An Analysis of Repeating-Division Type Cracking Pattern in Brittle Coating under Equi-Biaxial Tension

Abstract

In order to characterize the "Repeating-division type" cracking pattern which is often observed in the brittle coating on a ductile substrate under equi-biaxial tension, the bulge tests were carried out on steel disks with WC-Co coating which was deposited by high-velocity flame spraying. Moreover, an elastic-plastic analysis was applied to the division process of coating to derive the relation among crack interval, tensile stress and strain of substrate at the division, coating and substrate thickness, strength of coating, interfacial strength between coating and substrate, and material's constants. The characteristics of the division process calculated from the analytical equation agree semiquantitatively well with the experimental results that the crack interval decreases with increasing tensile stress and increases with increasing coating thickness.

The effect of defect location on coating fragmentation patterns under biaxial tension

“…(1). Finally, region III at the crack junctions experiences a complex stress distribution due to the proximity of two perpendicular cracks (approximate analytical expressions for stress distribution valid also in zone III can be found in [12]). Two principal fragmentation stages can be differentiated based on the relation between typical fragment linear dimension and the stress transfer length l (see, e.g.…”

“…by expanding M(s 1 ,s 2 ;t) in Taylor series about tZ0, Mðs 1 ; s 2 ; tÞ Z P N kZ0 ðv k Mðs 1 ; s 2 ; 0Þ=vt k Þðt k =k!Þ. For the monodisperse initial condition nðx; y; 0Þ Z dðx K LÞdðy K LÞ=L 2 (12) where L denotes the side length of the square coating; the solution is…”

Analysis and Simulation of Cracking Patterns in Ceramics Coating under Thermal Stress

“…The equations for the stresses in a cracked coating and along an interface between the coating and substrate under biaxial tension have been derived in the previous paper [4] on the model as is shown in Fig. 2.…”

“…The relations ¤ x1 = ¤ x2 , and ¤ y1 = ¤ y2 hold at the interface, where ¤ x2 and ¤ y2 are the strains of the substrate in the x and y directions, respectively. The stresses in the x and y directions in the coating, x1 and y1 , are derived from the following simultaneous partial-differential equations, which are similar to the equations without the thermal terms introduced in the previous paper [4]:…”

“…These equations show that x1 and y1 are unique functions of C x and C y which contain x2 , y2 and T. Therefore, C x and C y are called "Converted Thermal Strains" in the present paper, by which the expression of the thermo-elastic stress in the coating becomes simple. Similarly, shear stresses in the x and y directions along the interface between coating and substrate, zx i and zy i , are expressed by the following equation [4]: (5) In order to calculate the thermal stress in the coating of structures with complex shape, the present authors have already proposed the "Analysis/FEM Strain Accommodation Method" [5]. First, the strains x2 and y2 in the substrate with coating but without cracks in the coating are obtained by FEM.…”