Power-law characteristics of damage and failure of ceramic coating systems under three-point bending

Abstract

a b s t r a c t a r t i c l e i n f oDamage and failure of ceramic coatings bonded on alloy substrates was studied by observing crack evolution in the coating systems under in situ three-point bending tests with corresponding load-displacement curves. A damage and catastrophic failure model on the ceramic coatings was proposed based on our experimental results and the Taylor expansion of the controlling variable. The results indicate that the damage increases with increasing stress and obeys the power-law characteristics with the power exponent of 0.5, and the damage is 1 as the stress reaches the critical point corresponding to the failure of the coating systems. The damage rate increases rapidly when the stress is near the failure point and shows a power law singularity of −0.5. The experimental results of thin, thick, nanostructured, and conventional micrometer-scale microstructured coatings are all in agreement with the predictions based on the model.

Mode I Microscopic Cracking Process of Granite Considering the Criticality of Failure

“…For type 1 damage mode, the damage rate or damage factor showed a critical phase transition with a precursory acceleration as approaching failure (i.e., normalized load P ⋆ = 1). The critical cracking behavior of type 1 damage mode with power exponent n < 1 was pervasively observed for rock and other brittle materials (Bak & Tang, 1989; Hao et al., 2013; Liang et al., 2016; Salminen et al., 2002; Turcotte et al., 2003). Regarding type 2 damage mode, however, the damage rate decelerated progressively as approaching failure, showing no precursor of catastrophic failure.…”

“…In addition, the applied load P of cracking tests was selected as the controlling variable. Assuming that the controlling variable is continuous and derivable with the response variable, the applied load P can be expressed as the function of the damage factor D , that is, P ( D ), which can be given by the Taylor expansion (Jin et al., 2012; Liang et al., 2016): $$$P(D)={P}_{f}+{\left(\frac{dP}{dD}\right)}_{{D}_{f}}\left({D}_{f}-D\right)+\frac{1}{2}{\left(\frac{{d}^{2}P}{{d}^{2}D}\right)}_{{D}_{f}}{\left({D}_{f}-D\right)}^{2}+\mathcal{O}{\left({D}_{f}-D\right)}^{2}$$$ where P f is the failure load, which equals the maximum load P max of the cracking test. It is worth noting that the terms with order higher than two were omitted.…”

A Review on In Situ Mechanical Testing of Coatings

“…However, due to the simultaneously occurring diffusion induced, intermetallic layers formed at the coating/substrate interface leading to the initiation and propagation of micro-cracks in these layers. Liang et al [80,88] studied the failure of a YSZ coating deposited on a superalloy substrate by observing the crack evolution in the coating system using real-time threepoint bending tests and SEM imaging. The damage evolution of coatings with different thicknesses and microstructures were investigated, and different failure modes were identified for thinner-and thicker-coating specimens.…”

“…The major failure mode in thin coatings was multiple transverse cracks, while an interface cracking mode was shown in the thicker coatings [80]. In addition, a damage model to describe the catastrophic failure of brittle coatings was developed based on the conducted experimental tests [88]. Kiilakoski et al [18] investigated the effect of the coating deposit method (i.e., APS and highvelocity oxy-fuel (HVOF) thermal spraying) on the failure characteristics of Al 2 O 3 -ZrO 2 coatings through in situ three-point bending inside SEM (see Figure 20) and four-point bending with AE monitoring.…”

Interface Strength, Damage and Fracture between Ceramic Films and Metallic Substrates

“…Damage kinetics of thermal barrier coatings with thermal cycling oxidation time was analyzed by acoustic emission method [ 16 ]. Damage models based on the Taylor’s extension and energy analysis were developed to describe coating cracking and failure behavior [ 17 , 18 ]. How the crack modes in films depend on material properties and thickness ratio was studied by numerically analysis based on energy release rate [ 19 ].…”