Failure Analysis and Life Assessment of Coating: The Use of Mixed Mode Stress Intensity Factors in Coating and Other Surface Engineering Life Assessment

Abstract

Unlike metals, where failure analysis and life assessment methods are quite established, the failure analysis and life assessment of coatings are often underrated and disregarded. This research encourages failure analysts to realize and avail the opportunity provided by an alternative approach. The authors use energy density mechanics concepts to develop a new parameter in coating blistering. A mixed mode stress intensity factor is used as a basis for the derivation. This new parameter will be useful for the researchers and practitioners engaged in coating life assessment. It is recommended that the assessor combines field-determined adhesion strength values and blister evaluation, together with laboratory-derived strain energy density data, to quantitatively predict remaining coating life. This approach also provides a tool in failure analysis.

Appendix: Weight Function in Linear Elastic Fracture Mechanics

In this section, the application of the weight function in fracture mechanics is briefly described for the sake of reader’s convenience. Further discussion is available elsewhere [57]. Bueckner and Rice [57, 59–62] introduced the concept of the weight function (WF), which enables one to calculate the stress intensity factor (SIF) for certain loading system using a reference SIF for different loading systems. A WF exists for any crack problem specified by the geometry of the component and a crack type. If this function is known, then the SIF can be obtained by simply multiplying this function by the stress distribution and integrating it along the crack length.

Basic Relations: A crack of length a in a body may be loaded by tractions ${\mathbf{T}}(s) = (T_{y} ,T_{x} )^{\text{T}}$acting on acting normal to a curve Γ: see Fig. 4.

Fig. 4

Crack loaded by body tractions

The tractions are responsible for a stress field at the crack tip, which can be characterized by a SIF K^T, where the superscript T refers to the loading system. As Bueckner and Rice [57, 59–62] have suggested, one can write

$$ K^{\text{T}} = \int\limits_{\Upgamma } {{\mathbf{T}} \cdot {\mathbf{m}}\,ds} , $$

(A1)

where m is the vector of the weight function, ${\mathbf{m}} = (m_{y} ,m_{x} )^{\text{T}}$. Rice has shown that the weight function is related to the displacement field ${\mathbf{u}} = (u_{y} ,u_{x} )^{\text{T}}$ under an arbitrary reference load [8] by

$$ {\mathbf{m}} = \frac{H}{{K_{\text{ref}} }}\frac{{\partial {\mathbf{u}}}}{\partial a}. $$

(A2)

where H is the generalized Young’s modulus, equal to E for plane stress and E/(1 − ν ²) for plane strain. K _ref is the stress intensity factor for the chosen reference loading case. In most practical cases of Mode I loading, the stresses along the prospective crack line are of interest (see Fig. 5).

Fig. 5

Stress along a virtual crack

Therefore, referring to Fig. 5, from the distribution of the stress perpendicular to the crack area in the uncracked component along the location of the crack, σ(x), the SIF for this stress distribution is given by

$$ K = \int\limits_{0}^{a} {\sigma (x) \cdot h(a,x)dx} , $$

(A3)

Therefore, the WF depends only on the m, which is essentially independent of the stress state and depends only on the geometry.