February 2015 

NASA/TM–2015-218685 

Characterization of Residual Stress Effects on 

Fatigue Crack Growth of a Friction Stir Welded 

Aluminum Alloy 

John A. Newman and Stephen W. Smith 

Langley Research Center, Hampton, Virginia 

Banavara R. Seshadri 

National Institute of Aerospace, Hampton, Virginia 

Mark A. James, Richard L. Brazill, and Robert W. Schultz 

Alcoa Technical Center, Acola Center, Pennsylvania 

J. Keith Donald and Amy Blair 

Fracture Technology Associates, Bethlehem, Pennsylvania 
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February 2015 

NASA/TM–2015-218685 

Characterization of Residual Stress Effects on 

Fatigue Crack Growth of a Friction Stir Welded 

Aluminum Alloy 

John A. New and Stephen W. Smith 

Langley Research Center, Hampton, Virginia 

Banavara R. Seshadri 

National Institute of Aerospace, Hampton, Virginia 

Mark A. James, Richard L. Brazill, and Robert W. Schultz 

Alcoa Technical Center, Acola Center, Pennsylvania 

J. Keith Donald and Amy Blair 

Fracture Technology Associates, Bethlehem, Pennsylvania
Available from: 

NASA STI Program / Mail Stop 148 

NASA Langley Research Center 

Hampton, VA 23681-2199 

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Space Administration. 
1

Abstract

An on-line compliance-based method to account for residual 

stress effects in stress-intensity factor and fatigue crack growth 

property determinations has been evaluated. Residual stressintensity factor results determined from specimens containing 

friction stir weld induced residual stresses are presented, and the 

on-line method results were found to be in excellent agreement 

with residual stress-intensity factor data obtained using the cutcompliance method. Variable stress-intensity factor tests were 

designed to demonstrate that a simple superposition model, 

summing the applied stress-intensity factor with the residual 

stress-intensity factor, can be used to determine the total crack-tip 

stress-intensity factor. Finite element, VCCT (virtual crack closure 

technique), and J-integral analysis methods have been used to 

characterize weld-induced residual stress using thermal 

expansion/contraction in the form of an equivalent T (change in 

local temperature during welding) to simulate the welding process. 

This equivalent T was established and applied to analyze 

different specimen configurations to predict residual stress 

distributions and associated residual stress-intensity factor values.

The predictions were found to agree well with experimental results 

obtained using the crack- and cut-compliance methods. 

Introduction

The increased use of integral structures has been identified as critical for the development of 

improved aerospace structures [1]. Integral structures reduce the use of rivets and the need to 

create lap joints, the primary sources for the initiation of multi-site fatigue damage in airframe 

structures [2]. Additionally, the replacement of traditional riveting approaches permits modular 

fabrication of large sections of the airframe, which can result in reduced construction time, cost 

and weight. One primary method being examined to produce and join large modular sections of 

aluminum structure is solid state welding. Of particular interest to the aerospace industry is the 

use of friction stir welding (FSW), a solid-state process well suited for joining aluminum alloys. 

However, the residual stresses that result from FSW create complex crack propagation 

challenges, making it difficult to make accurate fatigue life predictions. This paper will explore a 

method to quantify residual stress for welded materials and explain how this information can be 

used to improve fatigue life predictions. Results are presented from multiple laboratories –

NASA Langley Research Center (herein referred to as LaRC), Alcoa Technical Center (Alcoa), 

and Fracture Technologies Associates (FTA) – to show repeatability of results.

Although friction stir welding is a solid-state process (meaning that it does not result in the 

local melting of material), there is sufficient heating and mechanical work to result in residual 

stress within welded components. The residual stress distribution about a friction stir weld in 

aluminum alloy (AA) 2024-T351 was characterized utilizing a hole-drilling method [3]. In this 

study, a tensile residual stress was observed along the centerline and a steep residual stress 

gradient existed perpendicular to the weld direction. Near the edge of the weld nugget, the 

residual stress was observed to decrease rapidly, becoming compressive and approaching zero 

further away from the nugget. Parallel to the weld direction, little change in the residual stress 
2

was observed, suggesting a consistent process as the weld advances. In addition to residual 

stress gradients, gradients of hardness and microstructure, specifically grain size, were also 

observed [3].

A tensile residual stress normal to a growing crack path will result in increased crack growth 

rates, while a compressive residual stress can dramatically reduce crack growth rates due to 

crack closure, even resulting in crack arrest [3-5]. In a weldment, which can exhibit large 

variations in residual stress as well as microstructure, residual stress has been shown to affect 

crack growth rates to a greater extent than the microstructural variations [3, 6-8].

The development of accurate fatigue life predictions requires the generation of appropriate 

fatigue crack growth rate data using mechanical test specimens. However, when a mechanical 

test specimen is extracted from a structure or a larger product containing residual stress, the 

residual stress will redistribute, resulting in a residual stress field in the test specimen that is 

very different from that within the structure [9]. Since residual stress can have a profound effect 

on fatigue crack growth [6-8], the use of data generated from a test specimen may not be 

appropriate to predict structural fatigue life. Further complicating this issue is the fact that the 

residual stress in a cracked body redistributes as the crack propagates, resulting in a variable 

effect [9]. This crack-induced residual stress redistribution will be different for a test specimen 

(depending upon the type of loading) than for a structure, particularly if the crack path simulated 

in the test specimen is not consistent with that produced for an in-service structure. 

In the examples described above, the residual stress is thought to bias both the property 

determination and the structural response. A more rigorous approach is to properly account for 

the residual stress effects on the crack driving force in both the property determination and the 

structural evaluation – that is, to separate the residual stress effects from the specimen during 

property determination for true fatigue crack growth (FCG) property data and to reintroduce the 

appropriate residual stress effects in the structural evaluation. As noted, the residual stress in a 

coupon excised from a structure will have different residual stress than the structure due to 

redistribution (from coupon removal), and crack growth testing likely also causes redistribution 

in the coupon. Other methods could be applied where the residual stress is measured in the 

specimen and then combined with analysis to evaluate efficacy; however, most methods are 

either destructive (e.g. slitting, hole drilling, etc.) and thus affect the residual stress distribution 

or are difficult to apply and costly for bulk residual stress in aluminum alloy materials (e.g. 

neutron diffraction).

This paper demonstrates a new in-situ test method [10] for the measurement of residual 

stress-intensity factor at a crack tip during fatigue crack growth rate testing. The method shows 

great promise as a tool for partitioning the residual stress effects that occur during FCG testing

on common specimens such as the compact or middle tension specimens. In combination with 

the new test method, the paper outlines a computational methodology that could be applied to 

quantify the residual stress distribution and fatigue life performance of a welded structure using 

the data obtained from a test specimen. Much of this work was presented at the Residual 

Stress Summit 2010 [11]. The experimental work presented here is similar to that subsequently 

studied by Olson and Hill [12].

Use of Compliance to Experimentally Determine Residual Stress-Intensity Factor

Compliance is a relationship of displacement at some location on a mechanical test 

specimen as a function of applied force and is a versatile tool for fatigue and fracture testing. 
3

Compliance-based measurements have been used to determine crack length [13] and closure 

loads [14, 15]. In this paper, the crack-compliance method [10] is demonstrated as a viable 

approach to determine the residual stress-intensity factor as a function of crack extension. 

Figure 1 is a schematic of a load-versus-displacement curve that represents compliance 

change during crack growth. Nonlinear effects such as crack closure have been omitted for 

clarity. As a crack grows in a residual stfor the ress free body, the compliance increases, but the 

displacements at zero load always return to the same value, as indicated in Figure 1. However, 

when the body has residual stress, the body load is redistributed as the crack grows, and this 

redistribution is reflected in a displacement translation, which in the sketch appears as a res

shift to the right denoting residual stress presence that acts to open the crack. Donald and 

Lados [10] showed that as a crack propagates through a residual stress field, there is a nonproportional effect as residual stresses are relieved, resulting in a shift of the load-versusdisplacement curve, residual (also illustrated in Figure 1). (Note that if crack closure is 

influencing the compliance data, the slope of the elastic portion of the load displacement curves 

(above the crack opening load) must be used.) Donald and Lados [10] showed that the residual 

stress-intensity factor during this increment of crack growth can be expressed as,



















max

max Δδ

Δδ K K

residual

residual

,

where Kmax is the maximum applied stress-intensity factor, Kresidual is the residual stress-intensity 

factor, residual is the shift in the crack opening displacement due to non-proportional residual 

stress effects, and max is the change in crack opening displacement due to crack growth. A 

more complete discussion of this method is given elsewhere [10]. 

Use of Computational Methods for Residual Stress Modeling

Computational methods have an essential role for integrating residual stress into a structural 

analysis because residual stress measurements are complex, expensive, and most importantly, 

usually limited to selected locations in a component. Often measurements are simply not 

feasible at critical locations of interest. As a result, a viable strategy for design analysis with 

residual stress is to use experiments to validate a residual stress model at selected locations in 

a component and in related components, then to use the validated model to predict the residual 

stress at the locations of interest for the component.

A variety of computational methods have been developed to estimate residual stress effects 

in structures. Broadly, the methods can be broken down into methods for estimating the 

residual stress in the body and methods for estimating the stress-intensity factor for a crack in a 

residual stress field. Some techniques have been developed using the weight function method

[16, 17], or finite element analysis using the least squares technique [18-20]. Previous efforts 

on this topic have focused on importing experimentally-determined residual stress data into 

FEM models [19, 20]. Neutron diffraction has been used for measurement of residual stresses 

in various types of materials [21] and specimen types [22, 23], and Liljedahl, et al., [22-24] used 

the neutron diffraction method and FEM to characterize the residual stresses in a welded 

aluminum alloy. The stress distribution was measured using the neutron diffraction technique 

which was input into the FE model as initial stress and allowed to equilibrate.
4

Load, P

Crack opening displacement, 

P

op

P

min

P

max

P

0



residual



max

Previous 

crack

length



res

New crack length

(No residual stress)

New crack length

(With residual stress)

Figure 1. Schematic of displacement data used for the crack-compliance method to determine residual 

stress.

The approach used here is often called the inherent strain method (also called Eigen-strain 

method) and was outlined by Hill and Nelson and others [25, 26, 27]. A similar approach was 

outlined by Liljedahl [22-24] to determine weld-induced residual stresses. 

Equivalent thermal loads are evaluated by defining initial strain due to welding along the 

length/width of the weld region. Using the elastic modulus, E, coefficient of thermal expansion, 

and change in temperature, T, equivalent thermal loads are calculated to produce the 

residual stress field. Conceptually, the residual stress field is determined by modeling the 

heating of the entire weldment volume to some temperature and then cooling to room 

temperature. The temperature change, T, is calibrated by comparing the predicted residual 

stress field to that measured for coupon test data. For a specific combination of material type 

and welding process, the same T may be used to predict the residual stress field for other 

configurations (specimen type, component, or panel size and shape) that contains a weld 

produced in the same manner as that used to calibrate the value of T. Note that a variety of 

limitations exist. The conceptual model assumes that the temperature history and cooling rates 

as well as the transient material response are equivalent for the original calibrated case and the 

predicted case. For instance, if the structural heat capacity is different due to the size of the 

structure, then the cooling rates could be different, which could affect the residual stress 

calibration. However, this simple linear elastic cooling model has worked well for many cases. 

In the current work, rather than directly comparing computational results to the residual stress 

field, the authors compare model-based calculated stress-intensity factor results with the 

experimentally determined Kresidual value (stress-intensity factor due to residual stress loading) 

as a function of crack length. Thus, the residual stress prediction is implicitly validated and the 

concept of residual stress-intensity factor and effect of stress redistribution with crack growth 

are validated directly.
5

Experimental Test Methods

To examine the residual stress produced from friction stir welding, an AA2024-T351 plate

was sectioned into three pieces and two butt welds were produced to create a single piece 

containing two parallel welds. The plate was initially 1 inch thick, but 0.25 inch was removed 

from both the top and bottom faces prior to welding, reducing the weld nugget size and 

satisfying the limitations for the FSW machine used in this study. Subsequent to welding, an 

additional 0.125 inch was removed from both the top and bottom faces to produce a more 

uniform through-the-thickness weld configuration in the welded plate (see Figure 2). Standard 

compact (C(T)) specimens, having width and thickness dimensions of 4.0 inches and 0.25 inch, 

respectively, were machined from the welded plate in the T-L orientation (loading in the long 

transverse direction and crack growth in the longitudinal direction), as shown in Figure 3a. 

Three configurations of specimens were machined from the AA2024-T351 material. Two of 

these configurations were machined such that the weld was in a different location within the 

specimen (see Figure 3b). Specifically, one configuration was designed such that the crack 

growth would initially occur in a tensile-dominated residual stress field and the other in a 

compressive-dominated residual stress field. The third configuration was machined from the 

base AA2024-T351 material and contained no weld. Note that only the component of residual 

stress normal to the crack plane (perpendicular to the loading direction) are used to characterize 

specimens as being either tensile-dominated or compression-dominated. While this approach 

seems reasonable for the relatively simple geometry considered, the effect of the full stress 

tensor should be considered in general [28]. 

Figure 2. Through-the-thickness schematic of FSW material.

Residual Stress-Intensity Factor Determination

A variety of techniques are documented in the literature to quantify residual stresses where 

the part being examined is altered by cutting, drilling, or some other destructive process [29-33]. 

In the current study, the cut-compliance method will be used because it produces data that can 

easily be transformed to calculate the residual stress-intensity factor of interest for this work. 

The results from this method will be compared to the new crack-compliance approach that is 

being evaluated in this study [10]. 

0.50 inch weld 0.25 inch
6

(a)

2.400"

2.500" 0.060"

2.000"

0.550"

0.400"

0.550"

hole diameter

0.800"

Hole dia. = 1.00 (2 places)

0.125”

4.00

5.00

1.10

1.10

4.80

0.25

2.00

(b)

3.96 

inches

2.90

inches

compressive

tensile

Figure 3. (a) Schematic of the compact tension specimen configuration used for this study. (b) The FSW

location within two specimen configurations are shown. All dimensions shown are in inches.
7

Cut-compliance Method

The cut-compliance method is described in detail elsewhere [29, 30], but is outlined here for 

convenience. Typically, specimens are cut (in a series of small increments) from the edge of 

the specimen along the direction of interest, which in this case is the anticipated crack growth 

direction for the C(T) specimens. After each cut increment, the change in strain is measured at 

predetermined locations. In the simplest case using Schindler’s method [29], the strain is 

measured at the specimen back-face, and the residual stress-intensity factor is calculated 

directly from the measured strain gradient without explicitly calculating the residual stress field. 

Prime [30] outlines additional methods where the residual stress is calculated and then the 

residual stress-intensity is calculated from the residual stress field, and the strain gages need 

not be at the specimen back face (to increase strain measurement sensitivity). For the current 

work, the strains were converted to the residual stress-intensity factor using Schindler’s method 

[29]. The typical cut increment was 0.078 inches, and a wire electrical discharge machining 

(EDM) process was used to produce the cut to minimize the potential for mechanical forces 

imparted on the specimen. Cut-compliance measurements were performed on specimens of 

the same overall dimensions and orientation as the C(T) specimens used for FCG testing 

(including pre-machined holes) but did not contain a pre-machined notch. 

Crack-compliance Method

The crack-compliance method is similar to the cut-compliance method, but new surface area 

is created via fatigue loading and fatigue crack growth rather than EDM slitting [10]. Here, 

compliance data are measured to determine crack length and the residual stress-intensity factor 

during automated fatigue crack growth (FCG) testing as described above. The crackcompliance method has the advantage of producing both residual stress-intensity factor data 

and crack growth data simultaneously. The method works equally well with either front-face 

clip-gage-based compliance or with back-face strain-gage-based compliance.

Fatigue Crack Growth Rate Testing

Fatigue crack growth rate testing, in accordance with ASTM standard E 647 [13], was 

performed on specimens with and without friction stir welds. All fatigue crack growth rate tests 

were performed utilizing computer-controlled servo-hydraulic load frames. A front-face clip 

gage was monitored during fatigue loading and the compliance data are analyzed to determine 

crack length and residual stress-intensity factor. The applied force was modified as a function 

of crack length to control the applied stress-intensity factor, which is also known as K-control 

testing. This allows a constant cyclic stress-intensity factor, constant-K, or a pre-determined 

variable-K to be applied to the specimen.

The ASTM E 647 test standard does not have provisions for residual stress, and as a result, 

assumes that the total crack-tip stress-intensity factor is equal to the applied stress-intensity 

factor. However, in the current work it is necessary to distinguish between applied, residual and 

actual crack-tip stress-intensity factors. For the purposes of this paper the following convention 

is used: “Applied” stress-intensity factor is the value calculated from the E 647 equations based 

on the applied force. “Residual” stress-intensity factor is the value due to residual stress. “Tip”

stress-intensity factor is the total value at the crack tip due to all body stresses acting on the 

crack (residual and applied). 
8

Constant Applied K Testing

Fatigue crack growth tests were performed under constant applied-K conditions. When the 

resulting test data are plotted as crack length versus cycle count, the slope of these data is the 

crack growth rate, da/dN. Constant applied-K test results for compression-dominated and 

tensile-dominated specimens are shown in Figure 4, plotted as crack growth rate (da/dN) versus 

crack length (a). In the absence of a residual stress field, the da/dN would be expected to 

remain constant; however, the variable growth rates presented in Figure 4 are a direct result of 

residual stress. 

The tensile-dominated data plotted in Figure 4 were generated at applied K = 13.5 ksiin 

and a load ratio of R = 0.11. The crack growth rate from the crack starter notch (approximately 

1.0 inch long) was nearly constant (da/dN approximately 1x10-5inches/cycle) until reaching a 

crack length of nearly 2.5 inches. As the crack approached the weld (starting at a crack length 

of approximately 2.8 inches), the crack growth rate decreased as Kresidual became compressive. 

The minimum value in da/dN (approximately 10-7inches/cycle) occurred at a crack length of 

nearly 3.1 inches, suggesting a maximum compressive Kresidual at that crack length. 

The compression-dominated data plotted in Figure 4 were started at applied K = 9.0 ksiin 

and R = 0.1. The crack growth rate from the crack starter notch (approximately 1.0 inch long) 

was approximately da/dN = 3x10-6inches/cycle, but rapidly decreased until crack arrest 

occurred at a crack length of nearly 1.5 inches. The applied loading was increased to obtain 

applied K = 13.5 ksiin (R = 0.1) which permitted an additional 0.25 inch of crack propagation 

before crack arrest occurred again. This behavior suggests that the crack is growing within an 

increasingly compressive residual stress field as the crack propagates.

Residual stress-intensity factor data for the tensile-dominated and compression-dominated 

specimen configurations are shown as Figures 5a and 5b, respectively. Testing was conducted 

by three laboratories (Alcoa, LaRC, and FTA) as indicated in the legend. Cut-compliance test 

results (performed at Alcoa) are shown as lines, and crack-compliance test results (performed 

at LaRC and FTA) are shown as symbols. Here, results are presented as the residual stressintensity factor, Kresidual, using the procedures described previously. Excellent agreement is 

observed between all sets of data, suggesting that the experimentally obtained residual stressintensity factor values are independent of test method or laboratory. 

As seen in Figure 5a, the tensile-dominated residual stresses are nearly zero at zero crack 

length (coinciding with the centerline of the pin holes) and gradually increase to a maximum 

Kresidual value of approximately 10 ksiin (tensile) near a crack length of 1.75 inches. Kresidual

decreases with further increase in crack/cut length to a minimum value of nearly -10 ksiin 

(compressive) near a crack length of 3.0 inches. The decreasing residual stress-intensity factor 

values are consistent with the crack length interval in which da/dN is observed to decrease in 

the tensile-dominated specimen presented in Figure 4. As the crack (or cut) reaches the edge 

of the weld (at a crack/cut length of approximately 3.5 inches), the Kresidual is nearly zero.

 

1 The load ratio, R, is defined as the ratio of the minimum to maximum values of applied load (Pmin/Pmax).
9

Figure 4 – Fatigue crack growth rate versus crack length for constant-K tests of tensile and 

compressive-dominated C(T) specimens. Data were generated at NASA Langley Research Center.

The Kresidual profile for the compression-dominated specimen (Figure 5b) is nearly zero at 

zero crack length, and gradually decreases (increasing compressive stress) with increasing 

crack length. The greatest value of Kresidual is approximately -20 ksiin (compressive), occurring 

near a crack length of 2.1 inches. The edge of the weld is at a crack/cut length of approximately 

2.3 inches. As the crack/cut progresses across the weld, the Kresidual values become less 

compressive and eventually become tensile as the crack/cut exits the weld at a crack length of 

approximately 3.3 inches. At this point in the tests, the crack-compliance and cut-compliance 

tests diverge, presumably due to the crack-tip plastic zone approaching the size of the 

remaining ligament on the specimen resulting in linear-elastic fracture mechanics being invalid. 

Note that both the cut-compliance and crack-compliance methods are subject to linear elasticity 

limitations. However, the crack-compliance method seems to be more prone to plasticity in this 

circumstance. It may be that the finite applied loads of the crack-compliance method create 

increasing plasticity effects in the small remaining specimen ligament as the crack tip 

approaches the back face of the specimen. The cut-compliance specimen has no externally 

applied loads, and as the ligament becomes small, the residual stress is relaxed to zero 

minimizing the plasticity effects.

Crack length, a (inch)

1.0 1.5 2.0 2.5 3.0 3.5

da/dN

(inches/cycle)

10-9

10-8

10-7

10-6

10-5

10-4

tension-dominated

compression-dominated

Kapp. = 13.5 ksiin

Kapp. = 9.0 ksiin

Kapp. = 13.5 ksiin

R = 0.1
10

(a) Tensile-dominated (b) Compression-dominated

Figure 5 – Experimental results from cut-compliance and crack-compliance test methods.

Constant Crack-Tip K Testing

Additional FCG testing was conducted to determine the effect of linear elastic superposition 

of the applied and residual stress-intensity factor. Using the premise that total crack-tip loading 

is a superposition of a non-cyclic Kresidual (recall Figure 5) onto the applied cyclic loading; tests 

were designed to maintain a constant cyclic crack-tip stress-intensity factor. Presumably, a 

constant crack growth rate, da/dN, can be maintained by compensating for the mean stress 

effect induced by the residual stresses. Based on the Kresidual profile of Figure 5a, a variable 

Kapplied test was designed to achieve a constant-Ktip state for the tensile-dominated specimen. 

The Kmax and R required to produce a constant-Ktip = 9 ksiin at R = 0.55 are plotted in Figures 

6a and 6b, respectively. In a similar manner, a constant-Ktip = 6.75 ksiin at R = 0.55 test was 

designed for compressive-dominated specimens and the corresponding Kmax and R values are 

plotted in Figures 7a and 7b, respectively. The applied K and R values were selected to insure 

that the applied Kmax would always be less than the fracture toughness of the base material. 

The fatigue crack growth rate data for tensile-dominated and compression-dominated 

specimens are plotted in Figures 8a and 8b, respectively, as crack length versus cycle count. A 

constant slope of these data corresponds to a constant crack growth rate. During the test of the 

tensile-dominated specimen, the crack growth rate remains nearly constant as the crack 

propagated across the entire specimen. A slight deviation in crack growth rate was observed at 

a crack length greater than 3.0 inches (note, the deviation from the dotted line in Figure 8a), 

possibly a result of local changes in the material microstructure and yield strength near the 

weld. The deviation from a constant FCG rate in Figure 8a corresponds to the largest gradients 

in the residual stress-intensity factor (Figure 5a). However, the change in growth rate is much 

less than those observed for the applied constant-K tests for the tensile-dominated specimen 

(Figure 4), suggesting that the effect of residual stress is much greater than any effect due to 

variation in material microstructure.

Crack length (inches)

0 1 2 3 4

Kresidual (ksiin)

-25

-20

-15

-10

-5

0

5

10

15

Crack (LaRC)

Crack (FTA)

Crack (Alcoa)

Cut (Alcoa)

Cut (Alcoa)

Crack length (inches)

0 1 2 3 4

Kresidual (ksiin)

-25

-20

-15

-10

-5

0

5

10

15 Crack (LaRC)

Crack (FTA)

Crack (Alcoa)

Cut (Alcoa)

Cut (Alcoa)
11

(a) K values (b) R values

Figure 6 – K and R values needed to maintain constant Ktip = 9 ksiin and Rtip = 0.55 for tensiledominated specimens.

For the constant-Ktip test on the compression-dominated specimen (Figure 8b), a nearly 

constant crack growth rate is observed up to a crack length of approximately 2.4 inches, which 

is nearly the same crack length as that corresponding to the peak applied loads. After this point 

in the test, a significant amount of crack closure was observed, likely causing the reduction in 

crack growth rate (slope of the curve). 

Crack length, a (inch)

Applied Kmax values to maintain Ktip = 20 ksiin

Crack length, a (inch)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

K (ksiin)

-10

-5

0

5

10

15

20

25

30

35 Kmax applied

Kresidual

Kmax tip

Applied R values to maintain Rtip = 0.55

Crack length, a (inch)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

R

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

R applied

R tip

weld

weld
12

(a) K values (b) R values

Figure 7 – K and R values needed to maintain constant Ktip = 6.75 ksiin and Rtip = 0.55 for 

compression-dominated specimens.

 (a) Tensile-dominated specimen (b) Compressive-dominated specimen

Figure 8 – Crack length versus cycle count data for Constant-Ktip condition tests.

Cycle count (x 1,000)

0 200 400 600 800 1000

Crack length, a (inches)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Cycle count (x 1,000)

0 50 100 150 200 250 300

Crack length, a (inches)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Slight deviation in crack

growth rates near weld

Reduction in da/dN

due to crack closure

Peak Kmax applied

weld weld

Applied Kmax to achieve tip loads of 

Kmax tip = 15 ksiin, Rtip = 0.55

Crack length, a (inches)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

K (ksiin)

-20

-15

-10

-5

0

5

10

15

20

25

30

35

Applied R to achieve tip loads of 

Kmax tip = 15 ksiin, Rtip = 0.55

Crack length, a (inches)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

R

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

weld

weld

Kmax applied

Kresidual

Kmax tip

R applied

R tip
13

The crack growth rates obtained for the tensile-dominated specimen (Figure 8a; 1.25 inches 

< a < 2.30 inches) and the compression-dominated specimen (Figure 8b; 1.25 inches < a < 2.75 

inches), are compared with constant-R = 0.55 FCG data for the base material (no weld; 

nominally free of residual stresses) in Figure 9. FCG testing of the base material was done in 

accordance with ASTM standard E647 [13], using a K-reduction (C = -2/inch) for applied K < 

6.75 ksiin, and a K-increasing test (C = +5/inch) for applied K > 6.75 ksiin. Excellent 

agreement is observed between the base material results (open symbols) and the constant-Ktip

data (closed triangular symbols). This observation suggests that residual stresses affect the 

crack-tip stress state as a superimposed non-cyclic component that acts similar to a mean 

stress, Ktip = Kapplied + Kresidual. 

Figure 9 – Comparison of constant-Ktip fatigue crack growth rate data for tensile and compressivedominated specimens with FCG data for baseline specimen.

Computational Study

Computational results are compared with experimental data from both cut-compliance 

(Alcoa) and crack-compliance (LaRC, Alcoa, and FTA). Here, the cut and crack-compliance 

methods produce a Kresidual profile as a crack grows, while the thermal load method results in a 

profile of residual stress for an uncracked body. Therefore, it is necessary to perform a 

numerical simulation to determine the resultant Kresidual for a growing crack in the estimated 

residual stress field, or alternatively, to determine the residual stress field that would produce 

the Kresidual profile measured using the cut- and crack-compliance methods. 

Stress-intensity factors were calculated using the virtual crack closure technique (VCCT) [34-

36] and J-integral [37] methods. The virtual crack closure technique was proposed for 2D crack 

R = 0.55

K (ksiin)

2 3 4 5 6 8 10 15 20

da/dN (inches/cycle)

10-9

10-8

10-7

10-6

10-5

10-4

Baseline data

FSW Constant-Ktip tests

Tension-dominated

specimen

Compression-dominated

specimen
14

configuration by Rybicki and Kanninen [34] and was extended to three dimensions (3D-VCCT) 

by Shivakumar, et al., [35]. The J-integral represents a way to calculate the strain energy 

release rate, or work (energy) per unit fracture surface area, in a material. The theoretical 

concept of J-integral was developed by Rice [37] who showed that an energetic contour path

was independent of the path around a crack. In the current study, both the J-integral and 3DVCCT techniques have been used to generate residual stress-intensity factor solutions [36]. 

Compact (C(T)) specimens exhibit two planes of symmetry, and consequently, only one 

fourth of the geometry is used for modeling. Iso-parametric eight-node brick elements were 

used in the model. All analyses were for 0.25 inch thick specimens. The width of the C(T) 

specimen is 4.0 inches measured from the centerline of the loading holes. The C(T) finite 

element analysis (FEA) model consisted of a total of 3,270 nodes and 1,516 brick elements. A 

typical finite element model of the C(T) specimen is shown in Figure 10 where the red shaded 

elements correspond to the weldment. AA2024-T3 was considered for all analyses with 

modulus E = 10,000 ksi (assumed linear-elastic deformation response) and coefficient of 

thermal expansion,  = 13.0x10-6in/inoF. The change in T, from the welding temperature to 

room temperature, was first estimated and a residual stress distribution was determined. Three 

dimensional finite element simulations were then performed. The residual stress profile along 

the symmetry plane for tensile dominated C(T) specimen was then compared to the results 

obtained from the experimental methods and T was modified until sufficiently reasonable 

agreement was obtained. The change in temperature, T, in the weld zone due to the friction 

stir weld process was empirically estimated to be -200oF, by fitting the predicted residual stress 

profile distribution to the experimentally measured values for the tensile-dominated 

configuration. Note that the value of T is negative as the weldment is at an elevated 

temperature during the processing, and the residual stress is a result of the weldment being 

cooled to room temperature. This same value of T was then applied to the analysis of the 

compressive-dominated specimen and the prediction results presented. 

Figure 10 – A typical finite element mesh for 4 inch wide C(T) specimen.
15

Crack growth simulations were then performed with crack increments of 0.4 inch. The Kresidual

at each increment was determined using VCCT technique [36, 37]. The calculated Kresidual profile 

was then compared to the results from the experimental methods. For the two weld locations 

(tensile-dominated and compression-dominated), Kresidual solutions were generated using the Jintegral and 3D-VCCT techniques [36, 37], and are shown in Figures 11 and 12. Both crackcompliance and cut-compliance experimental data are shown for comparison. The crackcompliance data are indicated by open and filled symbols and the cut-compliance data are 

represented by solid and dashed lines. In addition, a stress-intensity factor solution generated 

using the J-integral [37] method is represented by closed circles in Figure 11. The 

computationally-determined Kresidual solution generated using the VCCT technique (open 

squares in Figures 11 and 12) at various a/W values also compare well with experimental data. 

Figure 11 – Residual stress variation for tensile-dominated specimen. Experimental data are shown for 

comparison.

Crack length, a (inch)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Kresidual

, ksiin

-15

-10

-5

0

5

10

15

E = 10,000 ksi

T = -200 deg F

 = 13.0x 10 -6 in/in deg F

weld

FEA (ZIP3D)

Alcoa - spec.1

Alcoa - spec.2

LaRC

FTA

FEA (J-integral)

Cut-Compliance

Crack-Compliance

Analysis

(VCCT)
16

Figure 12 – Residual stress variation for compressive-dominated specimen. Experimental data are 

shown for comparison.

Discussion

Residual stresses in FSW coupons were determined experimentally using the wellestablished cut-compliance method and the relatively new crack-compliance method. Both of 

these test methods produced nearly identical residual stress-intensity factors, an indication that 

the crack-compliance test method produces valid results and is reproducible in different 

laboratories. The crack-compliance test has the inherent advantage of being conducted during 

an ongoing fatigue crack growth test such that fatigue crack growth rate data and residual 

stress-intensity data are obtained simultaneously. This advantage (over either FCG testing and 

cut-compliance testing as separate tests) is especially significant in cases where the available 

material for testing is limited or if significant variation in residual stresses may occur between 

specimens, such as from a die forging. Consider a scenario where the residual stress field 

varies between specimens; without crack-compliance testing, one specimen would be used to 

determine the residual stresses perpendicular to the crack path (cut-compliance) and another 

would be used to obtain FCG rate data. However, the use of multiple specimens and test 

methods to characterize the residual-stress-affected crack growth behavior requires specimento-specimen consistency in residual stress state. If significant differences in residual stresses 

exist between specimens, it would be difficult to accurately characterize the effect of residual 

stress on FCG using data obtained from multiple specimens.

The FSW specimens tested in this study were manufactured with a carefully-controlled 

welding process such that no significant residual stress differences existed between specimen 
17

types (i.e., all compressive specimens were nearly identical in terms of residual stress field). 

This observation permitted the constant-Ktip tests presented in this paper. Here, the Kresidual data 

obtained from a previous test were used to calculate applied loads such that the crack-tip would 

experience a nearly-constant stress state as the crack propagated across the specimen. This 

variable-applied-R test resulted in nearly constant crack growth rates, independent of the cracktip position with respect to the weld and independent of residual stress magnitude and 

associated Kresidual. Thus, the residual stress was shown to affect the crack tip much as an

increase in the (non-cyclic) mean stress whose value varies with the weld-induced residual 

stress field [38]. This observation allows laboratory results (determined from coupon testing) to 

be applied to larger structures for prediction of crack growth response.

A computational prediction of the weld-induced residual stress state was made based on 

thermal contraction/expansion of the weld material. A constant elevated temperature was 

assigned to the FSW in the absence of residual stress, and residual stresses were generated as 

the weldment was cooled to ambient conditions. Although the model was simple (linear-elastic 

material behavior and no variation in T across the weld region) and designed only to capture 

first-order effects, the predictions were in excellent agreement with the experimental data. The 

value of T was chosen to match the experimental result for one specimen configuration, and 

the same value of T was applied to another specimen configuration to predict a residual stress 

profile. Stress-intensity factors from the predicted profile were found to compare favorably with 

the experimental results for the original specimen configuration. It is believed that this model 

input (value of T) is primarily a function of the welding process, thus, coupon testing can be 

used (along with this modeling approach) to determine the residual stress state of a larger 

structure. With the combination of this computational approach and coupon test data, it is 

believed that the FCG response of large structures can be predicted. Specifically, the residual 

stress field of a complex geometry can be estimated using the equivalent T method, and its 

effect on fatigue crack growth predicted as an increase in crack-tip mean stress loading. 

Further study is required to fully validate this premise.

Finally, limitations of load redistribution and linear superposition are continual concerns in the 

fracture mechanics community. The testing here for the crack-compliance method and the 

variable-R provide experimental validation for linear superposition, and the results show that the 

crack-compliance method captures the load redistribution associated with crack growth as long 

as linear elastic fracture mechanics applies. However, as one might expect, crack-tip plasticity 

likely can invalidate results when the plastic zone is large relative to the remaining ligament for a 

given test specimen. Finally, although the crack compliance equation for the Kresidual calculation 

is remarkably simple, the sensitivity to data quality is very high. High quality Kresidual results 

require significantly better signal quality and algorithmic accuracy than are required for simple 

compliance crack length determination.

Summary

An experimental and computational study was conducted to determine residual stress effects 

on fatigue crack growth in aluminum coupons containing friction stir-weld (FSW) induced 

residual stresses. The effect of residual stress, calculated in terms of its contribution to the 

crack-tip stress-intensity factor, was obtained using a well-established cut-compliance method 

and a newly-developed crack-compliance method. Both test methods were found to produce 

nearly identical Kresidual results indicating that the new method (crack-compliance) delivers valid 

and accurate results. The on line crack-compliance method has the advantage of producing 

both conventional and residual-stress-corrected FCG data from a single test. Moreover, this 
18

method has the ability to partition and remove the residual stress contribution from the FCG test 

result.

FCG tests were conducted by continuously varying applied loads such that the combination 

of applied loading and residual stress resulted in constant crack-tip conditions (i.e., the 

superposition of applied and residual stress components of K is constant). This resulted in 

nearly constant fatigue crack growth rates, confirming that a constant cyclic crack-tip stress 

state was achieved, suggesting that the residual stresses affect FCG as a mean stress effect, 

and confirming linear superposition for the tested conditions (R >0). 

A thermal contraction/expansion model has been demonstrated to accurately predict residual 

stress distributions for specimens containing friction stir welds. Based on the results of the 

computational model for two configurations of welded coupons, this method is believed to be 

applicable to the prediction of FCG in welded both small and large structures. Further study is 

planned to validate this hypothesis.

Finally, the testing here for the crack-compliance method and the variable-R provide 

experimental validation for linear superposition, and the results show that the crack-compliance 

method captures the load redistribution associated with crack growth as long as linear elastic 

fracture mechanics applies.

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Characterization of Residual Stress Effects on Fatigue Crack Growth of a 

Friction Stir Welded Aluminum Alloy

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Newman, John A.; Smith, Stephen W.; Seshadri, Banavara R.; James, Mark 

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14. ABSTRACT

An on-line compliance-based method to account for residual stress effects in stress-intensity factor and fatigue crack growth property determinations has been 

evaluated. Residual stress-intensity factor results determined from specimens containing friction stir weld induced residual stresses are presented, and the 

on-line method results were found to be in excellent agreement with residual stress-intensity factor data obtained using the cut-compliance method. Variable 

stress-intensity factor tests were designed to demonstrate that a simple superposition model, summing the applied stress-intensity factor with the residual 

stress-intensity factor, can be used to determine the total crack-tip stress-intensity factor. Finite element, VCCT (virtual crack closure technique), and J-integral 

analysis methods have been used to characterize weld-induced residual stress using thermal expansion/contraction in the form of an equivalent ¿T (change in 

local temperature during welding) to simulate the welding process. This equivalent ¿T was established and applied to analyze different specimen 

configurations to predict residual stress distributions and associated residual stress-intensity factor values. The predictions were found to agree well with 

experimental results obtained using the crack- and cut-compliance methods. 

15. SUBJECT TERMS

Contraction; Crack closure; Fatigue; Friction; Residual concentration; Stress concentration; Thermal expansion; Welding

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