Samples: Materials and Spraying Conditions and Characterization
A commercially available CP titanium powder of grade 4 was used to spray samples for this study. The average particle size was 27 µm, while the powder size distribution and particle morphology are presented in Fig. 1(a).
A cold spray system (CGT KINETIKS 3000) with converging/diverging (de Laval) nozzle was used for direct fabrication of the Ti structures for this study. The nozzle geometries were 51.2 mm converging section, 2.7 mm throat diameter, 70.3 mm diverging section and 8.3 mm exit diameter. The nozzle was made of tungsten carbide. The deposition was carried out at 24 bars pressure and 800 °C spray temperature, with N2 as carrier gas. These parameters were chosen in relation to maximum capacity of the CGT KINETIKS 3000 cold spray system and in order to achieve the maximum particle velocity needed for deposition of a dense and low porosity material. The nozzle was mounted on a robotic arm to precisely control the cold spray supersonic jet motion during deposition. The transverse speed of the robotic arm was 80 mm/sec, and standoff distance was 45 mm. The overall procedure was almost is all details identical to the reported earlier (Ref 18, 19).
Two samples were produced using CS.
A CP titanium coating was sprayed onto stainless steel substrate
A CP titanium wall or bar was sprayed on Al substrate using a mask positioned between the nozzle and substrate to obtain a dumbbell shape deposit. For the purpose of stress analysis in the central cross section, the sample can be referred as a Ti bar deposited on an Al baseplate.
The final shapes and dimensions of the samples are reported in Fig. 2.
The microstructure of the sprayed Ti is shown in Fig. 1(b) and has a typical flattened splat or fish scale pattern. The mechanical characterization was focused on obtaining the elastic modulus, which is important if modeling of the stress state is attempted. Thus, a rectangular specimen was extracted from the bulk of the deposited material (approximate dimensions 40×5×2 mm3) and the Young’s modulus was determined using the impulse excitation technique (IET) accordingly to the ASTM standard E1876, which relies on measurements of the normal frequency. With the given sample dimensions, the value of the Young’s modulus was 68 GPa (for solid Ti, the bulk value is ~116 GPa) with statistical uncertainty less than 1%.
Neutron Residual Stress Measurements Strategy
With two different sample geometries and dimensions, the measurement strategies in the two cases were different and based on the following considerations regarding the expected stress state and required spatial resolution.
(1) The coating sample is a typical representative of a system that very accurately abides to the plane-stress condition. The applicability of the plane-stress condition in coated samples has been demonstrated practically but above that has a strong theoretical basis from the elasticity theory. First, the normal stress component (normal to the surface) is exact zero on both surfaces of the coated sample, σ33 = 0. (Here, x3 is the through-thickness dimension, while x1 and x2 are the in-plane coordinates.) Second, the condition for changing of σ33 in the through-thickness direction is determined by the existence of the gradient of other stress components stated by the following equation of equilibrium for the normal component:
∂ σ33∂x3 = − (∂ σ13∂x1 + ∂ σ23∂x2).
Thus, with uniform samples in x1 and x2 dimensions (no gradient), there must be no gradient of the σ33 in the thrugh-thickness direction. As a result, the plane-stress condition holds true through the whole thickness of a coated sample.
Of course, this condition breaks when location is close to the edge of a sample with large gradients in x1 and x2 dimensions.
Furthermore, when the spraying of particles is perpendicular to the surface, it is expected that symmetry of the process is reflected into the stress state of the sample. Thus, the normally expected stress state has the isotropic in-plane symmetry therefore the equal-biaxial stress state, 11 = 22. This assumption is not valid anymore when spraying is done under certain tilt angle to the surface, and in this case, a biaxial stress state is rather expected, 11 ≠ 22. Therefore, depending on the exact production conditions, the residual stress state is characterized by a one-dimensional, through-thickness dependence of one or two in-plane stress components that should be reconstructed from the measured strains.
(2) The bar sample represents a more difficult case. In general, it is expected that stress field is 3D, but limiting ourselves to a central transverse cross section (Fig. 2b) because its symmetry can provide some simplification. Three principal directions are the longitudinal (L), transverse (T) and normal (N) components, though locally (e.g., in the areas close to corners) they are not the principal directions anymore. For practical characterization, it is required to measure three normal components in the 2D cross section.
While these three components are allowed to have certain distributions from general elasticity theory point of view, due to large difference in dimensions some approximations might be contemplated. For example, 3.4 mm wall thickness can be considered as thin wall in comparison with longitudinal dimension of 40 mm; therefore, the transverse stress component is expected to be very weak (and it is exactly zero on the vertical walls) in comparison with the longitudinal one. A similar consideration regarding the normal component can also suggest that this component is going to be weak. Essentially, if looking at the cross section, the stress field in the deposit is supposed to be one-dimensional with only dependence along wall height. Nevertheless, our measurement strategy did not involve any of these simplifying assumptions and three normal stress components were determined in the central 2D cross section in order to prove or disprove the above considerations.
The stress distribution in the Al baseplate central cross section is expected to be more complex with through-thickness and transverse dimension dependence. To measure this field in any full manner would require too much of neutron beamtime. Only one central line was measured for control purposes and, nevertheless, that provided sufficient additional information to characterize and validate our numerical stress modeling attempts.
Neutron diffraction residual stresses measurements have been taken using the stress diffractometer KOWARI at the ANSTO OPAL research reactor (Ref 20). The instrument is equipped with Si(400) monochromator with changeable take-off angle that allows choosing a neutron wavelength accordingly to measured material.
(1) Coating sample. For through-thickness strain measurements in the middle part of the coating sample, a gauge volume with dimensions 0.5×0.5×20 mm3 was used. The use of the match-stick gauge volume elongated in the in-plane dimension allows full utilization of the planar sample geometry for maximizing the overall volume of the scattering material while maintaining the 0.5 mm through-thickness resolution. With 5 mm3 overall gauge volume, the count rate is sufficiently high for determining strain with typical statistical uncertainty of 5 × 10−5 within a reasonable measurement time. For materials like steel, it usually translates into 10 MPa uncertainty of the stress values. The exposure times were ~2 minute per position for the measurements in the Fe substrate and ~40 minutes per point for the Ti coating. Such big discrepancy is due to big difference in the neutron scattering properties of Fe and Ti: diffraction intensity of Ti is approximately 10 time smaller, while background is 10 times larger. Additionally, the cold spray materials have significant effect of peak broadening that further decrease the overall accuracy of the strain measurements and increase the measurement time.
The strain measurements in the steel substrate were taken using γ-Fe(311) reflection with a neutron beam wavelength of 1.54 Å, while Ti(103) reflection and wavelength of1.89 Å were used for strain measurements in Ti coating. The choice of different wavelengths was stipulated by requirement of providing approximately 90°-geometry for the both reflections that investigated, i.e., γ- and α-Fe(211) with the diffraction angles being 90° and 82°, respectively.
The strain measurements were taken in many through-thickness positions covering the entire sample thickness. The 0.5 mm spacing between points was chosen to be proportional to the overall thickness of 9.5 mm and gauge volume size of 0.5 mm. The strain measurement locations were determined from surface intensity scans (entry curves) to accuracy better than 0.03 mm.
Despite the prediction that equi-biaxial stress state was most likely expected, two in-plane directions and one normal direction were measured in order to reconstruct two in-plane stress principal components under the assumption of plane-stress condition as discussed above.
A “substrate only” sample was also measured with the same measurement protocol to quantify the pre-existing stress distribution in the substrate material due to production. It was subsequently subtracted from the coated system stress data so that the stress represents residual stress that is generated by the cold spray process only.
(2) Bar sample. Stress investigations were performed using a wavelength of 1.665 Å using take-off angle of 79º that put the Al(311) reflection close to the optimal 90°-geometry, while Ti(103) reflection is at ~80°. A cube-like gauge volume of dimensions 1×1×1 mm3 gauge volume was used to scan across central transverse cross section of the sprayed Ti bar with dimensions 3.4×5.4 mm (width × height) as well as for through-thickness scan of the Al substrate of 2.8 mm thickness. All measurements were taken with fully submerged gauge volumes. Strain accuracy of 100 μstrain was achieved against a data acquisition time of ~10 minutes per measurement point for Al and ~40 minutes per measurement point for Ti. Measurement locations were determined from surface entry curves to accuracy better than 0.05 mm. Measurements of three principal directions were taken to reconstruct three principal stress components in assumption of the constant d0.
For stress calculations from the measured strain in all cases, the isotropic elastic diffraction constants were used. They were evaluated in accordance with the material and (hkl) indices of the reflection from the corresponding single crystal elastic constants using IsoDEC program (Ref 21). After the calculations of the stress components, they were checked to insure the fulfillment of the available stress balance and boundary conditions.
Fitting Experimental Stress profiles with Analytical Models
The experimental stress profiles and maps are often misleading and confusing. For example, it is common to find a statement that cold spray generates compressive residuals stress. Although this is usually correct for the most surface layer of deposited material, there might be some interior layers of cold spray that are under tension; thus, this statement requires more accurate formulation and interpretation. Second, the magnitude and distribution of the residual stress always depend on the dimension of the sample and, for example, coated samples sprayed to different thickness will demonstrate different stresses. Not only the dimensions of the substrate but also the substrate material (or more precisely, the elastic and thermal properties of the substrate) that also plays a role in formation of the residual stress profiles. For example, the Young’s modulus of a substrate would be associated with amount of elastic constraint provided by the substrate in respect to the coating. Thus, the stress values in the experimental data represent a rather complex convolution of the substrate and coating material properties, dimensions and geometries with inherent parameters that are characteristic of the spray process and its truly attributes. The general approach to de-convolute different parameters of the elastic system is to model stress fields, analytically or through FEM, with explicit expression of the dimensional and material properties parameters. Due to complexity of the stress calculations for bodies of arbitrary shape, only an FEM approach can be recommended in general. However, in the case of our given simple sample geometries, a much easier analytical solution approach is attempted in the following ways.
(1) The coating sample was treated through use of the layer deposition model developed by Tsui & Clyne (Ref 13). This approach was tested and applied multiple times to stress analysis of coatings made by different techniques (Ref 22, 23), including the cold spray coatings (Ref 12, 24, 25). It is based on the one-dimensional stress distribution analysis of the coating-substrate system, which allows an analytical solution. This model gives an empirical description of the coating-substrate system with only two fitting parameters (while assuming that all thermal, elastic and dimensional properties of the coating and substrate are known):
The deposition stress σd. It is characteristic of the spray process; its sign and magnitude are determined by the spray process physical parameters (the main ones are particle temperature and velocity) as well as plastic properties of the sprayed material; it can be tensile (quenching) or compressive (peening).
The thermal mismatch Δεth. It accounts for the discrepancy in the thermal expansion coefficient (CTE) between materials of substrate and coating, Δεth = ΔαΔT, where ΔT is the temperature drop by at the end spraying process, while Δα is a difference in CTE. If the temperature is well monitored (known ΔT) and the materials CTE’s are also known (then known Δα), this parameter can be also fixed reducing the whole problem to one-parameter fitting.
Using this parametrization, the experimental through-thickness profiles can be fitted and these two parameters, σd and Δεth, can be extracted. Based on this approach, separate contribution into the final stress state can be quantified and then factorized.
(2) The bar sample poses more complex elasticity theory problem with potentially three nonzero stress components and 2D stress distribution in the sample cross section. However, with certain simplification, the same approach based on the same parametrization can be applied. We can consider the same two parameters:
The deposition stress σd to characterize the spray process, and
The thermal mismatch Δεth to accounts for the thermo-elasticity part if CTE’s of the coating and substrate materials are different.
However, the deposition model must be reassessed. While the layer deposition model deals with the case of a free-standing substrate, which is allowed to bend and deform during the deposition process, the more appropriate model for the additive manufacturing of a thin wall (or bar) is to consider a fixed substrate on which the wall was is deposited and only then the substrate bending constraints are released. This kind of scenario was considered and quantitatively validated on a similar additively manufactured thin-wall sample made by SLM (selective laser melting) (Ref 26). Assuming the wall to be thin eliminates the necessity of the transverse component to be analyzed—it should be very close to zero across the wall. However, this approximation depends on exact dimensional characteristics and at least requires an experimental verification, which has been done in this study.
Performing the above analysis allows parametrization and separation of different aspects of the CS process in its connection to the observed residual stress distribution. Also, the geometrical factors, such as thickness or material of substrate, can be eliminated and stress distribution can be reduced to few (one or two) parameters fully characterizing the elastic system and its stress field. In our case, those characteristic parameters, when extracted, allow to compare the deposition process for two samples despite their different geometries and dimensions. Furthermore, based on this parametrization approach, some prediction or recalculation of stress field can be made to the systems of wider class of sample geometries.