1]. Figure 15.7 shows
Residual stress (MPa)
100
the components of residual stresses parallel and perpendicular to the direction of treatment [15.12]. In this case
the x-ray diffraction method combined with layer removal was also used. The maximum compressive stress
in the direction of treatment was −427 MPa, In the perpendicular direction the maximum compressive stress
was −302 MPa. The depth of the compressive residual
stresses induced by UP was about 1.5 mm.
Neutron Diffraction Method
The neutron diffraction method relies on elastic deformations within a polycrystalline material that cause
changes in the spacing of the lattice planes from
their stress-free condition. The advantage of the neutron diffraction method in comparison with the x-ray
technique is its larger penetration depth. The neutron diffraction technique enables the measurement
of residual stress at near-surface depths of around
0.2 mm down to bulk measurements of up to 100 mm
in aluminum or 25 mm in steel [15.6]. With high
spatial resolution, the neutron diffraction method can
provide complete three-dimensional maps of the residual stresses in material. However, compared to other
diffraction techniques such as x-ray diffraction, the relative cost of application of neutron diffraction method
is much higher, mainly because of the equipment
cost [15.14].
The neutron diffraction method was applied for the
measurement of residual stresses in A572 Gr.50 steel
after ultrasonic impact treatment [15.12]. The three
components of residual stresses, parallel (x) and perpendicular (y) to the direction of treatment as well as
Residual stress (MPa)
300
0
200
–100
100
–200
0
–300
–100
Parallel
Perpendicular
–400
–500
–600
–200
Sxx (parallel)
Syy (perpend.)
Szz (deep)
–300
– 400
–500
0
0.2
0.4
0.6
0.8
1 1.2 1.4 1.6 1.8
Depth from surface (mm)
Fig. 15.7 Distribution of residual stresses as a function of
the distance from the treated surface of material received
by using of the x-ray diffraction method combined with
layer removal [15.12]
– 600
0
1
2
3
4
5
6
7
Depth from surface (mm)
Fig. 15.8 Distribution of residual stresses as a function of
the distance from the treated surface of material received
by using of the neutron diffraction method [15.12]
Residual Stress
a) ΔC/C x 10–3
b) ΔC/C x 10–3
2
2
1
1
0
0
0
–1
–1
–2
–200
C sx3
C sx2
CL
–100
0
100
–200
σ (MPa)
–2
–200
–100
377
c) ΔC/C x 10–3
2
1
–1
15.2 Residual Stress Measurement
0
100
–200
σ (MPa)
–2
–200
–100
0
100
–200
σ (MPa)
Fig. 15.9a–c Changes in the ultrasonic longitudinal (CL ) and shear wave velocities with orthogonal polarization (CSX3 ;
CSX2 ) depending on the mechanical stress σ in (a) steel A, (b) steel B, (c) and aluminum alloy [15.15]
sive external loads in steel and aluminum alloys are
presented in Fig. 15.9 [15.15]. As can be seen from
Fig. 15.9, the intensity and character of these changes
can be different, depending on the material properties.
Different configurations of ultrasonic equipment
can be used for residual stress measurements. In each
case, waves are launched by a transmitting transducer, propagate through a region of the material,
and are detected by a receiving transducer, as shown
in Fig. 15.10 [15.6]. The technique in which the same
transducer is used for excitation and receiving of ultrasonic waves is often called the pulse-echo method
(Fig. 15.10a). This method is effective for the analysis
of residual stresses in the interior of the material. In
a)
b)
15.2.3 Ultrasonic Method
for Residual Stress Measurement
One of the promising directions in the development of
nondestructive techniques for residual stress measurement is the application of ultrasound. Ultrasonic stress
measurement techniques are based on the acousticelasticity effect, according to which the velocity of
elastic wave propagation in solids is dependent on the
mechanical stress [15.16, 17]. The relationships between the changes of the velocities of longitudinal
ultrasonic waves and shear waves with orthogonal
polarization under the action of tensile and compres-
c)
Fig. 15.10a–c Schematic view of ultrasonic measurement configurations: (a) through-thickness pulse-echo,
(b) through-thickness pitch-catch, and (c) surface pitch-
catch
Part B 15.2
in the depth direction (z), are shown in Fig. 15.8. It can
be seen that the depth of the beneficial compressive residual stresses is 1.6–1.7 mm for all three components.
The maximum surface compressive residual stresses
was −458 MPa in the parallel to the treatment direction
and −416 MPa in the perpendicular direction.
There are various destructive and nondestructive
methods to detect and quantify the residual stresses
described in the technical literature. However, new
industrial problems, new geometrical and material complexities related to them, combined with a general need
for fast and economical residual stress measurements,
create a strong demand for new and effective techniques
and devices. The ideal technology must be reliable and
user-friendly, i. e., it should not require guessing and
intuition from the engineer/technician and it must be
computerized for quick analysis. The demand for sophisticated systems is increasing dramatically.
378
Part B
Contact Methods
Part B 15.2
this case the through-thickness average of the residual
stresses is measured.
In the configuration shown in Fig. 15.10c, the residual stress in a (sub)surface layer is determined. The
depth of this layer is related to the ultrasonic wavelength, often exceeding a few millimeters, and hence is
much greater than that obtained by x-ray method. Other
advantages of the ultrasonic technique are the facts that
the instrumentation is convenient to use, quick to set up,
portable, inexpensive, and free of radiation hazards.
In the technique proposed in [15.15], the velocities
of longitudinal ultrasonic wave and shear waves with
orthogonal polarization are measured at a considered
point to determine the uni- and biaxial residual stresses.
The bulk waves in this approach are used to determine
the stresses averaged over the thickness of the investigated elements. Surface waves are used to determine the
uni- and biaxial stresses at the surface of the material.
The mechanical properties of the material are represented by the proportionality coefficients, which can be
calculated or determined experimentally under external
loading of a sample of the considered material.
In general, the change in the ultrasonic wave velocity in structural materials under mechanical stress
amounts to only tenths of a percentage point. Therefore
the equipment for practical application of ultrasonic
technique for residual stress measurement should be of
high resolution, reliable, and fully computerized.
Ultrasonic Equipment and Software
for Residual Stress Measurement
The ultrasonic computerized complex (UCC) for residual stress analysis was developed recently based on
an improved ultrasonic methodology [15.15]. The UCC
includes a measurement unit with supporting software
and a laptop with an advanced database and expert sys-
Fig. 15.11 The ultrasonic computerized complex for the
measurement of residual and applied stresses
tem (ES) for the analysis of the influence of residual
stresses on the fatigue life of welded components. The
developed device with gages/transducers for ultrasonic
residual stress measurement is presented in Fig. 15.11.
The UCC allows the determination of uni- and biaxial
applied and residual stresses for a wide range of materials and structures. In addition, the developed ES can be
used for the calculation of the effect of the measured
residual stresses on the fatigue life of welded elements, depending on the mechanical properties of the
materials, the type of welded element, the parameters
of cyclic loading, and other factors.
The developed equipment enables the determination
of the magnitudes and signs of the uni- and biaxial residual and applied stresses for a wide range of materials
as well as stress, strain, and force in fasteners of various sizes. The sensors, using quartz plates measuring
from 3 × 3 mm to 10 × 10 mm as ultrasonic transducers,
are attached to the object under investigation by special
clamping straps (Fig. 15.11) and/or electromagnets.
The main technical characteristics of the measurement unit are:
•
•
•
•
•
•
•
stress can be measured in materials with thickness
2–150 mm;
the error in stress determination (from an external
load) is 5–10 MPa;
the error in residual stress determination is 0.1 σy
(yield strength) MPa;
stress, strain, and force measurement in fasteners
(pins) 25–1000 mm long;
independent power supply (accumulator battery
12 V);
the overall dimensions of the measurement device
are 300 × 200 × 150 mm3 ;
the weight of the unit with sensors is 6 kg.
The supporting software allows the control of the
measurement process, storage of the measured and
other data, and calculation and plotting of the distribution of residual stresses. The software also allows easy
connection with standard personal computers (PCs).
An example of the residual stress measurement data,
using the developed software, is shown in Fig. 15.12.
The software allows the comparison of different sets
of residual stress measurement data and transfer of selected data for further fatigue analysis. In Fig. 15.12,
the left side of the screen displays information on the
measured ultrasonic wave velocities as well as other
technical information on the sample. The right-hand
side of the screen displays the distribution of calculated
residual stresses.
Residual Stress
15.2 Residual Stress Measurement
379
Fig. 15.12 Screenshot showing the
distribution of residual stresses in
a low-carbon steel plate after local
heating [15.15]
σ (MPa)
200
the compression zone, located between the edge of
the plate and the center of the heating zone, the
longitudinal component of residual stress reaches
−140 MPa.
Examples of Residual Stress Measurements
Using the Ultrasonic Method
One of the main advantages of the developed technique
and equipment is the possibility to measure the residual and applied stresses in samples and real structure
elements. Such measurements have been performed for
a wide range of materials, parts, and structures. A few
examples of the practical application of the developed
technique and equipment for residual stress measurement based on the ultrasonic technique are presented
below.
Specimen for Fatigue Testing. The residual stresses
100
0
Local
heating
Fatigue
crack
–100
0
20
40
60
80
L (mm)
were measured in a 500 × 160 × 3 mm3 specimen made
of an aluminum alloy (σy = 256 MPa, σu = 471 MPa)
with a fatigue crack. The residual stresses were induced
by local heating at a distance of 30 mm from the center of the specimen. As can be seen from Fig. 15.13, in
the heating zone, both components of the residual stress
are tensile. In the compression zones, the longitudinal
component of residual stress reaches −130 MPa.
Fig. 15.13 Distribution of residual stresses induced by local
Compound Pipes and Pipes with Surfacing. Another
heating in a specimen made of an aluminum alloy with
a fatigue crack. L is the distance from the center of specimen [15.15]
example of measuring the residual stresses by the ultrasonic method is associated with compound pipes.
Compound pipes are used in various applications and
Part B 15.2
In the example of residual stress measurement
presented in Fig. 15.12, a plate made from lowcarbon steel, with a yield strength of 296 MPa, was
heated locally, with the focal point of heating located approximately 50 mm from the left side of the
plate. The distribution of both components of residual stresses in the specimen as a result of this
local heating are shown on the right-hand side of
Fig. 15.12. As can be seen, in the heating zone,
both residual stress components are tensile and reach
the yield strength of the considered material. In
380
Part B
Contact Methods
σ (MPa)
200
σ (MPa)
200
150
σx
100
σy
50
0
0
y
–50
–200
–100
x
1000
–150
–400
0
10
20
–
30
δ (mm)
+
Part B 15.2
Fig. 15.14 Residual stress distribution in a compound
ring with the following dimensions [15.15]. (inner ring
D1 = 160 mm and D2 = 180 mm; outer ring D1 = 180 mm
and D2 = 220 mm; D1 inner diameter, D2 outer diameter,
width of ring 16 mm)
a) σ (MPa)
b) σ (MPa)
160
160
80
80
0
0
–80
0
5
–
10 15
δ (mm)
+
–80
0
5
–
10
15 10
δ (mm)
+
Fig. 15.15a,b Residual stress distribution in rings with
inner surfacing [15.15]: (a) ring with D1 = 150 mm
and D2 = 180 mm; (b) ring with D1 = 180 mm and
D2 = 220 mm. (D1 inner diameter, D2 outer diameter,
width of ring 16 mm)
500
–200
–250
36
0
100
200
300
400
500
x (mm)
Fig. 15.16 Distribution of longitudinal (along the weld)
and transverse components of residual stresses along a butt
weld toe [15.18]
are made by fitting a pipe with a certain outer diameter inside a pipe with approximately the same inner
diameter under pressure. For residual stress measurement, rings were cut off from a number of compound
pipes of different diameters. The width of the rings was
16 mm. Residual stresses were measured across the prepared cross-sections in three different locations at 120◦
to each other with subsequent averaging of the measurement results. Depending on the differences between the
inner diameter D1 of the outer pipe and the outer diameter D2 of the inner pipe, the measurements were made
at three to five points along the radius. The distribution
of residual stresses as measured across the wall thickness of the compound pipe is presented in Fig. 15.14.
The results of residual stress measurement using the
ultrasonic method in rings cut off from a pipes with
inner surfacing are presented in Fig. 15.15.
Measurement of Residual Stresses in Welded Elements. The residual stresses were measured in a 1000 ×
500 × 36 mm3 specimen, representing a butt-welded element of a wind tunnel. The distribution of biaxial
residual stresses was investigated in the x- (along the
weld) and y-directions after welding and in the process
of cyclic loading of a specimen [15.18]. Figure 15.16
shows the distribution of longitudinal (along the weld)
and transverse components of residual stresses along the
weld toe. Both components of residual stress reached
Residual Stress
15.3 Residual Stress in Fatigue Analysis
381
b) σ (MPa)
a)
160
x2
σ22
x3
σ33
80
II
70
x1
σ11
III
I
I
0
II
III
900
σ22
σ11
–80
140
–160
c) σ (MPa)
0
20
40
60
80
100
120
140
x (mm)
d) x (mm)
75
120
80
Part B 15.3
σ22
σ11
40
35
σ11
σ33
0
–40
–80
0
20
40
60
80
100
0
–300
120
140
x (mm)
–200
–100
0
100
200
300
σ (MPa)
Fig. 15.17 (a) Welded specimen and (b) distribution of the residual stresses along the butt weld (I–I), (c) perpendicular to
the weld (II–II), and (d) through the thickness near the weld (III–III) [15.5]
their maximum levels in the central part of a specimen:
longitudinal – 195 MPa, transverse – 110 MPa.
The ultrasonic method was also applied for residual
stress measurement in a 900 × 140 × 70 mm3 specimen
of low-alloyed steel, representing the butt weld of
a structure [15.5]. The distribution of residual stress
components in the x3 (along the weld) and x2 (perpendicular to the weld) directions as well as through
the thickness of the specimen near the weld (x1 ) are
presented in Fig. 15.17.
15.3 Residual Stress in Fatigue Analysis
Despite the fact that the residual stresses have a significant effect on the strength and reliability of parts
and welded elements, their influence is not sufficiently
reflected in corresponding codes and regulations. This
is mainly because the influence of residual stresses on
the fatigue life of parts and structural elements depends
greatly not only on the level or residual stresses, but also
on the mechanical properties of the materials used, the
type of welded joints, the parameters of cyclic loading,
and other factors [15.1, 2]. Presently elaborate, timeand labor-consuming fatigue tests of large-scale specimens are required for this type of analysis.
Generally, in modern standards and codes for fatigue design, for instance, of welded elements the
presented data correspond to the fatigue strength of real
welded joints including the effects of welding tech-
382
Part B
Contact Methods
Part B 15.3
nology, type of welded element, and welding residual
stresses [15.19]. Nevertheless, in many cases there is
a need to consider the influence of welding residual
stresses on the fatigue life of structural components in
greater detail. These cases include the use of the results
of fatigue testing of relatively small welded specimens
without high tensile residual stresses, the analysis of the
effects of factors such as overloading, spectra loading,
and the application of improvement treatments. A few
examples of the analysis of the effect of residual stresses
on the fatigue life of welded elements based on fatigue
testing and computation are described below.
It is known that the tensile residual stresses induced
by welding can lead to drastic reduction of the fatigue
strength of welded elements [15.2]. Figure 15.18 illustrates the results of one of these studies in which butt
joints in low-carbon steel were tested using a symmetric loading cycle (stress ratio R = −1). There were three
types of welded specimens. Specimens of the first type
were cut from a large welded plate. Measurements of
the residual stresses revealed that in this case the specimens after cutting had a minimum level of residual
stresses. Additional longitudinal weld beads along both
sides in specimens of the second type created tensile
residual stresses close to the yield strength of the base
material in the central part of these specimens. These
beads did not change the stress concentration of the
considered butt weld in the direction of loading. In the
specimens of the third type the longitudinal beads were
deposited and then the specimens were bisected and re-
joined by butt-welding. Due to the small length of this
butt weld the residual stresses in these specimens were
very small (approximately the same as in the specimens
of the first type) [15.2].
Tests showed that the fatigue strength of the specimens of the first and third types (without residual
stresses) was practically the same as the limit stress
range 240 MPa at N = 2 × 106 cycles. The fatigue limit
of specimens with high tensile residual stresses (second
type) was only 150 MPa. In all specimens the fatigue
cracks originated near the transverse butt joint.
The reduction of the fatigue strength in this case
can only be explained by the effect of welding residual
stresses. These experimental studies also showed that,
at the level of maximum cycle stresses close to the yield
strength of the base material, the fatigue life of specimens with and without high tensile residual stresses
was practically identical. With the decrease of the stress
range there is a corresponding increase in the influence
of the welding residual stresses on the fatigue life of the
welded joint. In the multicycle region (N > 106 cycles)
the effect of residual stresses can be compared with the
effect of stress concentration [15.2].
The effect of residual stresses on the fatigue life of
welded elements can be more significant in the case of
the relief of harmful tensile residual stresses and the
introduction of beneficial compressive residual stresses
in the weld toe zones. Beneficial compressive residual
stresses at a level close to the yield strength of material
are introduced in the weld toe zones by the ultrasonic
Δσ (MPa)
Δσ (MPa)
3
450
400
350
400
350
300
300
250
250
200
1
2
200
150
150
log N = –3.183753 x log σ + 13.31484
10
5
10
2 3
6
N cycles
1
10
5
10
6
N cycles
Fig. 15.18 Fatigue curves of a butt-welded joint in low-
Fig. 15.19 Fatigue curves of non-load carrying fillet
carbon steel [15.2]: 1 – without residual stresses; 2 and
3 – with high tensile residual stresses (fatigue testing and
computation)
welded joint in high-strength steel [15.20]: 1 – in the aswelded condition; 2, 3 – after the application of ultrasonic
hammer peening (fatigue testing and computation)
Residual Stress
Δσ (MPa)
300
250
6
5
200
2
150
4
3
100
1
105
106
N cycles
Fig. 15.20 Fatigue curves of transverse loaded butt weld at
peening process. The results of fatigue testing of welded
specimens in the as-welded condition and after the
application of ultrasonic hammer peening (UP) are presented on Fig. 15.19. The fatigue curve of the welded
element in the as-welded condition (with high tensile
residual stresses) was also used as the initial fatigue
data for the computation of the effect of the UP. In
the case of a non-load-carrying fillet welded joint in
high-strength steel (σ y = 864 MPa, σu = 897 MPa), the
redistribution of residual stresses resulted in an approximately twofold increase in the limit stress range and
over tenfold increase in the fatigue life of the welded
elements [15.20].
The results of the computation of the effect of residual stresses correlates well with the results of fatigue
testing if the relaxation of residual stress is considered
during the cyclic loading of the welded elements, taking into account the effect of the stress concentration
created by the shape of weld (Figs. 15.18 and 15.19).
A significant increase in the fatigue strength of
welded elements can be achieved by the redistribution
of high tensile residual stresses [15.5]. The calculated
fatigue curves for a transverse-loaded butt weld with
different levels of initial residual stresses at R = 0 are
shown in Fig. 15.20. The fatigue curve of the welded
element will be located between lines 1 and 2 in the
case of partial relief of harmful tensile residual stresses
(lines 3 and 4). The decrease of the tensile residual
stresses from an initial high level to 100 MPa causes,
in this case, an increase of the limit stress range at
N = 2 × 106 cycles from 100 MPa to 126 MPa.
The relief of the residual stresses in a welded
element to the level of 100 MPa can be achieved, for example, by heat treatment or overloading of this welded
element at a level of external stresses equal to 0.52 σy .
As a result, this fatigue class 100 welded element becomes fatigue class 125 [15.19]. After modification of
the welding residual stresses, the considered welded element will have enhanced fatigue performance and, in
principle, could be used instead of a transverse-loaded
butt weld ground flush to plate (no. 211) or longitudinal weld (nos. 312 and 313) [15.19]. Introduction of
compressive residual stresses in the weld toe zone can
increase the fatigue strength of welded elements to an
even greater extend (lines 5 and 6 in Fig. 15.20).
15.4 Residual Stress Modification
In many cases, beneficial redistribution of residual
stresses can drastically improve the engineering properties of parts and welded elements. Detrimental tensile
residual stresses can be removed and beneficial compressive residual stresses introduced by the application
of heat treatment, overloading, hammer peening, shot
peening, laser peening, and low-plasticity burnishing.
A new and promising process for the effective redistribution of residual stresses is ultrasonic (hammer)
peening (UP) [15.1, 21–23]. The development of the
ultrasonic peening (UP) technology was a logical continuation of work directed towards the investigation and
further development of known techniques for surface
plastic deformation such as hammer peening, needle
peening, and conventional and ultrasonic shot peening.
UP is a very effective and fast technique for the relief
of harmful tensile residual stresses and the introduction
of beneficial compressive residual stresses in the surface
layers of parts and welded elements. Figure 15.21 shows
the results of the measurement of residual stresses in
a part produced by the electric discharge machining
(EDM) process. Application of the x-ray technique
showed that UP provided the relief of harmful tensile residual stresses and induced compressive residual
383
Part B 15.4
R = 0 [15.5]: 1 – with high tensile residual stresses; 2, 3,
4, 5, and 6 – with residual stresses of 0, 200, 100, −100,
and −200 MPa, respectively
15.4 Residual Stress Modification
384
Part B
Contact Methods
Residual stress (MPa)
600
UP treated surface
Zone C
0
0.01– 0.4 mm
400
–
Application of UP
Zone A
200
1–1.5 mm
0
Typical distribution of residual
stresses after UP
+
–200
Zone B
–400
–600
–800
15 mm and more
0
20
40
60
80
100
120
Treatment time (s)
Fig. 15.21 Relief of harmful tensile residual stresses induced by EDM, and the introduction of beneficial compressive residual stresses in the surface layers of a material by
UP [15.24]
Part B 15.4
stresses equal to the yield strength of material in the
surface layers of the considered part [15.24].
UP has been successfully applied to increase the
fatigue life of parts and welded elements, eliminate
distortions caused by welding and other technological
processes, relief residual stress, and increase the hardness of materials. Fatigue testing of welded specimens
has shown that UP is the most efficient improvement
treatment as compared with traditional techniques such
as grinding, TIG (tungsten inert gas)-dressing, heat
treatment, hammer peening, shot peening etc. [15.2].
The improvement in fatigue performance is achieved
mainly by the introduction of compressive residual
stresses into the surface layers of metals and alloys,
the decrease in stress concentration in weld toe zones,
and the enhancement of the mechanical properties of
the surface layer of the material. A schematic view of
Distance from surface
Fig. 15.22 Schematic view of the cross section of a mater-
ial/part improved by ultrasonic peening [15.21]
the cross section of a material/part improved by UP is
shown in Fig. 15.22 and a description of the benefits of
UP is presented in Table 15.1.
A compact system for ultrasonic peening (UP)
of materials, parts, and welded elements is shown
in Fig. 15.23.
The new optimized UP system (total weight 6 kg)
includes:
1. A hand tool, based on a piezoelectric transducer.
The weight of the tool is 2.8 kg and it is convenient
for use. A number of working head types have been
designed for different industrial applications.
2. Ultrasonic generator. The weight of the generator
is 3.2 kg with a power consumption of only 400 W.
Output frequency is ≈ 22 kHz.
3. A laptop with a software package for remote control
and optimum application of ultrasonic peening.
Table 15.1 Zones of material/part improved by ultrasonic peening
Zone
Description of zone
A
Zone of plastic deformation
and compressive residual stresses
Zone of relaxation
of welding residual stresses
Zone of nanocrystallization
(produced under certain conditions)
B
C
Penetration
(distance from surface) (mm)
1–1.5 mm
15 mm and more
0.01–0.1 mm
Improved characteristics
Fatigue, corrosion,
wear, distortion
Distortion,
crack propagation
Corrosion, wear, fatigue
at elevated temperature
Residual Stress
15.4 Residual Stress Modification
385
Δσ (MPa)
400
350
300
250
200
150
9
7
5
100
3
1
Fig. 15.23 Application of the ultrasonic peening system for
beneficial redistribution of residual stresses and fatigue-life
improvement of a tubular welded joint [15.23]
•
•
•
•
Determination of the maximum possible increase
in the fatigue life of the welded elements by UP,
depending on the mechanical properties of the material, the type of welded element, the parameters of
cyclic loading, and other factors
Determination of the optimum technological parameters for UP (maximum possible effect with
minimum labor and power consumption) for each
considered welded element
Quality monitoring of the UP process
Final fatigue assessment of the welded elements or
structures after UP, based on detailed inspection of
the UP-treated zones and computation
The developed software allows the assessment of
the influence of the residual stress redistribution caused
by the UP process on the service life of the welded
elements without having to perform time- and laborconsuming fatigue tests and to compare the results of
these calculations with the effectiveness of other improvement treatments such as heat treatment, vibration
treatment, and overloading.
The computation results presented in Fig. 15.24
show the effect of the application of UP on the fatigue
life of welded joints in steels of different strength. The
data for fatigue testing of non-load-carrying fillet weld
specimens in the as-welded condition (with high tensile
residual stresses) were used as initial fatigue data for
106
N cycles
Fig. 15.24 Fatigue curves of a non-load-carrying fillet
welded joint: 1 – in the as-welded condition for all types
of steel; 3, 5, 7, and 9 – after the application of UP to
steels 1–4 (see text)
calculating the effect of UP. These results are in agreement with the existing understanding that the fatigue
strength of a certain welded element in steels of different strength in the as-welded condition is represented by
a single fatigue curve [15.2, 19].
Four types of steels were considered for fatigue
analysis: steel 1 (σy = 270 MPa, σu = 410 MPa), steel 2
(σy = 370 MPa, σu = 470 MPa), steel 3 (σy = 615 MPa,
σu = 747 MPa), and steel 4 (σy = 864 MPa, σu =
897 MPa). Line 1 in Fig. 15.24 is the single fatigue
curve of the considered welded joint for all types of steel
in the as-welded condition, determined experimentally.
Lines 3, 5, 7, and 9 are the calculated fatigue curves for
the welded joint after the application of UP for steels
1–4, respectively.
As can be seen from Fig. 15.24, the stronger the
mechanical properties of the material, the higher the
fatigue strength of the welded joints after the application of UP. The increase in the limit stress range
at N = 2 × 106 cycles after UP for a welded joint in
steels 1–4 is 42%, 64%, 83%, and 112%, respectively.
These results show a strong tendency for increasing
fatigue strength of welded connections after the application of UP with increasing mechanical properties of
the material used.
The developed computerized complex for UP was
successfully applied in different applications for increasing of the fatigue life of welded elements,
eliminating distortions caused by welding and other
Part B 15.4
For optimum UP application, the maximum possible
increase in the fatigue life of the welded elements with
minimum labor and power consumption is desired.
The main functions of the developed software are:
105
386
Part B
Contact Methods
technological processes, relieving residual stress, increasing the hardness of the surface of materials, and
surface nanocrystallization. Areas/industries where UP
was applied successfully include railway and highway
bridges, construction equipment, shipbuilding, mining,
automotive, and aerospace.
15.5 Summary
Part B 15
1. Residual stresses play an important role in the operating performance of materials, parts, and structural
elements. Their effect on the engineering properties
of materials such as fatigue and fracture, corrosion
resistance, and dimensional stability can be considerable. Residual stresses should therefore be taken
into account during the design, fatigue assessment,
and manufacturing of parts and structural elements.
2. Various destructive and nondestructive techniques
can be efficiently used for the measurement of residual stresses in laboratory and field conditions in
many applications for a wide range of materials. In
many cases the residual stress analysis was successfully applied to increase the reliability and service
life of parts and welded elements in the construction industry, shipbuilding, railway and highway
bridges, nuclear reactors, aerospace industry, oil and
gas engineering, and in other areas during manufacturing, in service inspection, and the repair of real
structures.
3. Certain progress has been achieved during the past
few years in the improvement of traditional tech-
niques and the development of new methods for
residual stress measurement. A number of new engineering tools for residual stress management such as
the described ultrasonic computerized complex for
residual stress measurement, technology and equipment for ultrasonic hammer penning, and software
for the analysis of the effect of residual stresses on
the fatigue life of welded elements and structures
have recently been developed and verified for various applications.
4. The beneficial redistribution of residual stresses
is an efficient way of improving the engineering properties of parts and structural elements.
The application of ultrasonic hammer peening
causes a remarkable improvement in the fatigue
strength of parts and welded elements in various
materials: the stronger the treated materials, the
greater the efficiency of the application of ultrasonic peening. This allows more effective use of
the advantages of high-strength materials in parts
and welded elements that are subjected to fatigue
loading.
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15.2
15.3
15.4
15.5
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