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

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.


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 Materials 2024, 17, 2656 2 of 29 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 ∆K 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.
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 Tables 1 and 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].To establish the crack growth histories, the specimens were fatigue tested using six different marker block load spectra, as shown in Tables 1 and 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].
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 [67-69], 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
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]: 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 [67-69], and the change in the (three-dimensional) shape of the crack was computed using Equation (1).The advantage of using the threedimensional 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.
of the repaired structure.In this analysis, the Young's modulus and Poisson's ratio of 7 T7351 were taken to be 73,000 MPa and 0.3, respectively.The Young's modulus and P son's ratio of the cold spray deposit were taken from [16], and considered to be 69 MPa and 0.3, respectively.The maximum principal stress in the repaired specimen co sponding to a remote load of 30 kN, as determined using NASTRAN, is shown in Fig 3.

Comparison of the Measured and Computed Crack Growth Histories
The failure surfaces associated with these twelve fatigue tests, as well as the com isons between the measured and computed crack growth histories for each of the resul twenty-five cracks, are shown in Figures 4-39.The crack identifiers associated with e of the cracks shown in these figures are listed in Table 3, along with the starting crack s used in each of the analyses.

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 Figures 4-39.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.

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: 13.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).14.The computed and measured crack growth histories agree well for each of the twenty-five cracks.15.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]].16.Figures 12, 15, 24, 30 and 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

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 twentyfive cracks.(iii) Table 3 reveals that the value of ∆K thr associated with the majority of the twentyfive 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) Figures 12,15,24,30 and 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 ∆K thr often exhibit near exponential growth is given in a previous paper [21].Examples of 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].Figures 6 and 9 also reveal that, for the spectra investigated, cracks that have relatively small ∆K thr 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 ∆K 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 ∆K curve used in any crack growth assessment must be the worst-case curve.
The variability in the twenty-five da/dN versus ∆K 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 ∆K curve.It should be noted that this is the first time that the extent of the variability in the da/dN versus ∆K 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.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].Figures 6 and 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.

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 ∆K 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 ∆K 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.

Figure 1 .
Figure 1.Dimensions of the test specimen geometry.

Figure 2 .
Figure 2. A schematic diagram of marker block load spectrum 3.

Figure 2 .
Figure 2. A schematic diagram of marker block load spectrum 3.

Figure 3 .
Figure 3.The maximum principal stress in the specimen at a remote load of 30 kN.Only one ha the specimen is shown.

Figure 3 .
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 6 .
Figure 6.The measured and computed crack depth histories for specimen 75_1_NC_1_#1.

Figure 18 .
Figure 18.The measured and computed crack depth histories for specimen B_1_1_#1.

Figure 21 .
Figure 21.The measured and computed crack depth histories for specimen 75_1_NC_1_#3.

Figure 24 .
Figure 24.The measured and computed crack depth histories for specimen 75_1_NC_1_#4.

Figure 26 .
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.

Figure 26 .
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.

Figure 27 .
Figure 27.The measured and computed crack depth histories for specimen 75_1_NC_2_#4.

Figure 27 .
Figure 27.The measured and computed crack depth histories for specimen 75_1_NC_2_#4.

Figure 32 .
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.

Figure 38 .
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.

Figure 38 .
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.

Figure 39 .
Figure 39.The measured and computed crack depth histories for specimen 75_1_NC_1_#5.

Figure 39 .
Figure 39.The measured and computed crack depth histories for specimen 75_1_NC_1_#5.

Figure 40 .
Figure 40.The variability in the crack growth curves seen by the twenty-five cracks examined in the present study.

Figure 40 .
Figure 40.The variability in the crack growth curves seen by the twenty-five cracks examined in the present study.
* A schematic diagram of these particular test spectra is given in Figure2.

Table 2 .
The block loading spectra used in the various crack growth tests and the thicknesses of the cold spray.
Figure 1.Dimensions of the test specimen geometry.

Table 2 .
The block loading spectra used in the various crack growth tests and the thicknesses of the cold spray.

Table 3 .
The starting crack length and the values of ΔKthr (MPa √m) used in the crack growth pr tions.

Table 3 .
The starting crack length and the values of ∆K thr (MPa √ m) used in the crack growth predictions.
3.1.Measured and Computed Results for the Specimens Used Spectrum 1 3.1.Measured and Computed Results for the Specimens Used Spectrum 1 1.Specimen Number 75_1_NC_1_#1