Next Article in Journal
Taguchi Optimization of Wetting, Thermal and Mechanical Properties of Sn-1.0wt.%Ag-0.5wt.%Cu Alloys Modified with Bi and Sb
Next Article in Special Issue
A Finite Element Model for Simulating Stress Responses of Permeable Road Pavement
Previous Article in Journal
Thermal Reactivation of Hydrated Cement Paste: Properties and Impact on Cement Hydration
Previous Article in Special Issue
Numerical Simulation of Lost-Foam Casting for Key Components of A356 Aluminum Alloy in New Energy Vehicles
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Materials
Volume 17
Issue 11
10.3390/ma17112656
materials-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Durability Analysis of Cold Spray Repairs: Phase I—Effect of Surface Grit Blasting

by
Daren Peng
1,2,
Caixian Tang
3,
Jarrod Watts
3,
Andrew Ang
1,
R. K. Singh Raman
2,
Michael Nicholas
4,
Nam Phan
5 and
Rhys Jones
1,2,*
1
ARC Industrial Transformation Training Centre on Surface Engineering for Advanced Materials, Faculty of Science, Engineering and Technology, Swinburne University of Technology, John Street, Hawthorn, VIC 3122, Australia
2
Centre of Expertise in Structural Mechanics, Department of Mechanical and Aeronautical Engineering, Monash University, Wellington Rd, Clayton, VIC 3800, Australia
3
Rosebank Engineering Australia, 836 Mountain Highway, Bayswater, VIC 3153, Australia
4
US Army Research Laboratory, U.S. Army Combat Capabilities Development Command Weapons and Materials Research Directorate, Aberdeen Proving Ground, Aberdeen, MD 20852, USA
5
Structures Division, Naval Air Systems Command, Patuxent River, MD 20670, USA
*
Author to whom correspondence should be addressed.
Materials 2024, 17(11), 2656; https://doi.org/10.3390/ma17112656
Submission received: 17 April 2024 / Revised: 22 May 2024 / Accepted: 28 May 2024 / Published: 31 May 2024
(This article belongs to the Special Issue Artificial Intelligence in Materials Science and Engineering)
Browse Figures
Versions Notes

Abstract

:
This paper presents the results of an extensive investigation into the durability of cold spray repairs to corrosion damage in AA7075-T7351 aluminium alloy specimens where, prior to powder deposition, the surface preparation involved grit blasting. In this context, it is shown that the growth of small naturally occurring cracks in cold spray repairs to simulated corrosion damage can be accurately computed using the Hartman–Schijve crack growth equation in a fashion that is consistent with the requirements delineated in USAF Structures Bulletin EZ-SB-19-01, MIL-STD-1530D, and the US Joint Services Structural Guidelines JSSG2006. The relatively large variation in the da/dN versus ΔK curves associated with low values of da/dN highlights the fact that, before any durability assessment of a cold spray repair to an operational airframe is attempted, it is first necessary to perform a sufficient number of tests so that the worst-case small crack growth curve needed to perform the mandated airworthiness certification analysis can be determined.

1. Introduction

Cold spray, also known as supersonic particle deposition (SPD), is increasingly being used to repair both rotary and fixed-wing aircraft [1,2,3,4,5,6,7,8,9,10]. However, as delineated in the United States Joint Services Structural Guidelines JSSG2006 [11], MIL-STD-1530D [12], and USAF Structures Bulletin EZ-SB-19-01 [13], the airworthiness certification of a cold spray repair requires a durability assessment. Furthermore, as per MIL-STD-1530D and USAF Structures Bulletin EZ-SB-19-01, the durability and damage tolerance assessment should be based on linear elastic fracture mechanics (LEFM). Here, the term ‘durability’ is taken to be as defined in MIL-STD-1530D and JSSG2006: “Durability is the attribute of an airframe that permits it to resist cracking for a prescribed period of time”.
As such, the purpose of this paper is to illustrate how to perform an LEFM-based durability assessment of a cold spray repair using a “building block” approach that is consistent with that mandated in JSSG2006 and MIL-STD-1530D. In this context, it should be noted that [14,15,16,17] revealed that cold spray coatings are exceptionally damage tolerant and that failure often occurs due to the nucleation, and subsequent growth, of cracking at the intersection between the substrate being repaired and the cold spray repair. Furthermore, the damage tolerance of cold spray repairs to AA7075-T7351 substrates is such that even when the cold spray coating was notched, the failure was due to the nucleation and subsequent growth of cracks in the substrate, and that the cold spray deposition did not crack or delaminate until close to the final failure of the specimens [17].
As noted in MIL-STD-1530D and EZ-SB-19-01, analysis is the key to certification, and the role of testing is merely to validate or correct the analysis. However, there are only a few papers [10,16] that present a linear elastic fracture mechanics (LEM)-based durability analysis of a cold spray repair, where the initial crack length is of the order of the equivalent initial damage size (EIDS) that is mandated, namely 0.0254 mm (0.01 inch) [11,12,13]. Similarly, other than [10,16], there are no papers in which the predicted crack growth histories are compared with experimental measurements. However, in [10], the nucleating cracks are associated with corrosion pitting down the bore of a fastener hole that contains (existing) intergranular corrosion. As such, these cracks are not initiated either in the cold spray repair, or at the intersection between the cold spray and the substrate being repaired. Consequently, aside from the preliminary study [16] that presented an initial study of a small number of cold-spray-repaired specimens, there are currently no published papers presenting a durability analysis of cold spray repairs where failure was due to the nucleation and subsequent growth of cracks at the intersection between the cold spray coating and the substrate. There also no publications in which
(i)
the analysis was performed using LEFM;
(ii)
the initial crack sizes were smaller than or comparable to the mandated EIDS;
(iii)
the experimentally measured crack growth histories were compared with predictions;
(iv)
and the experimental test results were used to generate the variability in the da/dN versus ΔK curves that are needed to enable a worst-case analysis, as mandated in the NASA Fracture Control Handbook NASA-HDBK-1510 [18].
Consequently, the purpose of this paper is to illustrate how to perform the necessary durability analysis in a fashion that is consistent with USAF Structures Bulletin EZ-SB-19-01, MIL-STD-1530D, and Joint Services Structural Guidelines JSSG2006.
To achieve this objective, this paper presents the results of an extensive test program addressing cold spray repairs to simulated corrosion damage. To this end, tests on twelve cold spray repairs to AA7075-T7351 specimens containing a simulated width corrosion cut were performed. To enable the crack growth histories to be determined, the specimens were fatigue tested using six different marker block load spectra. This resulted in the nucleation and subsequent growth of twenty-five (25) fatigue cracks, which, as previously observed [14,15,16,17], nucleated in the AA7075-T7351 substrate at the interface between the substrate and the cold spray deposit.

2. Materials and Methods

2.1. The Geometric Dimensions and the Applied Marker Block Load Spectra

Tests on twelve cold spray repairs to AA7075-T7351 specimens containing a simulated width corrosion cut were performed. These specimens were labelled as follows: 75_1_NC_1_#2, 75_1_NC_1_#3, 75_1_NC_1_#4, 75_1_NC_1_#5, 75_1_NC_2_#3, 75_1_NC_2_#4, 75_1_NC_2_#5, B_1_1_#1, B_1_1_#2 and B_1_1_#3; see Table 1. The dimensions and geometry of the test specimens used in this study are shown in Figure 1.
The cold spray deposition was performed using the VRC Metal System Brolga mobile cold spray system [19]. This system was chosen as it is in use at the US Navy Fleet Readiness Center Southwest (FRCSW) [20]. The aluminium alloy 7075 had a particle size range of 15–53 µm. The cold spray parameters were optimized to produce a porosity level below 0.5% and a minimum adhesion strength of 26 MPa on a AA7075-T7351 substrate (The precise details associated with the deposit process are commercial in confidence). The coating hardness was measured as 82–84 HRB.
To establish the crack growth histories, the specimens were fatigue tested using six different marker block load spectra, as shown in Table 1 and Table 2. For all specimens, the nucleation and subsequent growth of the twenty-five fatigue cracks were found to be at the interface between the AA7075-T7351 substrate and the AA7075 cold spray deposit, and were consistent with previous experiments [14,15,16,17].
Table 1. Block loading spectrum.
Table 1. Block loading spectrum.
SpectrumPmaxCyclesRepeat
Blocks		CyclesRepeat
Blocks		CyclesRepeat
Blocks
kNR = 0.1R = 0.8R = 0.2R = 0.8R = 0.2R = 0.8
135500018,000To failure------
23050018,000To failure------
3 *3030015,000To failure------
426.7750018,000To failure------
526.7730015,000To failure------
626.7730015,0001520010,000151003000To failure
* A schematic diagram of these particular test spectra is given in Figure 2.

2.2. Stress Analysis and Durability Analyses

As in previous works [10,16] that also studied the growth of cracks in cold spray repairs to AA7075-T7351 aluminium alloy components, the analysis used the Hartman–Schijve crack growth equation [21] to compute the crack growth histories for each of the twenty-five cracks that nucleated and grew in these tests. This equation takes the following form:
da/dN = D (∆K − ∆Kthr)/√(1 − Kmax/A))n
Here, ∆K = Kmax – Kmin, where Kmax and Kmin are the maximum and minimum values of the stress intensity factor (K) in a cycle, ∆Kthr is the fatigue threshold, n and D are the material constants, and A is the apparent cyclic fracture toughness; see [21] for more details. The application of this formulation to a wide range of problems can be found in other journal papers [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]. The relationship between this formulation and crack-closure-based crack growth equations [41,42,43,44,45,46,47,48,49,50,51,52,53,54,55] is presented in [55]. A number of crack growth equations that are similar to Equation (1) can also be found in the literature [55,56,57,58,59,60,61,62,63,64,65,66].
As per the requirements delineated in JSSG206 [11], MIL-STD-1530D [12], and USAF Structures Bulletin EZ-SB-19-01 [13], to follow a “building block approach”, the coefficients D, A, and n in Equation (1) were taken from prior studies [10,16]: D = 1.86 × 10−9, n = 2 and A = 111 MPa √m.
The crack growth analysis of all twenty-five cracks in these specimens was performed using Equation (1). As in previous papers [10,16], at each stage in the analysis, the stress intensity factor distribution around the crack tip was determined using the three-dimensional finite element alternating approach [67,68,69], and the change in the (three-dimensional) shape of the crack was computed using Equation (1). The advantage of using the three-dimensional finite element alternating method is that the cracks are not modelled explicitly and, regardless of the shape of the crack, only the uncracked finite element model is needed [67,69]. As such, this approach is ideal for assessing fatigue crack growth. However, since Equation (1) is now available in the commercial finite element programs ABAQUS®, NASTRAN®, and ANSYS® via the Zencrack® software module [70], an alternative approach could have been to use conventional finite element analyses in conjunction with the Zencrack® software program.
Consequently, in order to determine the stress intensity factors for any given crack configuration, it was first necessary to develop a three-dimensional finite element model of the repaired structure. In this analysis, the Young’s modulus and Poisson’s ratio of 7075-T7351 were taken to be 73,000 MPa and 0.3, respectively. The Young’s modulus and Poisson’s ratio of the cold spray deposit were taken from [16], and considered to be 69,000 MPa and 0.3, respectively. The maximum principal stress in the repaired specimen corresponding to a remote load of 30 kN, as determined using NASTRAN, is shown in Figure 3.

3. Comparison of the Measured and Computed Crack Growth Histories

The failure surfaces associated with these twelve fatigue tests, as well as the comparisons between the measured and computed crack growth histories for each of the resultant twenty-five cracks, are shown in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30, Figure 31, Figure 32, Figure 33, Figure 34, Figure 35, Figure 36, Figure 37, Figure 38 and Figure 39. The crack identifiers associated with each of the cracks shown in these figures are listed in Table 3, along with the starting crack sizes used in each of the analyses.

3.1. Measured and Computed Results for the Specimens Used Spectrum 1

  • Specimen Number 75_1_NC_1_#1
Materials 17 02656 g004
Figure 4. Failure in the 75_1_NC_1_#1 specimen (failed 368,528 cycles).
Figure 4. Failure in the 75_1_NC_1_#1 specimen (failed 368,528 cycles).
Materials 17 02656 g004
Materials 17 02656 g005
Figure 5. SEM of Crack 1, which was the fastest-growing (i.e., the lead) crack in specimen 75_1_NC_1_#1.
Figure 5. SEM of Crack 1, which was the fastest-growing (i.e., the lead) crack in specimen 75_1_NC_1_#1.
Materials 17 02656 g005
Materials 17 02656 g006
Figure 6. The measured and computed crack depth histories for specimen 75_1_NC_1_#1.
Figure 6. The measured and computed crack depth histories for specimen 75_1_NC_1_#1.
Materials 17 02656 g006
2.
Specimen Number 75_1_NC_2_#2
Materials 17 02656 g007
Figure 7. Failure in the 75_1_NC_2_#2 specimen (failed 354,393 cycles).
Figure 7. Failure in the 75_1_NC_2_#2 specimen (failed 354,393 cycles).
Materials 17 02656 g007
Materials 17 02656 g008
Figure 8. SEM of crack in specimen 75_1_NC_2_#2.
Figure 8. SEM of crack in specimen 75_1_NC_2_#2.
Materials 17 02656 g008
Materials 17 02656 g009
Figure 9. The measured and computed crack depth histories for specimen 75_1_NC_2_#2.
Figure 9. The measured and computed crack depth histories for specimen 75_1_NC_2_#2.
Materials 17 02656 g009

3.2. Measured and Computed Results for the Specimens Tested under Spectrum 2

  • Specimen Number 75_1_NC_1_#2
Materials 17 02656 g010
Figure 10. Failure in the 75_1_NC_1_#2 specimen (failed 378,932 cycles).
Figure 10. Failure in the 75_1_NC_1_#2 specimen (failed 378,932 cycles).
Materials 17 02656 g010
Materials 17 02656 g011
Figure 11. SEM of the lead crack (Crack 1) in specimen 75_1_NC_1_#2.
Figure 11. SEM of the lead crack (Crack 1) in specimen 75_1_NC_1_#2.
Materials 17 02656 g011
Materials 17 02656 g012
Figure 12. The measured and computed crack depth histories for specimen 75_1_NC_1_#2.
Figure 12. The measured and computed crack depth histories for specimen 75_1_NC_1_#2.
Materials 17 02656 g012

3.3. Measured and Computed Results for the Specimens Using Spectrum 3

  • Specimen Number 75_1_NC_2_#3
Materials 17 02656 g013
Figure 13. Failure in the 75_1_NC_2_#3 specimen (failed 365,534 cycles).
Figure 13. Failure in the 75_1_NC_2_#3 specimen (failed 365,534 cycles).
Materials 17 02656 g013
Materials 17 02656 g014
Figure 14. SEM of the lead crack (Crack 1) in specimen 75_1_NC_2_#3.
Figure 14. SEM of the lead crack (Crack 1) in specimen 75_1_NC_2_#3.
Materials 17 02656 g014
Materials 17 02656 g015
Figure 15. The measured and computed crack depth for specimen 75_1_NC_2_#3.
Figure 15. The measured and computed crack depth for specimen 75_1_NC_2_#3.
Materials 17 02656 g015
2.
Specimen Number B_1_1_#1
Materials 17 02656 g016
Figure 16. Failure in the B_1_1_#1 specimen (failed 555,619 cycles).
Figure 16. Failure in the B_1_1_#1 specimen (failed 555,619 cycles).
Materials 17 02656 g016
Materials 17 02656 g017
Figure 17. SEM of the lead crack (Crack 1) in specimen B_1_1_#1.
Figure 17. SEM of the lead crack (Crack 1) in specimen B_1_1_#1.
Materials 17 02656 g017
Materials 17 02656 g018
Figure 18. The measured and computed crack depth histories for specimen B_1_1_#1.
Figure 18. The measured and computed crack depth histories for specimen B_1_1_#1.
Materials 17 02656 g018

3.4. Measured and Computed Results for the Specimens Used Spectrum 4

  • Specimen Number 75_1_NC_1_#3
Materials 17 02656 g019
Figure 19. Failure in the 75_1_NC_1_#3 specimen (failed 629,120 cycles).
Figure 19. Failure in the 75_1_NC_1_#3 specimen (failed 629,120 cycles).
Materials 17 02656 g019
Materials 17 02656 g020
Figure 20. SEM of the lead crack (Crack 1) in specimen 75_1_NC_1_#3.
Figure 20. SEM of the lead crack (Crack 1) in specimen 75_1_NC_1_#3.
Materials 17 02656 g020
Materials 17 02656 g021
Figure 21. The measured and computed crack depth histories for specimen 75_1_NC_1_#3.
Figure 21. The measured and computed crack depth histories for specimen 75_1_NC_1_#3.
Materials 17 02656 g021

3.5. Measured and Computed Results for the Specimens Used Spectrum 5

  • Specimen Number 75_1_NC_1_#4
Materials 17 02656 g022
Figure 22. Failure in the 75_1_NC_1_#4 specimen (failed 670,905 cycles).
Figure 22. Failure in the 75_1_NC_1_#4 specimen (failed 670,905 cycles).
Materials 17 02656 g022
Materials 17 02656 g023
Figure 23. SEM of the lead crack (Crack 1) in specimen 75_1_NC_1_#4.
Figure 23. SEM of the lead crack (Crack 1) in specimen 75_1_NC_1_#4.
Materials 17 02656 g023
Materials 17 02656 g024
Figure 24. The measured and computed crack depth histories for specimen 75_1_NC_1_#4.
Figure 24. The measured and computed crack depth histories for specimen 75_1_NC_1_#4.
Materials 17 02656 g024
2.
Specimen Number 75_1_NC_2_#4
Materials 17 02656 g025
Figure 25. Failure in the 75_1_NC_2_#4 specimen (failed 360,543 cycles).
Figure 25. Failure in the 75_1_NC_2_#4 specimen (failed 360,543 cycles).
Materials 17 02656 g025
Materials 17 02656 g026
Figure 26. SEM of the lead crack in specimen 75_1_NC_2_#4.
Figure 26. SEM of the lead crack in specimen 75_1_NC_2_#4.
Materials 17 02656 g026
Materials 17 02656 g027
Figure 27. The measured and computed crack depth histories for specimen 75_1_NC_2_#4.
Figure 27. The measured and computed crack depth histories for specimen 75_1_NC_2_#4.
Materials 17 02656 g027
3.
Specimen Number 75_1_NC_2_#5
Materials 17 02656 g028
Figure 28. Failure in the 75_1_NC_2_#5 specimen (failed 373,397 cycles).
Figure 28. Failure in the 75_1_NC_2_#5 specimen (failed 373,397 cycles).
Materials 17 02656 g028
Materials 17 02656 g029
Figure 29. SEM of the lead crack (Crack 1) in specimen 75_1_NC_2_#5.
Figure 29. SEM of the lead crack (Crack 1) in specimen 75_1_NC_2_#5.
Materials 17 02656 g029
Materials 17 02656 g030
Figure 30. The measured and computed crack depth histories for specimen 75_1_NC_2_#5.
Figure 30. The measured and computed crack depth histories for specimen 75_1_NC_2_#5.
Materials 17 02656 g030
4.
Specimen Number B_1_1_#2
Materials 17 02656 g031
Figure 31. Failure in the B_1_1_#2 specimen (failed 1,117,056 cycles).
Figure 31. Failure in the B_1_1_#2 specimen (failed 1,117,056 cycles).
Materials 17 02656 g031
Materials 17 02656 g032
Figure 32. SEM of the lead crack in specimen B_1_1_#2.
Figure 32. SEM of the lead crack in specimen B_1_1_#2.
Materials 17 02656 g032
Materials 17 02656 g033
Figure 33. The measured and computed crack depth histories for specimen B_1_1_#2.
Figure 33. The measured and computed crack depth histories for specimen B_1_1_#2.
Materials 17 02656 g033
5.
Specimen Number B_1_1_#3
Materials 17 02656 g034
Figure 34. Failure in the B_1_1_#3 specimen (failed 765,288 cycles).
Figure 34. Failure in the B_1_1_#3 specimen (failed 765,288 cycles).
Materials 17 02656 g034
Materials 17 02656 g035
Figure 35. SEM of the lead crack (Crack 2) in specimen B_1_1_#3.
Figure 35. SEM of the lead crack (Crack 2) in specimen B_1_1_#3.
Materials 17 02656 g035
Materials 17 02656 g036
Figure 36. The measured and computed crack depth histories for specimen B_1_1_#3.
Figure 36. The measured and computed crack depth histories for specimen B_1_1_#3.
Materials 17 02656 g036

3.6. Measured and Computed Results for the Specimens Used Spectrum 6

  • Specimen Number 75_1_NC_1_#5
Materials 17 02656 g037
Figure 37. Failure in the 75_1_NC_1_#5 specimen (failed 899,480 cycles).
Figure 37. Failure in the 75_1_NC_1_#5 specimen (failed 899,480 cycles).
Materials 17 02656 g037
Materials 17 02656 g038
Figure 38. SEM of the lead crack in specimen 75_1_NC_1_#5.
Figure 38. SEM of the lead crack in specimen 75_1_NC_1_#5.
Materials 17 02656 g038
Materials 17 02656 g039
Figure 39. The measured and computed crack depth histories for specimen 75_1_NC_1_#5.
Figure 39. The measured and computed crack depth histories for specimen 75_1_NC_1_#5.
Materials 17 02656 g039

4. Assessment of the Computed versus Measured Crack Growth Histories

There are a number of important conclusions that arise from this study, and these are as follows:
(i)
The sizes of the nucleating cracks are significantly smaller than the mandated minimum equivalent initial damage size (EIDS) given in [11,12,13], namely 0.254 mm (0.01 inch). Hence, the analysis could be used to compute the growth of cracks from the mandated size, i.e., EIDS = 0.254 mm (0.01 inch).
(ii)
The computed and measured crack growth histories agree well for each of the twenty-five cracks.
(iii)
Table 3 reveals that the value of ΔKthr associated with the majority of the twenty-five cracks falls within the range of 0.0 to (approximately) 0.3 MPa √m, which is commonly seen for small cracks in conventionally manufactured aluminium alloys [21,23,25,64,71], as well as for small naturally occurring cracks in additively manufactured parts [37,72,73,74,75].
(iv)
Figure 12, Figure 15, Figure 24, Figure 30 and Figure 36 reinforce the prior finding that the fastest-growing cracks, which are also called “lead cracks” [76,77], in cold spray repairs to simulated corrosion damage have a crack growth history that is approximately exponential.
The fracture mechanics explanation as to why small naturally occurring cracks that have a small value of ΔKthr often exhibit near exponential growth is given in a previous paper [21]. Examples of this phenomenon are also given [73,74,75] for the growth of small naturally occurring cracks in additively manufactured metals. This phenomenon can also be seen in the study by Gallagher et al. [78], which used the USAF Characteristic K approach, as delineated in the USAF Damage Tolerant Design handbook [79], together with the assumption that the fatigue threshold was zero to analyse the crack growth in 7075-T7451 specimens subjected to six different combat aircraft flight load spectra. Further examples of the ability of the Hartman–Schijve crack growth equation and the characteristic K approach, or variants thereof, to accurately represent the growth of small naturally occurring cracks in conventionally built metals and the resultant exponent nature of the crack growth history are discussed by Molent [80]. At this point, it should also be noted that exponential growth is consistent with the growth of lead cracks seen in both USAF and Royal Australian Air Force (RAAF) operational aircraft [77,81].
Figure 6 and Figure 9 also reveal that, for the spectra investigated, cracks that have relatively small ΔKthr values can yield a crack growth history that has a “staircase”-like shape, i.e., has changes in slope as the loads change within a given load block.

Variability in the Crack Growth Curves and NASA-HDBK-5010

As previously noted, the MIL-STD-1530D mandates that the airworthiness certification of an airframe must be based on linear elastic fracture mechanics, and USAF Structures Bulletin EZ-SB-19-01 states the same thing for additively manufactured parts and modifications. USAF Structures Bulletin EZ-SB-19-01, which addresses the airworthiness certification requirements for AM parts and, by implication, for cold spray repairs, highlights the importance of accounting for the variability in crack growth. In this context, it should also be noted that the study by Virkler, Hillberry and Goel [82] is acknowledged as being one of the first to highlight the extent of the variability in the da/dN versus ΔK curves associated with ASTM E647 [83] fatigue tests on long cracks in conventionally manufactured metals. On the other hand, previous work in [84] was the first to show the extent of this variability for cracks that emanated from etch pits that had an EIDS similar to that mandated in MIL-STD-1530D and USA Structures Bulletin EZ-SB-19-01. As a result of the acknowledged variability in the growth of cracks in conventionally manufactured materials, NASA Fracture Control Handbook NASA-HDBK-5010 [18] mandates that the da/dN versus ΔK curve used in any crack growth assessment must be the worst-case curve.
The variability in the twenty-five da/dN versus ΔK curves determined in the current study is shown in Figure 40. This enables us to determine the NASA-HDBK-5101 mandated worst-case da/dN versus ΔK curve. It should be noted that this is the first time that the extent of the variability in the da/dN versus ΔK curves associated with cold spray repairs, where the nucleating crack lay at the intersection between the cold spray deposit and the substrate, has been shown. This worst-case curve is also shown in Figure 40.
The (relatively large) variation in the crack growth curves associated with low values of da/dN highlights the fact that, before any durability assessment of a cold spray repair to an operational airframe is attempted, it is first necessary to perform a sufficient number of tests so that the worst-case crack growth curve needed to perform the mandated airworthiness certification assessment can be determined.

5. Conclusions

MIL-STD-1530D notes that analysis is the key to certification, and that the role of testing is merely to validate and assist in correcting the analysis. USAF Structures Bulletin EZ-SB-19-01, MIL-STD-1530D and the US Joint Services Structural Guidelines JSSG2006 mandate that a durability analysis must result in an EIDS of no greater than 0.254 mm (0.01 inch). Furthermore, the durability analysis must be consistent with the building block approach outlined in MIL-STD-1530D and the US Joint Services Structural Guidelines JSSG2006.
This study has confirmed the ability to accurately compute the crack growth histories, i.e., to accurately perform the durability analyses mandated in JSSG2006, MIL-STD-1530Dc, and USAF Structures Bulletin EZ-SB-19-01, associated with twenty-five naturally occurring cracks that had nucleated and subsequently grown from the material discontinuities associated with cold spray repairs to simulated corrosion damage. Furthermore, in these tests, the size of the nucleating cracks was either comparable to, or smaller than, the equivalent initial damage size (EIDS) mandated in the JSSG2006, MIL-STD-1530D, and USAF Structures Bulletin EZ-SB-19-01. It should also be noted that the durability analysis described in this study has followed the building block approach outlined in MIL-STD-1530D and in the US Joint Services Structural Guidelines JSSG2006, and that the variability in the crack growth histories is captured by allowing for variability in the local fatigue threshold.
We also illustrate the extent of the variability in the da/dN versus ΔK curves associated with cold spray repairs; to the best of the authors’ knowledge, this is the first time that this variability has been reported. The relatively large variation in the da/dN versus ΔK curves associated with low values of da/dN highlights the fact that, before any durability assessment of a cold spray repair to an operational airframe is attempted, it is first necessary to perform a sufficient number of tests so that the worst-case small crack growth curve needed to perform the mandated airworthiness certification analysis can be determined.

Author Contributions

Project methodology and test direction—R.J.; Funding procurement, fractography and 1st draft—A.A.; Fractography, testing—D.P. and R.K.S.R.; Resources at Rosebank and supervision of testing at Rosebank—J.W.; Experimental testing and specimen test program definition—C.T. and D.P.; Funding and overall direction—N.P. and M.N. All authors have read and agreed to the published version of the manuscript.

Funding

R.J. and A.A. would like to acknowledge funding provided by the US Army International Technology Center, Indo-Pacific (ITC-IPAC), Tokyo, Contract No. FA520923C0010.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The data will be made available at the completion of the project.

Acknowledgments

The findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the ITC-IPAC.

Conflicts of Interest

Authors Caixian Tang and Jarrod Watts was employed by the company Rosebank Engineering Australia. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

  1. Jones, R.; Matthews, N.; Baker, A.; Champagne, V. Aircraft Sustainment and Repair; Butterworth-Heinemann Press: Oxford, UK, 2018; ISBN 978008100548. [Google Scholar]
  2. Champagne, V.K. The Cold Spray Materials Deposition Process Fundamentals and Applications; Woodhead Publishing Ltd.: Cambridge, UK, 2007; ISBN 978-1-84569-181-3. [Google Scholar]
  3. Champagne, V., Jr.; Matthews, N.; Champagne, V., III. Chapter 14: Introduction to Supersonic Particle Deposition. In Aircraft Sustainment and Repair; Jones, R., Matthews, N., Baker, A., Champagne, V., Eds.; Butterworth-Heinemann Press: Oxford, UK, 2018; pp. 799–844. ISBN 9780081005408. [Google Scholar]
  4. Matthews, N. Chapter 15: Additive Metal Technologies for Aerospace Sustainment. In Aircraft Sustainment and Repair; Jones, R., Matthews, N., Baker, A., Champagne, V., Eds.; Butterworth-Heinemann Press: Oxford, UK, 2018; pp. 845–862. ISBN 9780081005408. [Google Scholar]
  5. Bagherifard, S.; Guagliano, M. Fatigue performance of cold spray deposits: Coating, repair and additive manufacturing cases. Int. J. Fatigue 2020, 139, 105744. [Google Scholar] [CrossRef]
  6. Champagne, V.; Helfritch, D. Critical Assessment 11: Structural repairs by cold spray. Mater. Sci. Technol. 2015, 31, 627–634. [Google Scholar] [CrossRef]
  7. Widener, C.A.; Ozdemir, O.C.; Carter, M. Structural repair using cold spray technology for enhanced sustainability of high value assets. Procedia Manuf. 2018, 21, 361–368. [Google Scholar] [CrossRef]
  8. Yin, S.; Cavaliere, P.; Aldwell, B.; Jenkins, R.; Liao, H.; Li, W.; Lupoi, R. Cold spray additive manufacturing and repair: Fundamentals and applications. Addit. Manuf. 2018, 21, 628–650. [Google Scholar] [CrossRef]
  9. Pathak, S.; Saha, G.C. Development of Sustainable Cold Spray Coatings and 3D Additive Manufacturing Components for Repair/Manufacturing Applications: A Critical Review. Coatings 2017, 7, 122. [Google Scholar] [CrossRef]
  10. Kundu, S.; Jones, R.; Peng, D.; Matthews, N.; Alankar, A.; Singh, R.K.R.; Huang, P. Review of Requirements for the Durability and Damage Tolerance Certification of Additively Manufactured Aircraft Structural Parts and AM Repairs. Materials 2020, 13, 1341. [Google Scholar] [CrossRef] [PubMed]
  11. Department of Defense Joint Service Specification Guide, Aircraft Structures. JSSG-2006. October 1998. Available online: http://everyspec.com/USAF/USAF-General/JSSG-2006_10206/ (accessed on 2 May 2024).
  12. Department of Defense Standard Practice Aircraft Structural Integrity Program (ASIP). MIL-STD-1530D. 13 October 2016. Available online: http://everyspec.com/MIL-STD/MIL-STD-1500-1599/MIL-STD-1530D_55392/ (accessed on 27 May 2024).
  13. Durability and Damage Tolerance Certification for Additive Manufacturing of Aircraft Structural Metallic Parts; Structures Bulletin EZ-SB-19-01; Wright Patterson Air Force Base: Dayton, OH, USA, 2019; Available online: https://daytonaero.com/usaf-structures-bulletins-library/ (accessed on 2 May 2024).
  14. White, B.; Story, W.; Brewer, L.; Jordon, J.B. Fatigue behaviour of fastener holes in high-strength aluminum plates repaired by cold spray deposition. Fatigue Fract. Eng. Mater. Struct. 2019, 43, 317–329. [Google Scholar] [CrossRef]
  15. Yandouzi, M.; Gaydos, S.; Guo, D.; Ghelichi, R.; Jodoin, B. Aircraft Skin Restoration and Evaluation. J. Therm Spray Technol. 2006, 23, 1281–1290. [Google Scholar] [CrossRef]
  16. Peng, D.; Tang, C.; Matthews, N.; Jones, R.; Kundu, S.; Singh Raman, R.K.; Alankar, A. Computing the Fatigue Life of Cold Spray Repairs to Simulated Corrosion Damage. Materials 2021, 14, 4451. [Google Scholar] [CrossRef]
  17. Peng, D.; Jones, R.; Matthews, N.; Tang, C. On the role of the interface on the damage tolerance and durability of cold spray repairs to AA7075-T7351 aluminium alloy wing skins. Appl. Surf. Sci. Adv. 2020, 3, 100052. [Google Scholar] [CrossRef]
  18. Fracture Control Handbook for Payloads, Experiments, and Similar Hardware. NASA-HDBK-5010. May 2005, Revalidated 2012. Available online: https://standards.nasa.gov/standard/nasa/nasa-hdbk-5010 (accessed on 14 April 2024).
  19. Available online: https://vrcmetalsystems.com/brogla-002-mobile-cold-spray-system/ (accessed on 21 May 2024).
  20. Available online: https://www.navair.navy.mil/news/Rise-Cold-Spray-Technology-Fleet-Readiness-Center-Southwest/Thu-12142023-1318 (accessed on 21 May 2024).
  21. Jones, R. Fatigue crack growth and damage tolerance. Fatigue Fract. Eng. Mater. Struct. 2014, 37, 463–483. [Google Scholar] [CrossRef]
  22. Tan, J.L.; Chen, B.K. Prediction of fatigue life in aluminum alloy (AA7050-T7451) structures in the presence of multiple artificial short cracks. Theor. Appl. Fract Mech. 2015, 78, 1–7. [Google Scholar] [CrossRef]
  23. Tan, J.L.; Chen, B.K. Coalescence and growth of two coplanar short cracks in AA7050-T7451 aluminium alloys. Eng. Fract. Mech. 2013, 102, 324–333. [Google Scholar] [CrossRef]
  24. Tan, J.L.; Chen, B.K. A new fracture area method for predicting the growth of a newly coalesced crack in AA7050-T7451 aluminium alloy. Theor. Appl. Fract. Mech. 2015, 75, 146–150. [Google Scholar] [CrossRef]
  25. Main, B.; Evans, R.; Walker, K.; Yu, X.; Molent, L. Lessons from a Fatigue Prediction Challenge for an Aircraft Wing Shear Tie Post. Int. J. Fatigue 2019, 123, 53–65. [Google Scholar] [CrossRef]
  26. Godefroid, L.B.; Moreira, L.P.; Vilela, T.C.G.; Faria, G.L.; Candido, L.C.; Pinto, E.S. Effect of chemical composition and microstructure on the fatigue crack growth resistance of pearlitic steels for railroad application. Int. J. Fatigue 2019, 120, 241. [Google Scholar] [CrossRef]
  27. Kovarik, O.; Cizek, J.; Klecka, J. Fatigue Crack Growth Rate Description of RF-Plasma-Sprayed Refractory Metals and Alloys. Materials 2023, 16, 1713. [Google Scholar] [CrossRef] [PubMed]
  28. Khudiakova, A.; Brunner, A.J.; Wolfahrt, M.; Pinter, G. Quantification Approaches for Fatigue Crack Resistance of Thermoplastic Tape Layered Composites with Multiple Delaminations. Materials 2021, 14, 1476. [Google Scholar] [CrossRef]
  29. Riedl, G.; Pugstaller, R.; Wallner, G.M. Development and implementation of a simultaneous fatigue crack growth test setup for polymeric hybrid laminates. Eng. Fract. Mech. 2002, 267, 108468. [Google Scholar] [CrossRef]
  30. Simon, I.; Banks-Sills, L.; Fourman, V. Mode I delamination propagation and R-ratio effects in woven DCB specimens for a multi-directional layup. Int. J. Fatigue 2017, 96, 237–251. [Google Scholar] [CrossRef]
  31. Arhant, M.; Lolive, E.; Bonnemains, T.; Davies, P. Effect of aging on the fatigue crack growth properties of carbon-polyamide 6 thermoplastic composites using the multi ΔG-control method. Compos. Part A Appl. Sci. Manuf. 2022, 161, 107105. [Google Scholar] [CrossRef]
  32. Clerc, G.; Brunner, A.J.; Niemz, P.; Van De Kuilen, J.W.G. Feasibility study on Hartman-Schijve data analysis for mode II fatigue fracture of adhesively bonded wood joints. Int. J. Fatigue 2019, 221, 123–140. [Google Scholar] [CrossRef]
  33. Sanaei, N.; Fatemi, A. Defect-based multiaxial fatigue life prediction of L-PBF additive manufactured metals. Fatigue Fract. Eng. Mater. Struct. 2021, 44, 1897. [Google Scholar] [CrossRef]
  34. Sanaei, N.; Fatemi, A. Defect-based fatigue life prediction of L-PBF additive manufactured metals. Eng. Fract. Mech. 2021, 244, 107541. [Google Scholar] [CrossRef]
  35. Markham, M.J.; Fatemi, A.; Phan, N. Mixed-Mode Small Fatigue Crack Growth Rates and Modeling in Additively Manufactured Metals. Int. J. Fatigue 2024, 183, 108258. [Google Scholar] [CrossRef]
  36. Sanaei, N.; Fatemi, A. Defects in additive manufactured metals and their effect on fatigue performance: A state-of-the-art review. Prog. Mater. Sci. 2021, 117, 100724. [Google Scholar] [CrossRef]
  37. Dastgerdi, J.N.; Jaberi, O.; Remes, H.; Lehto, P.; Toudeshky, H.H.; Kuva, J. Fatigue damage process of additively manufactured 316L steel using X-ray computed tomography imaging. Addit. Manuf. 2023, 70, 103559. [Google Scholar] [CrossRef]
  38. Markham, M.J.; Fatemi, A. Multiaxial Fatigue Life Predictions of Additively Manufactured Metals using a Hybrid of Linear Elastic Fracture Mechanics and a Critical Plane Approach. Int. J. Fatigue 2024, 178, 107979. [Google Scholar] [CrossRef]
  39. Ye, J.; Syed, A.K.; Zhang, X.; Eimer, E.; Williams, S. Fatigue crack growth behaviour in an aluminium alloy Al-Mg-0.3Sc produced by wire based directed energy deposition process. Fatigue Fract. Eng. Mater. Struct. 2023, 46, 3927–3938. [Google Scholar] [CrossRef]
  40. Shamir, M.; Zhang, X.; Syed, A.K. Characterising and representing small crack growth in an additive manufactured titanium alloy. Eng. Fract. Mech. 2021, 253, 107876. [Google Scholar] [CrossRef]
  41. Elber, W. Fatigue crack cyclic closure under cyclic tension. Eng. Fract. Mech. 1970, 2, 37–45. [Google Scholar]
  42. ASTM STP 486; The Significance of Crack Closure. ASTM International: West Conshohocken, PA, USA, 1971; pp. 230–242.
  43. Kemp, R.M.J. Fatigue Crack Closure—A Review, Royal Aerospace Establishment; Technical Report 90046; Procurement Executive, Ministry of Defence: Farnborough, UK, 1990; Available online: https://apps.dtic.mil/sti/pdfs/ADA236760.pdf (accessed on 20 April 2024).
  44. Paris, P.C.; Tada, H.; Donald, J.K. Service load fatigue damage—A historical perspective. Int. J. Fatigue 1999, 21, S35–S46. [Google Scholar] [CrossRef]
  45. Paris, P.C.; Lados, D.; Tada, H. Reflections on identifying the real ΔKeffective in the threshold region and beyond. Eng. Fract. Mech. 2008, 75, 299–305. [Google Scholar] [CrossRef]
  46. Kujawski, D. Enhanced model of partial crack closure for correlation of R-ratio Effects in aluminium alloys. Int. J. Fatigue 2001, 23, 95–102. [Google Scholar] [CrossRef]
  47. Ribeiro, V.; Correia, J.; Lesiuk, G.; Gonçalves, A.; De Jesus, A.; Berto, F. Application and discussion of various crack closure models to predict fatigue crack growth in 6061-T651 aluminium alloy. Int. J. Fatigue 2021, 153, 106472. [Google Scholar] [CrossRef]
  48. Schijve, J. Some formulas for the crack opening stress level. Eng. Fract. Mech. 1981, 14, 461–465. [Google Scholar] [CrossRef]
  49. Zhang, S.; Marissen, R.; Schulte, K.; Trautmann, K.K.; Nowack, H.; Schijve, J. Crack propagation studies on Al7475 on the basis of constant amplitude and selective variable amplitude loading histories. Fatigue Eng. Mater. Struct. 1987, 10, 315–332. [Google Scholar] [CrossRef]
  50. Kumar, R.; Singh, K. Influence of stress ratio on fatigue crack growth in mild steel. Eng. Fract. Mech. 1995, 50, 377–384. [Google Scholar] [CrossRef]
  51. Newman, J.C., Jr. A crack opening stress equation for fatigue crack growth. Int. J. Fatigue 1984, 24, 131–135. [Google Scholar] [CrossRef]
  52. ASTM STP 748; A Crack-Closure Model for Predicting Fatigue Crack Growth under Aircraft Spectrum Loading. American Society for Testing and Materials: Philadelphia, PA, USA, 1981; pp. 53–84.
  53. Skorupa, M. Load interaction effects during fatigue crack growth under variable amplitude loading—A literature review. Part II: Qualitative interpretation. Fatigue Fract. Eng. Mater. Struct. 1998, 22, 905–926. [Google Scholar] [CrossRef]
  54. Donald, K.; Paris, P.C. An evaluation of ∆K estimation procedure on 6061-T6 and 2024-T3 aluminum alloys. Int. J. Fatigue 1999, 21, S47–S57. [Google Scholar] [CrossRef]
  55. Jones, R.; Ang, A.; Phan, N.D.; Nicholas, M. On the Link between Plastic Wake Induced Crack Closure and the Fatigue Threshold. Metals 2024, 14, 523. [Google Scholar] [CrossRef]
  56. Ishihara, S.; McEvily, A.J. Analysis of short fatigue crack growth in cast aluminium alloy. Int. J. Fatigue 2002, 24, 1169–1174. [Google Scholar] [CrossRef]
  57. Zheng, X.; Hirt, M. Fatigue crack propagation in steels. Eng. Fract. Mech. 1983, 18, 965–973. [Google Scholar]
  58. Chapetti, M.D. Fatigue propagation threshold of short cracks under constant amplitude loading. Int. J. Fatigue 2003, 25, 1319–1326. [Google Scholar] [CrossRef]
  59. Wang, H.; Wang, F.; Cui, W.; Hayat, T.; Ahmad, B. Prediction of short fatigue crack growth of Ti-6Al-4V. Fatigue Fract. Eng. Mater. Struct. 2014, 37, 1075–1086. [Google Scholar] [CrossRef]
  60. Masuda, K.; Oguma, N.; Ishihara, S.; McEvily, A.J. Investigation of subsurface fatigue crack growth behavior of D2 tool steel (JISSKD11) based on a novel measurement method. Int. J. Fatigue 2020, 133, 105395. [Google Scholar] [CrossRef]
  61. Durán, A.R.; Castro, J.T.P.; Filho, J.C.P. Fatigue crack propagation prediction by cyclic plasticity damage accumulation models. Fatigue Fract. Eng. Mater. Struct. 2003, 26, 95–184. [Google Scholar] [CrossRef]
  62. de Castro, J.T.P.; Meggiolaro, M.A.; de Oliveira Miranda, A.C. Fatigue crack growth predictions based on damage accumulation calculations ahead of the crack tip. Comput. Mater. Sci. 2009, 46, 115–123. [Google Scholar] [CrossRef]
  63. Miranda, A.C.O.; Meggiolaro, M.A.; Castro, J.T.P. Path and life prediction sunder mixed Mode I-Mode II complex loading. In Mechanics of Solids in Brazil 2007; Alves, M., da Costa Mattos, H.S., Eds.; Brazilian Society of Mechanical Sciences and Engineering: Águas de Lindóia, Brazil, 2007; ISBN 978-85-85769-30-7. Available online: https://www.researchgate.net/profile/Heraldo-Da-Costa-Mattos/publication/271384775_ABCM_Symposium_series_in_solid_mechanics_-_Solid_Mechanics_in_Brazil_2007/links/54c6835a0cf2911c7a58f9bc/ABCM-Symposium-series-in-solid-mechanics-Solid-Mechanics-in-Brazil-2007.pdf (accessed on 13 April 2024).
  64. Dixon, B.; Fayek, H.; Hodgen, C.; Wiley, T.; Barter, S. Optimising fatigue crack growth predictions for small cracks under variable amplitude loading. Int. J. Fatigue 2004, 185, 108339. [Google Scholar] [CrossRef]
  65. McEvily, A.J.; Ishihara, S. On the dependence of the rate of fatigue crack growth on the σna (2a) parameter. Int. J. Fatigue 2001, 23, 115–120. [Google Scholar] [CrossRef]
  66. McEvily, A.J.; Eifler, D.; Macherauch, E. An analysis of the growth of short fatigue cracks. Eng. Fract. Mech. 1991, 40, 571–584. [Google Scholar] [CrossRef]
  67. Vijayakumar, K.; Atluri, S.N. Embedded Elliptical Crack, in an Infinite Solid, Subject to Arbitrary Crack-Face Tractions. J. Appl. Mech. 1981, 48, 88–96. [Google Scholar] [CrossRef]
  68. Nishiok, T.; Atluri, S.N. Analytical solution for embedded elliptical cracks, and finite element alternating method for elliptical surface cracks, subjected to arbitrary loadings. Eng. Fract. Mech. 1983, 17, 247–268. [Google Scholar] [CrossRef]
  69. Wang, L.; Atluri, S.N. Recent advances in the alternating method for elastic and inelastic fracture analyses. Comput. Methods Appl. Mech. Eng. 1996, 137, 1–58. [Google Scholar] [CrossRef]
  70. Available online: https://www.zentech.co.uk/zencrack_publications.htm (accessed on 15 February 2024).
  71. Jones, R.; Singh Raman, R.K.; McMillan, A.J. Crack growth: Does microstructure play a role? Eng. Fract. Mech. 2018, 187, 190–210. [Google Scholar] [CrossRef]
  72. Jones, R.; Molaei, R.; Fatemi, A.; Peng, D.; Phan, N. A note on computing the growth of small cracks in AM Ti-6Al-4V. Procedia Struct. Integr. 2020, 28, 364–369. [Google Scholar] [CrossRef]
  73. Peng, D.; Champagne, V.K.; Ang, A.S.M.; Birt, A.; Michelson, A.; Pinches, S.; Jones, R. Computing the Durability of WAAM 18Ni-250 Maraging Steel Specimens with Surface Breaking Porosity. Crystals 2023, 13, 443. [Google Scholar] [CrossRef]
  74. Jones, R.; Cizek, J.; Kovarik, O.; Ang, A.; Champagne, V. Observations on comparable aluminium alloy crack growth curves: Additively manufactured Scalmalloy® as an alternative to AA5754 and AA6061-T6 alloys? Addit. Manuf. Lett. 2022, 2, 100026. [Google Scholar] [CrossRef]
  75. Peng, D.; Jones, R.; Ang, A.S.M.; Michelson, A.; Champagne, V.; Birt, A.; Pinches, S.; Kundu, S.; Lankar, A.; Singh Raman, R.K. Computing the durability of WAAM 18Ni 250 Maraging steel specimens. Fatigue Fract. Eng. Mater. Struct. 2022, 45, 3535–3545. [Google Scholar] [CrossRef]
  76. Molent, L.; Barter, S.A.; Wanhill, R.J.H. The lead crack fatigue lifing framework. Int. J. Fatigue 2011, 33, 323–331. [Google Scholar] [CrossRef]
  77. Berens, A.P.; Hovey, P.W.; Skinn, D.A. Risk Analysis for Aging Aircraft Fleets—Volume 1: Analysis, WL-TR-91-3066, Flight Dynamics Directorate, Wright Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, October 1991. Available online: https://apps.dtic.mil/sti/citations/ADA252000 (accessed on 14 April 2024).
  78. Gallagher, J.P.; Molent, L. The equivalence of EPS and EIFS based on the same crack growth life data. Int. J. Fatigue 2015, 80, 162–170. [Google Scholar] [CrossRef]
  79. Gallagher, J.P.; Giessler, F.J.; Berens, A.P.; Engle, R.M. USAF Damage Tolerant Design Handbook: Guidelines for the Analysis and Design of Damage Tolerant Aircraft Structures; AFWAL-TR-82-3073; Air Force Research Laboratory, Wright-Patterson Air Force Base: Dayton, OH, USA, 1984; Available online: https://apps.dtic.mil/sti/citations/ADA153161 (accessed on 3 May 2024).
  80. Molent, L. Aircraft Fatigue Management; Springer Briefs in Applied Sciences and Technology; Springer Nature Singapore Pty Ltd.: Berlin/Heidelberg, Germany, 2023; ISBN 978-981-99-7467-2/978-981-99-7468-9 (eBook). [Google Scholar] [CrossRef]
  81. Main, B.; Molent, L.; Singh, R.; Barter, S. Fatigue crack growth lessons from thirty-five years of the Royal Australian Air Force F/A-18 A/B Hornet Aircraft Structural Integrity Program. Int. J. Fatigue 2020, 1330, 105426. [Google Scholar] [CrossRef]
  82. Virkler, D.A.; Hillberry, B.M.; Goel, P.K. The statistical nature of fatigue crack propagation. Trans ASME 1979, 101, 148–153. [Google Scholar] [CrossRef]
  83. ASTM E647-23b; Standard Test Method for Measurement of Fatigue Crack Growth Rates. ASTM International: West Conshohocken, PA, USA, 2023.
  84. Jones, R.; Rans, C.; Iliopoulos, A.P.; Michopoulos, J.G.; Phan, N.; Peng, D. Modelling the Variability and the Anisotropic Behaviour of Crack Growth in SLM Ti-6Al-4V. Materials 2021, 14, 1400. [Google Scholar] [CrossRef]
Materials 17 02656 g001
Figure 1. Dimensions of the test specimen geometry.
Figure 1. Dimensions of the test specimen geometry.
Materials 17 02656 g001
Materials 17 02656 g002
Figure 2. A schematic diagram of marker block load spectrum 3.
Figure 2. A schematic diagram of marker block load spectrum 3.
Materials 17 02656 g002
Materials 17 02656 g003
Figure 3. The maximum principal stress in the specimen at a remote load of 30 kN. Only one half of the specimen is shown.
Figure 3. The maximum principal stress in the specimen at a remote load of 30 kN. Only one half of the specimen is shown.
Materials 17 02656 g003
Materials 17 02656 g040
Figure 40. The variability in the crack growth curves seen by the twenty-five cracks examined in the present study.
Figure 40. The variability in the crack growth curves seen by the twenty-five cracks examined in the present study.
Materials 17 02656 g040
Table 2. The block loading spectra used in the various crack growth tests and the thicknesses of the cold spray.
Table 2. The block loading spectra used in the various crack growth tests and the thicknesses of the cold spray.
Specimen IDBlock Loading SpectrumThickness of Cold Spray Deposit (+/−0.005 mm)
75_1_NC_1_#110.785
75_1_NC_1_#220.755
75_1_NC_1_#340.76
75_1_NC_1_#450.73
75_1_NC_1_#560.72
75_1_NC_2_#210.818
75_1_NC_2_#330.735
75_1_NC_2_#450.74
75_1_NC_2_#550.73
B_1_1_#130.935
B_1_1_#250.925
B_1_1_#350.14
Table 3. The starting crack length and the values of ΔKthr (MPa √m) used in the crack growth predictions.
Table 3. The starting crack length and the values of ΔKthr (MPa √m) used in the crack growth predictions.
Specimen IDCrack IDSimplified Specimen and Crack IdentifierStarting Crack Length (mm)ΔKthr (MPa √m)
75_1_NC_1_#111-10.02460.64
21-20.02800.69
31-30.02690.61
75_1_NC_1_#212-10.03270.09
22-20.03530.10
75_1_NC_1_#3 13-10.02600.10
23-20.02610.173
75_1_NC_1_#4 14-10.01800.135
24-20.03300.176
34-30.07800.33
75_1_NC_1_#5 15-10.04630.29
75_1_NC_2_#2 16-10.01800.47
75_1_NC_2_#3 17-10.03000.06
27-20.02750.07
37-30.03100.05
47-40.04100.07
75_1_NC_2_#4 18-10.07260.23
75_1_NC_2_#5 19-10.02630.150
29-20.03420.252
39-30.02550.143
B_1_1_#1110-10.08000.268
210-20.08390.32
B_1_1_#2111-10.04000.275
B_1_1_#3112-10.04800.20
212-20.01200.05
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Peng, D.; Tang, C.; Watts, J.; Ang, A.; Raman, R.K.S.; Nicholas, M.; Phan, N.; Jones, R. Durability Analysis of Cold Spray Repairs: Phase I—Effect of Surface Grit Blasting. Materials 2024, 17, 2656. https://doi.org/10.3390/ma17112656

AMA Style

Peng D, Tang C, Watts J, Ang A, Raman RKS, Nicholas M, Phan N, Jones R. Durability Analysis of Cold Spray Repairs: Phase I—Effect of Surface Grit Blasting. Materials. 2024; 17(11):2656. https://doi.org/10.3390/ma17112656

Chicago/Turabian Style

Peng, Daren, Caixian Tang, Jarrod Watts, Andrew Ang, R. K. Singh Raman, Michael Nicholas, Nam Phan, and Rhys Jones. 2024. "Durability Analysis of Cold Spray Repairs: Phase I—Effect of Surface Grit Blasting" Materials 17, no. 11: 2656. https://doi.org/10.3390/ma17112656

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop