Hindawi Publishing Corporation ISRN Polymer Science Volume 2013, Article ID 321489, 11 pages http://dx.doi.org/10.1155/2013/321489 Research Article Fatigue Failure Model for Polymeric Compliant Systems Theddeus T. Akano and Omotayo A. Fakinlede Department of Systems Engineering, University of Lagos, Akoka, Lagos 101017, Nigeria Correspondence should be addressed to Teddeus T. Akano; manthez@yahoo.com Received 21 January 2013; Accepted 28 February 2013 Academic Editors: H. M. da Costa, A. Mousa, and A. Uygun Copyright © 2013 T. T. Akano and O. A. Fakinlede. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Fatigue analysis and lifetime evaluation are very important in the design of compliant mechanisms to ensure their safety and reliability. Earlier models for the fatigue prediction of compliant mechanisms are centred on repeated and reversed stress cycles. Compliant mechanisms (CMs) are now being applied to situations where the fatigue is caused by random varying stress cycles. It is, therefore, necessary to consider fatigue resulting from random varying stress cycles and damage caused to the compliant material. A continuum damage mechanics (CDM) model is proposed to assess the fatigue life of polymeric compliant mechanisms. Te elastic strain energy is computed on the basis of a nearly incompressive hyperelastic constitution. Te damage evolution equation is used to develop a mathematical formula that describes the fatigue life as a function of the nominal strain amplitude under cyclic loading. Low density polypropylene (LDP) is used for the fatigue tests conducted under displacement controlled condition with a sine waveform of 10 Hz. Te results from the theoretical formula are compared with those from the experiment and fatigue sofware. Te result from the prediction formula shows a strong agreement with the experimental and simulation results. 1. Introduction Fatigue is one of the major failure mechanisms in engineering structures [1]. Time-varying cyclic loads result in failure of components at stress values below the yield or ultimate strength of the material. Fatigue failure of components takes place by the initiation and propagation of a crack until it becomes unstable and then propagates to sudden failure. Te total fatigue life is the sum of crack initiation life and crack propagation life. Fatigue life prediction has become important because of the complex nature of fatigue as it is infuenced by several factors, statistical nature of fatigue phenomena and time-consuming fatigue tests. Tough a lot of fatigue models have been developed and used to solve fatigue problems, the range of validity of these models is not well defned. No method would predict the fatigue life with the damage value by separating crack initi- ation and propagation phases. Te methods used to predict crack initiation life are mainly empirical [2] and they fail to defne the damage caused to the material. Stress- or strain- based approaches followed do not specify the damage caused to the material, as they are mainly curve ftting methods. Te limitation of this approach motivated the development of micromechanics models termed as local approaches based on continuum damage mechanics (CDM). Te local approaches are based on application of micromechanics models of fracture in which stress/strain and damage at the crack tip are related to the critical conditions required for fracture. Tese models are calibrated through material specifc parameters. Once these parameters are derived for particular material, they can be assumed to be independent of geometry and loading mode and may be used to the assessment of a component fabricated from the same material. For some compliant structures, the desired motion may occur infrequently, and the static theories may be enough for the analysis [3]. However, by the defnition of compliant mechanisms, defection of fexible members is required for the motion. Usually, it is desired that the mechanism be capable of undergoing the motion many times, and design requirements may be many millions of cycle of infnite life. Tis repeated loading cause fuctuating stresses in the members and can result in fatigue failure. Failure can occur at stresses that are signifcantly lower than those that cause static failure [3]. A small crack is enough to initiate the fatigue failure. Te crack progresses rapidly since the stress concentration efect becomes greater around it. If the stressed