ALL THERMO-MECHANICAL manufacturing
processes--such as forging, extrusion, casting,
heat treatment, welding, coating, and machining---
create residual stresses in industrial
products. There are situations when such stresses
can be beneficial and are intentionally created,
for example, compressive stresses on the outer
surface of a component subjected to fatigue
loads, autofrettage in gun barrels, and prestressed
pressure vessels; even bolted connections and
prestressed concrete can be included in this category.
In many other situations, however, the presence
of residual stress is detrimental to the integrity
of the product under service conditions.
Examples in this category include: tensile
stresses on the outer surface of a component subjected
to fatigue loads, tensile stresses on the
inner surface of an austenitic stainless steel pipe
caused by welding leading to intergranular stresscorrosion
cracking in boiling water reactors, interlaminar
stresses in coatings leading to their
spallation, premature yielding or fracture (especially
in brittle materials), and part distortion or
dimensional instability. The presence of residual
stresses in a part is also known to affect its machinability.
For these reasons, mechanical and
manufacturing engineers have long been interested
in understanding the source of such stresses,
their control, and relief (Ref 1-4).
In the case of metallic products, the selection of
material is generally dictated by functional requirements
such as the ability of the product to
withstand service loads, resistance to wear or
corrosion, and so forth. It is rare that the magnitude
and distribution of residual stresses is a matter
of primary consideration while selecting the
material to manufacture a metallic part. The issue
facing the manufacturing engineer is to control
the residual stresses in the product once the material
(and often the manufacturing process) has
already been selected. In the case of a composite
or coated product, however, minimization of residual
stresses is a prime consideration while
selecting the constituent materials. This article
primarily deals with metallic products.
A logical way to control residual stresses in a
product should consist of the following steps:
1. Understanding the fundamental sources of
stress generation
2. Identifying the parameters that can cause residual
stresses in a particular manufacturing
process
3. Understanding the relative significance of
each one of these parameters
4. Experimenting with the most significant process
parameters until a suitable combination is
obtained that results in the desired magnitude
and distribution of residual stresses
If the residual stresses in the product are still higher
than acceptable, the only recourse left is the use of
one of the various techniques of stress relief or the
inducement of a su'ess pattern more favorable than
the original.
The fundamental sources of residual stresses in
a product can best be understood with the help of
the disciplines of solid mechanics, heat transfer,
and metallurgy, as discussed in the section "Fundamental
Sources of Residual Stresses" in this
article. The identification of process parameters
comes from an engineer's knowledge of and experience
with a particular manufacturing process.
Finally, to understand the relative significance of
each process parameter and to arrive at their optimal
combination one can use either of two
approaches: trial and error on the shop floor combined
with a suitable method of stress measurements,
or computer simulation, especially one
based on the finite element method. Both of these
approaches have some advantages and limitations.
In general, computer simulation offers a
more economical and efficient means of performing
a parametric study. It also helps in understanding
the behavior of the product at various
intermediate stages of its manufacture. For example,
in case of forging, it is possible to monitor
stresses during the entire duration of the die motion,
as well as after the die removal. Computer
simulation also helps in monitoring other phenomena
of interest, such as the flow of material
during forging. However, the trial-and-error approach
offers only one opportunity to see the
effect of changing a process parameter, for example,
after the die removal. On the other hand, trial
and error requires less investment in personnel
training and development of a material properties
database. Also, the use of physical modeling in a
laboratory coupled with residual-stress measurements
is still needed to verify the results of computer
simulation until full confidence in the accuracy
of simulation code and personnel skill is
attained.
Until recently, the trial-and-error approach has
played a more prominent role in the control of
residual stresses in industrial products, as compared
to its simulation counterpart. However, in
recent years, considerable progress has been
made in computer simulation of several manufacturing
processes, for example, casting, forging,
quenching, and postweld heat treatment. In such
processes, it is expected that computer simulation
will soon be used routinely on the shop floor.
Until then, a judicious combination of computer
simulation and trial and error appears to be the
most prudent approach to control the residual
stresses. On the other hand, in the case of shot
peening and some other processes, computer
simulation is either not mature enough or is too
uneconomical to be used as an alternative to trial
and error, at least in the foreseeable future.
It is important to note that, before attaining its
final shape, a product often undergoes a series of
primary and secondary operations; for example,
it may involve forging as the primary operation
and quenching, aging, and machining as the secondary
operations. Each of these operations affects
the state of residual stresses in the part.
Therefore, in order to control the residual stresses
in a finished product, it appears logical to apply
the aforementioned techniques (either trial and
error or computer simulation) for each operation.
In some cases (e.g., forging followed by quenching),
it may be argued that the final manufacturing
operation is mainly responsible for the state
of residual stresses in the part and, hence, the
effort to control them should focus on the final
operation. However, this argument does not apply
if the sequence of quenching and machining
is considered. Hence, it should not be used as a
general rule.
This article is an introduction to the subject of
control of residual stresses. Its objectives are to:
• Introduce the various fundamental sources of
residual stresses common to most manufacturing
processes
• Explain the effect of material removal on residual
stresses and distortions in a part
Provide a summary of commonly used techniques
of measuring residual stresses
• Provide a summary of the finite element
method used for predicting residual stresses
• Demonstrate the application of the above to a
few selected manufacturing processes
Because the number of manufacturing processes is
too large, it is not possible to cover them all in a short
article. Also, a listing of rules for control of residual
stresses in various manufacturing processes is not
attempted in this article, because an indiscriminate
application of such roles without proper appreciation
of the basic concepts could lead to adverse
results.
It is hoped that the article provides some insight
to a manufacturing engineer into the cause
of residual stresses in a product and assists in
identifying key process parameters responsible
for such stresses. The article is also expected to
assist in making a choice between the trial-anderror
and computer-simulation approaches (or a
combination of the two) for the control of residual
stresses.
Fundamental Sources of
Residual Stresses
In manufacturing processes, residual stresses
are caused by a combination of some or all of the
following fundamental sources:
• Inhomogeneous plastic deformation in different
portions of the product due to mechanical
loads or constraints
• Inhomogeneous plastic deformation due to
thermal loads
• Volumetric changes and transformation plasticity
during solid-state phase transformation
A mismatch in the coefficients of thermal expansion
The mechanics related to these sources is explained
in the remainder of this section. Also, an important
concept related to the effect of material removal
(e.g., a casting mold, a forging die, or the material
removed during machining) on the magnitude and
distribution of residual stresses in the workpiece is
introduced.
Mechanical Loads. Generation of residual
stresses due to mechanical loads can be understood
by consideration of the example shown in
Fig. 1 (Ref 5). It consists of an assembly of three
bars, each 254 mm (10 in.) long with a cross
section of 25.4 mm (1 in.) square. The bars are
spaced 25.4 mm (1 in.) apart, center to center. The
two outer bars are made of the same material with
an elastic modulus of 207 GPa (30 x 106 psi),
yield strength of 207 MPa (30 ksi), and plastic
modulus of 41 GPa (6 x 10 ° psi). The middle bar
has a higher yield strength of 414 MPa (60 ksi),
but the same elastic and plastic moduli as the two
outer bars. The upper ends of the three bars are
fixed and not allowed to move in any degree of
freedom; their lower ends are tied to a rigid but a
weightless block. Also, the assembly carded a
load P in the center, as shown in Fig. 1.
Now consider two different loading histories.
In the In:st case, the load P is gradually increased
from 0 to 400 kN (90 kips), and then brought
back to zero. When P is 400 kN (90 kips), each
bar shares 133 kN (30 kips) and the stress in none
of them exceeds the yield strength. On unloading,
the original zero stress state in each bar is restored,
and no residual stresses are introduced.
In the second case, P is increased from 0 to 534
kN (120 kips) and then brought back to zero. The
entire history of stresses in the three bars is shown
in Fig. l(b). When P exceeds 400 kN (90 kips),
the two outer bars deform plastically and, be-
cause of the reduced modulus, begin to share less
load. The stress in the two outer bars follows the
path ABCD, whereas that in the middle bar follows
the path ABEF. It can be seen that when P is
again zero (unloading), the stresses in the three
bars do not go back to zero. Instead, the middle
bar has a residual tensile stress of 78.8 MPa (11.4
ksi), and each of the two outer bars has a residual
compressive stress of 39.4 MPa (5.7 ksi). Because
there is no external load on the assembly,
the residual stresses in the three bars are in selfequilibrium.
A comparison of the two loading
histories indicates that the presence of inhomogeneous
plastic deformation in the three bars is
responsible for the generation of residual
stresses. Similarly, mechanical residual stresses
occur in any component when the distribution of
plastic deformation in the material is inhomogeneous,
such as the surface deformation in shotpeening
operation.
Thermal Loads. A similar three-bar model explaining
the generation of residual stresses due to
inhomogeneous plastic deformation caused by
thermal loads is discussed by Masubuchi (Ref 6,
presumably adopted from Ref 7). In this model,
three carbon-steel bars of equal length and crosssectional
area are connected to two rigid blocks
at their ends. The middle bar is heated to 593 °C
(1100 °F) and then cooled to room temperature,
while the two outer bars are kept at room temperature.
Some of the details are not clearly explained
in Ref 6, but the problem is very similar
to the previous example. When the temperature in
the middle bar is raised, the requirements of compatibility
and equilibrium imply that a compressive
stress be generated in the middle bar and
tensile stresses in the two outer bars; the stress in
each of the two outer bars being half of that in the
middle bar. If the temperature in the middle bar is
so high that its stress exceeds yield but in the two
outer bars the stresses are still below yield, residual
stresses will occur in the three bars when the
temperature of the middle bar is brought back to
room temperature (i.e., on unloading). Similarly,
if the stresses in all three bars exceed yield but by
different amounts, residual stresses will still occur
when the temperature of the middle bar is
brought back to room temperature. Indeed, this
case is very similar to that of a cylinder immersed
vertically in a quenchant where, during the initial
stages of quenching, the temperature in the outer
layer is much lower than that in the inner core.
The three-bar model can be further utilized to
explain the generation of residual stresses due to
the mismatch in coefficients of thermal expansion.
For example, suppose the two outer bars
represent the layers of matrix in a composite
lamina and the inner bar represents a layer of
fibers. The coefficient of thermal expansion of
the two outer bars is equal but, in general, different
from that of the middle bar. It is assumed that
the initial temperature of all the three bars is
equal, which corresponds to a certain processing
temperature much higher than room temperature.
When the assembly is brought to room temperature,
the requirements of compatibility and equilibrium
will be satisfied if a system of forces
(residual stresses) is established such that the sum Fig. 3
of the forces in the two outer bars is equal and
opposite to that in the middle bar. In this case, the
presence of unequal plastic deformation is not a
prerequisite for the generation of residual
stresses. This explains why, while selecting the
constituent materials for a composite or for a
coating, the designers try to minimize the mismatch
between their coefficients of thermal expansion.
Solid-State Transformation. In quenching,
welding, and casting processes, many metals
such as steels undergo one or more solid-state
transformations. These transformations are accompanied
by a release of latent heat, a change in
volume, and a pseudoplasticity effect (transformarion
plasticity). All of these affect the state of
residual stresses in the part. The release of latent
heat during solid-state transformation is similar
to that during the liquid-to-solid transformation,
albeit of a smaller amount. The change (increase)
in volume occurs due to the difference in mass
densities of the parent phase (e.g., austenite) and
the decomposed phases (pearlite, ferrite, bainite,
and martensite). In steels, the volumetric change
due to phase transformation is in contrast to the
normal contraction or shrinkage during cooling
(Ref 8).
A simple example of transformation plasticity
is shown in Fig. 2, which is based on the results
of a constrained dilatometry experiment (Ref 9).
The figure shows that during cooling in the phase
transformation regime, the presence of even a
very low stress may result in residual plastic
strains. Two widely accepted mechanisms for
transformation plasticity were developed by
Greenwood and Johnson (Ref 10) and Magee
(Ref 11). According to the former, the difference
in volume between two coexisting phases in the
presence of an external load generates microscopic
plasticity in the weaker phase. This leads
to macroscopic plastic flow, even if the external
load is insufficient to cause plasticity on its own.
According to the Magee mechanism, if martensite
transformation occurs under an external load, (a)
martensitic plates are formed with a preferred orientation
affecting the overall shape of the body.
Material Removal. A fact that is often overlooked
in discussing residual stresses caused by
various manufacturing processes is the effect of
material removal on the state of stresses in the
product. Consider, for example, that a casting
mold must be finally broken and removed, or a
forging die must be retracted. Likewise, in making
a machined part some of the material has to
be removed. All of these operations change the
state of stress in the part. In order to fully understand
this concept, three examples discussed in
Ref 5 should be considered.
The first example entails an assembly of two
concentric springs of slightly different lengths, L i
and L o, as shown in Fig. 3(a); the subscripts i and
o refer to inner and outer springs, respectively.
The bottom ends of the two springs are fixed.
Then, the upper ends are tied to a rigid block that
is free to move only in the vertical direction. The
two springs adopt a compromise length, L, which
is in between L i and L o, as shown in Fig. 3(b). As
a result, the two springs develop equal and opposite
forces: compressive in the longer inner spring
and tensile in the outer shorter spring. The assembly
of the two springs may be viewed as analogous
to the assembly of a cast part and its mold or
to the assembly of the forged part and the die, or
to a machined part before some portion of it is
removed. Then, the removal of the outer spring
becomes analogous to removal of material during
machining (Ref 5, 12), of the casting mold (Ref
13-16), or of the forging die (Ref 17). Two cases
are considered. In the first case, the stresses in
both springs are assumed to be within their elastic
limits. When the outer spring is removed, the
force acting on it is transferred to the inner spring
in order to satisfy equilibrium and the inner
spring returns to its original length. In the second
case, it is assumed that the inner spring has undergone
a certain amount of plastic deformation.
When the outer spring is removed, the inner
spring does not return to its original length, L i. In
either case, because the two springs and, therefore,
the forces, are concentric, the residual stress
in the inner spring becomes zero when the outer
spring is removed.
For the second example, reconsider the threebar
model from the section "Mechanical Loads"
in this article. After creating residual stresses in
the three bars by loading and unloading the assembly,
bar 3 is removed, by (for example) machining.
As shown in Fig. 4(a) and (b), a redistribution
of stresses in the remaining two bars takes
place. The resultant stresses at the centroids of the
two bars become -14.8 MPa (-2.14 ksi) in bar 1,
and 14.8 MPa (2.14 ksi) in bar 2. Also, the assembly
rotates (distorts) by an angle of 4.3 x 10 -3
radians.
The third example in Ref 5 is of a thick-walled
cylinder with an internal diameter of 101.6 mm
(4 in.) and an outer diameter of 203.2 mm (8 in.)
as shown in Fig. 5(a). Both ends of the cylinder
are restrained axially, and the cylinder is subjected
to an internal pressure. A 25.4 mm (1 in.)
thick (along the axis) slice of the cylinder is
analyzed by subdividing it into 10 equal finite
elements (5.08 mm, or 0.2 in., thick each) in the
radial direction (Fig. 5b). The residual stresses
are created by increasing the pressure from zero
to 345 MPa (50 ksi), and then back to zero. The
elements 1 and 2 are removed successively. The
variation of the three stress components along the
radius is shown in Fig. 6, before material removal
(i.e., the residual stresses) and after removing the
two layers. It may be noted that in an overall
sense, the level of residual stresses goes down as
the material is removed. However, this is not
necessarily true in a local sense. Consider, for
example, the circumferential stress at the centroids
of elements 3 and 4 in Fig. 6(b); it increases
as the material is removed.
Important conclusions from the three examples
discussed above can be summarized as follows:
• When the material removal is symmetric with
respect to the stress distribution (Fig. 3), the
residual stresses in the remainder of the assembly
or part are very small or even zero.
• When the material removal is not symmetric
with respect to the stress distribution (Fig. 4,
6), the residual stresses in the remainder of the
assembly or part are not necessarily small.
• Material removal may result in an increase in
stresses at some locations of the assembly or
the part (Fig. 6).
Computer Prediction of
Residual Stresses
In recent years, the finite element method has
become the preeminent method for computer prediction
of residual stresses caused by various
manufacturing processes. A transient, nonlinear,
thermomechanical analysis software is generally
employed for that purpose. Some of the mathematics
that form the basis of such software is
common for all manufacturing processes. Such
common mathematics is summarized by this section.
However, because every process is unique,
some mathematical requirements are, in turn, dependent
on the process. Also, for the simulation
of certain processes a sequential thermomechani-
cal analysis is adequate, whereas for others a
coupled analysis may be preferred or even essential.
Such subtleties are pointed out later when
individual processes are discussed.
Ignoring convection, the following conduction
heat-transfer equation is solved with appropriate
initial and boundary conditions:
• aT
v . (kw3 + Q~ =pcp aTt (Eq t)
where Tis the temperature at an arbitrary location in
the workpiece at time t, k is the thermal conductivity
of the material, Qc is the rate of heat generated per
unit volume p is the density (7_ is the specific heat
• ' . . ' l / . ' and V is the differential operator; all material properties
are assumed to vary with temperature. The
term Qc accounts for the release of latent heat during
liquid-to-solid transformation in casting and welding
processes or during solid-state phase transformation
in quenching, welding, or casting processes.
It also accounts for the heat of plastic deformation
in forging and other bulk deformation processes.
The initial and boundary conditions are process
dependent. Details of converting Eq 1 into its finite
element form and of numerical solution are available
in a number of technical papers and textbooks
and are not repeated here. For a general treatment of
the subject, the reader is referred to Ref 18 to 21.
The transient temperatures computed above
are used as loading for the subsequent transient
stress/displacement analysis. Using the incremental
theory, the total strain increment {Ae} at
time t can be divided into various components
(Ref 22-26):
{Ae} = {Ae e} + {AE t} + {Ae p} + {Ae or} + {Ae v} + {AE tr} (Eq 2)
where superscripts e, t, p, cr, v, and tr refer to elastic,
thermal, plastic, creep, volumetric change, and
transformation plasticity components, respectively.
The first three strain terms are needed in the simulation
simulation
of every manufacturing process discussed here,
whereas the use of the other three terms is dependent
on the process and are pointed out as appropriate.
Also, mathematical details for the first four strain
terms are discussed in most standard references (Ref
22, 23), whereas the details for the last two terms are
discussed often in the context of the simulation of
quenching and welding processes (Ref 24-26).
In forging and other large deformation processes,
the term Qc in Eq 1 represents the heat of
plastic deformation and leads to a coupling between
Eq 1 and 2.
At present, no single computer code is capable
of predicting residual stresses caused by all
manufacturing processes. However, several general-
purpose finite element codes are capable of
predicting these stresses to a reasonable degree of
accuracy for at least some of the manufacturing
processes (Ref27-29). In addition, some of these
codes permit customized enhancements leading
to more reliable results for a specific process.
Before attempting to predict residual stresses due
to a manufacturing process, it is advisable to
compare the capabilities of two or three leading
codes and use the one most suited for the simulation
of the process in consideration. Examples of
such comparisons are given in Ref 12 and 13 for
forging, quenching, and casting processes. It
must be noted that, due to continuous enhancement
in these codes, it is always advisable to
compare the capabilities of their latest versions.
Measurement of Residual Stresses
It is generally not possible to measure residual
stresses in a product during its manufacture; instead,
they are measured after the manufacturing
process is complete• Smith et al. (Ref 30) have
divided the residual stress measurement methods
into two broad categories: mechanical and physical.
The mechanical category includes the stressrelaxation
methods of layer removal, cutting,
hole drilling, and trepanning, whereas the physical
category includes x-ray diffraction (XRD),
neutron diffraction, acoustic, and magnetic. The
layer-removal technique as originally proposed
by Mesnager and Sachs (Ref4) is only applicable
to simple geometries such as a cylinder with no
stress variation along its axis or circumference, or
to a plate with no variation along its length or
width. Thus, whereas it could be used to measure
quench-induced residual stresses in a cylinder or
a plate, it is not suitable for measuring complex
stress patterns such as those caused by welding.
The layer removal and cutting techniques, however,
have been applied to pipe welds in combination
with conventional strain gages and XRD
measurements. The layer-removal technique is
also used to measure residual stresses in coatings.
Hole-drilling and trepanning techniques can be
used in situations where the stress variation is
nonuniform, but they are generally restricted to
stress levels of less than one-third of the material
yield strength. Also, these two techniques can be
unreliable in areas of steep stress gradients and
require extreme care while drilling a hole or ring
in terms of its alignment as well as the heat and
stress generation during drilling (Ref 31). For
such reasons, and others, these two techniques
have found little application in the measurement
of weld-induced residual stresses.
Of the methods in the physical category, XRD
is probably the most widely used method, the
neutron diffraction method being relatively new.
These two methods measure changes in the dimensions
of the lattice of the crystals, and from
these measurements the components of strains
and stress are computed. The XRD technique has
undergone many improvements in recent years.
With the development of small portable x-ray
diffractometers, the technique can be used for
on-site measurement of residual stresses. It
should be noted, however, that this technique is
capable of measuring strains in only a shallow
layer (approximately 0.0127 ram, or 0.0005 in.,
thick) at the specimen surface. To measure subsurface
residual stresses in a workpiece, thin layers
of materials are successively removed and
XRD measurements are made at each exposed
layer. For reasons discussed in the section "Material
Removal" in this article, the measurements at
an inner layer should be corrected to account for
the material removed in all the previous layers.
Reference 32 gives analytical expressions for
such corrections in cases of simple geometries
and stress distributions. For more complex cases,
it still remains difficult to determine subsurface
residual stresses accurately.
In contrast to the x-rays, neutrons can penetrate
deeper into the metals. For example, in iron the
relative depth of penetration at the 50% absorption
thickness is about 2000 times greater for
neutrons than for x-rays. Only a few materials,
such as cadmium and boron, absorb neutrons
strongly. However, to gain the advantage of
greater penetration of neutrons requires the component
to be transported to a high flux neutron
source (Ref 30), which limits the use of the technique.
Residual Stresses Caused by Various
Manufacturing Processes
Casting. In the past, little attention has been
paid to the control of residual stresses in casting;
much of the interest was focused on the prediction
and control of porosity, misruns, and segregation.
A review of the transactions of the American
Foundrymen's Society or of earlier textbooks
on casting (e.g., Ref 33) reveals practically no
information on the subject; even the ASM Handbook
on casting (Ref 34) provides little insight. In
a recent book, Campbell (Ref 35) has included a
brief discussion of residual stresses summarizing
the work done by Dodd (Ref 36) with simple
sand-mold castings. Dodd studied the effect of
two process parameters: mold strength, by changing
water content of sand or by ramming to different
levels, and casting temperature. The conclusions
of these costly experiments could have been more
economically and easily arrived at by using the
basic concepts discussed in the section "Fundamental
Sources of Residual Stresses" and further amplified
in the following paragraphs.
When a casting is still in its mold, the stresses
are caused by a combination of the mechanical
constraints imposed by the mold, thermal gradients,
and solid-state phase transformation. Also,
creep at elevated temperature affects these
stresses. Finally, when the casting is taken out of
its mold, it experiences springback that modifies
the residual stresses.
As discussed in Ref 13 to 16, the computer
prediction of residual stresses in castings requires
a software that is capable of performing coupled
transient nonlinear thermomechanical analysis
(see the section "Computer Prediction of Residual
Stresses" in this article). In addition, it should
be able to account for the following:
• Release of latent heat during liquid-to-solid
transformation, that is, in the mushy region
• Mechanical behavior of the cast metal in the
mushy region
• Transfer of heat and forces at the mold-metal
interface
• Creep at elevated temperatures under condition
of varying stress
• Enclosure radiation at the mold surface to
model the investment-casting process
• Mold withdrawal to model directional solidification
• Mold (material) removal
The author and his coworkers have recently
modified a commercial finite element code and
have analyzed simple sand-mold castings (Ref
15, 16). Computer simulation of these castings
indicates that: (1) for an accurate prediction of
transient and residual stresses, consideration of
creep is important; creep is also found to make
the stress distribution more uniform; and (2) just
prior to mold removal the stresses in the casting
can be extremely high, but after the mold removal
they become very small (owing to the springback
discussed in the section "Material Removal") except
in the areas of stress concentration. The
residual stresses after the mold removal will not
necessarily be small if the casting is complex and
the mold removal is asymmetric with respect to
the stress distribution. Also, small variations in
mold rigidity are not found to have any noticeable
effect on residual stresses, which confLrrns the observations
based on trial and error using greensand
molds with various water contents (Ref 35).
Although very little work is published thus far
on the subject of control of residual stresses in
castings, finite element simulation methodology
is now sufficiently advanced to enable the study
of the effect of various process and design parameters
on the residual stresses in castings, for
example, superheat, stiffness and design of the
mold, design of the feeding system and risers, and
the design of the part itself. Also, residual stresses
caused by different casting practices such as
sand-mold, permanent-mold, investment casting,
and so forth, can be determined. As the manufacturers
and end-users of cast products become
more aware of the status and benefits of the computer-
simulation methodology, it can be expected
to play a very important role in controlling residual
stresses in complex industrial castings. At
present, the biggest limiting factor in the use of
simulation is the lack of thermophysical and mechanical
properties data for the cast metal and the
mold materials.
Forging. As with the casting process, little attention
has been paid in the past to the control of
residual stresses caused by forging; most of the
interest was in predicting the filling and the direction
of material flow. Now, due to recent advances
in computer-simulation techniques, it is
possible to predict and control the residual
stresses in forged pans.
Large plastic flow of the workpiece material is
inherent in the forging process. The material
flow is influenced by a number of factors including
the die shape and material, forging temperature,
die speed, and lubrication at the die/workpiece
interface. Therefore, finite element
simulation software used to predict and control
residual stresses in the part should be capable of
accounting for these factors. Because a significant
amount of energy is dissipated during forging
in the form of heat due to plastic deformation,
a coupled thermomechanical analysis becomes
necessary especially for nonlsothermal forging.
Other factors contributing to the complexity of
the finite element simulation of this class ofproblems
are: temperature-dependent thermal and
mechanical properties of the materials (especially
for a nonisothermal forging); the choice of solution
algorithm and remeshing due to large plastic
deformation in the workpiece; and mathematical
treatment of the die/workpiece interface that includes
heat transfer, lubrication, and contact. The
last two terms in Eq 2 need not be considered in
the simulation of the forging process.
Finite element simulation of the forging process
with simple geometries and of a two-dimensional
idealization of the thread-rolling process
(Ref 17) showed that, although the stresses in the
workpiece are high during the deformation stage,
the stresses after retraction of the die (residual
stresses) are no longer high except in the regions
of stress concentration. Again, similar to the
simulation of the casting processes, it is premature
to generalize this conclusion but it is clear
that the technique of computer simulation of
forging and many other bulk deformation processes
has advanced to a stage where it can assist
in controlling the residual stresses in the part by
performing a detailed parametric study with
much less investment of time and capital than
trial and error on the shop floor.
Quenching involves heating of the workpiece
to the heat treatment temperature followed by
rapid cooling in a quenchant (e.g., air, water, oil,
or salt bath) in order to impart the desired metallurgical
and mechanical properties. The choice of
a quench medium is the key element; it should be
such that it removes the heat fast enough to produce
the desired microstructure, but not too fast
to cause transient and residual stresses of excessive
magnitude or of an adverse nature (e.g.,
tensile instead of compressive). The heat removal
characteristic of a quenchant is known to be affected
by a number of factors including the size,
shape, orientation of the workpiece (even for
simple shapes such as plates and cylinders, the
heat removal is different at the bottom, top, and
side surfaces); the use of trays and fixtures to hold
the workpiece in the quenchant; composition of
the quenchant; size of the pool and its stirring,
and so forth (Ref 37-39). Additional difficulties
arise when, due to economic reasons, quenching
is performed in a batch process.
In the past, using trial and error, shop-floor
personnel have come up with some interesting
strategies to control the residual stresses (and
warpage), for example, air delay or an intentional
delay while transporting the workpiece from the
heating furnace to the quenchant, and time
quenching or performing the quenching operation
in two steps. In the first step, the part is
quenched in a medium such as a salt bath until the
part has cooled below the nose of time-temperature
transformation curve, followed by quenching
in second medium such as air to slow the
cooling rat& Obviously, perfecting the quenching
operation by trial and error can be an extremely
time-consuming task.
At first glance, computer simulation of the
quenching process may appear to be simple. It
involves an uncoupled transient nonlinear small
deformation thermomechanical analysis (as outlined
in the section "Computer Prediction of Residual
Stresses" in this article), with due consideration
to solid-state transformation effects (Ref
9, 24, 25); creep is generally ignored. However,
the major difficulty lies (for reasons discussed in
the preceding paragraph) in a lack of knowledge
of the heat removal characteristic of various
quenchants, which is mathematically represented
as the convective heat transfer coefficient at the
outer boundary of the workpiece. Other difficulties
arise due to the lack of thermophysical and
mechanical properties of the workpiece material
at elevated temperatures. Still, at least in the
United States, major aircraft engine manufacturers
and their forging vendors have been using
computer simulation to control quench-related
cracking and residual stresses for some time. One
such example involving a turbine disk is discussed
in Ref 40. The reported work was performed
without the benefit of sophisticated simulation
software that could account for solid-state
transformation effects. For proprietary reasons,
few such cases are published in the open literature.
Machining. Many complex parts in aerospace
and other key industries are made by machining
forgings, castings, bars, or plates to their net
shapes. The presence of residual stresses in the
workpiece affects its machinability and, on the
other hand, the machining process also creates
residual stresses and undesired distortions in the
part and alters the already existing stress state. In
order to minimize or eliminate these adverse effects,
machine-shop personnel often experiment
with a number of process parameters, for example,
depth of cut, speed of the cutting tool, and
coolant. For single-point turning, they frequently
flip the workpiece in order to balance the distortions
and stresses evenly on the two sides. This
trial and error is frequently combined with statistical
process control.
A serious problem associated with machining
and residual stresses is often manifested in the
form of part distortion. For example, consider the
example in Table 1 (Ref 12). The table shows the
results of a dimensional check on 30 samples of
an aircraft engine part that was made by machining
heat treated forgings procured from three
different vendors (10 samples each). The location
at which the dimensional check was performed is
identified on the figure included in the table. It
was found that: (1) for all forgings from any one
vendor, the drop was almost identical; (2) the
drop in forgings from vendor B was within the
specifications, but not so in the case of the other
two vendors; and (3) the drop in forgings from
vendors A and C was on the two opposite sides of
that from vendor B. It was recognized that all heat
treated forgings contained residual stresses.
When these forgings were machined to net
shapes, distortions occurred for two reasons: the
release of residual stresses from the removed portion
of the workpiece and the machining process
itself. The former can be easily modeled using
the finite element method if the magnitude of
residual stresses in the forgings prior to machining
is known (Ref 5). However, to this author's
knowledge, no serious attempt has so far been
made to predict residual stresses in a workpiece
due to the machining process itself. If an attempt
of this type is to provide reliable results, it must
take into account such factors as: depth of cut,
speed of the cutting tool, interaction between the
tool and the workpiece (heat and force), coolant,
and clamping/unclamping of the workpiece. It
must also recognize the fact that the location of
contact between the tool and the workpiece
moves as the machining process progresses. If
such technology could be developed, it would
become possible to predict and control the overall
distortions and residual stresses in a part after
machining, thereby reducing scrap.
Welding. The residual stress distribution in
welded joints depends on a number of process
and design parameters such as the heat input,
speed of the welding arc, preheat, thickness of the
welded part, groove geometry, and weld schedule.
Welding engineers have long used trial and
error to obtain a suitable combination of these
parameters in order to control the residual
stresses.
The role of computer simulation in the prediction
of residual stresses in weldments is the subject
of a recent review (Ref 14). Major elements
of computer simulation of the process are:
• Mathematical representation of the heat input
from the welding source
• A transient thermal analysis
• A transient stress/displacement analysis; the
flow of molten metal and thermal convection
in the weld pool are generally ignored
Following Rosenthal (Ref 41), a semisteady state
approach is often used, although some attempts at
full three-dimensional analysis have also been
made. As mentioned earlier, it is now possible to
account for volumetric change and transformation
plasticity effects. Because of the short time periods
involved, creep is ignored. In the case of a singlepass
weld or a weld with few passes (e.g., four or
five), it is now possible to predict residual stresses
with reasonable accuracy. But, as the number of
passes increases (e.g., 20 or 30), it becomes computationally
intractable to model each pass. The
scheme of lumping several passes into one layer has
been employed with less than satisfactory results. In
addition to excessive computation time, other major
difficulties with the simulation of a mulfipass weld
ale: the numerical errors tend to accumulate with
each pass, and the changes in metallurgical and
mechanical properties of material in previously deposited
layers during deposition of a subsequent
layer are difficult to quantify and to account for in
the finite element analysis. The technique of lumping
several layers together aggravates these problems.
Between the mid 1970s and early 1980s, the
Electric Power Research Institute (EPR1) in the
United States sponsored a program to systematically
study the effects of various process and
geometric parameters such as the heat input,
welding method (gas tungsten arc welding, submerged
arc welding, laser, and plasma), speed of
the welding arc, diameter and thickness of the
pipe, and groove geometry, on residual stresses in
pipe welds (Ref42-51). In addition, various thermal
processes such as heat-sink welding, backlay
welding, and induction heat treatment were investigated
to verify if the residual stresses on the
inner surface of the pipe could be changed from
tensile to compressive to avoid intergranular
Stress-corrosion cracking. Both experimental and
finite element methods were used in the study.
The results of this effort are summarized in Ref
52.
A very interesting effort related to in-process
control and reduction of residual stresses and
distortions in weldments is being pursued (Ref
53, 54). The effort aims at moving beyond mere
analysis of residual stresses and distortions to
aggressively controlling and reducing them. To
accomplish this objective, the effort is subdivided
into the development of the following three primary
capabilities: prediction, sensing, and control.
For prediction purposes, a series of computer
programs have been developed, include simple
but fast one-dimensional programs that analyze
only the most important stress component, that is,
the one parallel to the weld line. Sensing capability
refers to a set of devices including a laser
interferometer to measure minute amounts of distortions,
a laser vision system to measure large
amounts of distortions, and a mechanical system
to measure radi of curvature. Finally, to control
the residual stresses, various techniques including
changes in heating pattern and application of
additional forces have been attempted. References
53 and 54 provide further examples of the
application of this methodology in reduction of
residual stresses in weldments in high-strength
steels and girth-welded pipes.
Coating. Coatings are being used extensively
in aerospace, marine, automobile, biomedical,
electronics, and other industries. For example, in
modem jet aircraft engines, approximately 75%
of all components are coated. Some of the reasons
for the application of coatings are: thermal bartier,
wear resistance, corrosion resistance, oxidation
protection, electrical resistance, and repair or
dimensional restoration of worn parts. A variety
of methods are used for the deposition of coatings
on a substrate; the following discussion is limited
primarily to the thermal spray process.
The prediction of residual stresses in a coating/
substrate system is in its infancy. These
stresses result from the difference in the coefficient
of thermal expansion of the coating and
substrate materials and from plastic deformation
of the substrate material. The limited number of
numerical studies conducted thus far have been
related to small button-type specimens where the
coating material was assumed to be fully molten
and deposited instantaneously. These efforts have
ignored several important factors, for example:
• The presence of partially molten particles in
the spray
• A nonuniform deposition of coating material
normal to the axis of the plasma jet
• A liquid-to-solid and solid-state transformation
• Imperfect bond between the coating and the
substrate
• The relative motion between the spray and the
substrate
Also, because a layer of coating consists of
several successive passes, the effect of any new
pass on its adjacent previously deposited pass in
terms of partial remelting, additional material
buildup, solute diffusion, and redistribution of
residual stresses could be important and should
be accounted for. If more than one layer is involved,
for example, in functionally graded coatings,
modeling the effect of a whole new layer of
material on the previously deposited layer would
be computationally prohibitive. Also, due to the
morphology of the coating material on deposition,
its thermal and mechanical properties are
extremely difficult to measure and, thus, are generally
unavailable for simulation purposes. Due
to such reasons, end-users of coated products still
rely on the methods of trial and error and statistical
process control for the selection of an optimal
combination of process parameters in order to
control the residual stresses in coated parts (Ref
55).
Stress-Relief Methods
The basic premise of a stress-relief method is
to produce rearrangement of atoms or molecules
from their momentary equilibrium position
(higher residual stress state) to more stable positions
associated with lower potential energy or
stress state. These methods can be classified into
three broad categories: thermal, mechanical, and
chemical (Ref 4, p 134). The following concern
the methods in the first two categories.
Thermal stress-relief methods include annealing,
aging, reheat treatment (e.g., postweld heat
treatment), and others. In general, a stress-relief
operation involves heating the part to a certain
temperature, holding at the elevated temperature
for a specified length of time, followed by cooling
to room temperature. Primary reduction in
residual stresses takes place during the holding
period due to creep and relaxation. Thus, computer
simulation of a thermal stress-relief method
generally entails a thermal-elastic-plastic-creep
analysis of the part. A simple, one-dimensional
computer analysis of residual stresses in thin
plates along with experimental verification is discussed
by Agapakis and Masubuchi (Ref 56).
More sophisticated thermal-elastic-plastic-creep
simulations of the annealing of single pass and
multipass girth-butt welds in pipes are presented
in Ref57 and 58.
A number of subcategoties of mechanical
stress-relief methods are listed in Ref 4. Of these,
the methods in the static-stressing subcategory
such as stretching, upsetting, bending and
straightening, and autofrettage are common, and
these should not pose much difficulty in simulation
by the finite element method. Similarly, in
the mechanical surface treatment subcategory, it
should be possible to model the surface-rolling
method. However, within the same subcategory,
method) is likely to be difficult to simulate; and
to this author's knowledge, no realistic attempt
has yet been made to do so. The obvious reason
is that, whereas it should be possible to model a
single impact, modeling multiple impacts will be
difficult,just as it is for modeling multipass welding.
In recent years, the method of vibratory stress
relief (especially in the subresonant region) has
received considerable attention (Ref 59, 60). The
basic premise of this method is that the presence
of residual stresses in a part changes (increases)
its natural resonant frequency. When the part is
subjected to vibrations below its new frequency,
the metal absorbs energy. During this process, the
stresses redistribute gradually and the resonant
frequency shifts back to the point corresponding
to a residual stress-free (or almost free) state. The
process does not change the metallurgical or mechanical
properties of the material. The technique
has been found successful in relieving residual
stresses induced by thermal processes such as
welding and casting, but not those induced by
cold working. It has also been applied to reduce
residual stresses in parts prior to machining in
order to minimize distortions. It has been found
particularly beneficial in low- and medium-carbon
steels, stainless steels, and aluminum alloys,
but not in copper alloys. In view of the fact that
the technique is much simpler, quicker, and more
inexpensive than the thermal-relief methods, it
merits further study.
ACKNOWLEDGMENT
The author would like to thank H.A. Kuhn for
providing many valuable technical suggestions.
1 comment:
Great write-up
Keep it up
Charlie
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