Origins of Residual Stress

Residual macrostress in a coating combines the intrinsic stress and the thermal stress acting in the coating plane parallel to the coating/substrate interface:

where ot is the total macrostress, and oi and oth are intrinsic stress and thermal stress, respectively. Intrinsic stress results from the growth processes, depending primarily on deposition parameters, whereas thermal stress arises from a mismatch in coefficients of thermal expansion between the coating and the substrate.

Many phenomenological models have been proposed to explain the occurrence of intrinsic stresses by correlating them with a variety of coating microstructure and process features. To varying degrees, the intrinsic stress of a coating is associated with these deposition conditions and coating features:

• Incorporation of residual gas atoms in the coating

• Grain size, microvoid, and dislocation density in the coating

• Energetic particle bombardment during coating growth

• Lattice misfit between the substrate and the growing coating

• Combined effect of surface tension and growth process at grain boundaries

• Deposition temperature relative to the melting temperature of the coating material

• Annealing and shrinkage of disordered material buried behind the advancing surface of a growing coating

Although many studies have described the intrinsic stresses, information on the corresponding structural details is limited. It seems unlikely that one can formulate a generalized model of intrinsic stress for various coating materials and deposition processes.

Any coating that is prepared at elevated temperatures (T2) and then cooled to room temperature (stress measurement temperature, T1) will be thermally stressed because of the difference in the coefficients of thermal expansion between the coating and the substrate. Assuming no deformation of the substrate, the magnitude of the thermal stress in the coating is:

where ac and as are the coefficients of thermal expansion for the coating and the substrate, respectively, and Ec and vc are the Young's modulus and Poisson's ratio of the coating, respectively. A coating deposited at an elevated temperature exhibits compressive stress if as > ac, but tensile stress if as < ac. In the case of as > ac, the substrate shrinks more than the coating does during cooling from the deposition temperature and compresses the coating to maintain dimensional compatibility.

In some cases, thermal stress is the primary residual stress of the coating. For example, a titanium nitride coating can be deposited on a cemented carbide substrate (tungsten carbide-1 wt.% tantalum-10 wt.% cobalt) via a CVD process at 1000 °C (1830 °F). With the values of as = 5 x 10"6/K, ac = 9.54 x 10"6/IC, EjiN = 411 GPa (60 x 106 psi) and v™ = 0.24, the stress in the coating, as calculated from Eq 2, is 2.39 GPa (0.35 x 106 psi) in tension at 25 °C (77 °F).

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