Designing damage-resistant brittle-coating structures: I. Bilayers

Abstract

A FEA study of coating/substrate bilayers is conducted as a foundation for damage analysis. Attention is focused on the stresses along the contact axis immediately adjacent to the bilayer interface, where radial cracking or yield in the coating, or yield in the substrate, tend to occur. The stress analysis is used to determine critical loads to initiate each damage mode in terms of basic material properties and coating thickness. Controlling material parameters are strength (brittle mode) and yield stress or hardness (plastic mode). The critical loads are shown to have a simple quadratic dependency on coating thickness, but more complex dependencies on elastic modulus mismatch ratio. Simplified explicit modulus functions afford a route to prediction of the critical loads for design purposes. Implications concerning the design of bilayers for specific applications are discussed.

Introduction

Laminate structures with functional stiff and hard outer layers (typically ceramics) on compliant or soft support bases (polymers, metals, or even soft ceramics) are representative of many engineering coating systems (cutting tools, thermal barrier coatings, ceramic armor, laminated windows, eye glasses, electronic packaging devices, hard disks) and biomechanical systems (shells, teeth, dental crowns) [1]. The simplest form of such structures is a bilayer—a coating on a substrate. In some functional systems (e.g. dental crowns) the structure is a trilayer (or even multilayer), with an intermediate support core layer. The outer layers shield the underlying substrate from external loads, but any one layer may be susceptible to damage above some critical applied load. Because adjacent layers may consist of different material types—ceramic, metal, polymer or composite—the damage modes can be varied and complex. An understanding of these modes is critical to the design of longer-lifetime systems.

Several damage modes have been identified in bilayers in concentrated loading. Near-contact modes, e.g. cone (or outer ring) cracking or quasiplasticity, can occur in the top surfaces, as in monoliths [2], [3], [4], [5]. However, such top-surface modes are dominant only in thicker coatings [2], and can in any case be avoided by ensuring sufficiently blunt or soft contacts, so we shall regard them as secondary. More insidious in thinner, brittle coatings are subsurface radial cracks [1], [2], [3], [5], [6]. Radial cracks initiate at the coating/substrate interface, and are associated with coating flexure beneath the contact. They can extend long lateral distances with increasing load. In softer coatings, fracture at the undersurface may be supplanted by local yield. Yet another important mode is yield in the substrate itself, particularly in soft metals. In cases where the substrate is stiffer than the coating (e.g. porcelain/metal crowns), substrate yield can act as an essential precursor to radial cracking in the overlying coating [7]. Such plasticity may also cause delamination of the coating/substrate interface. Whereas the activation of any one damage mode may not lead to immediate failure of the bilayer, it signals the beginning of the end of the useful lifetime of the structure (especially biomechanical structures)—the issue is then one of damage prevention rather than damage containment [1], [3].

Accordingly, a primary goal in the analysis of bilayers is the development of explicit relations for the critical loads to activate subsurface coating cracking or yield, and substrate yield, in terms of key geometrical and material variables. Existing relations suggest a common quadratic dependency of the critical loads on coating thickness (typical of point-contact and flexure fields), and somewhat slower dependencies on modulus ratio [1]. However, these dependencies, especially those associated with modulus mismatch, remain to be fully validated. The same relations also predict a linear dependence on fracture strength [4] or yield stress [7] of the coating and substrate materials, depending on the damage mode.

The present study is divided into two parts. Part I deals with bilayers, Part II with trilayers. Finite element analysis (FEA) is used to evaluate the important stress components in the layers, and thence to determine critical load relations for the different damage modes by equating maximum tensile and shear stress components to material strength (fracture) or yield stress (plasticity). The bilayer solutions are used to validate the quadratic coating thickness dependency in the existing critical load relations, and to examine further the modulus dependency. Apart from their intrinsic importance, bilayer solutions provide an essential starting point for analysis of trilayers. As we shall indicate in Part II, trilayers are subject to similar damage modes, in either outer or inner layers depending on thickness and modulus ratios [1]. Finally, consideration will be given as to how the results may be used as a basis for materials design of layer structures.