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Theoretical prediction of residual stresses induced by cold spray with experimental validation

Dibakor Boruah (Faculty of Engineering, Environment and Computing, Coventry University, Coventry, UK) (National Structural Integrity Research Centre (NSIRC), TWI Ltd, Cambridge, UK)
Xiang Zhang (Faculty of Engineering, Environment and Computing, Coventry University, Coventry, UK)
Matthew Doré (Integrity Management Group, TWI Ltd, Cambridge, UK)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 3 April 2019

Issue publication date: 18 April 2019




The purpose of this paper is to develop a simple analytical model for predicting the through-thickness distribution of residual stresses in a cold spray (CS) deposit-substrate assembly.


Layer-by-layer build-up of residual stresses induced by both the peening dominant and thermal mismatch dominant CS processes, taking into account the force and moment equilibrium requirements. The proposed model has been validated with the neutron diffraction measurements, taken from the published literature for different combinations of deposit-substrate assemblies comprising Cu, Mg, Ti, Al and Al alloys.


Through a parametric study, the influence of geometrical variables (number of layers, substrate height and individual layer height) on the through-thickness residual stress distribution and magnitude are elucidated. Both the number of deposited layers and substrate height affect residual stress magnitude, whereas the individual layer height has little effect. A good agreement has been achieved between the experimentally measured stress distributions and predictions by the proposed model.


The proposed model provides a more thorough explanation of residual stress development mechanisms by the CS process along with mathematical representation. Comparing to existing analytical and finite element methods, it provides a quicker estimation of the residual stress distribution and magnitude. This paper provides comparisons and contrast of the two different residual stress mechanisms: the peening dominant and the thermal mismatch dominant. The proposed model allows parametric studies of geometric variables, and can potentially contribute to CS process optimisation aiming at residual stress control.



This publication was made possible by the sponsorship and support of the Lloyd’s Register Foundation, which is a charitable organisation that helps to protect life and property by supporting engineering-related education, public engagement and the application of research.


Boruah, D., Zhang, X. and Doré, M. (2019), "Theoretical prediction of residual stresses induced by cold spray with experimental validation", Multidiscipline Modeling in Materials and Structures, Vol. 15 No. 3, pp. 599-616.



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Copyright © 2019, Emerald Publishing Limited

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