Residual stress and thermo-mechanical properties of cold spray metal coatings

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Acta Materialia 59 (2011) 1259–1270 www.elsevier.com/locate/actamat

Residual stress and thermo-mechanical properties of cold spray metal coatings V. Luzin a,⇑, K. Spencer b,c, M.-X. Zhang b,c a

The Bragg Institute, Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia Division of Materials, School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia c ARC Centre of Excellence for Design in Light Metals, Australia

b

Received 19 May 2010; received in revised form 25 October 2010; accepted 27 October 2010 Available online 22 November 2010

Abstract The residual stress profiles in Cu and Al coatings cold sprayed using kinetic metallization have been studied using neutron diffraction. To interpret results and to describe them quantitatively, the measured profiles were fit to Tsui and Clyne’s progressive coating deposition model, which demonstrated that the residual stresses are largely due to kinetic and not thermal effects. The residual stress state of the coatings was found to depend mainly on the deformation behaviour and properties of the coating material, and the kinetic parameters of the cold spray process. Young’s modulus and impact strain were measured and used along with published material data for Cu and Al to approximate the residual stresses, using a model developed for shot peening. The properties of the Cu coatings such as Young’s modulus and porosity were found to be closer to their bulk values than in the case of the Al coatings, and this was related to the amount of particle deformation on impact. Crown Copyright Ó 2010 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Cold spray; Residual stress; Neutron diffraction

1. Introduction Cold spray [1] is a rapidly developing technology for depositing materials in the solid state. In this process the feedstock material, which should have a metallic powder as the principal component, is injected into a gas stream and accelerated to speeds from 500 to 1000 m s1 and is impacted onto a metallic substrate. If the powder reaches a critical velocity defined by the material properties and process conditions, then metallurgical bonding is obtained and the properties of the deposit approach those of the equivalent bulk material. The primary application of cold spray coatings is for the surface enhancement of metals to improve properties such as wear and corrosion resistance, electrical/thermal conductivity, etc. Due to the low temperature of the process ⇑ Corresponding author. Tel.: +61 2 9717 7262; fax: +61 2 9717 3606.

E-mail address: [email protected] (V. Luzin).

it is suitable for depositing thermally sensitive materials, and little or no oxidation is thought to occur during the spray process. The low temperature also makes this process suitable for coatings on light metal substrates such as magnesium alloys. In all such applications coating integrity is important, which may be loosely defined as the quality of bonding between particles within the coating, and between the coating and the substrate. Coating integrity may be influenced by the residual stresses present in the coating, and in the case of thermal spray coatings residual stresses have been shown to lead to peeling and delamination of the coating [2]. Among other factors, understanding, prediction and control of internal stress accumulation can contribute to improved coating performance. To date there is a limited amount of data detailing the residual stresses in cold spray coatings [3,4]. Also, there have been no attempts to interpret the measured values based on the kinetics of the spray process and material properties other than straightforward finite element calculations.

1359-6454/$36.00 Crown Copyright Ó 2010 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.actamat.2010.10.058

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A distinct feature of the cold spray process is the compressive residual stress that arises during the deposition process. A state of compressive residual stress on the surface is generally thought to be beneficial for fatigue resistance, and several surface treatment processes are designed to produce this state of stress such as shot peening, laser shock peening, low plasticity burnishing, ultrasonic impact treatment, etc. In all of these methods the compressive stress is produced through plastic deformation of the surface region. In a similar manner, the cold spray process induces compressive stress by high speed impact of the sprayed particles on the surface, causing a peening effect. In Ref. [4] the role of the particle kinetic energy in the accumulation of residual stress was studied, by comparing the internal stress in coatings produced by “high thermal impact” spray processes such as plasma spray to those produced by “high kinetic impact” spray processes such as cold spray or the high-velocity oxy-fuel process. As far as experimental studies are concerned, several experimental techniques have been used to study residual stress in coatings and films produced by very different techniques and methods. Historically, the curvature measurement technique has been employed first for studying stress in the electrolytically deposited thin metallic films [5] and it was a major stress measurement technique in coatings for the following decades [6]. In its original formulation, the Stoney formula, the method works well for thin films; for thicker coatings some significant corrections are required [7]. The modern versions of this technique are still in use and known as the continuous curvature measurement [8] or in situ curvature measurement [9–12] and allow even through-thickness stress profile reconstruction but with some experimental and numerical difficulties. The main drawbacks of the method are apparent – it is impossible to retrace stresses in the samples with no recorded in situ thermal/displacement history, and it works only for samples of certain geometry and design. A group of material removal techniques, which includes the layer removal method [2], slitting method, hole drilling [13] and some other variations, can overcome these problems but at the price of sample destruction. Although these methods have been applied successfully, extraction of the residual stress might require considerable numerical computations, especially for the samples of complex geometry, and accuracy might suffer. The neutron diffraction technique is non-destructive and the most direct way of stress determination in coatings thicker than 0.5 mm. Because of their penetration power, neutrons can be used for stress measurements in relatively thick deposits (cm) and/or with fine resolution (better than 0.5 mm). Through-thickness stress profiles have been experimentally determined with success for different types of coatings nature (metals, ceramics and composites) produced by different spraying techniques [14,15]. Unlike the two mechanical methods described above, the neutron diffraction technique is phase sensitive and stresses can be assessed for each phase independently [16]. In addition, no special sample/surface prep-

aration is required. Although laboratory X-rays do not have the penetration power of neutrons and are not suited for stress profiling, they are indispensable for stress measurements on the surface of coatings and films [17] or the stress measurements in individual splats [18], or they can be adapted for the through-depth stress profiling in lmthin films [19]. In the present work we present the results of residual stress measurements obtained by using all discussed advantages of the neutron diffraction with the focus on stress profiling. Cold spray coatings produced using different coating/substrate material combinations have been studied. Through-thickness stress profiles are fit to the progressive deposition model of Tsui and Clyne [20–22], which has been used to assess the relative importance of thermal vs. kinetic effects in the accumulation of residual stresses during the cold spray process. Observations of the coating microstructure are used to interpret the measured stresses, which may be qualitatively predicted using an analogy to shot peening. This is done using a physically based model incorporating readily available material parameters. 2. Experimental procedures and material characterization 2.1. Materials Copper and aluminium were selected as coating and substrate materials. Different combinations of the substrate and coating materials enabled an analysis of the different factors influencing the residual stress state. Four samples in total were produced forming a 2  2 matrix, two coating materials vs. two substrate materials, Al/Al, Al/Cu, Cu/Cu and Cu/Al. The substrate materials used were electrical grade pure copper sheet and 5xxx Al–Mg alloy sheet, chosen because their grain size of 20–30 lm enables reasonable counting times for the neutron diffraction stress measurements. The thickness of the Cu and Al substrates was 3.1 mm and 2.6 mm respectively. Before spraying they were cut into square coupons 30  30 mm, sized to obtain a state of balanced biaxial plane stress in the central part. Prior to spraying the substrate surface was ground using 1200 grit SiC paper and rinsed with ethanol. The feedstock powders used were commercially pure copper and aluminium powders. The particle size for each material was measured using a laser diffraction particle size analyser, with the volume-weighted average given in Table 1. Both powders were produced using an atomization process, and are almost perfectly spherical in shape. 2.2. Spraying procedure The cold spray coatings were produced using a kinetic metallization (KM) system, which is a commercially available cold spray variant (Inovati, Santa Barbara, CA, USA). Whereas a conventional cold spray system uses a convergent–divergent nozzle to accelerate the process gas

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Table 1 Process parameters used for cold spray experiments. Powder material

Average particle size (lm)

Driving pressure (kPa)

Nozzle temperature (°C)

Powder feed rate (g min1)

Estimated particle exit velocity (m s1)

Al Cu

15 6

620 620

140 200

15 15

585 645

to supersonic speeds between Mach 1 and Mach 3 [23], KM uses a convergent barrel nozzle to accelerate the process gas to Mach 1 [24]. In order to increase the impact velocity, helium was used as the process gas, as the speed of sound in helium is almost three times that in nitrogen. Furthermore, we have used a smaller particle size than is typical in supersonic cold spray systems. Therefore, in this work the particle exit velocities are similar to those attained in a conventional supersonic cold spray system. The process conditions and resultant particle velocities are detailed in the next section. Useful comparisons of convergent vs. convergent–divergent nozzles in cold spray are given in Refs. [25,26].

between horizontal nozzle movement lines of the spray nozzle. We assume that this is due to dynamic effects of the spraying process. At first, small surface irregularities form because of non-uniformities in flux density across the stream of particles. As deposition progresses, these initial undulations are amplified: hills become bigger since they are exposed to more particle flux, but the valleys do not fill in because they are shadowed by hills, and they become relatively deeper. This defect is observed only in very thick coatings; in the present case they were made thick specifically to enable easier neutron stress measurements. Usually in practical applications the coating thickness is less then 0.5 mm, and this pronounced pattern is not developed.

2.3. Spraying conditions 2.4. Neutron powder diffraction measurements All coatings were sprayed using a temperature optimized for maximum deposition efficiency while avoiding fouling of the nozzle. The process parameters used are as follows. The nozzle standoff distance from the substrate was 12 mm and the nozzle traverse speed was 50 mm s1. The nozzle temperature was measured in the mixing chamber just upstream of the nozzle throat (Table 1). This temperature is used to estimate the exit velocity of the particles from the nozzle using a one-dimensional isentropic model based on that of Dykhuizen and Smith [27]. In a simple convergent barrel nozzle the gas speed through the barrel is less than Mach 1 due to friction effects. In the KM system the barrel of the nozzle has a slight divergence to compensate for friction [28]; therefore, the velocity along the barrel is Mach 1, which simplifies calculation of particle speed. The gas properties are calculated assuming ideal gas behaviour, and the average particle size is used. The particle drag coefficient is calculated using the correlation of Henderson [29], based on the change in particle Reynolds number as it accelerates through the nozzle. The process parameters are summarized in Table 1. It should be noted that the nozzle temperature is in fact the stagnation temperature of the mixed gas/particle stream just prior to being accelerated through the nozzle throat. The resultant thickness of the deposited coatings was 3 mm to enable through-thickness stress measurements using a reasonable diffraction volume. It is typical that thick cold spray coatings have an uneven surface, as shown in Fig. 1. A pattern appears with streak-like features in the direction of nozzle movement. Quantitatively, roughness has been estimated through maximum profile height, Rt = 1.0 mm, and average Ra = 0.2 mm. The spatial period of the ripples is 1 mm and this conforms to the 0.5 mm step

Neutron powder diffraction was used to measure the oxide volume fraction of the sprayed coatings, to compare it against the feedstock powder, and to confirm the chemical purity of the feedstock powders. Neutron diffraction was chosen over X-ray diffraction because the latter method is surface quality sensitive and can bias the result toward a higher oxide content. Also, the oxide content of the coating surface may be different from that of the coating bulk, and neutron diffraction enables a better average measurement. Neutron diffraction data were collected ˚ from the high resolution using a wavelength of 1.622 A powder diffractometer ECHIDNA at the ANSTO OPAL

Fig. 1. General appearance of the surface of the Al/Cu cold sprayed sample. Inset: the top coating surface profile obtained by digitizing of the sample cross-section.

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research reactor [30]. The phase volume fraction was determined using the GSAS Rietveld refinement software [31] with the EXPGUI front-end [32] for the Al and Cu feedstock powders and corresponding coatings. 2.5. Neutron diffraction stress measurements The bulk of the neutron diffraction residual stresses measurements have been carried out at the NIST Center for Neutron Research using the residual stress diffractometer BT8 [33]. A gauge volume 0.5  0.5  18 mm was chosen as a result of the fine balance between different competing factors: (i) it should be small enough to provide necessary through-thickness resolution and avoid edge effects; (ii) at the same time it should be large enough to produce a count rate sufficiently high such that experimentally determined strains can be measured with statistical uncertainty better than 5  105, within a reasonable measurement time. Since Cu is a stronger scatterer than Al the measurement time was varied correspondingly: 10 min per measurement point for Cu and 90 min for Al. The measurements were done in several different through-thickness locations to cover the entire sample thickness, forming a line profile with 0.3 mm spacing between points. In order to optimize localization of the gauge volume, the take-off angle 2hM of the Si (400) monochromator was varied to maintain a 90° geometry (2hB  90°). The instrument settings are summarized in Table 2. For each measurement point, d-spacings (diffraction peak positions) were measured in the two principle directions, normal to the surface and in-plane. From the measured d-spacings in-plane stresses were calculated using the assumption of a balanced biaxial plane stress state following the procedure described in Ref. [3]. The diffraction elastic constants used for stress calculation were computed using the self-consistent method of Kro¨ner [34], and are reported in Table 2. To separate stresses originating from the cold spray process from pre-existing stresses (e.g. residual stress from cold rolling of the substrate) neutron stress measurements were done on the uncoated substrate. They were treated as separate samples and measured using the same procedure. One sample, a Cu coating on an Al substrate, was measured on a different neutron diffractometer – the KOWARI strain scanner at the ANSTO OPAL research reactor. The measurement protocol was kept as close as possible to what is described above with only one major difference: for measurements in the copper coating the Cu (222) reflection was used. Use of the appropriate diffraction elastic constants, S1 = 1.94 and ½S2 = 8.23 TPa1, however, should ensure there is no practical difference.

2.6. Thermo-mechanical properties The planar geometry of the coatings and their small thickness make it difficult to obtain specimens large enough for direct mechanical tests. However, two methods were found to be appropriate to measure the Young’s modulus of the coatings: (i) Microindentation tests were performed on the polished cross-section of the specimens using a UMIS 200 universal material tester together with IBIS software to analyse the indentation data. The Bercovich test was employed in load control mode using a maximum load of 250 mN in the case of Al and 100 mN for Cu. The Young’s modulus was extracted by analysing indentation curves (unloading–displacement). Indents were made in several different locations to obtain an average value and a standard deviation. (ii) The Young’s modulus was also measured in rectangular specimens (27  5  2 mm for Cu and 32  5  2 mm for Al) using the impulse excitation technique (IET) according to the ASTM standard E1876. The accuracy of this method is generally high and limited in the present case by the parallelism of the specimen faces and the uncertainty of the smallest dimension. It was estimated that the accuracy was better than 0.5%. The coefficient of thermal expansion (CTE) was measured using a dilatometer. Samples were measured in the temperature rage of 22–300 °C in steps of 0.5 °C with a heating ramp rate of 5 °C min1. The CTE behaviour above 180 °C was the most stable, so it was used to judge the closeness of the CTE of the cold spray coatings to the equivalent bulk value. The rectangular specimens used to measure Young’s modulus in (ii) were also used to calculate coating porosity using Archimedes’ method. Bulk specimens of Cu and Al were used to assess the accuracy of the method, and the results are within 1% of published values. 3. Numerical modelling of the residual stress The basis of our analysis of residual stress accumulation is according to Tsui and Clyne’s progressive coating deposition model [20]. A given spraying process such as cold or thermal spray is complex; however, it has been demonstrated that the model is applicable to the prediction of the stress distribution in coatings produced by different techniques under various spray conditions [4]. Thus, we can consider that the progressive deposition model is ade-

Table 2 Instrument setting and material constants for the measured reflections. ˚) ˚) d (A 2hM (°) k (A

2hB

S1 (TPa1)

½S2 (TPa1)

t (min)

Cu (311) Al (311)

89.7° 89.5°

3.38 5.16

12.58 19.57

10 90

1.10 1.22

70.0 79.8

1.55 1.72

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quate to physical process and it adequately describes the elastic stress state in coatings unless stress development during the deposition process reaches yield conditions. In this case, plastic effects intervene and should be addressed in a more general elasto-plastic model, see e.g. Ref. [35]. Although the model was originally developed to model the residual stress accumulation in thermal spray coatings, it has been found to work equally well for cold spray coatings in the present work. Similar to the model applications used before in the case of the thermal spray for separation of quenching stress from thermal stress [12,15], in our study we use the same model to separate the peening stress from the thermal stress. In the model, two components of the spray process are accounted for separately using two different fitting parameters: (i) The coating deposition process is considered as the formation of a new, nth layer on the top of the previously formed system comprising the substrate plus all previously deposited coating layers. This new layer is formed with a characteristic deposition stress rd. For thermal spray coatings rd is treated as a tensile “quench” stress originating from shrinkage of a solidifying splat on the surface. For cold spray coatings this stress is compressive, characteristic of a peening process. (ii) The coating process occurs at or above room temperature. If after coating deposition the substrate + coating system is cooled to room temperature, then a thermal misfit term De is needed to account for thermal stresses arising from a difference in thermal expansion coefficients of the substrate and coating materials, De = DaDT. The significance of this term depends on the cooling range and difference in thermal expansion coefficients of the coating and substrate materials. Determination of the two physical parameters of the model can be made by studying the coating formation process on the microscopic scale. In the present case it was found more practical to obtain rd and De from the experi-

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mentally measured stress profiles; this serves to validate the microscopic modelling approach. The fitting process enables the relative significance of rd and De to be determined for a given coating, and also to evaluate the significance of these terms for different materials. This can be used to assess the importance of the thermal vs. kinetic components of the coating process, and the sensitivity of a given system to accumulating residual stress. 4. Results 4.1. Microstructure Secondary electron micrographs of a Cu coating on a Cu substrate and an Al coating (removed from a Cu substrate for etching) are shown in Fig. 2. Macroscopically, both coatings are uniform and free of large voids or cracks. At higher magnification some details of the microstructure are clear: while there is some deformation of the particles from their original spherical shape, the overall structure is still granular, as compared to the typical splat-like microstructure of thermal spray coatings. There was virtually no observable porosity in the Cu coatings, and a small amount of porosity in the Al coatings. The oxide content of the feedstock powders and coating materials is given in Table 3, as measured by neutron powder diffraction. The oxide content of the Al powder and coating was below the resolution of the measurement, 0.5 vol.%. Table 4 gives the porosity of the Cu and Al coatings estimated using Archimedes’ method. The oxide content of the coatings in Table 3 was used to correct the measurement, and measurements of the substrate materials were done Table 3 Results of powder diffraction phase analysis for different coating materials.

Cu powder vs. coating Al powder vs. coating

Oxide species

Oxide content (vol.%)

Cu2O Al2O3

5 ± 0.7 vs. 4 ± 0.7 <0.5 vs.<0.5

Fig. 2. Secondary electron micrographs of the cross-section of: (a) Cu coating on a Cu substrate and (b) Al coating on an Al substrate.

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Table 4 Porosity measurements for the cold spray coatings. q (g/cm3)

qref (g/cm3)

Vol.%

8.951 8.670 2.528

8.954 (Cu 100%) 8.806 (Cu 95% + Cu2O 5%) 2.700 (Al 100%)

99.96 ± 0.3 98.5 ± 0.5 93.6 ± 0.6

to verify the accuracy of the technique. Higher porosity in the Al coatings was expected because of the use of coarser powder (15 lm) than for the Cu coatings (6 lm). Although the use of a mixture of powders or finer powder can reduce the porosity of Al coatings to the level of 1–2%, the finer powders agglomerate and do not feed as consistently. 4.2. Thermo-mechanical properties The Young’s modulus measurements of the cold spray coatings are given in Table 5. They are closer to those of a bulk material than is found in the case thermal spray coatings. For example, a plasma sprayed Cu coating has a typical Young’s modulus of 30–40 GPa, while it is 100 GPa in the cold spray coatings examined here. In thermal spray coatings the deviation of mechanical properties from those of a bulk material is mainly caused by imperfections in interparticle bonding, oxidation of the splat surface and, to a lesser extent, coating porosity. While the indentation test and impulse excitation test give similar modulus values for the Cu coating, the two techniques give significantly different modulus values for the Al coating. Any calculations in the present work requiring Young’s modulus were done using the values obtained from the impulse excitation measurements, as this is generally considered the most accurate measurement of elastic constants. The difficulty of Young’s modulus measurements in coatings by indentation technique is known but with certain precautions can be successfully employed [36–38]. Issues such as the presence of a splat-like microstructure, the presence of porosity as well as surface preparation can impact results. The better agreement between results obtained by indentation and IET in the Cu coatings is in accord with the fact that the Cu coating is denser than the Al coatings, so for the Cu coatings porosity had a smaller influence on the measurements. Thus, the modulus value measured by the indentation technique can be more distorted in the case of the Al coatings and larger measurement errors are observed, as shown in Table 5. The thermal expansion coefficient was measured for both the coatings and the substrate material and a compar-

CTE [x10 -6 1/K]

Cu substrate Cu coating Al coating

30

25

Al

20

Cu 15

10 200

250

300

temperature,°C Fig. 3. Comparison of the temperature dependence of CTE of the sprayed material (solid line) and bulk value (dashed line).

ison of expansion behaviour is given in Fig. 3. There is no significant difference between the coating and substrate behaviour. The thermal expansion coefficient values obtained are summarized in Table 5, and are equivalent to those of a bulk material. 4.3. Residual stress The in-plane residual stress profiles determined by neutron diffraction are shown in Fig. 4a–d. Both Cu coatings show a significant compressive residual stress at the surface 50–80 MPa, while the surface residual stress of the Al coatings is less than 10 MPa. The overall stress profile of the two Cu coatings is similar, regardless of the substrate material, and the same can be said of the Al coatings. Some internal stress was measured in the freestanding Al substrate before the cold spray coating was applied, and this was subtracted to isolate stresses induced by the cold spray process. There was no significant residual stress in the freestanding Cu substrate. The error bars in Fig. 4 comprise both neutron counting statistical error and positioning error, and each of these gives approximately equal contributions to the total uncertainty. The achieved uncertainties of 5–10 MPa are typical of this type of experiment. In the points close to the free surface or the coating/substrate interface the measured stress values can be biased due to the edge effect in neutron stress measurements, and it is difficult to eliminate all of the error from this effect in the measurements. With these issues in mind, the stress balance condition is fulfilled for the experimental data: the volume integral of the residual stress adds to zero, which gives added confidence regarding the accuracy of the stress profiles. The stress profiles were used as an input to fit experimental data with the model of Tsui and Clyne as described

Table 5 Experimental values of the thermal and mechanical properties for coating materials. CTE (106 K1)

Young’s modulus (GPa)

Cu coating Al coating a

Indentation test

Impulse excitation technique

Bulk material value

Measured value

Bulk material value

98 ± 10 74 ± 20

104.0 ± 0.5 49.4 ± 0.2

124a 71

17 22

17 22

This value was also measured by IET on the specimen taken from the Cu substrate.

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(b)

100 80 60 40 20 0 -20 -40 -60 -80 -100

stress,MPa

stress,MPa

(a)

Cu substrate

-3

-2

Cu coating

-1

0

1

100 80 60 40 20 0 -20 -40 -60 -80 -100

2

(c)

Cu coating

-1

0

1

through-thickness position,mm

(d)

60 40

60 40

stress,MPa

stress,MPa

Al substrate

-2

through-thickness position,mm

1265

20 0 -20 -40

20 0 -20 -40

Cu substrate

-60 -3

-2

Al coating

-1

0

-60

1

2

through-thickness position,mm

Al substrate

-2

-1

Al coating

0

1

2

through-thickness position,mm

Fig. 4. Measurement (symbols) and model fit (solid lines) of the through thickness in-plane stress distributions for (a) Cu/Cu sample, (b) Cu/Al sample, (c) Al/Cu sample and (d) Al/Al sample.

previously, using the fitting parameters rd and De, which are characteristics of the deposition stress and thermal mismatch respectively. All other parameters such as coating thickness and elastic modulus were taken from measured values. The fitting parameters are given in Table 6 and the corresponding stress profiles are shown in Fig. 4a–d as solid lines. The fitted stress profiles are almost entirely determined by rd, with De having relatively little effect: the small shift resulting from setting De to zero is less than the experimental error (5 MPa) in the neutron diffraction stress measurements. 5. Discussion 5.1. Interpretation of the result in terms of empirical model parameters The fitted stress profiles in Fig. 4 are almost entirely shaped by rd. Its negative sign (compression) is indicative of “peening” on impact and the evidence of a certain degree of plastic strain of the sprayed material. It is the accumuTable 6 Fitting parameters of the model and the quality of fit of the experimental data. Coating/substrate

rd ± error (MPa)

De ± error (l strain)

v2

Cu/Cu Cu/Al Al/Cu Al/Al

41 ± 12 85 ± 20 9 ± 2 9 ± 2

150 ± 200 140 ± 200 140 ± 200 3 ± 200

2.0 2.4 0.8 2.2

lated peening stress from successive deposited layers that is largely responsible for the residual stress. The evidently higher values of rd in the case of the Cu coatings suggest the amount of plasticity on impact is more significant than in the Al coatings, leading in part to higher residual stress accumulation. The thermal mismatch term De has a minimal effect on the fitted residual stress profiles. This is due to the small macroscopic variation in temperature during the spray process of 100 °C, which is discussed in Appendix A (ii.2) and this makes the thermal mismatch term De = DaDT almost negligible. In the case of high-velocity oxy-fuel coatings both impact and thermal effects play a role in the accumulation of residual stresses. In contrast, the residual stress accumulation in the cold spray coatings examined here is primarily a result of plastic deformation resulting from particle impact, and thermal effects are relatively minor. Macroscopically, the residual deposition stress in the coatings rd is the net result of the stress resulting from shock loading, then unloading with, in general, reverse yielding and then possible stress relief due to recovery and relaxation processes. The microscopic interpretation of rd (in terms of micromechanics, on the scale of a particle) is less straightforward and requires the knowledge of many details of the deposition process such as non-uniform local deformation and recrystallization, that can be studied by some experimental methods such as EBSD [39] and TEM [40], multiple modes of stress relaxation, etc. (see the Appendix A for further discussion). Such complexity in the cold spray process makes it attractive to use finite

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element methods for numerical simulation [41,42], rather then analytical models. The task of establishing an accurate link between macroscopically available experimental data and phenomena at the microscopic level may ultimately require the use of statistically meaningful averaging procedures difficult for practical applications. In the next section an intermediate approach is described. In an attempt to establish a link between the micro- and macro-scales we discuss the importance of some factors and the relative insignificance of others based on available experimental data and easily attainable estimates. 5.2. Interpretation of the result in terms of physical process parameters While the fit of Tsui and Clyne’s empirical model to the residual stress data in Fig. 4 demonstrates the relative importance of kinetic aspects of the cold spray processes on residual stress formation and provides quantitative measure of the accumulative result, it would be useful to understand why the residual stress is so much larger in the Cu coatings, namely, why rd is larger in Cu than in Al. Given the complexity of the cold spray process a finite element simulation is best able to capture details the mechanics of residual stress accumulation. Several publications detail the use of finite element simulation to calculate the temperature and stress inside individual impacting particles [42,43], or a small number of successive impacting particles [44,45], in order to gain an understanding of the cold spray bonding process. Surprisingly there has been no attempt to extract residual stress data from any of these simulations, even though they incorporate the details of impact pressure, stress accumulation using a rate sensitive material model, and elastic unloading, e.g. Ref. [46]. In principle it should be possible to calculate at least the average residual stress in the coating and substrate respectively. While a finite element simulation should be able to predict residual stresses with reasonable accuracy, it is often difficult to extract simple predictive relationships from the results. In the present work a physically based approach will be used instead, incorporating data that are either measured or easily estimated. An analogy of the cold spray process to a Taylor impact test [47] will be used to estimate some process parameters, combined with a model of residual stress accumulation in the shot peening process, since this process has many similarities to cold spray. The relevant process parameters are given in Table 7. The particle impact velocity was calculated as described in Section 2.3. The impact strain was measured metallo-

graphically by fitting the deformed particles to an oblate ellipsoid, which is the closest regular shape with a reasonable fit. The deformation from a sphere to an ellipsoid of a given aspect ratio gives the average impact strain. Although there is generally strain localization at the particle boundaries, for the purpose of estimating the average residual stress it is the macroscopic particle strain that is of interest, since strain localization occurs over a relatively small volume of the particle. The final deformed state of the particles in a cold spray coating is the result not just of the initial particle impact, but also of successive particle impacts as the coating is built up. This is a similar situation to shot peening, where the substrate material is subject to multiple impacts. Using the calculated particle velocity and impact strain, the impact duration can be estimated by assuming the impacting particle decelerates linearly, as is done with the analysis of a Taylor impact test [47]. This also gives the average strain rate. The average impact pressure is calculated based on momentum transfer over the calculated impact time, as done in Ref. [48]. Of interest are the short impact duration, 10– 30  109 s, and the high average strain rate of 107 s1 (local strain rates can be even higher). The other interesting point is that the impact strain is significantly larger in the Cu coating than in the Al coating. Papyrin et al. have observed that the impact strain in cold spray coatings of different materials can be fit empirically to the ratio of the kinetic impact energy to the dynamic flow stress [49], and this makes sense when considering dissipation of the impact energy through plastic deformation. This ratio is higher in the case of Cu, so a larger impact strain is expected. The maximum impact pressure can be roughly estimated based on consideration of momentum transfer, by assuming impact of a moving plate against a fixed, stationary plate of the same material and size [47]. For the impact speeds in Table 7 this gives maximum impact pressures of 12.7 GPa and 4.5 GPa for Cu and Al respectively, well beyond the Hugoniot elastic limit (HEL) for both materials, of 0.6 GPa. As a result, the impact will propagate through the material in the form of a plastic shock wave. It is important to note that this calculation assumes a planar geometry. Since the impacting particle is roughly spherical during the impact process, attenuation of the plastic shock wave will occur as it traverses the particle [49]. As a result the pressure will rapidly drop and it is unlikely that the entire particle will deform plastically. However, once a given particle (now incorporated into the coating) is impacted by another particle, complete plastic

Table 7 Estimated impact parameters based on linear momentum transfer on impact. Material

Density (kg m3)

Particle size (lm)

Impact speed (m s1)

True impact strain

Impact duration (s)

Average strain rate (s1)

Average impact pressure (MPa)

Maximum impact shock pressure (MPa)

Al Cu

2700 8930

15 6

585 645

0.6 0.95

23  109 11  109

2.7  107 7.5  107

680 2020

4520 12,730

V. Luzin et al. / Acta Materialia 59 (2011) 1259–1270

deformation is likely to result. The average impact pressure should better incorporate these effects, and the magnitude of the average impact pressure for Al and Cu in Table 7 are very close to the interface pressures calculated by Grujicic et al. for Al and Cu using a numerical simulation [50]. The deformation in cold spray involves very high average strain rates on the order of 107–108 s1, and local strain rates as high as 109 s1 [49]. It is interesting to compare the strain rate in cold spray to other plastic deformation processes such as low plasticity burnishing (101 s1), deep cold rolling (102 s1), shot peening (104 s1), laser shock peening (106 s1), and combustion spray (1010 s1). In spite of a variation in strain rate of nine orders of magnitude, the surface compressive residual stresses in all cases depend almost entirely on the material and not the process, e.g. Refs. [51,52]. This is because the dynamic flow stress of metals exceeds the static yield stress by a factor 61.5–2.0 [53], due to limitations imposed by dynamic recovery at temperatures at or above ambient. When considering the accumulation of surface residual stresses we consider it reasonable to neglect the relative rate sensitivity of materials. With these points in mind the model of residual stress accumulation in shot peening due to Li and co-workers is appropriate [54], based on Hertzian contact and assuming plastic deformation on loading–unloading developed for the case of the shot peening. The present work uses a modified form [55,56] of the same formalism which is readily applied to the case of cold spray coatings. This approach assumes a material volume has been impacted with 100% coverage, and this is analogous to the problem in cold spray of a particle deformed partly by its own impact energy, and partly by the impact of successive particles that form the coating. The assumption is that the final amount of plastic deformation is more important than the deformation sequence. While it is not possible to make an exact analytical prediction of the residual stress in the cold spray coatings, it is at least possible to rationalize the results. The analysis can be reduced to the prediction of the maximum residual stress at the surface [55]: rmax ¼  ð0:333 þ 0:286abÞð1  abÞ½ð1  2abÞrs þ k  ab  pmax   1=5 2 5 4 2 pE qV pmax ¼ p 4 

ð1Þ ð2Þ

where pmax is the maximum pressure calculated in the assumption of Hertzian contact, rs is the yield stress, q is the density, V is the velocity of the particle upon impact, E* is the equivalent modulus, E ¼ E=2ð1  m2 Þ, and k is a constant close to 1. Two parameters, a and b, are coupled

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into a product that describes in simple terms the elastoplastic state of the deformed material: a is the ratio of the strain hardening rate (tangent modulus) to the Young’s modulus, and b is the ratio of the true plastic strain to the true elastic strain. As can be seen from Eqs. (1) and (2) the impact stress is the result of several competing factors: spray kinetic conditions (qV2), elastic material properties (E, m), and plastic material properties (ab and rs). The input parameters in Eqs. (1) and (2) are readily determined. The average impact pressure from Table 7 is used for pmax in Eq. (2) in order to roughly account for plastic shock wave attenuation effects. With these points in mind the following can be stated: – Cu is more dense than Al and Cu will have a higher impact pressure. – The flow stress of Cu is higher than that of Al over a wide range of strain rates [57–59]. – This higher impact pressure leads to a greater amount of plastic strain in the case of Cu, despite its higher dynamic flow stress. – Al shows minimal shock hardening compared to Cu [60]. Table 8 gives the estimated residual stress from Eq. (1). The estimated surface residual stresses for Al and Cu are qualitatively correct compared to the measured values, and it is thought that this analysis should hold true for other metals. While this is by no means an accurate quantitative prediction, it provides a useful estimate of the residual stresses when considering different coating materials, based on readily available material property data and some simple calculations. Even if a more accurate estimate is possible within this approach, the practical value of it might not be great until a degree of influence of some other factors on the residual stress (such as dynamic and static recovery, rate sensitivity, Bauschinger effects, the role of particle size, etc.) is clarified as discussed in the Appendix A. 5.3. Coating quality and performance through mechanical properties The results of the deformation modelling are relevant to the porosity measurements in Table 4 and the Young’s modulus measurements in Table 5. It is clear that the physical properties of Cu enable it to form a higher integrity coating than Al. Compared to Al, the higher density of Cu enables a higher impact pressure, without a corresponding increase in dynamic flow stress. This enables more plastic deformation on impact in the Cu coatings, and the

Table 8 Estimated residual surface stresses with corresponding input parameters. Material

Yield strength (MPa)

ab

Average impact pressure (MPa)

Estimated residual stress (MPa)

Measured residual stress (MPa)

Al Cu

30 60

0.01 0.04

680 2020

12 45

9 60

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porosity and Young’s modulus measurements for the Cu coatings are closer to their bulk values than those of the Al coatings. Higher deformation within the coating should lead to better interparticle bonding arising from conformal metal/metal contact by break-up of the particle’s external oxide layer. The relatively poor interparticle bonding in the Al coatings is likely why the Young’s modulus measurement based on the indentation test gives results that are so different from the impulse excitation test, with a rather large error. Another observation can be made on the basis of the comparison of our results with experimental data obtained on the thermal spray coatings and published in the literature. It has been demonstrated that, in the case of thermal spray, there is a correlation between the coating’s Young’s modulus and residual (quenching) stress [10–12]. The same was also demonstrated for two phase coatings [16]. This is not surprising considering the nature of the quenching stress: under cooling, with a temperature drop DT quench , a splat experiences the thermal misfit Deth ¼ acoat DT quench , where acoat is the thermal expansion coefficient of the coating material. If we consider the quenching temperature drop to be from the melting point then, for any material, the thermal misfit is Deth  1–2%. Because for thermal spray processes the thermal misfit is so high, it exceeds the yield strain (for metals) or the brittle fracture limit (for ceramics) by an order of magnitude since both of these limits have the typical value of De0  0:1–0:2%. Only this limited strain can be preserved as the elastic strain while the rest of the total thermal misfit is accommodated through inelastic mechanisms (microcracking, sliding, yielding, creeping, etc.), which eventually are reflected in the coating microstructure. Thus, the maximum quenching stress which a coating can withhold is rq ¼ Ecoat De0 , i.e. proportional to the Young’s modulus of the coating material. In case of cold spray, however, Eq. (1) suggests a different functional relationship between stress and Young’s modulus than a simple linear proportion. This is the manifestation of the different stress generation mechanism by complex plastic deformation accumulated throughout the full loading–unloading history of individual splats. The result of that must be connected not only to elastic (e.g. Young’s modulus) but also plastic (e.g. hardening rate) properties of the material. For instance, for different aluminium alloys cold sprayed in the same conditions, the correlation between the peening stress and UTS is more plausible, while the Young’s modulus values for different coatings are expected to cluster in a very narrow band. Experimental verification of this prediction in the case of cold spray coatings will require a larger series of samples sprayed at different conditions. 6. Conclusions The residual stresses profiles have been measured in Cu and Al cold spray coatings in neutron diffraction stress experiments. The experimental residual stress distributions

were treated empirically using Tsui and Clyne’s progressive deposition model to demonstrate that the residual stresses accumulate mainly by kinetic and not thermal effects, and these effects were characterized quantitatively. The interpretation of the measured compressive residual stresses is that they are determined almost entirely by the plastic deformation process (peening) of the particles of the spray material. An attempt has been made to explain the higher residual in-plane stress in the Cu coatings by using a physically based model of residual stress accumulation in a shot peened surface. Calculations within this model in the case of Al and Cu demonstrate that the balance between the elasto-plastic properties of the material and the spraying conditions defines the resultant residual stress. It is believed this interpretation can be applied generally for a range of materials providing a close numerical estimate. The higher plastic strain on impact of the Cu particles results in higher residual stress in the Cu coatings and better compaction, ensuring the mechanical properties of the Cu coatings are closer to their equivalent bulk values than is the case with Al coatings. Appendix A

(i) Although in the preceding arguments we neglected the strain rate dependence of the material flow stress, at such strain rates the effects of strain hardening, and strain-rate-dependent hardening coupled with heat transfer, can become important. The rate sensitivity of Cu and Al at the strain rates found in cold spray impact have not been measured experimentally, and the accuracy of results based on extrapolating material data one or several orders of magnitude in strain rate is questionable. On the other hand, in many simulations the Johnson–Cook or Zerilli–Armstrong material models [61] are used up to strain rates of 109 s1, but none of the data used for verification the model parameters extends beyond 105–106 s1 (achieved in the laser peening process). Available data on strain rate sensitivity show that the flow stress of Cu is roughly double that of Al, at any strain rate lower then 105 s1 [57–59]. (ii) Some of the initial impact stress is relaxed either during or immediately after the impact process through recovery and recrystallization. Dynamic recovery and recrystallization are expected to lead to stress relaxation, probably more so in Al coatings than in the Cu coatings. Recovery processes are poorly understood and a quantitative description requires knowledge of the dislocation density and spatial arrangement, which is beyond the scope of the present work (see, e.g. [62]). Roughly, one can estimate the relative operation of recovery processes in the two coatings as follows: 1. Because the thermal conductivity of Cu is higher than that of Al, the impact conditions are expected to be less adiabatic in the case of Cu.

V. Luzin et al. / Acta Materialia 59 (2011) 1259–1270

2. Under the impact conditions the average temperature of the Cu and Al as a fraction of the melting temperature are estimated as 0.35 and 0.44 respectively but during impact it may rise to as much as 0.9 locally, as suggested by numerical simulation of single particle impacts [41,42,50]. This sudden temperature rise is short, 107 s, and due to heat conduction and dissipation this does not in general lead to melting in Cu and Al coatings, as confirmed by numerous detailed microscopic examinations, e.g. Refs. [40,63,64]. The nozzle temperatures given in Table 1 are a measure of the gas temperature immediately before entering the nozzle throat, where some cooling takes place. The particle temperature will be lower than the gas temperature, though there is general heating resulting from plastic dissipation of the impact energy. It was possible to hold the samples immediately after spraying, which suggests that the average temperature rise was not very high. In the absence of detailed information on the thermal history of the material during the cold spray process, it can simply be stated that Al will likely be affected more by thermally activated recovery processes than Cu during cold spray. (iii) A variety of experimental data shows that the flow stress begins to increase rapidly beyond a strain rate of 105 s1 due to a change from thermal activation to drag-controlled motion of dislocations (e.g. Ref. [57]); however, this point has been debated (e.g. Refs. [47] and [58]). (iv) The Bauschinger effect can be important because of large plastic deformation in cold spray, and importance of yielding upon unloading process. (v) The role of particle size on the resultant stress is unclear. It can be speculated, however, that this role might be significant. At a minimum it can be said that particle size has a significant impact on the defect microstructure and, together with particle velocity, determines critical conditions for particle adhesion.

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