Defense Date


Document Type


Degree Name

Doctor of Philosophy


Mechanical and Nuclear Engineering

First Advisor

Gary Tepper


Under certain loading conditions, surfaces topography coupled with materials degree of brittleness can significantly compromise the mechanical performance of structures. The foregoing remains valid even if roughness is intentionally introduced for engineering reasons. In either case, stress can concentrate. The case of the stress concentration in surfaces having randomly distributed pits is a problem that, although being very practical, yet it remains unsolved. The complexity of a random configuration renders difficult the problem of analytically finding relationships between surface parameters and markers indicative of mechanical failure. Another difficulty is the reproducibility of replicates of specimens possessing random rough surfaces, for destructive testing followed by statistical analysis. An experimental technique to produce highly controlled replicates of random rough surfaces (including modeling of degradation growth) was developed. This method was used to experimentally and statistically study the effects on fracture of early randomly degraded surfaces of poly methyl methacrylate (PMMA) versus topographical parameters. Growth of degradation was assumed to go from an engineering surface to one whose heights are normally distributed. (Early stage of degradation is meant to be that level of roughness which is in the neighborhood of the critical flaw size for a given material). Among other findings, it was found that neither stress nor strain alone can be used to predict fracture at this early stage of degradation. However, fracture location was found to be strongly correlated to the ratio of the root-mean square roughness (RMS) to auto correlation length (ACL), above some RMS threshold. This correlation decreases as the material becomes less brittle (i.e., decrease of Young’s modulus or increase of percent of elongation). Simultaneously, a boundary value problem involving traction-free random rough surfaces was solved using a perturbation method, assuming elastic and isotropic conditions. For small RMS/ACL ratio, the solution for the RMS stress concentration factor, kt was found to be: kt = 1 + 2*SQRT(2)*(RMS/ACL), which agrees very well with the experimental work. Finally, a generalization of stress concentration factor formulas for several geometrical configurations and loading conditions into the Modified Inglis Formula was proposed. Finite element analysis was carried out and comparison was made with both experimental and analytical results. Applications of these results are broad. In surface engineering, for example, our analytical solution can be coupled with Fick’s Law to find critical conditions under which a film could become unstable to random roughness. Additionally, in design and maintenance of surfaces in service, it can be used to preliminarily assess how stress concentrates in surfaces where well defined notches cannot be used as an approximation.


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