Prolonging fatigue life of structural components through shape changes

Abstract

About half of mechanical failures are due to repeated loading. Most of the failures are fatigue related and the fatigue problem has been of major concern in the design of structures. The failure due to fatigue is a function of, among other factors, the external loads, material behavior, geometry of the structure and the crack characteristics. In this paper, the relationship between structural geometry and number of life cycles to failure is investigated. The linear elastic fracture mechanics (LEFM) approach is integrated with shape optimal design methodology. The primary objective of the design problem is to enhance the life of the structure. The results from LEFM analyses are used in the fatigue model to predict the life of the structure before failure is deemed to have occurred. The shape of the structure is changed using the natural shape optimal design procedure where gradient-based nonlinear programming (NLP) techniques are used with the supplied sensitivity information to predict the required shape changes. Relevant issues such as problem formulation, finite element modeling, mesh generation and regeneration are discussed. Two design examples are solved and the results show that with proper shape changes the life of structural systems subjected to fatigue loads can be enhanced significantly. INTRODUCTION About half of mechanical failures are due to repeated loading [Fuchs & Stephens, 1980]. Most of the failures are fatigue related and the fatigue problem has been of major concern in the design of structures. Engineers have been developing many approaches to deal with the problem of fatigue. The majority of such investigations usually focus on the relationship between crack growth and applied loads such as the applied stress range, strain range and mean stress. This relationship characterizes fatigue life which is defined as the total number of cycles or time to induce fatigue damage and to initiate a dominant fatigue flaw that propagates to final failure [Suresh, 1991]. An economic study estimated the cost of failures due to fracture in the United States in 1978 at $119 billion (in 1982 dollars) or about 4% of the GNP [Duga et. al, 1983]. This study estimated that if the current technology were applied the annual cost could be redcued appreciably and that further fracture mechanics research could reduce this figure by $28 billion. Failures can be reduced to a larger extent through improved design practice. The fatigue failure phenomenon is still an active area of research. The early research focused on discontinuities in the material to explain fatigue crack growth. Empirical relationships were developed and the material constants in the expressions were usually obtained through experimental data. Research in the last two decades [Jono and Song, 1987; Kaleta and Zietek, 1994; Faanes and Fernando, 1994] have shown that various factors such as energy dissipation, early growth of short cracks and friction contribute to fatigue crack growth. It should be noted that a crack growth is not independent of structural geometry. In this research, the relation between structural geometry and fatigue life is investigated by integrating LEFM approach with shape optimal design optimization tools [Gani, 1996]. The major thrust of this paper is to discuss the methodology aimed at improving the life of a structural system or component through appropriate design changes. Achieving this objective requires the understanding of fracture mechanics, material behavior, finite element analysis, geometric modeling, mesh generation, design optimization and design principles to name a few. There are three key issues that need to be dealt with in order to achieve the aforementioned objectives an understanding of the LEFM approach that provides the basis for computing the fatigue life of a structural system, the design problem formulation that is necessary to solve the problem with the available optimization methodologies and the finite element modeling and analysis needed to compute the LEFM parameters. The rest of the paper deals with these three topics with the primary focus on the latter two topics.