~ TTERWORTH I N E M A N N Int. J. Fatigue Vol. 17, No. 6, pp. 385-398, 1995 Copyright © 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0142-1123/95/$10.00 0142-1123(95)00005-4 Development of a finite element based strain accumulation model for the prediction of fatigue lives in highly stressed Ti components I.V. Putchkov, Y.M. Temis, A.L. Dowson* and D. Damrit Central Institute of Aviation Motors, 2 Aviamotornaya St, Moscow, 111250, Russia *IRC in Materials for High Performance Applications, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK tRolls Royce plc, PO Box 31, Derby DE2 8B J, UK (Received 24 October 1994; accepted 16 January 1995) Low-cycle fatigue studies have been conducted on the near-alpha IMI 829 Ti alloy under constant- amplitude and variable-amplitude load- and strain-controlled loading conditions, and fundamental data have been generated relating to the effects of cyclic loading on elastic modulus, yield stress and plastic strain development. The results of these studies have been used to develop a finite element based damage accumulation model, which is capable of predicting both the stress and strain distributions in cyclically loaded components, and the time to failure (time to first crack) in critical regions of high stress and/or strain concentration. The model has been successfully validated using LCF tests conducted on notched specimens (Kt = 2.8 and 3.2) at ambient (20 °C) temperature. (Keywords: life prediction; Ti alloys; strain accumulation; cyclic stress--strain curves; low-cycle fatigue; FE model) Mathematical and numerical procedures capable of modelling the physical processes that underwrite the fracture behaviour of engineering materials and struc- tures are now well established 1-3. Such procedures have become essential tools in both the design process and in the definition of life prediction philosophies for safety-critical aeroengine components4's. As such they promote the concepts of safe-life design3`s and can reduce the need for investment in expensive materials and component evaluation trials. Their application, however, has been dependent on the development of a detailed understanding of the micro- structure and mechanical parameters that influence failure, and on the development of life prediction philosophies that are capable of handling the complex stress and strain histories associated with in-service loading. Because of their high strength-to-weight ratio and their capacity for thermomechanical processing, Ti- based alloys have found widespread application throughout the aerospace industry6,7, particularly within the compressor and low-pressure regions of the gas turbine engine, where component life is often governed not by static properties but rather by the damage processes associated with cyclic changes in both temperature and load. Under such conditions the fundamental parameters that influence failure are the cyclic stress-strain response of the material, and the associated resistance to crack initiation and subsequent growth. Conventionally, the cyclic stress-strain response of a material is described in terms of a simple power-law-type relationship similar to that originally proposed by Ramberg and Osgood 8. Assuming Masing- type behaviour9, Moskvitin1° has recently shown that this relationship may be modified such that the stress, 0-,,* and strain e,,* coordinates during any half cycle, n, may be related directly to the monotonic stress-strain curve by a relationship of the form • J( :t or. = a (1) \ a,/ where f represents the initial stress-strain response of the material under monotonic loading (i.e. n = 0), and a, is a transformation coefficient that, analogous with the Bauschinger effectn, takes into account cyclic changes in the stress-strain curve. This relationship was further developed by Gusenkov 12 and Schneiderovitch and Gusenkov 13, who suggested a generalized form of the stress-strain curve such that: { <* e* = S*, S* -- S,s S* + An[f-l(pS*/2) - al s*. > sL e*n e*~ . or n = --,S. - (2) 13s o's where ~rs and es are the initial stress and strain values 385