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Thermo-Mechanical Deformation History and the Residual Stress Distribution in Cold Spray

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Abstract

In cold spray, high gas temperatures and high velocity impact of particles introduce complex thermal and stress histories in the coating layers and the substrate. It is crucial to understand the interplay between temperature evolution and residual stress development as the residual stresses could potentially cause distortion and/or delamination. In this study, a system-level cold-spray deposition model is developed. The model includes a moving heat source, material addition and thermo-mechanical stress analyses. The heat source model is first validated by qualitatively comparing the thermal history with experimental measurements from literature. The system-level model is then used to calculate the residual stresses and distortion in the cold-sprayed Cu/steel system. The influence of the spray path on the residual stress development is systematically analyzed. The corresponding interface residual stress states are also examined for the different spray paths. Simulation results indicate that the thermo-mechanical analysis using the developed system-level model can provide an effective way to assist in optimizing the cold-spray coating deposition strategy and improve the coating performance.

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Abbreviations

ε:

Emissivity

\(\sigma\) :

Boltzmann constant (1.3806 × 10−23 J/K)

\(\rho\) :

Material density (\({\text{kg}}/{\text{m}}^{3}\))

\(C_{p}\) :

Specific heat capacity (\({\text{J}}/{\text{kg}} \cdot {\text{K}}\))

\(k\) :

Thermal conductivity of the solid materials (\({\text{W}}/{\text{m}} \cdot {\text{K}}\))

\(\varvec{n}\) :

Unit normal vector to the substrate surface

\(f_{c} ,f_{r}\) :

Convective and radiative heat flux (W/m2)

\(h\) :

Heat transfer coefficient used for forced convection (\({\text{W}}/{\text{m}}^{2} \cdot {\text{K}}\))

\(h_{g}\) :

Heat transfer coefficient used in Eq (6) (\({\text{W}}/{\text{m}}^{2} \cdot {\text{K}}\))

\({\text{Nu}}\) :

Nusselt number (\({\text{Nu}} = h_{g} D/k_{g} )\)

\(D\) :

Nozzle diameter (m)

\(k_{g}\) :

Gas thermal conductivity (\({\text{W}}/{\text{m}} \cdot {\text{K}}\))

\(T_{g}\) :

Gas temperature on the substrate surface used in Eq (6) (K)

\(T_{{}}\) :

Substrate temperature (\({\text{K}}\))

\(T_{\infty }\) :

Air temperature (\({\text{K}}\))

\(T_{s}\) :

Radiation reference temperature (\({\text{K}}\))

\(\dot{Q}_{\text{impact}}\) :

Thermal energy generation rate due to the particle impact (\({\text{W}}/{\text{m}}^{3}\))

\(\dot{E}_{k}\) :

Power of particle kinetic energy (\({\text{W}}\))

\(\dot{m}_{p}\) :

Powder feeding rate (\({\text{kg}}/{\text{s}}\))

\(\overline{{v_{p} }}\) :

Averaged particle impact velocity (\({\text{m}}/{\text{s}}\))

\(R_{e}\) :

Kinetic to thermal energy conversion factor

\(V_{\text{dep}}\) :

Volume of deposited coating block (\({\text{m}}^{3}\))

Y :

Yield stress, JC model (Pa)

A :

Initial yield stress, JC model (Pa)

B :

Strain hardening coefficient, JC model (Pa)

n :

Strain hardening exponent JC model

C :

Strain-rate hardening coefficient, JC model

m :

Thermal-softening exponent, JC model

T r :

Reference temperature, JC model (K)

T m :

Melting temperature, JC model (K)

\(\varepsilon_{\text{p}}\) :

Plastic strain, JC model

\(\dot{\varepsilon }_{\text{p}}\) :

Plastic strain rate, JC model

\(\dot{\varepsilon }_{0}\) :

Reference strain rate, JC model

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Acknowledgment

This work was sponsored in part by the Army Research Laboratories under the Grant Number W911NF-15-2-0026. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the US Government.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, 02115, USA

    Enqiang Lin, Ozan C. Ozdemir & Sinan Müftü

  2. United States Army Research Laboratory, Aberdeen Proving Ground, Maryland, 21005, USA

    Isaac Nault, Victor K. Champagne Jr. & Aaron Nardi

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  1. Enqiang Lin
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Correspondence to Sinan Müftü.

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This article is part of a special topical focus in the Journal of Thermal Spray Technology on Advanced Residual Stress Analysis in Thermal Spray and Cold Spray Processes. This issue was organized by Dr. Vladimir Luzin, Australian Centre for Neutron Scattering; Dr. Seiji Kuroda, National Institute of Materials Science; Dr. Shuo Yin, Trinity College Dublin; and Dr. Andrew Ang, Swinburne University of Technology.

Appendix

Appendix

Two data storage frequencies (4 times and 50 times during a scan) were used to save the temperature and deposition history during heat transfer analysis step, in order to study the effects on the stress development along path-1, in thermo-mechanical simulations. Figure 15 shows that when the storage frequency increases to 50, the discontinuity in the stress along the scan-path is significantly reduced during the immediate scan (first scan), and the stress almost immediately reaches the steady state. The stress is slightly changed after the second scan only near the two edges. These observations confirm that the stress in the newly deposited coating ribbon is mainly determined by the immediate scan and the next scan.

Fig. 15
figure 15

Effects of coating save frequency on the stress evolution along path-1. Each curve is plotted at the moment when the individual scan is completed

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Lin, E., Nault, I., Ozdemir, O.C. et al. Thermo-Mechanical Deformation History and the Residual Stress Distribution in Cold Spray. J Therm Spray Tech 29, 1424–1436 (2020). https://doi.org/10.1007/s11666-020-01034-5

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