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Keywords:

  • crack growth;
  • cold expansion;
  • fatigue;
  • machining;
  • peening;
  • relaxation;
  • residual stress;
  • welding

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

Many manufacturing processes can induce residual stresses in components. These residual stresses influence the mean stress during cyclic loading and so can influence the fatigue life. However, the initial residual stresses induced during manufacturing may not remain stable during the fatigue life. This paper provides a broad and extensive literature survey addressing the stability of surface and near-surface residual stress fields during fatigue, including redistribution and relaxation due to static mechanical load, repeated cyclic loads, thermal exposure and crack extension. The implications of the initial and evolving residual stress state for fatigue behaviour and life prediction are addressed, with special attention to fatigue crack growth. This survey is not a critical analysis; no detailed attempt is made to evaluate the relative merits of the different explanations and models proposed, to propose new explanations or models or to provide quantitative conclusions. Primary attention is given to the residual stresses resulting from four major classes of manufacturing operations: shot peening and related surface treatments, cold expansion of holes, welding and machining.


NOMENCLATURE
A

function of material and temperature

C

empirical constant

CX

cold expansion

DOD

Department of Defence

DR

deep rolling

EP

electropolished

FAA

Federal Aviation Administration

FCG

fatigue crack growth

FE

finite element

FTI

Fatigue Technology, Inc.

GBP

glass bead peening

GP

gravity peening

JSSG

Joint Service Specification Guide

k

Boltzmann's constant

LBP

low plasticity burnishing

LCF

low-cycle fatigue

LSP

laser shock peening

m

empirical constant

Q

effective activation energy for residual stress relaxation

R

stress ratio

S-N

Stress-Life

SP

shot peening

SR

stress relieved

t

time

T

Temperature

USAF

United States Air Force

WP

water peening

σRS

residual stress

3D

three-dimensional

INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

Background

The fatigue behaviour of a mechanical or structural component is a strong function of the load history that it experiences. The amplitude of the applied load cycles is a primary variable influencing the fatigue lifetime, and the mean (or maximum) value of the load in each cycle is a secondary variable that can also have a major influence on fatigue.

However, the stresses resulting from applied service loading are not the only stresses of significance for fatigue. Many components also contain residual stresses that were established prior to placing the component into service and which remain in place during the service life. These residual stresses do not cycle as the applied loads cycle—they are effectively ‘static’—and so they do not directly influence the amplitude of the in-service cyclic loading. They do influence the mean or maximum value of the load in each cycle, and therefore they can have a major influence on fatigue. It should also be noted that these residual stresses are generally self-equilibrating. They do not induce a net external force on the component, so any regions of compressive residual stress are counterbalanced by other regions of tensile residual stress.

Residual stresses can arise from many sources. Some residual stresses are an inherent byproduct of the manufacturing process. Welding, machining, forming, hardening, casting and forging can all cause residual stresses to remain in the finished product (see, for example, the many review articles in the Handbook of Residual Stress and Deformation of Steel.1) In some cases, additional steps are added to the manufacturing process for the specific purpose of inducing beneficial compressive residual stresses (which reduce the mean stress and increase the fatigue life) at fatigue critical locations. Shot peening and related surface treatments such as laser peening, low plasticity burnishing and deep rolling are the most common examples of this approach. Cold expansion of holes and autofrettage of thick cylinders are also widely employed. Finally, other residual stresses can result from pre-service and in-service loading. A proof test (typically to some specified load or pressure above the normal maximum service conditions) or a maximum load in-service can cause local yielding at stress concentrations that cause residual stresses to form and remain.

The conventional wisdom is that the fatigue nucleation life (the number of cycles required to form fatigue microcracks) is a function of the alternating stress amplitude but not the mean stress, while the growth rates of fatigue cracks are a function of both the stress amplitude and mean stress. This paradigm implies that residual stresses have relatively little influence on fatigue crack nucleation, but potentially a significant influence on fatigue crack growth. The influence on fatigue crack growth may be especially pronounced when the fatigue cracks are relatively small and the driving force for fatigue crack growth is near the grow/no-grow threshold; in this case, a residual stress may be the critical difference between a fatigue microcrack growing or arresting. It follows, then, that the effect of residual stresses on stress-life behaviour (commonly characterized as the number of fatigue cycles required to fracture a smooth laboratory specimen at different constant applied stress amplitudes and mean stresses) is complex. To the extent that the S-N curve is driven by crack nucleation behaviour, the effects may be small, but to the extent that the S-N curve is driven by crack growth, including the growth of microcracks, the effects of residual stresses may be large. As will be noted later, manufacturing processes that induce residual stresses may also induce other material changes—for example, changes in surface roughness or microstructural deformation—that have independent effects (beneficial or deleterious) on fatigue crack nucleation and growth, and so the true effects of residual stress may not always be obvious.

However, one of the biggest complications is that the initial residual stress field inherent in or induced by the manufacturing process may not remain stable throughout the service life. The residual stresses can relax and redistribute due to a variety of mechanisms. A single applied load that causes yielding in a region of residual stress (due to the superposition of residual and applied loads of the same sign) will result in changes in the residual stresses upon removal of the applied load. Repeated cyclic loading can also cause gradual changes in the residual stresses over time, even if no single fatigue cycle induces local yielding. Exposure to elevated temperatures can also relax residual stresses. Finally, extension of a fatigue crack through an initial residual stress field can cause significant changes in the residual stress field under some conditions.

Residual stresses can create a dilemma for operators and regulators of mechanical and structural components, especially in safety-critical applications. On the one hand, compressive residual stresses are often beneficial and can result in substantial improvements in fatigue life. However, it can be challenging to consistently impose the same initial residual stress state from part to part during the manufacturing process, and more challenging still to ensure through process control and measurement that the assumed or designed residual stress state is, in fact, actually present in each as-manufactured component. The potential for changes in the residual stress state in service can raise further questions, including the continuing challenge of measuring or monitoring the evolving residual stress state.

As a result, it is the official policy of some operators and regulators that official ‘credit’ will not be granted for beneficial residual stresses. In other words, the designed component must meet all required life and reliability goals without considering the beneficial effect of the residual stress, effectively assuming that it is not present. For example, the United States Air Force (USAF) Handbook for Damage Tolerant Design2 provides the following guidance for the specific case of fastener holes:

In practice, the growth of flaws from fastener holes can be retarded by the use of interference fit fasteners, special hole preparation such as cold work, and to some degree, by joint assembly procedures like friction due to joint clamp-up. Because these procedures delay flaw growth, the slow crack growth lives (or intervals) can be significantly longer than those obtained from structure containing conventional low torque clearance fasteners.

Experience has shown that to achieve the beneficial effects of these techniques consistently, exceptionally high quality process control is required during manufacture. However, this is not always obtained. As a result, it is thought unwise to consider all interference or hole preparation systems effective in retarding crack growth.

As stated in JSSG-2006 [DOD Joint Service Specification Guide-Aircraft Structures] paragraph A3.12.1.g, to maximize safety of flight and to minimize the impact of manufacturing errors, the damage tolerance guidelines should be met without considering the beneficial effects of specific joint design and assembly procedures such as interference fit fasteners, cold expanded holes, and joint clamp-up.

The actual existence of the residual stress is regarded as an additional safety factor, and the manufacturer will generally continue to impose the residual stress—even without official ‘credit’—because experience has shown that it makes their parts last longer and their end-use customers safer and happier. In practice, some operators and regulators do give some official credit for beneficial residual stresses—as the USAF Handbook for Damage Tolerant Design acknowledges in the paragraph following the quotation cited above, ‘Exceptions to this policy can be considered’—and such credits have become standard in certain applications. Some rule-of-thumb methods have been developed to guide these credits, but such rules-of-thumb are not always based on rigorous engineering analysis.

Existing production design paradigms and tools often do not address residual stresses explicitly, or do not address them through rigorous analytical methods, and (as noted earlier) neither do some certification regulations. However, there are a number of current motivations to change this situation. First of all, as aging systems (in which beneficial residual stress treatments were routinely applied) approach the end of their certified design lifetimes (such original design lifetimes not including residual stress effects), residual stress effects offer a potential sound engineering rationale for life extension. Second, several new life enhancement methods—including laser shock peening and low plasticity burnishing—may provide deeper and more stable compressive residual stresses, and so the potential benefit for fatigue lifetime assurance may become too prominent and too promising to dismiss. Third, an increased awareness of inherent residual stresses—perhaps beneficial, perhaps detrimental—in some manufactured components is evolving. If these inherent residual stresses are present in the components, but not present in the same measure in the baseline tests used to generate the material design properties, and not considered explicitly in the design scheme, then the resulting designs may sometimes be non-conservative relative to calculated life limits.

Purpose and scope of this article

This article provides a broad literature survey of the current understandings of significant residual stress issues for fatigue lifetime. The survey focuses explicitly on the stability of the residual stress fields under fatigue conditions, including redistribution and relaxation due to static mechanical load, repeated cyclic loads, thermal exposure and crack extension. The implications of the initial and evolving residual stress state for fatigue behaviour are addressed, with special attention to fatigue crack growth. The bias towards fatigue crack growth rather than stress-life or strain-life behaviour is consistent with an emphasis on damage tolerance, but this bias also concedes the significant complications (cited earlier) associated with the complex effects of some life enhancement methods on fatigue crack formation and early growth. Brief attention is given, where appropriate, to the major approaches to fatigue crack growth life analysis proposed and practiced in the literature. Relatively little attention is paid to the detailed analysis of initial residual stress states (especially for life enhancement methods that involve substantial changes to the material state) and to the experimental methods used to measure residual stresses. Both of these topics are large and complex, and were judged to be beyond the scope of the present investigations. There is a strong focus on surface and near-surface residual stresses (as opposed to bulk residual stresses, such as might be formed in the interior of a thick component due to thermal or mechanical deformation mechanisms during manufacturing). This focus is consistent with the observation that critical fatigue damage and fatigue cracking typically initiates and progresses at (or very near) the component surface, and these surface and near-surface issues have received the vast majority of the attention in the scientific literature.

The literature survey is based on a comprehensive (but not exhaustive) bibliography assembled over a period of several years and currently containing well over 300 citations. Computer searches of the major technical journals and other significant publication databases were employed widely, in addition to the usual tracing of cited references in each new article as it was catalogued. The bibliography has been limited to English language journal articles and conference papers that are available to the general public. Foreign language articles, academic theses and dissertations and technical reports with limited circulation were not included. In most cases, the significant results first reported in these other media (or at least the highlights thereof) were eventually published in the traditional English language technical literature. A majority (but not all) of the articles in the bibliography are cited in this survey.

This literature survey is not a definitive critical review. No attempt was made to evaluate the relative merits of the different explanations and models proposed, and no attempt was made to provide clear answers on important issues, beyond reporting the preponderance of the published opinions. These are worthy and needed goals, but the technical scope of the present effort was too broad and the available resources too limited to go into critical depth in any or all topics. That effort is left for future work. A short discussion at the end of the survey document summarizes some of the major trends and repeated observations from the survey.

The scope of the survey is generally very broad. Primary attention is given to the residual stresses resulting from four major classes of manufacturing operations: peening and related surface treatments, cold expansion of holes, welding and machining (and in that order of dramatically decreasing breadth). Within those four major areas, a wide variety of metallic materials are considered. Major applications include aircraft gas turbine engines, aircraft structures, welded steel structures, automotive components and machinery.

Most cited articles focus exclusively on one of the four major residual stress-inducing manufacturing processes (peening, cold expansion, welding, machining). However, a few review articles address issues that cut across multiple processes. Notable among these are an early review by Rosenthal;3 a classic treatment by Vöhringer4,5 updated more recently in Löhe and Vöhringer;6 two additional articles by Löhe et al.7 and Lu8 in the Totten et al. Handbook1 and recent articles by Fitzpatrick and Edwards9 and Webster and Ezeilo.10 Schulze11 has very recently published an extensive volume addressing mechanical surface treatments (different peening methods and deep rolling) and associated residual stresses. Some additional information is scattered throughout the large Handbook on Residual Stress edited by Lu.12

Slightly less than half of the articles in the bibliography directly address the stability of residual stresses. The remaining articles provide supporting information on initial residual stress fields or the impact of the residual stresses on fatigue or fatigue crack growth behaviour.

PEENING AND RELATED SURFACE TREATMENTS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

Shot peening (SP) is perhaps the most widely used mechanical treatment to modify the surface state of metallic materials, and it is often used for the specific purpose of improving the fatigue strength and the fatigue life. Shot peening causes inhomogeneous plastic deformation of the near-surface layers that induces numerous changes in the material state, including not only residual stresses but also microhardness, dislocation density, surface roughness, surface defects and phase composition. Vöhringer13 has reviewed these changes, their characterization and their relationship to various peening parameters.

For convenience, this survey will simultaneously consider a number of related mechanical surface treatments including glass bead peening (GBP), water peening (WP) and laser shock peening (LSP), along with deep rolling (DR) and low plasticity burnishing (LPB). Although the specific mechanics and mechanisms of these techniques vary, they share the common characteristic that localized plastic deformation of arbitrary engineering surfaces is used to induce compressive residual stresses near the surface. Some of the salient differences in the results of the various techniques will be highlighted in later discussions.

The stability of peening residual stresses has been studied in a wide range of metallic materials, including titanium alloys, nickel-based superalloys, many different steels and aluminium alloys. Over 90 articles have been identified to date that provide data and/or models specifically addressing the stability of residual stresses induced by peening and related mechanical treatments in all materials.

Initial residual stress fields

Many investigations have characterized the initial residual stress fields resulting from peening and related treatments, and a comprehensive treatment of these investigations is outside the scope of the current survey. Nearly all of the articles cited later on various stability issues also provide some quantitative data on the initial residual stress state prior to mechanical or thermal loading.

Representative experimental data on initial residual stress fields due to shot peening, laser shock peening and low plasticity burnishing of IN-718 were published by Zhuang and Wicks,14 as shown in Fig. 1. Several general trends can be noted. The peak compressive residual stress occurs slightly beneath the surface, decreasing slightly immediately at the surface. The compressive stresses then decay deeper beneath the surface, eventually becoming slightly tensile due to self-equilibration. Residual stresses due to SP are shallower than the corresponding profiles due to LSP or LPB, although the magnitudes of the peak compressive stresses are often comparable.

image

Figure 1. Representative initial residual stress profiles in IN-718 due to shot peening, laser shock peening and low plasticity burnishing.14

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Representative experimental data on initial residual stress fields due to SP in several different gas turbine engine alloys were provided by Ezeilo et al.,15 as shown in Fig. 2. Again, several common trends may be noted. The peak compressive residual stresses near the surface (the residual stresses at the surface itself are not shown in this figure) are often on the order of the yield strength of undeformed material. The tensile residual stresses deeper beneath the surface are generally of much smaller magnitude and decay towards zero slowly with increasing depth. The two curves for Udimet 720 are due to different shot peening conditions, and they serve as a reminder that the initial residual stress profile is a strong function of various SP parameters, including the type, density, shape, diameter and size distribution of the shot; the velocity or pressure; the exposure time or coverage; the impact angle, mass flow and nozzle diameter; and the distance from the nozzle to the workpiece.13

image

Figure 2. Representative initial residual stress profiles in various gas turbine alloys due to shot peening, adapted from Ref. [15]

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Numerical models to predict these initial residual stress profiles have been developed16,17 but are much less common than experimental measurements. Tufft18 has proposed a simple functional form that she claims can empirically describe the initial profile of SP residual stresses for many materials, if experimental data are available to which the equation can be fitted. Robertson19 has proposed a different functional form for the same purpose.

Fatigue life effects

Stress-life behaviour

The most common reason for peening is to improve the fatigue life, and there is extensive evidence of this effect in the literature. For example, early research by Reed and Viens20 found a 25% improvement in the endurance limit due to GBP of Ti-6Al-4V. Dorr and Wagner21 showed life improvements ranging from 5× to 100× in various specialty titanium alloys. Lautridou and DuQuenne22 found 2× to 5× improvements for a nickel-based powder metallurgy alloy. Happ et al.23 published early data for elevated temperature LCF of peened René 95 bolt hole specimens showing 10× life improvements compared to unpeened specimens at lower stress levels (see Fig. 3). Lee and Mall24,25 studied the effect of SP on fretting fatigue of Ti-6Al-4V. Everett et al.26 documented the beneficial effects of SP and LSP on the fatigue life behaviour of Al 2024 and 4340 steel. Nikitin et al.27 compared the effects of deep rolling and LSP on fatigue for as-received and electropolished specimens of 304SS at two temperatures. Nalla et al.28 compared the effects of deep rolling and LSP on the fatigue life of Ti-6Al-4V at two temperatures. Prevéy et al.29–31 evaluated the effects of several different surface treatments on the fatigue life of Ti-6Al-4V first-stage blades and vanes and Ti-6-2-4-6 compressor blades. Many of the papers cited later in discussions of thermal and cyclic stability also provide data for the effects of peening and related surface treatments on fatigue life.

image

Figure 3. Effect of shot peening on fatigue behaviour of René 95 disk bolt hole specimens, adapted from Ref. [23]

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Wagner32 has demonstrated that the effects of shot peening on fatigue life are actually much more complex than just residual stresses. He systematically shot peened, stress relieved (SR) and electropolished (EP) rotating beam fatigue specimens of an equiaxed Ti-6Al-4V alloy. Selected results are summarized in Fig. 4. He found that SP alone significantly increased the fatigue strength and fatigue life compared to EP without SP. However, SP followed by SR to remove the residual stresses resulted in a significant decrease in fatigue strength, attributed to increases in surface roughness. A subsequent EP step (now SP + SR + EP) resulted in a net increase in fatigue strength compared to the original EP condition, even though no residual stresses remained, and this benefit was attributed to cold work of the surface layers. However, SP + SR + EP was not as beneficial as SP alone (residual stresses remaining), and SP + EP to remove surface roughness without changing residual stresses gave similar results to SP alone.

image

Figure 4. Effect of various surface conditions on fatigue life in Ti-6Al-4V.32

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Sridhar et al.33 published results showing a decrease in fatigue life for the titanium alloys IMI685 and IMI318 (Ti-6Al-4V) at both ambient and elevated temperatures due to glass bead peening, attributing the differences to residual stress relaxation and increased surface roughness.

It must be emphasized that most of the studies cited above were academic investigations in which peening and testing conditions were chosen to illustrate various effects. Surface treatments were generally not optimized for maximum fatigue benefit, and testing conditions were generally not optimized for maximum fidelity to service conditions. Therefore, the specific quantitative conclusions should not be regarded as being entirely general, but qualitative observations about various issues and effects are nevertheless instructive.

Fatigue crack growth behaviour

Shot peening can also have a beneficial effect on the growth rates of fatigue cracks emanating from the treated surface, although less attention has been given to the FCG problem compared to stress-life fatigue approaches. Burck et al.34 apparently published one of the earliest such studies, evaluating glass bead blasting effects in the wrought nickel-based superalloy Udimet 700, and finding dramatic decreases in FCG rates. Elber35 studied shot peening effects on FCG and fracture in D6AC steel, deriving a simple superposition model to rationalize FCG rates with and without SP residual stresses. Hack and Leverant36 performed a detailed investigation of the substantial effects of SP compressive residual stresses on the crack-opening and growth rate behaviours of surface fatigue cracks, pointing out that such effects are more pronounced than the effects of SP on fatigue crack nucleation. The effects of SP on small fatigue cracks have been addressed directly by Misumi and Ohkubo,37 De Los Rios et al.38 and Natkaniec-Kocanda et al.39 Turnbull et al.40 investigated SP effects on FCG rates in Waspaloy, and Ruschau et al.41 studied LSP effects on FCG in Ti-6Al-4V. Other data for SP effects on FCG have been published by Mutoh et al.,42 De Los Rios et al.43 and Honda et al.44 for aluminium alloys; Everett et al.26 for Al 2024 and 4340 steel; Berns and Weber45 for a medium carbon steel and De Los Rios et al.46 for 316 SS. Everett et al.26 also studied LSP effects. Nalla et al.28 published limited data for deep rolling effects on FCG rates. Continuing the theme first introduced by Hack and Leverant,36 Zhu and Shaw47 and Ruschau et al.41 employed closure models to correlate FCG rate data with and without SP residual stresses.

The analysis of FCG behaviour in complex residual stress fields induced by SP and related techniques is not necessarily as simple as invoking superposition or closure arguments to modify traditional FCG analysis methods. The residual stress fields also distort the shapes of the resulting fatigue cracks so that conventional semi-elliptical shapes are no longer representative. Prevéy et al.48 have published a particularly striking example of a fatigue crack growing in a residual stress field induced by low plasticity burnishing; see Fig. 5 (here different symbols indicate replicate measurements). Wilks et al.49 commented on the same phenomenon in their review article.

image

Figure 5. Effect of low plasticity burnishing on residual stresses and fatigue crack shape development in IN-718.48

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Residual stress stability

Thermal relaxation

The stability of peening residual stresses during thermal exposure is especially important for gas turbine engine applications. Numerous researchers have investigated thermal stability in both common titanium and nickel alloys. This survey will first focus on residual stress stability at elevated temperature without simultaneous mechanical loading or cycling, and then consider those synergisms in a later section.

Leverant et al.50 were the first to report on residual stress stability in Ti-6Al-4V. They found that 600 °F (316 °C) thermal exposure alone caused only a small (perhaps 20%) relaxation in surface and near-surface residual stresses from SP. Vöhringer et al.51 found no relaxation of SP residual stresses at the surface in Ti-6Al-4V at temperatures up to 572 °F (300 °C) for annealing times up to 60  000 min. At higher temperatures, ranging from 752 °F (400 °C) up to 1112 °F (600 °C), they found progressively greater relaxation—from 50% after 10& 000 min at 752 F (400 °C) up to nearly complete relaxation at 932 °F (500 °C) and above. Gray et al.52 published limited data later reprinted by Wagner32,53 showing some relaxation at 662 °F (350 °C) after only 30 h and much greater relaxation at 932 °F (500 °C) and 1112 °F (600 °C). Lee and Mall24 found only about 10% relaxation of SP residual stress at the specimen surface after 24 h at 212 °F (100 °C), about 30% relaxation at 500 °F (260 °C) and 95% relaxation at 698 °F (370 °C).

Prevéy et al.54 compared thermal relaxation in Ti-6Al-4V for residual stresses produced by shot peening, gravity peening (GP) and laser shock peening. Shot peening parameters were deliberately chosen to produce a high level of cold work (75% at the surface), while GP and LSP processes yielded much lower levels of cold work (5 to 10%). Residual stresses from SP relaxed somewhat at 615 °F (325 °C) and extensively at 890 °F (475 °C) after 600 min. GP residual stresses were stable at 615 °F (325 °C) but relaxed significantly at 890 °F (475 °C). LSP residual stresses were relatively stable at both 615 °F (325 °C) and 795 °F (425 °C). Data at 615 °F (325 °C) for all three peening processes are shown in Fig. 6.

image

Figure 6. Thermal relaxation at 615 °F (325 °C) of residual stress in Ti-6Al-4V induced by shot peening (top left), gravity peening (top right) and laser shock peening (bottom), along with the corresponding changes in cold work percentage.54

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Nalla et al.28 compared thermal relaxation at 842 °F (450 °C) in Ti-6Al-4V for residual stresses produced by deep rolling and laser shock peening. Exposure of only 45 min caused significant reductions—50% or more—in residual stress for both DR and LSP.

Prevéy et al.31 compared thermal relaxation after 100 h at 700 °F (371 °C) for SP and low plasticity burnishing of Ti-6246. The SP residual stresses relaxed about 50% at the surface but were stable at all depths below about 0.002 in., and the LPB residual stresses (which were initially 50% lower at the surface than for the corresponding SP treatment) were stable everywhere.

Berger and Gregory55 studied thermal relaxation of shot peening residual stresses in the β-titanium alloy Timetal 21 s at 662 °F (350 °C) and 842 °F (450 °C). Relaxation of surface residual stresses was significant at both temperatures and increased with increasing aging time through 1000 min.

Nickel-based superalloys such as Inconel 718 are designed for higher temperature applications. Khadhraoui et al.56 studied thermal relaxation in Inconel 718 after 10 and 100 h at 1112 °F (600 °C) and 1202 °F (650 °C) for two different shot peening conditions. Residual stresses relaxed substantially (50 to 75%) at the surface but were more stable with increasing distance beneath the surface. Prevéy et al.54,57 compared the thermal stability of residual stresses from SP, GP and LSP in Inconel 718 at 980 °F (525 °C) and 1240 °F (670 °C) at times up to 2000 min. Residual stresses from SP relaxed roughly 50% at the surface but were again more stable with increasing distance from the surface. Gravity peening residual stresses were slightly more stable—decreasing only 30% or less—and LSP residual stresses were relatively unchanged. See Fig. 7. As in their previously cited study of Ti-6Al-4V, Prevéy et al.54 noted that peening with higher percentages of cold work was less stable. Prevéy et al.48 compared the thermal stability of peening residual stresses in Inconel 718 at 1112 °F (600 °C) after 1 h and 10 h for SP and three LPB conditions. Residual stresses relaxed substantially at and near the surface for SP but were somewhat stable for LPB, again attributed to differences in cold work percentage. Cammett et al.58 directly addressed the effects of different SP coverages on residual stress, cold work and thermal stability in Inconel 718 after 10 h at 977 °F (525 °C). Although heavier coverage induced somewhat higher initial residual stresses, the resulting relaxed residual stress fields after thermal exposure were relatively insensitive to coverage, although heavier coverage tended to be associated with slightly lower relaxed residual stresses. Relaxed stresses were generally 30 to 50% lower than initial residual stresses at the surface, and more stable with increasing distance from the surface.

image

Figure 7. Thermal relaxation at 980 °F (525 °C) of residual stress in Inconel 718 induced by shot peening (top left), gravity peening (top right) and laser shock peening (bottom), along with the corresponding changes in cold work percentage.54.

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Isolated thermal stability results are available for other nickel-based superalloys. Cao et al.17 reported residual stress measurements for Astroloy. At 1022 °F (550 °C), slight relaxation occurred in the near-surface layer only during the first hour, remaining stable thereafter through 100 h. More relaxation (50 to 70% at the surface) occurred during the first hour at 1202 °F (650 °C) with only slight changes at longer times. Tufft18 showed thermal exposure results for René 88DT after 5 h or 100 h at 1000 °F (538 °C), 1150 °F (621 °C) and 1300°F (704°C). Surface and near-surface residual stresses relaxed from 40 to 60%. Masmoudi and Castex59 published limited measurements of surface residual stresses in IN100 at exposure temperatures ranging from 932 °F (500 °C) to 1292 °F (750 °C). Relaxation varied from 50% at the lower temperatures to almost 100% at the higher temperatures, and nearly all changes occurred within the first 10 h. Buchanan et al.60 have more recently presented additional studies on IN100 at temperatures of 1202 °F (650°C) and 1300 °F (704 °C) with exposure times ranging up to 300 h. Surface residual stresses relaxed by roughly 50% but stabilized quickly (after about 1 h), while interior residual stresses continued to relax slowly with increased exposure time, as shown in Fig. 8. Gabb et al.61 examined residual stresses in production René 95 turbine disks removed from T700 helicopters after serving full lives, and then subjected the disks to additional thermal exposure at 593 °C, 650 °C and 704 °C (1100 °F, 1200 °F and 1300 °F). Residual stress relaxation increased with greater exposure temperature, time, initial compressive stress and initial cold work.

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Figure 8. Residual stress distribution in IN-100 versus exposure time at 1300 °F (704 °C), adapted from Ref. [60]

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Thermal stability of SP residual stresses has also been investigated in selected steels. Hoffmann et al.62 considered three different heat treatments of a 0.45% C plain carbon steel at exposure temperatures ranging from 392 °F (200 °C) to 1022 °F (550 °C) and exposure times up to 1000 min. Relaxation of surface stresses was a strong function of temperature, and only limited information was shown for subsurface stresses. Schulze et al.63 published similar results for 4140 steel at temperatures ranging from 482 °F (250 °C) through 842 °F (450 °C) and exposure times up to 6000 min. Surface stresses relaxed from 15 to 85% with increasing temperature, but again only limited information was shown for subsurface stresses. Menig et al.64 later added a comparison with thermal relaxation of LSP surface stresses at 572 °F (300 °C) and 842 °F (450 °C). Prevéy and Cammett65 studied thermal relaxation for different shot peening coverages in 4340 steel at 475 °F (246 °C) after 24 h. Surface and near-surface relaxation was minor (10 to 30%) and residual stresses were generally stable below a depth of about 0.004 in. Tufft18 found only minor changes in SP residual stresses for Marage 250 steel after 16 h at 250 °F (121 °C), 400 °F (204 °C) and 600 °F (316 °C). Krull et al.66 studied thermal stability of shot peening and water peening residual stresses in austenitic and martensitic phases of 316SS at 392 °F (200 °C), 572 °F (300 °C), and 752 °F (400 °C). Childs67 observed substantial decreases in SP residual stresses in 403 stainless steel in times as short as 1 h at temperatures as low as 300 °F (150 °C), with comparable or larger decreases at longer times and temperatures up to 1100 °F (595 °C).

Roth and Wortman68 found that exposure temperatures of 250 °F (121 °C) associated with adhesive bonding heat cycles of 1 h duration induced a relaxation of SP residual stresses in the aluminium alloy 7050-T7451 that was maximum at the surface and about 30%. Exposures up to 12 h at 185 °F (85 °C) caused no noticeable relaxation. Potter and Millard69 found no thermal relaxation in 7075-T6 after about 20 h at 200 °F (93 °C), but significant relaxation for similar time scales at 225 °F (107 °C) and 250 °F (121 °C).

Two primary approaches have been proposed for modelling the thermal stability of peening residual stresses. Vöhringer et al.51 and his colleagues (for example, Hoffmann et al.,62 Schulze et al.,63 Eigenmann et al.,70 Berger and Gregory,55 and Menig et al.64) at the Institut für Werkstoffkunde, University of Karlsruhe, Germany, have widely used a so-called Zener–Wert–Avrami function4 of the general form

  • image(1)

where A is a function of material and temperature according to

  • image(2)

to fit experimental data for surface residual stresses. This is still something of an empirical rather than predictive approach, and the parameter m has been found to change with aging temperature. This approach does not appear to have been extended to subsurface changes in residual stresses.

Khadhraoui et al.56 and Cao et al.17 have published some details of a more sophisticated numerical approach to modelling thermal stability, while also treating initial residual stress formation and cyclic stability. Their method, which has been implemented in the ‘Shotpeen’ software, includes an Avrami-type formulation to describe the kinetics of recovery. Published results include predictions of the entire residual stress profile in agreement with experimental measurements. Exercising the model requires information about the limiting state of recovery and the integrated width of X-ray diffraction peaks, so additional predictive capability appears to be required for the model to be practical in an engineering context.

It must be emphasized strongly, as was noted earlier in passing, that the thermal stability of peening residual stresses is dependent on several critical peening parameters, including coverage, intensity and the resulting cold work. Therefore, the individual experimental results cited above cannot be regarded as being entirely general. In fact, in several cases, the researchers noted that peening parameters were selected to highlight relaxation phenomena, and some of these conditions may not be representative of common peening practice in production environments.

Static relaxation

Relaxation and redistribution of residual stress occurs when the summation of the residual stress and applied stress due to subsequent mechanical loading exceeds the yield condition of the material. Simple mechanics models for this phenomenon have been outlined in classic review papers by Vöhringer.4,5 Several specific studies of the effects of quasi-static mechanical loading on peening residual stresses in 4140 steel have been published by Vöhringer and his colleagues at Karlsruhe, including Hanagarth et al.,71 Eigenmann et al.,70 Eigenmann,72 and Holzapfel et al.73–75 Kirk76 reported similar studies in a variety of materials and Cammett et al.77 did the same for 301 stainless steel. More recently, Prevéy et al.78 briefly investigated overload relaxation of SP and LPB residual stresses in Ti-6Al-4V. Smith et al.79 compared experimental measurements and finite element analyses of the changes in peening residual stresses following simple tensile loading and a single fatigue cycle for an En15R steel. Static effects are also included in numerous studies of cyclic relaxation cited below, and will be discussed further in that context.

Cyclic relaxation

The more significant issue for many mechanical components is the potential effect of repeated fatigue cycling on residual stress relaxation and redistribution, even when the individual mechanical load cycles do not cause macroscopic plastic deformation. This topic has received extensive attention in the literature. To date over 65 articles have been identified that address the cyclic stability of peening residual stresses, including numerous investigations focused on titanium alloys, nickel-based superalloys, aluminium alloys and a wide range of steels. Synergisms with other relaxation mechanisms, such as thermal activation, are also considered.

The landmark Leverant et al.50 paper was again the first investigation of this phenomenon in titanium alloys. They experimentally observed additional relaxation of residual stresses in Ti-6Al-4V with fatigue cycling at 600 °F (316 °C) compared to thermal exposure alone (which caused only mild relaxation), and the extent of relaxation increased with increasing cyclic strain amplitude (±0.3 vs. ±0.6%, both with positive mean strains). Vöhringer et al.51 found only limited residual stress relaxation during continued fatigue after the first cycle (on which more substantial relaxation occurred, due to static effects) for cyclic bending of Ti-6Al-4V sheet. Recent studies of Ti-6Al-4V80–82 found extensive relaxation of surface residual stresses from deep rolling at the fatigue half-life for high temperature fatigue (460 MPa stress amplitude, R=−1, 842 °F [450 °C]). More detailed Ti-6Al-4V data published by Nalla et al.28 showed relaxed residual stress profiles following fatigue cycling at several different temperatures for both DR and LSP. As shown in Fig. 9, room temperature cyclic relaxation was minimal for LSP and moderate for DR, but extensive for both processes at 842 °F (450 °C) and for DR at 482 °F (250 °C). Since all cycling was at R=−1, these data likely include both static and cyclic effects, because the superposition of compressive residual stresses and compressive applied stresses will induce further yielding, especially at elevated temperatures. Prevéy et al.30 found mild (perhaps 10 to 30%) relaxation of LPB residual stresses following room temperature fatigue cycling of Ti-6Al-4V single-edge vane feature specimens at two fully reversed stress amplitudes. Cheong et al.83 performed LCF tests at R= 0.05 on disk bore feature specimens of Ti-6Al-4V, finding about a 20% reduction in surface residual stress from shot peening and little or no change in LPB residual stresses, which were initially about 3× smaller than SP residual stresses. Lee and Mall24,25 observed significant relaxation of SP residual stresses under fretting fatigue at elevated temperature.

image

Figure 9. Residual stress profiles before and after fatigue cycling in Ti-6Al-4V for laser shock peening (left) and deep rolling (right) at various temperatures.28

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Relatively few studies of cyclic stability are available for nickel-based superalloys. Cao et al.17 studied SP residual stresses in Astroloy and found that elevated temperature fatigue cycling at R= 0 caused only small amounts of additional relaxation compared to thermal exposure alone for 1202 °F (650 °C). Tufft18 found progressive relaxation with elevated temperature fatigue cycling in René 88DT, although the effects of cycling did not appear to be much more severe than the effects of temperature alone. Zhuang and Halford84 have published models of SP residual stress stability in IN718 without validating experimental measurements. Boggs and Byrne85 performed some early work on cyclic stability of SP stresses in two nickel–cobalt alloys, noting moderate relaxation in one alloy and little relaxation in the other, but providing few details.

Berkley et al.86,87 measured surface residual stresses on 305 Waspaloy superalloy disks (both compressor and turbine) from the F100 and T56 engines, varying in life from zero to greater than 8000 engine cycles. Data scatter was considerable, but most disks with 4000–8000 cycles generally exhibited 30 to 60% relaxation of surface residual stresses. Further discussion on the scope and significance of this work is available in Ref.[88]. Belassel et al.89,90 performed a limited number of laboratory coupon tests in a companion study.

Limited information is available on cyclic relaxation of peening residual stresses in aluminium alloys, but the available data suggest minimal-to-moderate relaxation. Seppi91 published one of the very earliest investigations in a short paper where he noted a 20% reduction in residual stresses following tension fatigue cycling of 7075-T6. Potter and Millard69 found no significant cyclic relaxation of SP stresses at either R=−1 or R= 0.5 in 7075-T6, and Hammond and Meguid92,93 observed no significant relaxation following rotating bending in 7075-T6. Rasouli Yazdi and Lu94 reported moderate relaxation of SP residual stresses in 7075 at different fatigue stress amplitudes, but most changes occurred on the first cycle. Bonnaféet al.95 found little SP relaxation in 7075-T7351 at two different stress amplitudes (R= 0.1) but more substantial relaxation in 2024-T351. Fontanari et al.96 reported only mild (5 to 20%) relaxation of SP surface stresses and less relaxation of subsurface stresses following R= 0.1 bending fatigue in 6082-T5. Zinn and Scholtes97 studied SP residual stress stability in several aluminium alloys (including 2017, 5083, 5754, 6082 and 7020) with reversed bending and found that surface stresses typically relaxed 30 to 40% by the end of the fatigue life, but that stress relaxation was the most pronounced during the first cycle (again, likely a static effect). Bathias et al.98 observed moderate (10 to 40%) relaxation of peening residual stress in both 2024 and 7075 during the first 20 cycles for both high-cycle fatigue and low-cycle fatigue, and mostly stable behaviour thereafter, until late in life when additional relaxation occurred due to microcrack formation. Relaxation was slightly greater at the higher applied stresses.

Extensive information is available on the stability of peening residual stresses in steels. The relevant literature is summarized in Table 1, which indicates the authorship, date, specific grade of steel(s) considered and any special issues in the investigation. Unless otherwise specified, researchers performed axial fatigue tests on smooth shot peened specimens. A detailed analysis and discussion of these collective data is beyond the scope of the current effort, but some selected observations are in order. Notable work includes the early research of Taira and Murakami,99 Esquivel and Evans100 and Kodama;101 and the extensive investigations on 4140 by the group at the University of Karlsruhe (Eigenmann, Schulze, Holzapfel, Wick, Menig, Vöhringer and their colleagues70,74–75,102–107).

Table 1.  Summary of published research on cyclic relaxation of peening residual stress in steels
AuthorsDateSteel GradeSpecial Notes
Taira and Murakami991960S40C medium CReversed bending
Esquivel and Evans10019684130 
Kodama1011972JIS SS41Reversed bending
Neff1171981cast 0.28CFour-point bending, R= 0
McClinton and Cohen11119821040 
Bergström and Ericsson11819844140Smooth and notched, R= 0 & −1
Bergström and Ericsson10819864140Smooth and notched, R= 0 & −1
Berns and Weber45198650CrV4Bending
Bergström and Ericsson11919874140Smooth and notched, R= 0 & −1
Bignonnet et al.1201987E460 and E550Welded T-joints
Bignonnet116198735 NCD 16Four different loading types
Misumi and Ohkubo371987S45CReversed bending with small hole
Qiu and Wang1131987GC-4 superhigh strength 
Cao and Castex12119884135Plane bending
Meguid and Hammond931989080M40 (medium C) 
Hammond and Meguid921990080M40 (medium C) 
Cammett et al.771993301 SS 
Zeller1101993Ck 45, X5 CrNiMo 18 10Rotating bending
Eigenmann et al.7019944140 
Farrahi et al.122199560SC7 spring steelTorsion, R=–1
Iida and Taniguchi1231996S45CReversed bending
Schulze et al.10219964140Stress control vs. strain control
Holzapfel et al.7419964140Bending, elevated temperature
Holzapfel et al.7519984140Bending, elevated temperature
Iida and Hirose10919990.45% C carburizedReversed bending
Wick et al.10319994140Warm peening, cyclic bending
Wick et al.10419994140Warm peening, cyclic bending
Wick et al.10520004140Warm peening, cyclic bending
Batista et al.1242000Carbo-nitrided 4130Contact fatigue (gears)
Smith et al.792001En15RTension-compression cycling
Menig et al.10620024140Warm peening, torsion
Menig et al.10720024140Warm peening, diff heat treats
Torres et al.11520024340Rotating bend, diff hardnesses
Torres and Voorwald11420024340Rotating bend, diff SP intensities
Teodosio et al.1122003API 5L X70, 31803 SSComplex changes in weldments
Capello et al.1252004C45, 39NiCrMo3R=–1
Nikitin et al.272004304SSLSP, DR at elevated T, R=–1

A general theme of many papers is that residual stress relaxation is more pronounced for larger cyclic stress or strain amplitudes (for example, Bergström and Ericsson,108 Eigenmann et al.70 and Wick et al.105). Under some conditions, little or no relaxation of peening residual stresses occurs, especially for small fatigue stress amplitudes.100,109 Complete or nearly complete relaxation of residual stresses is rare and occurs only for severe cycling, sometimes with an additional influence from elevated temperature (e.g., see Ref. [75] and [110]). McClinton and Cohen111 reported unique results for R= 0 (zero-tension) fatigue cycling with the maximum stress on the order of the yield strength, resulting in the originally compressive surface residual stress changing to tensile (this did not occur for their fatigue cycling at lower stress amplitudes). Teodosio et al.112 observed complex fluctuations in residual stresses during fatigue cycling of a peened weldment.

Several studies that employed reversed bending found significant relaxation of the compressive surface residual stress on the first fatigue cycle, followed by a much more gradual relaxation with continuing cycling (e.g., see Ref. [99], [101], [105] and [113]). The large change on the first cycle is apparently due to the static effect discussed earlier, when the superposition of residual stress and applied stress of the same sign exceed the yield condition. Subsequent changes are attributable to true cyclic effects. The remaining residual stress as a fraction of the original residual stress often decreased linearly with the logarithm of the cycles during this second stage of relaxation.

The rate and extent of cyclic residual stress relaxation was observed to depend on many parameters, including the shot peening intensity and coverage,114 peening temperature,105,106 the original hardness of the material115 and the loading type.116

Representative results of Wick et al.105 for room temperature peening of 4140 are shown in Fig. 10. Here the measured surface residual stress is shown after 1 cycle and after 104 cycles of fatigue loading at different stress amplitudes, compared to an initial as-peened value of about 600 N/mm2 (compressive). Note the systematic decrease in residual stress with stress amplitude on the first cycle above a critical stress amplitude, and the additional systematic decrease with further cycling above a second (higher) critical stress amplitude. Relaxation is negligible at the lowest fatigue stress amplitude and extensive at the highest fatigue stress amplitude.

image

Figure 10. Surface residual stress as a function of fatigue stress amplitude after 1 cycle and 104 cycles.105

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Several researchers have developed models to characterize or predict cyclic relaxation of peening residual stresses in various materials. The most common model is an empirical form based on the observation (cited earlier) that residual stress often decreases linearly with the logarithm of the fatigue cycles after initial static relaxation.70,74,75,101,108,117 The two constants in this power-law equation are typically determined by fitting the available experimental data, and are themselves functions of other variables such as the stress amplitude.

The other common approach is a sophisticated numerical model, generally based on finite elements. Lu, Flavenot and their colleagues94,126–128 apparently developed the first such model, a simplified inelastic analysis based on finite elements and employing a group of internal parameters that characterize local inelastic mechanisms. They applied the model to predict cyclic relaxation of peening and machining stresses in various steels and an aluminium alloy. Cao and colleagues developed another early numerical model for residual stress relaxation with particular attention to material cyclic softening and applied it to steels121 and nickel-based superalloys,17 also incorporating thermal relaxation effects (see also Ref. [56]). Batista et al.,124 Zhuang and Halford84 and more recently Meguid et al.129 have each published numerical models implemented in finite element contexts. Detailed discussion of these numerical models is beyond the scope of the present survey. All have shown some apparent success in predicting experimentally observed relaxation, but all require the determination of multiple material parameters, complicating their practical use in a production engineering environment.

COLD EXPANSION OF HOLES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

Holes in structural members create local stress concentrations that can become preferred sites for fatigue crack initiation and growth. To mitigate this tendency, methods for ‘cold expansion’ of the hole have been developed as a means of inducing compressive residual stresses around the edge of the hole.

While a number of cold expansion (CX) processes have been developed, the split-sleeve process130 has been the most widely used. This process involves placing a longitudinally split sleeve within the hole and then drawing an oversized tapered mandrel through the assembly. The hole is expanded to an extent sufficient to cause permanent plastic deformation. Upon removal of the mandrel, the surrounding elastic material attempts to return to its undeformed state, producing a self-equilibrating residual stress field. This residual stress is compressive (and therefore beneficial) in an annular region adjacent to the hole, and slightly tensile farther away from the hole. The growth of fatigue cracks may be significantly delayed, if not arrested altogether, by these compressive residual stresses. This split-sleeve method has been successfully commercialized by Fatigue Technology, Inc. (FTI), Seattle, Washington, including other derivatives of the split-sleeve approach, and many CX researchers cite FTI methodologies explicitly in their published studies.

The CX process has been most widely applied to aircraft structures, and so it should not be surprising that the great majority of the scientific literature on CX residual stresses addresses high-strength aluminium alloys. However, Rufin131 has published an overview of CX technology for aircraft engine applications. Sha et al.132 published selected results from an early USAF-funded study at Pratt & Whitney of the fatigue behaviour of cold expanded holes in Ti-6246, and Ezeilo et al.133 reported work (with Rolls-Royce connections) on IN-718. Rich and Impellizzeri134 included a mill-annealed Ti-6Al-4V in their aircraft-motivated study. A limited number of papers have addressed CX behaviour in steels.135–139 The literature also includes attention to non-aerospace applications such as rails.140 The autofrettage method employed to induce compressive residual stresses in the bores of cannons and thick-section gun barrels141–144 can also be regarded as an alternative form of CX.

Initial residual stress fields

The CX process is much simpler from a mechanics perspective than peening, welding or machining, and so is amenable to simpler analytical approaches. Hsu and Forman145 and Rich and Impellizzeri134 were among the first to propose simple radial expansion models for the CX process, and others146–150 developed models of increasing complexity and accuracy. Ball150 provides a thorough yet concise review of these various models.

Numerical approaches such as the finite element (FE) method have also been employed to characterize the initial residual stresses resulting from CX. Sha et al.132 reported on an early MARC analysis, and Armen et al.151 published one of the first detailed FE investigations. Heller et al.152 included the effects of a pre-existing crack in their FE study. These earlier efforts and some later ones153,154 employed two-dimensional plane stress or plane strain models that neglected through-thickness variations in the resulting residual stress fields.

Poussard et al.155 also performed plane stress and plane strain FE analyses, but further developed axisymmetric models in a first attempt to explore variations through the thickness. Pavier et al.156 went on to simulate the actual process of pulling the mandrel through the hole in his axisymmetric FE models and added a fully three-dimensional (3D) model of the same process shortly thereafter.157 His axisymmetric and fully 3D models gave very similar results. Figure 11157 demonstrates this agreement and also the substantial differences in residual stresses between the entrance face, mid-thickness and the exit face. Papanikos and Meguid158 and Chakherlou and Vogwell159 published 3D models with lower resolution, and Kang et al.160 added finish reaming to his 3D FE simulation. Zhang, Edwards and Fitzpatrick161 have written a brief yet thorough comparison of various 2D and 3D FE models, including selected comparisons with X-ray measurements.

image

Figure 11. Residual tangential stress fields following cold expansion as predicted by 3D and axisymmetric finite element analyses.157

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Özdemir and Edwards162 and Wang and Edwards163 used the modified Sachs method and neutron diffraction methods, respectively, in attempts to measure experimentally the actual variations in residual stress, both through the thickness and around the perimeter of the hole, resulting from the split-sleeve CX method. They confirmed that the actual distributions of residual stress are quite complex, and they qualitatively confirmed the trends from the numerical modelling. Stefanescu et al.164 later showed relatively good agreement between neutron and X-ray diffraction measurement methods. Zhang, Fitzpatrick and Edwards165 employed the contour method to investigate 3D effects on the crack plane.

Fatigue life effects and models

The conventional wisdom is that CX of holes has a relatively small effect on the number of cycles required to initiate a fatigue crack at an open hole (e.g., see Ref. [153] and [166]). The primary fatigue benefit accrues during the crack growth phase of life. For this reason, and because of the historical emphasis on damage tolerance methods for aircraft structures, most of the studies and models for CX effects have focused on the FCG problem.

The classical approach to FCG life prediction for cold expanded holes is to combine an analytical estimate of the residual stresses normal to the crack plane with a weight function method to calculate the stress intensity factor, in which the weight function is directly integrated with the residual stresses along the length of the crack. The effects of (remote) applied loading are linearly superimposed with the (local) static residual stresses to determine the total stress intensity factor range. Grandt and his colleagues performed some of the ground-breaking studies following this paradigm.167–169 Similar approaches were followed later by Chandawanich and Sharpe,166 Clark148 and Ball and Lowry.153 Sample results from Ball and Lowry153 are shown in Fig. 12. In the top figure, experimental measurements of residual stresses are compared with various analytical and numerical models, and in the bottom figure, the resulting predictions of crack growth are compared with fatigue test data for three levels of interference ratio, I0. Note that the residual stresses in this paradigm are typically taken to be the initial residual stresses, prior to any loading, crack growth or thermal exposure.

image

Figure 12. Comparisons of analytically predicted versus experimentally measured values for residual stress normal to the crack plane (top) and crack length as a function of fatigue cycles (bottom).153

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Pavier et al.170 developed a sophisticated finite element analysis of the fracture mechanics problem to compute effective stress intensity factors for cracks emanating from the edge of a cold worked hole. This work was a response to various concerns about the applicability of the classical superposition—weight function method, including stress relaxation and redistribution effects due to crack growth. Pavier et al. concluded that the traditional weight function method generally underestimated the effective stress intensity factor and therefore could lead to non-conservative life predictions.

The three-dimensional variations in CX residual stresses (especially through-thickness variations) cited earlier have a significant implication for the practical FCG analysis problem. Traditional FCG life analysis assumes that the fatigue cracks have idealized, regular shapes such as quarter-elliptical corner cracks and straight through cracks. Common stress intensity factor solutions for cracks at holes are based on these geometric simplifications. However, real fatigue cracks at CX holes have been shown to have complex shapes. This was shown clearly by the early work of Pell et al.,171 who published photographs of cracks with distinct ‘P’ shapes indicative of highly non-uniform growth rates across the thickness. More recently Kokaly et al.172 has published numerous fractographs of fatigue cracks growing from CX and non-CX holes in plates of different thicknesses, demonstrating a variety of complex shapes. Others such as Saunder and Grandt173 have documented only the significant differences in surface crack lengths on the entry and exit sides.

Residual stress stability

It is noteworthy that all of the residual stress models and fatigue crack growth predictions cited above are based exclusively on the initial residual stress field for a cold expanded hole, with no adjustments for any residual stress relaxation or redistribution. Several early researchers speculated about the possibility of changes in the residual stress field (e.g., see Ref. [132] and [174]) but had no data to evaluate their suspicions. Only a handful of more recent researchers have directly addressed the stability of CX residual stresses.

Static relaxation

One of the simplest and most significant effects on CX residual stresses is the effect of significant applied mechanical loads, especially in compression. These compressive excursions, which can occur frequently in spectrum loading of aircraft structures, can substantially decrease the compressive residual stress field at the edge of the hole. The change occurs because the sum of residual and applied compressive stresses exceeds the yield strength of the material, but the total stress is limited by the yield surface of the material. When the applied compressive stress is removed, the local elastic unloading results in a decreased compressive residual stress. This effect was cited by Ball and Lowry153 as an interpretation of unpublished life results. The same effect was investigated more directly, albeit with limited scope, by Stefanescu et al.,175 who measured residual stress fields at CX holes before and after single compressive loads. The applied compressive loads were relatively small—only a fraction of the material yield strength—but the changes in the residual stress field were substantial, as shown in Fig. 13.

image

Figure 13. Residual stresses measured by X-ray diffraction along the transverse direction of a cold expanded hole specimen on the (a) inlet face and (b) outlet face before and after compressive loading.175

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Cyclic relaxation

Three studies have been found to date that investigated cyclic relaxation of CX residual stresses. Hermann and Moffatt176 performed R= 0.05 fatigue tests on the aluminium–lithium alloy 2091 following FTI cold expansion. They measured significant relaxation after 106 fatigue cycles at an applied maximum stress of 70 MPa (nominally 210 MPa at the edge of the hole, in comparison to a material yield strength of 350 MPa) but only minimal further relaxation with additional cycling. Ezeilo et al.133 reported noticeable reductions in residual stress with fatigue cycling in IN-718, but provided relatively few quantitative details in their short paper. Özdemir and Edwards177 studied cyclic relaxation effects at R= 0.1 in reamed 4% FTI expanded holes in 7050-T76. They found no discernable relaxation when applied cyclic stresses were below the fatigue limit (150 MPa), but a clear effect at higher loads. Selected results are shown in Fig. 14. When cycled at the fatigue limit, residual stresses continued to relax with additional numbers of cycles.

image

Figure 14. Residual hoop stress distributions at reamed 4% FTI expanded holes fatigued for 50 000 cycles at different applied stresses.177

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Thermal relaxation

Since the preponderance of published research on CX residual stresses has focused on aluminium alloys and aircraft structural applications, little work has been done on the thermal relaxation issue. Clark and Johnson178 investigated stress relaxation in 7050-T7451 at temperatures ranging from 71 to 104 °C (approximately one-half of the melting temperature of the alloy). They found little relaxation (5 to 15%) after 250 h, and relatively small changes in fatigue lives, although their experiments were complicated by several other issues.

Lacarac et al.179 and Garcia-Granada et al.180 investigated a new high temperature aluminium alloy 2650 developed for advanced supersonic transport applications. Studies were conducted at 150 °C with 1000 h exposures. As shown in Fig. 15, the creep exposure resulted in significant residual stress changes at the exit face (where the CX residual stresses were the highest) but only minimal changes at the entrance face. Since fatigue cracks typically initiate and grow most quickly at the entrance face (where the compressive residual stresses are the lowest), it appears that the creep exposure would have relatively little effect on the growth of these small corner cracks. Once the cracks grow and transition to become through cracks, the residual stress relaxation would have more of an effect, and this was confirmed by subsequent FCG testing.179 The relaxation effects appeared to be slightly more pronounced when the elevated temperature exposure was accompanied by tensile loading, and substantially more pronounced when high temperatures were superimposed with compressive loading. The latter effect is presumably linked to the effect of static compressive loads discussed previously.

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Figure 15. Hoop residual stresses measured using X-ray diffraction after cold expansion and 150 °C exposure.179

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No studies of thermal relaxation effects on cold expanded holes in gas turbine engine alloys at operating temperatures were found in the open literature. Sha et al.132 speculated that these effects could be significant for Ti-6246 applications, but their limited LCF testing of bolthole specimens with a superimposed dwell period demonstrated increased lives, perhaps attributable to other factors. Work cited earlier on cold expanded holes in IN-718133 considered only room temperature conditions.

The thermal relaxation models developed to address elevated temperature exposure of shot peening and related surface enhancement residual stresses (as discussed earlier) should be applicable to elevated temperature exposure of cold expanded holes, but this does not appear to have been investigated and reported in the open literature.

Relaxation due to crack growth

Stefanescu181 has recently reported some interesting work on the apparent effects of fatigue crack growth on CX residual stresses. His data suggested systematic changes in residual stress fields with crack extension, as shown in Fig. 16. Companion tests with EDM slots simulating crack extension found more pronounced changes in residual stress fields. Subsequent predictions of FCG rates based on classical weight function techniques agreed more closely with experimental measurements when the evolving residual stress field was used rather than the initial residual stress field,182 as illustrated in Fig. 17. As Stefanescu noted, this result stands in apparent contradiction to the numerous successful predictions by earlier researchers using only the initial residual stress field. The mechanisms by which the residual stress change occurs with crack extension are not clear. When residual stresses are tensile, the mechanism for relaxation with crack growth is obvious (see later discussion of welding residual stresses) but this argument does not appear to be immediately applicable to crack growth in compressive residual stress fields. Stefanescu suggested the changes were related to the localized plastic deformation around the crack during fatigue cycling but proposed no working model.

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Figure 16. Residual stresses measured using X-ray diffraction for different average fatigue crack lengths at the (a) inlet face and (b) outlet face.181

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Figure 17. Comparisons of measured FCG rates for thickness-averaged crack lengths with predictions based on initial or evolving residual stress fields.182

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WELDING

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

In peening and cold expansion, beneficial compressive residual stresses are deliberately induced into the final manufactured part for the specific purpose of enhancing fatigue performance. In contrast, welding residual stresses are an inherent and largely unavoidable byproduct of the manufacturing process itself, and they are largely deleterious to fatigue performance. After solidification of the weld bead, the bead is prevented from contracting during cooling by the surrounding parent material. The parent material thus undergoes compression due to contraction forces in the weld, and correspondingly the weld bead and heat-affected zone are put into tension. The maximum tensile residual stresses in the welded joint itself may approach the yield strength of the parent material.

The majority of the scientific literature addressing residual stress effects on weldment fatigue has focused on steels, although some limited attention has been given to alloys of titanium183 and aluminium.184–186 Most researchers have emphasized fatigue crack growth behaviour rather than crack formation or S-N behaviour.

Fatigue life effects and models

Calculation of the initial residual stress field via numerical analysis of the welding process is a challenging effort beyond the scope of the current survey. Terada187 developed a simple functional form for the residual stress field at a weld bead in a wide plate as a first step in deriving stress intensity factors for cracks perpendicular to the weld bead. Tada and Paris188 and later Smith189 proposed alternative functional forms and, in turn, derived alternative expressions for the stress intensity factor. Terada and Nakajima190 used the same residual stress fields to develop K solutions for a crack approaching the weld bead. Rybicki et al.191 proposed another simple functional form and corresponding K solutions for girth-welded pipes.

Adams183 was apparently among the first to propose a simple superposition approach using weight function methods to determine the net effect of residual stresses and applied loads on fatigue crack growth in welded joints. Similar approaches were employed with general success by Glinka,192,193 Parker194 and Nelson.195 Parker194 noted that special attention is needed when weight function superposition methods infer physically inadmissible interpenetration of opposing crack faces. Miyazaki et al.196 reported successful applications of the superposition approach but also proposed an inherent strain method for more complex problems.

Numerous other researchers have proposed that a crack closure approach is a superior means of addressing residual stress effects on crack growth in weldments. This approach assumes that the residual stress field influences the crack opening stress (the stress at which the fatigue crack tip first becomes fully open during the loading cycle), and that the resulting changes in the effective stress intensity factor range correlate with changes in the fatigue crack growth rate. The crack opening levels are determined using either experiment or analysis. Miyamoto et al.197 focused his pioneering work in FE analysis of fatigue crack closure on the welding problem, and Fukuda and Sugino198 employed a similar numerical approach to predict how welding residual stresses influenced crack opening behaviour. Nelson195 applied a simpler closure analysis method and critically compared the results with the superposition approach for some of the Glinka192 data, suggesting that the closure approach was sometimes superior. Glinka193 himself later suggested that the two approaches should give similar results under many conditions. Fukuda et al.199 and later Itoh et al.200 and Kang et al.201,202 measured crack opening levels experimentally and then used these values to correlate crack growth rate data. Kang et al.202 pointed out that closure approaches must address the complex partial opening that can occur when fatigue cracks grow from compressive to tensile residual stress regimes. Itoh et al.200 as well as Ohta et al.203,204 observed that cracks growing in tensile residual stress fields under tensile applied stress ratios exhibit no effect of the tensile residual stress field on crack growth rates, because the crack tip is already fully open during the entire fatigue cycle. Beghini and Bertini205 and Beghini et al.206 suggested a simple approach to modify the traditional superposition method to account for certain closure effects. Wang207,208 extended a strip-yield fatigue crack growth model for plasticity-induced crack closure to address residual stresses in weldments.

Residual stress stability

Most of the fatigue crack growth analyses cited above did not address changes in the residual stress field in their formulation, although some researchers (e.g., see Ref. [193] and [195]) speculated on the potential effect of these changes. However, numerous other researchers have directly addressed changes in residual stress distributions due to a variety of mechanisms, including static loading, cyclic loading and crack extension. Thermal relaxation of welding residual stresses has not been addressed explicitly in this survey, although it should be noted that post-weld heat treatment is often performed for the explicit purpose of relieving deleterious tensile residual stresses in the weldment.

Static and cyclic relaxation

Numerous researchers have reported significant relaxation and redistribution of residual stresses on the first loading cycle, followed by minimal further relaxation on subsequent cycles. Iida et al.209 and Iida and Takanashi210 reported this result for both R= 0 and R=−1 cycling on notched specimens, and then Takanashi et al.211 found a similar result for smooth butt welds, proposing a simple mechanics model as explanation. Typical results for the change in the residual stress at a single point near the weld centre line with cycling are shown in Fig. 18210. Note that the magnitude of the decrease in the residual stress on the first cycle corresponds with the magnitude of the applied static stress, indicating a simple shakedown behaviour. Typical changes in the residual stress profile after fatigue cycling at two different stress amplitudes are shown in Fig. 19211. Note that both the tensile and compressive residual stresses are relaxed towards zero, although the changes are more pronounced for the tensile stresses.

image

Figure 18. Change in longitudinal residual stress at a distance 10 mm from the weld center line with application of static or fatigue loads.210

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image

Figure 19. Transverse distributions of longitudinal residual stresses in smooth butt welded joint before and after fatigue cycling.211

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Nitschke-Pagel and Wohlfahrt212 experimentally measured a relaxation of residual stresses in welded high-strength steel in proportion to the magnitude of a single applied static tensile load, but minimal changes with further cycling, and minimal changes with static compressive loads. Lachmann et al.213 confirmed the same general trends with corresponding Barkhausen Noise measurements of residual stress. Han et al.214 found a large change in residual stresses on the first load cycle for a low-strength steel, but very small changes with further cycling. Dattoma et al.215 developed a finite element model of residual stress relaxation in weldments that predicted significant changes on the first cycle but no further changes after 10 cycles. Blom216 reported experiments in which residual stress measurements were performed before cycling and at two different numbers of fatigue cycles, neither of which was a single cycle. He found some appreciable relaxation between the two cycle counts in some tests, although the largest relaxation (50 to 80% of the initial value) was recorded at the first cycle count. Lopez Martinez et al.217 published maps of residual stress distributions measured by neutron diffraction for as-welded and TIG-dressed specimens with and without static loading or spectrum fatigue cycling. They concluded that the static load caused appreciable relaxation and that the variable amplitude fatigue showed the same degree of relaxation as the static load case, suggesting that the fatigue relaxation occurred early during the fatigue loading and was correlated to the occurrence of maximum load in the spectrum. Khanna et al.218 studied residual stresses in spot welds using Moiré interferometry methods and reported that residual stress decreased at weld centre but increased at the weld edge after 1000 to 10  000 cycles; no data were reported after only one cycle. James et al.186 recently reported an interesting result based on detailed synchrotron diffraction measurements of the full residual stress distribution; they claimed significant increases in tensile residual stress with fatigue cycling, but offered no potential explanations.

Relaxation due to crack growth

Fukuda and Tsuruta219 were apparently the first to study the effect of fatigue crack extension on the tensile residual stress fields resulting from the welding process. They experimentally measured a progressive decrease in the residual stresses as a through-thickness fatigue crack extended under R= 0 cycling, as shown in Fig. 20. The amplitude of the applied stress cycle was small enough that relaxation of the residual stress field due to purely static or cyclic load mechanisms was not significant, as confirmed by measurements performed before and after substantial fatigue cycling (without cracking).

image

Figure 20. Changes in welding residual stress profile with crack extension, adapted from Ref. [219].

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Fukuda220 later developed a simple analytical method to predict the redistribution of tensile residual stress with crack extension, and showed good agreement with experimental measurements. Park et al.221 developed a numerical model for a similar purpose. Terada222 has recently published another equation for tensile residual stress redistribution with crack extension and shown favourable agreement with limited experimental data.

MACHINING

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

Machining techniques for metallic materials such as cutting, grinding and turning typically induce residual stresses at the part surface as a byproduct of the thermal cycling, microstructural transformations and deformation associated with material separation. Although these residual stresses are typically of much smaller magnitude (at least for good machining practice) than the residual stresses resulting from peening, cold expansion or welding, they are sometimes large enough to become significant for fatigue behaviour. These machining-induced residual stresses are also subject to potential relaxation and redistribution.

The available information in the scientific literature about the stability of machining residual stresses is very limited, although this may be indicative of the limited significance of the issue. There is a broader literature on the formation and measurement of the initial residual stress state due to machining, but this survey did not attempt to address that literature comprehensively. Some limited information is also available on fatigue life effects, mostly focused on S-N behaviour, because the depth of the machining residual stress fields is generally too shallow to affect fatigue crack growth behaviour except for the smallest crack sizes. However, it should be noted that machining effects on S-N behaviour also involve surface roughness and other factors, not simply residual stress effects.

The most extensive work on the stability of residual stresses induced by machining was performed by James;223 see also Ref. [224]. He studied surface milling as part of a broader study of residual stress formation and stability in Al 2219-T851, and characterized the changes in the surface residual stress with R=−1 fatigue cycling at different stress amplitudes (all significant fractions of the yield strength). A simple model was proposed to predict the results.

Bathias et al.98 investigated the relaxation of tensile residual stresses due to milling of Al 2024 and 7075, finding a rapid and nearly total relaxation during the first few cycles of fatigue loading.

Flavenot and Skalli225 performed experimental measurements of the initial and cyclically relaxed residual stress profiles in 42CD4 grade steel due to different grinding conditions. Lu, Flavenot and Turbat128 used their finite element model (cited earlier in the treatment of peening residual stresses) to predict this relaxation behaviour.

Kuhn et al.226 published data on relaxation of residual stresses due to milling of 1045 steel in various heat treat conditions and with various stress concentrations. Residual stresses relaxed substantially, especially in softer conditions and at larger fatigue stress amplitudes. Alam et al.227 reported only limited information about relaxation of residual stresses due to turning of XC80 steel.

OTHER PROCESSES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

It is useful to cite, for completeness, a few published studies on residual stress relaxation under other conditions. One set of these studies focuses on the relaxation of mean stress during strain-controlled fatigue, while another set addresses the relaxation of residual stresses induced by different mechanical deformation processes. Some of the studies were published many years ago and were particularly significant in the historical development of the topic.

Mean stress relaxation

Morrow and colleagues performed the landmark early research on cyclic relaxation of mean stresses228–230 in careful experimental studies of 4340 (in three different heat treat conditions) and A286 steels. He performed displacement-controlled fatigue tests on axial specimens with an imposed mean stress and measured the change in the mean stress with continued cycling for different values of constant applied stress amplitude. Morrow then developed an empirical equation in the general form of a power law on the logarithm of applied cycles to describe the observed behaviour. Martin et al.231 and Jhansale and Topper232 later continued this line of research by applying their more general inelastic deformation models to treat mean stress relaxation in steels. Taira et al.233 independently performed some early investigations of mean stress relaxation during torsional fatigue of a plain carbon steel. More recent work on mean stress relaxation in steels has been reported by Gong and Norton234 and Lindgren and Lepistö.235

Mechanical deformation

One of the earliest studies of the cyclic stability of mechanically induced residual stresses was documented in a classic paper by Pattinson and Dugdale.236 They bent beams of mild steel or a hard aluminium alloy to a known curvature and then straightened them to introduce a controlled residual stress. Following various amounts of flexural cycling, the remaining residual stress in the beam was measured. Residual stress faded rapidly in the mild steel at low numbers of cycles, but fading was pronounced in the aluminium alloy only after about 107 cycles.

Gould and Pittella237 imposed a residual stress in 1100 Al by cold working and then measured the decay of this residual stress during double bending fatigue tests. Applied loads were relatively severe, and observed decreases in residual stress were substantial.

Radhakrishnan and Prasad238 applied a tensile pre-strain to axial specimens of 0.23% C steel to generate a residual stress due to differences in deformation between surface and core. Relaxation of this residual stress during subsequent R= 0 fatigue cycling was observed to follow a power-law relationship with respect to the logarithm of the elapsed cycles.

Underwood et al.239 induced residual stresses in bend specimens of a nickel–chromium–molybdenum steel by localized plastic indentation, and then performed fatigue crack growth tests. Residual stress redistribution due to the effects of notching and crack extension had to be addressed to obtain accurate analyses.

Almer et al.135,136 studied the effects of residual stresses induced by pre-strain on fatigue crack initiation and growth in 1080 steel. Microscopic (localized) residual stresses faded rapidly and had little impact on fatigue behaviour. Macroscopic residual stresses were more significant for fatigue, especially as their fading and/or redistribution interacted with fatigue crack growth.

DISCUSSION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

It is clear from the sheer volume of this survey that a great deal has been observed, measured, modelled and learned during the past 50 years about the stability of residual stresses in many engineering metals. The major sources of induced and inherent residual stress—peening and related surface treatments, cold expansion of holes, welding and machining—have all received appropriate levels of attention, although a few specialized combinations of factors (e.g., cyclic relaxation of residual stresses from cold expansion of holes in engine materials at elevated temperature) have not been investigated in any depth.

The body of knowledge, while extensive, has not yet provided definitive observations, explanations and models for all relaxation phenomena. Nevertheless, a critical reading of the literature incorporated in this survey leads naturally to a series of general observations and conclusions that should provide a solid foundation for further study, model development and practical implementation.

First of all, it is clearly important to discern and separate the different relaxation phenomena. Residual stress relaxation can occur due to thermal effects, static mechanical load effects, cyclic load effects and crack extension effects. The specific mechanisms are different for each of these different effects, and the various effects often superimpose. For example, the first cycle of fatigue loading often induces static relaxation effects, while subsequent load reversals can induce cyclic relaxation effects. Fatigue cycling at elevated temperature can invoke both thermal and cyclic phenomena. A failure to discern and separate these different effects can lead to some confusion, and some researchers appear to have fallen victim to such confusion. From a more positive perspective, discernment and separation of the different phenomena facilitate simpler and more accurate modelling of each individual effect, and these simple models can be superimposed in some situations.

The available literature provides some general insight into the significance of the various relaxation phenomena. For example, thermal relaxation effects do not appear to be extremely large for most practical application temperatures for common engineering metals. Some academic studies subjected materials to temperatures greater than their normal operating envelope and observed substantial relaxation, but relaxation at normal operating temperatures tended to be moderate.

Static relaxation effects appear to be relatively easy to identify and characterize based on knowledge of the initial residual stress field and the applied service loading. In general, compressive loading tends to relax beneficial compressive residual stress fields in proportion to the magnitude of the applied loading. Tensile loading typically has no effect on compressive residual stresses unless the applied loads are so large as to cause yielding when superimposed with the self-equilibrated tensile residual stress fields.

Many of the pronounced cyclic relaxation effects identified in the literature appear to be static effects on the first loading cycle (compressive loads relaxing compressive peening residual stresses, or tensile loads relaxing tensile welding residuals, for example). Once these static effects are set aside, the remaining true cyclic relaxation tends to be gradual and moderate unless the applied fatigue stress amplitudes are large. However, no generalized quantitative criterion appears to be available yet to characterize “moderate” and “large” in this last statement.

The effects of crack extension on tensile residual stress fields are relatively easy to identify and understand. The effects of crack extension on compressive fields are not so clear and require further study. Only limited data are available to suggest that such an effect even exists.

No effort was made in this survey to perform a quantitative evaluation of the various models that have been proposed to characterize or predict thermal, static, cyclic or crack extension effects on residual stress. However, some general observations are in order. Simple thermal activation models have been developed to treat thermal relaxation effects, although their generality and truly predictive nature has not yet been established. It should not be difficult to formulate a general treatment of static relaxation based on simple mechanics arguments (superposition of two known stress fields and comparison with an established cyclic yield criterion). This does not appear to have been done yet outside of simple, idealized profiles or a general finite element treatment. Empirical models may be useful for focused, well-characterized cyclic relaxation problems. The more general numerical models proposed for cyclic relaxation are encouraging but require some further detailed study to evaluate their practicality. Tractable models have been proposed for relaxation of tensile residual stresses due to crack extension, but no well-established theory has yet been laid out for crack extension effects on compressive fields.

The available evidence suggests that, in practical engineering applications, induced residual stresses due to cold expansion, peening or related manufacturing techniques rarely relax fully to zero. Although some relaxation commonly occurs due to one or more mechanisms, and so final residual stress fields are rarely the same as the initial stress fields, some significant fraction of the initial residual stress field often remains at the end of the relevant fatigue exposure. Static effects appear to be the most deleterious, and these should be easily predictable in most cases. Most of the severe degradation of residual stresses reported in the literature appears to be attributable to unrealistically severe thermal or mechanical loading conditions.

Having said that, characterizing and employing the correct residual stress field is essential for accurate life modelling. It is clear that residual stress effects on S-N lifetimes and fatigue crack growth lives can be very substantial. A life prediction based on an incorrect assumption about residual stress may be seriously in error. In view of the uncertainties associated with residual stresses, appropriately conservative assumptions are in order. Some further investigation of the probabilistic aspects of residual stress analysis appears to be warranted.

Established methods for modelling the growth of fatigue cracks in residual stress fields using weight function stress intensity factors and superposition techniques appear to provide satisfactory accuracy in many cases. Special attention must be given to the effects of stress ratio on crack growth, and appropriate crack closure methods may also be satisfactory for this purpose. Several issues can complicate the analysis and may require further attention, including the multi-dimensionality of stress fields, non-elliptical crack shapes and crack face contact.

Finally, it is important to remember that the effects of peening and related techniques, cold expansion, welding and machining on fatigue behaviour are not limited to residual stress effects, and this is especially true for S-N behaviour. The same manufacturing processes that induce residual stresses can also influence the surface quality, microstructure and material condition, all of which may independently influence fatigue life. Residual stress effects appear to be dominant for many fatigue crack growth problems, but this may require experimental confirmation. The most significant complication in fatigue crack growth is perhaps the possibility of substantial changes in the stable fatigue crack shape, which can greatly complicate the accurate characterization of the stress intensity factor and hence the accurate prediction of FCG rate.

Acknowledgement

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES

This work was supported by the Federal Aviation Administration (FAA) under Grant 99-G-016. Joe Wilson (FAA Technical Center project manager) and Tim Mouzakis (FAA Engine and Propeller Directorate) are thanked for their sustained encouragement. Many researchers graciously provided information in support of the survey, including (in alphabetical order) Dale Ball, Dennis Buchanan, Lyndon Edwards, Reji John, Paul Prevéy, Rob Ritchie, Volker Schulze, Danut Stefanescu, Jack Telesman, and Wyman Zhuang. Alberta Matthews provided exceptional clerical support in the preparation of the bibliography and manuscript.

Figure 1 is reprinted with the permission of ASME International. Figure 4 is © TMS (The Minerals, Metals, and Materials Society), Warrendale, PA, and is reprinted with the permission of TMS. Figures 6 and 7 are reprinted with permission of ASM International®, all rights reserved (http://www.asminternational.org). Figures 9, 10 and 15 are reprinted with permission from Elsevier. Permission to reproduce Figs. 11, 13, 16 and 17 is granted by the Council of the Institution of Mechanical Engineers. Figures 12 and 14 are reprinted with permission from Blackwell Publishing. Figures 18 and 19 are reprinted with the kind authorization of the International Institute of Welding (IIW).

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. PEENING AND RELATED SURFACE TREATMENTS
  5. COLD EXPANSION OF HOLES
  6. WELDING
  7. MACHINING
  8. OTHER PROCESSES
  9. DISCUSSION
  10. Acknowledgement
  11. REFERENCES
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