A review of testing methods for thermal spray coatings

Non-destructive methods

Non-destructive methods can be grouped into two categories. The first category employs electromagnetic radiation directed towards a coating in the form of X-ray diffraction, ^172,173 neutron diffraction ^174,175 or laser beam excitation spectroscopy. ¹⁷⁶ Diffraction methods are based on the measurement of the lattice plane spacing and are capable of determining the stress state of specific coating phases. The laser beam excitation spectroscopy method explores the shifts in the Raman bands ¹⁷⁷ or Cr³⁺ luminescence peaks. ¹⁷⁶ Electromagnetic radiation methods are often adopted due to the simple experimental setup, but care needs to be taken with respect to the specimen thickness requirement and the detection depth limitations, Table 9.

The use of laboratory X-ray diffraction (XRD) methods employs the reflection-based sin²ψ technique. Changes in crystal lattice plane d-spacing are measured with respect to the coating surface. Shifts in d-spacing from the original diffraction peaks and the specimen tilt angle, ψ, are correlated with internal strains in the coating. Thus, coating stress can be calculated with the use of appropriate elastic constants. ¹⁷³

The conventional laboratory XRD method is limited due to the shallow penetration of the X-ray beams, typically in the several micrometres range. It is possible to determine a coating’s through-thickness residual stress profile by performing XRD measurements that require progressive mechanical or chemical layer removal. ⁶⁸ However, this procedure compromises the non-destructive character of the XRD method; the details of which are provided in the next section.

Synchrotron or high energy X-rays offer 20–300 keV photons that are over a thousand times more penetrating than laboratory X-rays. Among the synchrotron techniques, transmission high energy X-rays have been used to determine localised phase composition and strains in plasma sprayed coatings. ¹⁸⁰ This method is also based on the sin²ψ concept, but allows for diffraction of discrete volumes of coating material through the coating thickness and uses an area detector to capture the full Debye diffraction cone from polycrystalline coatings. ¹⁸¹ The transmission technique requires cross-sectional samples with limited thickness but does not require material removal for discrete measurements throughout the entire thickness of the coating.

The neutron diffraction methods are capable of providing a through-thickness stress profile analysis up to centimetres, without the need of successive layer removal or cross-sectioning. This method uses a pulsed polychromatic neutron beam to measure Bragg reflections at fixed scattering angles and the time of flight of each diffracted neutron defines its wavelength. Two apertures, one before and one after the specimen, define the size of incident and diffracted beams. ¹⁷⁸ Their intersection defines the ‘gauge volume’ and is the volume being probed by the neutrons. From a set of lattice spacings in different orientations, and a stress-free lattice spacing, an elastic strain tensor can be found. Subsequently, using Hooke’s law, the stress tensor component can be established. At least six measurements in different orientations are required for the determination of the six independent stress tensor components. ¹⁸²

While neutron diffraction is not limited by penetration depth, the low spatial resolution (∼0·3 mm) necessitates long scanning times ^178,185 of about tens of minutes per measurement point. Neutron-based depth profiling near the interface is usually not representative of the coating. ^186,187 Also, the surface ‘vertical scan’ arrangement is preferred, in which the coated specimen is moved up or down in the ‘z’ direction for the depth profiling of strain in the coating and substrate material. ¹⁸⁸ In this arrangement there is no change in diffraction angle and, hence, no pseudo-strains generated since the gauge volume is consistently referenced with respect to the surface. A comparison of these methods ^178,179,181 is presented in Table 9.

The second category of non-destructive methods to measure residual stress involves substrate curvature monitoring by optical or mechanical means. The residual stresses can be calculated by comparing the curvature of strip-shaped samples before and after spraying. ¹⁸⁹ The in-situ curvature monitoring method, proposed by Kuroda et al., ^117,120 can provide information of (i) intrinsic quenching stresses during coating deposition and (ii) the differential thermal contraction stresses created during the cooling process. Variations of this method have been implemented across laboratories ^190,191 to monitor the residual stress build-up during the deposition and cooling stages.

Quenching stresses are determined from knowledge of the coating thickness and the gradient of curvature response during deposition. The quenching stress, σ_q, can be determined by using Brenner and Senderoff’s formula ¹⁹² (4) where ΔR is the change in radius of curvature caused by quenching stresses in a deposited layer of thickness Δt _D; and are the effective Young’s moduli of the substrate and deposit respectively; β is the ratio of and t _s is the substrate thickness. Tsui and Cyne ¹⁹³ developed models to predict the quenching stress for several geometric shapes. The models assume a layer-by-layer coating build up process such that the misfit strain was accommodated after each additional layer. Since curvature changes after each torch pass can be monitored, the quenching stress can be inversely deduced. ^193,194

After the deposition process, the differential thermal contraction stresses can be evaluated ¹⁹⁰ from equation (3). An example of temperature–curvature data of a plasma sprayed molybdenum coating is shown in Fig. 14. ¹⁹⁵ The different sub-processes such as preheating, deposition and cooling can be identified. Furthermore, the effect of the deposition condition is observed to influence the evolution of the coating stress states.

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14.

Reproduced from Ref. 195

Destructive methods

In destructive tests, the thermal spray coating is subjected to strain release as a result of material removal. The measurement of change in the stressed coating microstructure can be performed by means of (i) conventional, physically attached strain gauges, ^196,197 (ii) XRD, ⁶⁸ or (iii) optical displacement measurements. ^198,199 The destructive techniques are unable to differentiate the source of the induced stress. In addition, challenges exist in removing the material in a controlled manner. Plastic deformation or damage of the coating microstructure, especially ceramic coatings, implies that the assumption of a linear elastic change in the through-thickness stress state is invalid.

The hole drilling method that employs a strain gauge rosette is based on Mathar’s observation ²⁰⁰ that the shape of a circular hole drilled into a stressed structure will change. It is the most common practical technique for determining residual stresses in bulk materials. ²⁰¹ Reference 202 details its execution. The hole drilling procedure, shown in Fig. 15a , involves two stages (i) removal of the stressed material by drilling a small hole into the surface of the body at the centre of a special strain gauge rosette, and (ii) measurement of the relaxation strain occurring around the hole location. It is possible to calculate the strain state by means of an analytical model. ¹⁹⁷

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15.

Schematic representation of strain gauge methods to measure thermal spray residual stress; a hole drill method, ¹⁹⁷ and b modified layer removal method ¹⁹⁶

However, since thermal spray coatings display non-uniform through-thickness residual stresses, it is recommended to measure the stress profile through the coating. Therefore, the technique can be modified to perform incremental hole drilling. This method involves drilling a series of small steps of about 20–40 μm in depth ^203,204 that produce measurable strain relaxation. Analytical evaluation of the detected strain data using an ‘integral method’ is considered to be the most suitable ^204,205 data analysis method. It considers simultaneously the contribution of the measured strain relaxation of the stresses at all depths and also provides a separate evaluation of the residual stresses with each depth increment.

An alternate method was proposed by Greving et al. ^196,206 that involves the controlled removal of the coating via either electropolishing or wet polishing and monitoring the changes in strain on the substrate side (see Fig. 15b ). The method is based on the concept that the removed layer from the surface of a stressed plate or beam will release a force and moment acting on the remaining sample. The removed layer has to be insignificantly small so that (i) sufficient depth resolution is achieved, and (ii) the material removal process does not induce strain artefacts. Accordingly, the recorded strain data and thickness changes are used as inputs to calculate the residual stresses. ¹⁹⁶

Although low energy XRD methods offer high spatial resolution, there is a 10–50 μm depth detection limitation owing to the effective penetration of the radiation source wavelength and coating material. ¹⁷⁹ Thus, the strain measured on an as-sprayed coating relates to (i) a depth of no greater than its surface roughness, and (ii) is within a region subjected to substantial stress relaxation. ¹¹⁸ Methods that combine the residual stress measurements from coatings of varying thicknesses are not an accurate representation of the through-thickness stress profile.

Therefore, to allow the residual stress depth profile analysis of a single thermal spray coating sample, controlled removal of the coating layers using electropolishing for metals or cermets and wet polishing for ceramics has been combined with a reflective-based X-ray technique. ^68,207 Transmission high energy X-rays also can be applied to cross-sectioned samples for residual stress measurements. ²⁰⁸ This technique allows diffraction from discrete volumes of coating material through the coating thickness and uses an area detector to capture the full Debye diffraction cone from a polycrystalline coating. ¹⁸¹

Other residual stress measurement methods that have been applied include Moiré interferometry with cutting relaxation, ¹⁹⁸ probing surfaces with an indenter ²⁰⁹ and digital image correlation with focussed ion beam milling techniques. ¹⁹⁸

Types of hardness test for thermal spray coatings

Indentation tests ²¹⁰ have been used widely for thermal spray coatings to quantitatively measure their resistance to deformation under an applied load. Mechanical properties such as hardness, ^211–213 elastic modulus, ^164,214 fracture toughness, ^109,215 and interfacial adhesion or cohesion strength ^216,217 can be determined by performing variations of the indentation test method.

Reference 218 describes hardness test methods for most materials. Both of these indentation methods are commonly used for thermal spray coating characterisation. Essentially, the type of indenter (i.e., Knoop or Vickers) yields the associated hardness number. Specifically, for the indentation testing of advanced ceramics, there are five unique standards as shown in Table 10.

These standards highlight that ceramic materials have a tendency to develop cracks during testing as opposed to metal materials. Therefore, indentation at a small test load (typically less than 1000 gf) or microindentation hardness testing is recommended for ceramic materials. It is also necessary to allow sufficient spacing in between successive indents and implement a procedure to reject indents that develop excessive cracking. These details are covered within ASTM standards C1326 ²¹⁹ and C1327 ²²⁰ and are also represented in Fig. 16.

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16.

Guidelines for acceptance of indentations for Knoop (left) and Vickers (right) microhardness tests ^219,220

Another reason to avoid macroindentation hardness tests, which use loads between 1 and 100 kg, on thermal spray coatings concerns the size of the indent imprint. Typical thermal spray coatings have thicknesses less than 1 mm; thus macroindentation hardness tests on the coating top surface cannot be applied because the depth ratio of the imprint to coating thickness must be at least*4 10. ^219,220 Similarly, if the macroindentation hardness tests were performed on cross-sectioned coating samples, the imprint diagonal lengths will most likely exceed the dimension of the coating surface under examination. Under a load of 1 kg (i.e. 9·81 N) the Vickers indent diagonal length for materials of 300–800 HV is between 78 and 48 μm. The depth of imprints on cross-sectioned coatings should preferably not be greater than the splat geometry since the deformation response of the underlying layer cannot be resolved. On the other hand, microindentation hardness tests have the attribute of a small indent imprint; therefore specific phases or constituents and regions can be evaluated. Such information would be lost if a macroindentation test was performed.

Vickers and Knoop hardness tests

The Vickers indentation test uses a square-based, pyramidal-shaped diamond indenter with an included angle between opposite faces of 136°. Indentation is carried out at a predetermined load onto the surface of the polished coating. The Vickers hardness, HV in units of GPa, is determined from using the following relationship (5) where P is the test load (in newtons), θ is the included angle between opposite indenter faces (136°), and d is the average length (in millimetres) of the two diagonals of the indentation measured. It is meaningful to point out that the use of SI units, GPa, is consistent with the reporting format of scientific papers; although the use of the Vickers hardness scale is a more familiar format for engineers. A similar Knoop hardness scale also exists.

The SI unit of GPa is similar to that of pressure, tensile strength or elastic moduli and suggests that hardness may be correlated with the intrinsic material properties. ^210,221 There is such a correlation between the hardness values and elastic modulus. ^222,223 However, hardness is a more complex property than elasticity since it involves plastic deformation and brittle failure. ²²¹ Therefore, interpretation of a hardness value without relating this number to the microstructure may lead to a poor understanding of structure–property relationships.

A Knoop indentation test involves using a calibrated machine to force a pointed rhombic-based, pyramidal-shaped diamond indenter with specified face angles, under a predetermined load into the coating surface. Figure 17 illustrates the geometrical dimensions of the Vickers and Knoop indenters and sketches their indention impressions. Unlike a Vickers hardness test, Knoop indentations only require the measurement of the long diagonal of the resulting impression.

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17.

‘t’ is the coating thickness; ‘h’ is the penetration depth of the indentation; ‘d’ and ‘a’ are the diagonal impression lengths for the Vickers and Knoop microhardness tests, respectively

Another difference in comparison to the Vickers test concerns the calculation of Knoop hardness, which is the ratio of the applied test load to the projected area on the indented surface. The Knoop calculation assumes that the elastic recovery of the narrow diagonal is negligible. The mathematical relationship of Knoop hardness, in GPa, is given as (6) where P is the test load (in newtons), A _p is the projected area of the indentation (in square millimetres), a is the length of the major diagonal of the indentation measured (in millimetres).

The diagonal lengths of a Vickers indent are approximately 2·8 times shorter than the major diagonal of a Knoop indent for the same specimen at a similar test load. The indentation depth of the Vickers indent is approximately 1·5 times more deep than the Knoop indent. ²²⁰

The deeper Vickers indents are, therefore, more likely to cause cracks in ceramics than Knoop indents. The cracks may influence the measured hardness by fundamentally altering the deformation process that contributed to the formation of the impression. Generally, the cracks impair the measurement of the diagonal length because of distortion at the indent tip and edges. On the other hand, the long slender tip edge of the Knoop indentation is more difficult to discern precisely; especially for thermal spray coatings that have revealed multiple phases.

The Vickers and Knoop hardness measurements exhibit dissimilar indenter geometries and, thus, different impressions on the coating surface. Thus, forming relationships between these hardness scales is not recommended. In other words, there is no numerical equivalency between the Knoop and Vickers hardness scales and empirical conversions between these scales have no basis in scientific rigour.

Microstructural relationships in hardness testing.

The hardness values should be independent of the test load since the impressions made by the indenter are geometrically similar. However, it has been reported ^224,225 that lower test loads are more affected by localised microstructural variations than higher test loads. The ensuing hardness–load dependence was also found for microhardness testing of bulk ceramics and is known as the indentation size effect (aka ‘ISE’). ²²⁶ The ISE states that hardness will usually decrease with increasing indentation test load until it reaches a constant, ²²⁷ assuming that there are no substrate-induced effects. The phenomenon has been associated with factors such as the lamellar microstructure, surface energy and indenter shape. The ISE was more pronounced during hardness testing of thermal spray coatings due to the heterogeneous microstructure. The scatter experienced with the void systems, as well as the different phases of solidified splat layers, influenced the elastic response of the indent.

Therefore, the test load should be reported with the hardness value. The recommended choice of test load for both indentation methods should be sufficiently large to allow good indent observations but not cause excessive cracking at the surface. Typical microhardness test loads used for thermal spray coatings are 1 N (100 gf), 3 N (300 gf) and 5 N (500 gf). Lower test loads should not be used unless accompanied with suitable microstructural evaluation and the ISE should be taken into account during the reporting of such data.

The materialographic preparation before testing can influence the hardness results. In most cases, measurements were made with the test indent on the cross-section of the lamella structure. Thus, similar to porosity measurements by IA, the accuracy of the hardness test depended on the surface roughness that arises from the grinding and polishing procedures. An appropriate method of sample preparation for thermal spray coatings is described by Ref. 228.

Berndt and Leigh ¹⁰⁵ have shown that the Knoop hardness in the plane of the coating surface was about 1·5 times higher than indents made perpendicular to the substrate; i.e., on the coating cross-section. This can be explained by the anisotropic architecture of thermal spray coatings on the two orthogonal planes of symmetry. Thus, as illustrated in Fig. 18, indentations carried out (i) parallel to the spray direction, and (ii) perpendicular to the spray direction, should yield different values due to the splat piling orientations. The distinct void network and the volume of material under indentation loading account for the relative differences in hardness values.

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18.

Indentation test perpendicular to spray direction (coating top section) and parallel to spray direction (cross-section)

The most common orientation for an indentation test is on the cross-section of the thermal spray coating. However, the literature makes little mention of the indenter orientation with respect to the thermal spray lamellar microstructure. Thus, the indenter alignment can exhibit two prime orientations where the pyramid axes are rotated by 90°. It can be appreciated that the indent orientation may influence the test results; for instance, the axis of the indenter can be aligned (i) along the lamellar layers, or (ii) across the lamellar layers. Therefore, under such testing conditions the coating cross-section might reflect anisotropic behaviour.

It was expected that there would be scatter in the hardness data for a thermal spray coating because the random distribution of the pore and crack network influences the indent hardness values. Subsequently, the reliability of the entire data depends on the number of indentations performed. Ten indentations are recommended by the ASTM standards for Vickers and Knoop hardness tests. However, the heterogeneous nature of thermal spray coatings indicates that more indents are necessary. The associated coefficient of variance; i.e., standard deviation divided by the mean, should also be reported with the calculated mean. ²²⁷ Berndt et al. ²¹¹ and Valente et al. ²¹² further suggested that the hardness data could be assessed by using statistical tools such as the Student’s test and Weibull distribution analysis. The data scatter can be reduced by performing tests on carefully selected regions that appear to have no void defects. However, it must be cautioned that preferentially choosing dense areas within the coating for indentation will bias the data to high values and is not recommended.

Another indent technique uses a spherical indenter ²²⁹ that is intended to reduce coating damage during indentation. The stress field under such a blunt Hertzian indenter is quite different from that generated under a sharp indenter. ^230,231 Thus, comparisons of data generated by these two different test methods are not valid. A similar argument can be made concerning Rockwell hardness tests that employ a brale, 120° diamond cone, indenter.

Individual splats and lamellae can be characterised by using nanoindentation techniques that employ a 3-sided pyramid-shaped Berkovich tip. ²³² Nanoindentation is highly sensitive to the material phases and structural defects within the splat and is, thus, defect sensitive. The nanoindentation technique has also measured the material properties of singular nano-sized splats in coatings. ^233–235 In these tests, the nano-sized indents lie entirely within a single lamellar and it is expected that the indent depth is less than 1/7 of the lamellar thickness. Thus, these indent tests measure intrinsic material properties and represent the maximum value in coating characteristics. The influence of crack and pore networks that are micrometre-sized are not measurable by nanoindentation methods.

Elastic modulus measurements

The elastic modulus is traditionally evaluated from the slope of the initial linear portion of the stress–strain curve. Beyond the elastic limit, the sample undergoes plastic deformation, yielding and finally fracture. For bulk ceramic materials, the associated elastic limit, elastic modulus and fracture strength is a well-defined value.

However, for thermal spray ceramics or composite coatings, the elastic modulus is influenced by factors such as cohesion of the lamellae as well as the distribution of void and crack networks. The inhomogeneous architecture of a coating is likely to cause pseudo ductility because the lamellae may slide over each other. ²⁶⁸ In response to the external loading, the elastic energy dissipation will be governed by crack growth and fracture. Therefore, the determination of the precise elastic limit, as well as estimating the linear portion of the stress–strain curve can be a challenge. Consequently, there is a wide range of values for E _c for similar coating compositions deposited by an identical thermal spray method. These values can differ significantly from the equivalent bulk material. ^269,271

The stiffness result is sensitive to the test direction due to the anisotropic nature ¹⁶⁴ of the coating. In other words, it is important to remember the relative orientation of mechanical testing since the elastic moduli of thermal spray coatings are different in a direction parallel to the coating surface compared to the perpendicular direction.

The E _c measurement for thermal spray ceramics is difficult to execute because of the limited coating thickness and the brittle nature of the coating. There are different methods to measure the coating stiffness and most relate to the coating stiffness parallel to the substrate. Elastic modulus in thermal spray coatings can be categorised into destructive and non-destructive test methods, Table 12.

The two common techniques used by researchers to obtain elastic modulus values of thermal spray coatings are by the indentation ¹⁶⁴ and flexural bend tests, ²⁷⁶ which are the first two methods presented in Table 12. These techniques are used due to the simple specimen preparation procedures as well as the ease of executing the experiments and calculations. Another notable test that provides in-situ measurement values is the cantilever beam test ^117,190 that tracks the curvature profile of a thin substrate during the thermal spray process.

Indentation methods to measure modulus

The indentation test of thermal spray coatings undergoes the same procedure as a conventional indentation hardness test. The fundamental principle is based on the resistance of a solid material against the penetration of the indenter under load. An elastic–plastic field develops during the indentation process and the deformed coating is comprised of reversible, or elastic; and irreversible, or plastic, behaviour.

The Marshall et al. ²²³ method to calculate modulus assumes elastic recovery of the in-surface dimension of a Knoop indentation. Elastic modulus was hence determined by measuring the major and minor diagonals of the Knoop indent on the sample. In the fully loaded state, the ratio of the diagonal dimensions, a (major) and b (minor) of the Knoop contact area was defined by the indenter geometry, a/b = 7·11. Elastic recovery during the unloading cycle reduced the length of the diagonals and indentation depth. The reduction in length was evident for the minor diagonal, b′, while the major diagonal change, a′, was negligible. Therefore, on modelling the Knoop indent as an elliptical hole subjected to uniaxial stress, the relationship of the displacement can be summarised as follows (7)

The elastic modulus, E, is derived by rearrangement of equation (7). (8) where H _k is the Knoop hardness (in GPa) and α is a constant determined by Marshall et al. ²²³ to be 0·45. Since the measurement depends on the elastic recovery of the minor diagonal, b′, its alignment with respect to the coating microstructure can be used to measure anisotropic behaviour. The extent of recovery depended on the hardness to modulus ratio and the ratio of a/b′ was always greater than 7·11. Although, the Knoop indenter caused less damage among other sharp indenter geometries, it was critical to select the most appropriate test load. For example, an excessive indentation load may cause extensive cracking around the indent impression. However, crack-free measurements require low load indentation. The observation of small indent dimensions may require the use of SEM.

The alternative to the Marshall method is the Oliver and Phar method ²²² that used depth sensing indentation measurements. In this method, the applied load P, and penetration depth, h _i, curve are recorded simultaneously for the complete loading and unloading cycle. Different sharp indenter tips (i.e., Vickers and Berkovich geometries) and spherical indenters can be used and the apparent elastic modulus of the indenter specimen system (also known as reduced modulus, E*) can be defined as (9) where is the contact area of the indenter, dP/dh _i is the slope of the P–h _i curve of the initial stage of unloading from P _max. The constant c* = 1·142 for the Vickers, 1·167 for the Berkovich, and 1·128 for circular conical indenters. ²⁹¹ The contact area at peak load was determined by the geometry of the indenter and the depth of the contact. Subsequently, the elastic modulus of the coating was determined by accounting for the elastic effects of the non-rigid indenter. Mathematically, (10)

Rearranging for elastic modulus, E (11)

The characteristic material properties of the indenter, E _in and v _in, can be obtained from the equipment manufacturer. The use of the Oliver and Pharr method ²²² requires knowledge of Poisson’s ratio for the thermal spray coating. However, Poisson’s ratio values have not been determined widely for thermal spray materials and are often assumed to follow those of bulk dense materials that range between 0·20 and 0·30. Poisson’s ratio values for thermal spray materials are discussed further in ‘Poisson's ratio of thermal spray coatings’ section.

The size of the indent relates to the difference in measuring the elastic properties of the consolidated coating microstructure or the individual splats. Nano-sized indentations are most likely related to the local splat properties of the sprayed coating since the indents are sufficiently small to probe the individual splat. Local material phases and their elastic properties within a splat can be measured but the effects of micrometre-sized pores and cracks are not measured.

Thermal spray coatings are more appropriately measured with the use of micrometre-sized indents. Conventional microindentation will result in impressions that span across several splat layers, various void morphologies and the crack network. An appropriate indentation load must be selected that does not cause excessive cracking or localised densification of the coating. ²⁷⁷ The resulting micrometre-sized indent is, therefore, considered a more direct representation of the elastic and plastic mechanical responses of a thermal spray coating. It is cautioned that the interaction of indenter geometry with the microstructure under investigation must be considered when interpreting or comparing nanoindentation and microindentation results.

Bending test methods to measure modulus

The flexural test method can be used for either coated substrates or free standing coatings, in either the tension or compression modes. Producing free standing coatings can be arduous and the following discussion applies to flexural testing on a coating that has been sprayed onto a substrate.

The major difference between three-point and four-point flexural tests is the location of the bending moment. While three-point bending can be performed, the disadvantage is that there is a linear variation of the bending moment from a maximum at the loading point to zero at the two supports. This load pattern predetermines the failure location in the tested thermal spray coating; i.e., the failure locus is positioned under the loading nose.

The four-point bending method allows for uniform bending moment distribution between the two inner loading noses. In this case, the thermal spray coating fails at its weakest point within a large volume of the sample. In other words, four-point bending is able to measure the structural weaknesses within the coating loaded between the inner load noses and is a preferred test method for measuring thermal spray coating strength.

Nonetheless, the elastic modulus via the flexural method is determined from the measurement of applied force and sample deflection curves. There are mechanics of materials approaches that can be used for calculations. For three-point bending, the flexural elastic modulus of a beam under loading is related to the deflection w measured (12) where P is the force applied, L is the length of the outer supports (or ‘noses’), b is the specimen width and h is the beam thickness. The slope of the load versus deflection curve, , can also be used to calculate the flexural elastic modulus of the beam.

The formula for the flexural elastic modulus of a beam under four-point bending requires calculations that depend on the location of the loading span. There are 2 commonly adopted configurations, (i) the loading span is 1/3 of the support span (i.e., a = b), or (ii) the loading span is 1/2 of the support span (i.e., 2a = b). The deflection is related to two loads acting simultaneously and E _beam can be calculated by applying the principle of superposition (13)

The calculation for the 1/3 support span configuration is (14)

The calculation for the 1/2 support span configuration is (15)

The coating modulus is deconvoluted from the beam modulus by applying the rule of mixtures between the thermal spray coating and substrate. The elastic modulus of the thermal spray coating can be calculated from the following equation (16)

The use of equation (16) is valid for both modes of flexural bending and has provided estimates for the coating elastic modulus. ²⁸¹

A second method is derived from a mathematical relation of the bending mechanics of a bi-material beam. For flexural testing, the entire coated specimen bending modulus, E _beam, is expressed by (17) where h _t is the entire specimen thickness and subscripts ‘c’ and ‘s’ denote coating and substrate, respectively. The apparent elastic modulus, E^* , includes both bending deflection and shear deflection while the true modulus includes only the bending deflection. Their relationships are (18) (19)

The elastic modulus of the substrate, E _s, can be predetermined by conducting a bending test on an uncoated calibration coupon. The apparent modulus can be solved by relating the relevant equation, (12) or (13) with equation (17). Finally, the coating elastic modulus can be found by relating the apparent elastic modulus to the true elastic modulus.

The methods presented above are generally employed in cases for the flexural testing of a thermal spray coating–substrate system. Different variants of the test orientation ^278,292 and calculation methods exist but are not covered here.

The elastic moduli of thermal spray coatings depend on the concentration, shape, continuity, and the spatial distribution of the different phases in a composite or multi-phase coating. Consider the simple case of a composite comprised of two elastically isotropic phases, wherein the applied load causes equal strains in each of the phases at all times. In the case of a two phase structure, the overall composite stress is the sum of the stresses carried by each phase. The composite modulus is the weighted average of the moduli of two constituents ²⁸⁰ (20)

The subscripts represent the elastic modulus of the particular phase and vol is the volume fraction of that phase. Equation (20) is applicable to thermal spray coatings in which multi phases often exist within a coating microstructure due to the rapid melting and quenching of splats. This physical effect accounts for the differences in elastic moduli of coatings with similar chemical composition but processed by distinct thermal spray parameters that could alter the proportion of metastable phases.

Reported literature elastic modulus values for thermal spray coatings are presented in Table 13. A comparison of these values reveals that although indentation methods were often employed, these tend to exhibit higher elastic modulus readings compared to other methods. This is probably attributed to indents that are most likely placed in dense regions of the coating to enable a well-defined deformation for measuring purposes. Subsequently, the coating stiffness values will appear high since the test is measuring a sample region where the void content is low. This example highlights the subjective nature of the indentation technique that may present large errors if applied inappropriately.

In addition, thermal spray coatings also perform differently with respect to the load direction; coating stiffness in compression is usually higher than that measured in tension. ²⁷⁷ Under compressive stresses, the elastic closing of the pore and crack network tends to cause a gradual decrease of the microcrack density or increase in coating density. However, under tensile stresses, there is a coalescence of these microcracks; and such inelastic processes reduce the effective coating elastic modulus. ²⁹⁴

Models to calculate modulus

The methods to calculate the elastic modulus of the coating are derived, mostly, from the literature on dense sintered materials. Prior knowledge of structural features such as splat dimensions, degree of inter-lamellar bonding, porosity type and distribution are required for their application to thermal spray coatings.

For instance, porous materials can be considered as two phase structures, whereby the second phase is the void network; i.e. E = 0. The elastic modulus of this microstructure was found to conform to an empirical relationship such as (21) where E _o was the modulus of the dense material, ρ the volume fraction of porosity, and k a material constant. This relationship relates the volume fraction of voids to the coating microstructure and has ignored the influence of void morphology; that is, the effect of cracks contrasted to pores on the overall elastic modulus. ²⁷¹ The following expression has been used ¹⁶⁴ on the basis of pores and cracks that interact (22) where, ‘c’ is the axis parallel to the stress direction and ‘a’ is the plane perpendicular to ‘c’. P _s is the porosity. The model was used to explain the effects of oriented spheroidal-shaped pores on the thermal spray coating. Coatings with orientated spheroidal pores underwent a larger decrease in overall elastic modulus perpendicular to the major axis of the spheroidal pores. However, the model; i.e., equation (22), cannot be applied to practical situations.

Appropriate models encompassing the effects of the orientation and shape of voids on the elastic value of thermal spray coatings have been discussed by Nakamura et al. ²³¹ and Sevostianov et al. ¹⁰⁸ These models were effective in describing the anisotropic character of thermal spray coatings. By adapting these models, Kroupa et al. ²⁹⁴ modelled coating properties as a function of (i) globular pores, (ii) inter-splat horizontal pores/cracks, and (iii) intra-splat vertical cracks.

For instance, within a representative volume element V of a thermal spray coating there are N randomly distributed spherical pores of radii R _k and the coating porosity P _s is given by (23)

According to this model, cracks contribute to porosity P. The family of horizontal cracks and vertical cracks each have unique representative functions. ²⁹⁵ For a family of approximately N ₃ circular and randomly distributed horizontal micro-cracks of radii r _3k their scalar crack density p ₃ is (24)

The p ₃ function can be used to represent the crack network parallel to the substrate surface, which mimics imperfect bonding between splats along the interface. Similarly, for a family of approximately N ₁ circular and randomly distributed vertical micro-cracks of radii r _1k the scalar crack density p ₁ is (25)

The microstructural characteristics of thermal spray coatings with respect to anisotropy of the elastic moduli in the in-plane E _ip and through thickness E _tt directions are expressed as (26) (27) where the positive constants c ₁, a ₁, c ₃ and a ₃ depend on the Poisson’s ratio, v _o. (28) (29) (30)

It can be deduced from these equations that coatings with the same porosity levels (P _s) and scalar crack density values (i.e., p ₁ = p ₃) may exhibit anisotropic behaviour with respect to the two-dimensional elastic moduli, as shown in Fig. 21. The net effects of void size and shape dependencies are reflected in the ratios of its elastic moduli E _ip/E ₀ on p ₁ and E _tt/E ₀ on p ₃.

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21.

Graphic plots of equations (26) and (27) to show the ratio of coating modulus with respect to the intrinsic modulus. A constant volume of spherical pores of 0·1 is assumed. The levels of vertical and horizontal cracks are plotted on the x-axis. The variation in Poisson’s ratio is represented by each individual line

Another theoretical model of the relationship between the coating elastic modulus and structural parameters was proposed by Li et al. and McPherson et al. ^271,296 It was assumed that when a load was applied perpendicular to the deposit plane, then the stress would be transferred from one lamella to the other through the bonded interface area. Under such loading conditions, lamellae would experience tension at the bonded interface area and bending at the non-bonded regions. Thus, neglecting the effects of vertical cracks, this analysis showed that the elastic modulus of an idealised thermal spray coating perpendicular to the coating plane consisted of two components. These being:

Using circular plate theory for an idealised microstructure consisting of the stacking of micrometre-sized lamellae; the Young’s modulus in the through thickness direction, E _tt, can be determined as (31) (32)

Where 2R is the diameter of the single splat, 2a is the size of the bonded region, δ is the mean lamellar thickness and α is the bonding ratio between lamellae. The term f(β) is a function of the interface bonding ratio. There are two components of elastic strain for the coating under tensile stress; one arising from localised elastic strain at regions of ‘true’ contact between lamellae and the other arising from elastic bending of the lamellae between the contact regions.

The modelling of micro-cracks as a distribution of flat hollow rotational ellipsoids as shown in Fig. 22 should not be interpreted as the actual micro-crack distribution. Physically, the inter-splat boundary structure exhibited regions of good bonding, surrounded by interconnected non-bonded regions of complex shapes. Similarly, ignoring micro-crack formation to achieve an idealised thermal spray microstructure is not experimentally possible. Nevertheless, the models developed can be considered as useful theoretical treatments, to explain the low values of Young’s moduli and elastic anisotropy of thermal spray deposits.

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22.

Theoretical model of the idealised microstructure in relation to Li’s model ²⁷¹

The Griffith concept

The fracture mechanics approach for assessing thermal spray coatings is based on linear elastic fracture mechanics (LEFM) that was pioneered by Griffith. ²⁹⁸ The Griffith theory indicates that the fracture work per unit crack extension at the onset of unstable fracture is balanced by the strain energy release rate from the surrounding elastically strained material. In other words, the fracture zone absorbs a large amount of additional energy and this must be balanced by the energy required to create a new fracture surface. ^237,299,300

In particular, the ‘strain energy release rate concept’ will be introduced to further clarify the quantity of energy released from a fracture. Two terms need to be defined:

The condition for spontaneous fracture is reached when the strain energy release rate, G equals G _c. The mathematical relationship relating the strain energy release rate for the crack tip is (33) where σ_c is the stress level and 2a _c is the crack length at fracture. E is the elastic modulus of the material.

The problem can also be formulated in terms of the concept known as ‘stress intensity’, leading to the terms of (i) stress intensity factor, K, (i.e., K _I for plane stress) and (ii) critical stress intensity factor, K _c, (i.e., K _Ic). The quantities such as K _c and K _Ic are commonly referred to as the material fracture toughness. Linear-elastic fracture toughness of a material in plane stress or plane strain, K _Ic, is related to G _Ic and the material Poisson’s ratio, v (34)

The equations (33) and (34) can be rewritten to describe the tensile stress that corresponds to initiating a crack of length a _c (35)

Application to thermal spray coatings

For thermal spray coatings, the σ_c from the above equation relates to the strength of the microstructure of the sprayed material under the influence of the pore and crack network. ²⁶⁸ It is shown in Fig. 23 that the initial crack a ₀ grows to the critical crack length a _c for coating failure. The coating elastic modulus, E, depends on the porosity and contact between the lamellae. Therefore, G _Ic would also depend on these microstructural features because a crack can propagate between areas of weak contact within the splats. In other words, the fracture strength of a coating is related to its microstructure by E and G _Ic. The largest pores or micro-cracks produced during spraying would be expected to act as fracture initiating defects ²⁶⁸ and, thus, influence strength through a _c.

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23.

Illustration showing crack growing from an initial crack length to a critical crack length. An inter-splat boundary has been overlaid onto this image to indicate potential fracture initiation sites

The focus of discussion on fracture toughness has been on plane stress loading or fracture in ‘mode I’. The subscript ‘Ic’ denotes ‘mode I’ crack opening under a normal tensile stress perpendicular to the crack. Other modes of fracture, Fig 24a , include the shear (mode II) or the tearing (mode III). However, thermal spray ceramic coatings typically exhibit a much higher compressive strength than tensile strength; therefore, they do not fail in shear modes under loading normal to the coating surface. That is K_IIc and K_IIIc are much higher than K _Ic. ²⁹⁹ For this reason, the testing of thermal spray coating fracture toughness has been limited mostly to ‘mode 1’ or determining K _Ic or G _Ic, ²³⁸ although ‘mode 2’ fracture studies have been performed. ³⁰¹ The complex splat interactions also dictate the crack path. As depicted in Fig. 24b , the initial crack, a ₀, can propagate through defects within the coating.

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24.

a Possible fracture modes for thermal spray coatings. b ‘a _c’ represents the initiation cracks. Three potential cracking mechanisms are suggested

The methods to determine fracture toughness has been detailed by Lin and Berndt ^237,238 and include (i) the double cantilever beam (DCB) test, (ii) the double torsion test, (iii) a flexural bending test, (iv) the scratch test, (v) the indentation test method, and (vi) the tensile test. Table 14 compiles several of these methods and identifies the related quantity of measure, K_Ic or G _Ic.

The locality of measurement is determined by the fracture path of the specimen. By controlling the locus of fracture, it is possible to carry out fracture toughness tests for either the coating–substrate interface or within the coating structure itself. One example is the DCB test, in which carefully orientated grooved edges are machined during the specimen assembly. ²³⁷ The DCB testing of plasma sprayed alumina coatings measured values of G _Ic = 10–15 J m⁻² for adhesive and G _Ic = 16–25 J m⁻² for cohesive failures. ²³⁷ The preference for fracture at the coating–substrate interface during four-point bend methods implies that fracture toughness values reflect the microstructure’s interface strength. Modified four-point bend measurements on APS YSZ coatings have shown that the interfacial fracture toughness ^304,306 is about G _Ic = 17–50 J m⁻² but can increase to about ∼120 J m⁻² after accounting for sintering effects after high temperature exposure. ³⁰⁶ Similar values for DCB testing of APS YSZ coatings, G _Ic = 20–80 J m⁻², have been obtained by Heintze and McPherson. ³⁰⁹

The TAT data are a measure of coating fracture; hence it is possible to correlate the TAT results to the fracture toughness of thermal spray coatings. The TAT geometry can be considered as a bar with circumferential cracks; therefore, permitting a fracture mechanics interpretation of the adhesive/cohesive strength of the coating. Berndt ²⁴³ proposed that the tensile strength can be transformed into fracture toughness by the relationship ³¹⁰ (36) where P is the TAT specimen failure force, D is the outside diameter of the bar and d _i is the inside diameter in the circumferentially notched bar. It was assumed that the notch in the bar was conferred by pre-existing defects such as splat boundaries and other defects.

Indentation methods

Fracture toughness measurements for thermal spray coatings can be performed by the indentation method. However, it must be pointed out that the location of the indent determines the region of the microstructure that is measured. Importantly, the coating fracture toughness should not be confused with its interface fracture toughness. Thus, the interface fracture toughness refers to indentation along the coating–substrate interface. ²¹⁶ On the other hand, an overload indentation test measures an average fracture toughness of the coating that is not localised to a specific microstructural feature.

Failure is most likely to occur along the interface between the bond coat and substrate interface for the majority of fracture toughness measuring techniques. If a particular feature of a coating microstructural volume is the artefact of interest, then crack propagation must be deliberately controlled to cause the specified fracture mode. For the DCB test, ³¹¹ a groove can be placed within the coating to promote cohesive failure. Similarly, Vickers indents ¹⁰⁹ may be placed within the microstructural volume of the coating to obtain the fracture toughness of this specified element without the influence of the substrate.

The difference in interface fracture toughness and coating fracture toughness is highlighted in Fig. 25. The indentation fracture toughness of a thermal spray coating microstructure can be calculated by several methods. The methods of (i) Lawn et al., ^109,312 and (ii) Niihara et al. ^307,313 are listed below: (37) (38) where a is the diagonal length of the indent, E _c is the elastic modulus of the sprayed coating, P is the indenter load, c is the total crack length, and H _v is the measured Vickers hardness value. In both methods, a median crack type ³¹² is assumed; and c/a≧2⋅5. It should be emphasised that Lawn et al. intended this method to be employed for dense ceramics and never applied this relationship to sprayed coatings. However, the method has been adopted by scientists and engineers in the thermal spray community.

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25.

‘a’ refers to the diagonal length and ‘c’ is the total crack length; (i) Parallel cracks within the coating lamellae; (ii) perpendicular cracks within the coating lamellae; (iii) crack along the coating–substrate interface

Chicot and coworkers ²¹⁶ have investigated the interface fracture toughness. They found that for a given coating and substrate couple, there exists a load that is independent of the coating thickness and which corresponds to the cracking ability of the interface. The Vickers indent was deliberately placed along the axis of the substrate–coating interface, inducing semi-circular shaped cracks localised along this interface. The measurement of the crack formation was proportional to the substrate–coating interface fracture toughness values (39) where P _c was the critical indenter load and was considered to be representative of the adhesive properties of the coating on its substrate. The term H _a was the apparent hardness at that indenter load, E _a was the apparent elastic modulus and C _IFT was the length of crack induced along the interface. The interfacial fracture toughness of flame sprayed alumina coatings on steel substrate ²¹⁷ was found to be between 0·7 and 1·9 MPa m^0·5.

The cracking behaviour of a coating is influenced strongly by its anisotropic microstructure. Therefore, the orientation and placement of indents must be appropriately considered for the indentation fracture toughness testing of thermal spray coatings.

It was mentioned that the elastic modulus of thermal spray coatings was lower than that of the bulk material because of its porosity network and diminished contact area that results from splat overlays. Similarly, the effective fracture surface energy, (G _c)_eff, would be lower than that of the bulk material G _c since a crack would pass from one region of good contact to another.

McPherson et al. ²⁶⁸ proposed a simple model to describe the effective strain energy release rate in a typical thermal spray microstructure. Since (G _c)_eff was related to the bonding ratio between the neighbouring splats, fracture would not be expected to occur by propagation of a single crack in a coating. The mathematical relation is: (40) where α is the bonding ratio between lamellae; that is the fraction of the lamellae surfaces in contact with other lamellae, and m _c is a factor describing the multiplication of crack branching that would increase the crack surface area. G _{Ic_dense} is the fracture surface energy of a dense material.