International Journal of Fatigue 21 (1999) 909–923 www.elsevier.com/locate/ijfatigue Simulation of damage evolution in a uni-directional titanium matrix composite subjected to high cycle fatigue Rainer Echle a , George Z. Voyiadjis b,* a HILTI Servicegesellschaft GbR, Hiltistr. 2, 86899 Kaufering, Germany b Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA Received 18 May 1998; received in revised form 28 December 1998; accepted 27 May 1999 Abstract Among the advanced material systems under consideration for use in gas turbine engines special consideration is given to the family of metal matrix composites especially the Titanium matrix composites. This is attributed mainly to the superior stiffness to weight ratio as compared to other conventional materials. The lack of appropriate material models capable of simulating the material behavior realistically is a major drawback in the success of this material system. In the current research the results of numerical simulations for the damage evolution in a uni-directional Titanium matrix composite subjected to high cycle fatigue loading are presented. The employed micro-mechanical fatigue damage model has been developed previously by the authors. Results obtained from the numerical simulations include those from parametric studies on the influence of various model parameters as well as those for damage evolution in the constituents during the material lifetime. Comparison of the final results for the number of cycles to failure for room temperature fatigue with those obtained from experimental investigations show good agreement.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Metal matrix composites; Fatigue; Damage; High cycle fatigue; Titanium matrix composites 1. Introduction With the ever advancing technology in the aerospace industry and of modern aerospace vehicles the design factors, such as weight and material strength, play an increased role in design philosophies. A major goal her- eby is the increase in performance through the enhance- ment of fuel efficiency of turbine engines and/or the development of more advanced material systems which are able to sustain the arising loads and to perform safely under conditions such as those occurring during flight, while retaining their structural integrity. Among the many advanced material systems under consideration, the Metal Matrix Composites (MMCs) have been con- sidered for such applications. Especially continuous fiber reinforced Titanium Matrix Composites (TMC) are fav- ored for such applications due to the fact that they are * Corresponding author. Tel.: + 1-225-388-8668; fax: + 1-225-388- 8662. E-mail address: cegzvl@unixl.sncc.lsu.edu (G.Z. Voyiadjis) 0142-1123/99/$ - see front matter.  1999 Elsevier Science Ltd. All rights reserved. PII:S0142-1123(99)00082-1 able to maintain their excellent strength to density ratio even at elevated temperatures. It is this intrinsic material property which makes it a candidate material in the gas turbine engine manufacturing industry for potential use in a new generation of gas turbine engines. Titanium matrix composites offer higher mechanical properties, better dimensional stability, and strength retention even at elevated temperatures as compared to their monolithic counterparts. However there still exists a certain reluc- tance against a general use of MMCs due to the high production/manufacturing costs, and furthermore the lack of a thorough understanding of the material system in order to be able to employ it for vital structural components with a predictable margin of risk. Considerable experimental as well as theoretical research efforts during the last two decades have focused on the analytical modeling of the real material behavior using the concept of continuum damage mechanics (CDM). The concept of continuum damage mechanics describes analytically the phenomenon of progressive material degradation during the loading process due to damage development. Such material degradation may