Modeling the strain-rate dependence of fatigue life of hot- pressed silicon nitride Vinod Sharma, S. Nemat-Nasser * , Kenneth S. Vecchio Center of Excellence for Advanced Materials, Department of AMES, 9500 Gilman Drive, University of California, San Diego, La Jolla, CA 92093-0416, USA Received 22 March 1997; revised version received 5 March 1998 Abstract This paper presents the results of a micromechanical model used to explain the strain-rate dependence of the com- pression fatigue lives of amorphous and crystalline grain boundary phase; denoted by ABP and CBP silicon nitrides, respectively. When the strain-rate is changed from 400 to 0.01/s, the fatigue lives of both materials, evaluated at a peak stress of 3.2 GPa, increased by more than two orders of magnitude (Sharma et al. (1996a,b)). The model is based on the dynamic and quasi-static microstructural damage mechanisms observed in both materials. The microstructure of ABP and CBP silicon nitrides is modeled as a simple composite in which silicon nitride grains are embedded in a continuous network of the grain boundary phase. Since the subsurface fatigue cracks in both materials nucleate mainly from the contact region between silicon nitride grains, contact stresses between adjacent silicon nitride grains are obtained, and the frequency dependence of the fatigue lives of ABP and CBP silicon nitrides is explained on the basis of the strain-rate sensitivity of the grain boundary phase. Ó 1998 Elsevier Science Ltd. All rights reserved. 1. Introduction In recent work by the authors (Sharma et al. (1996a,b)), the results of an experimental investi- gation of the eects of the grain boundary phase on the dynamic and quasi-static compression fa- tigue life of hot-pressed silicon nitrides are present- ed. The compression fatigue lives of amorphous grain boundary phase (ABP) and crystalline grain boundary phase (CBP) silicon nitrides are evaluat- ed at strain-rates of 0.01, 0.1 and 400/s. Table 1 summarizes the results of the experiments. ABP silicon nitride was ¯uxed with 6 wt% Y 2 O 3 and 3 wt% Al 2 O 3 , whereas CBP silicon nitride was ¯uxed with 8 wt% Y 2 O 3 and 1 wt% Al 2 O 3 . At a strain- rate of 400/s, the fatigue life of ABP silicon nitride (104 cycles) is observed to be superior to the fa- tigue life of CBP silicon nitride (44 cycles). When the strain-rate is decreased from 400 to 0.01/s, the fatigue lives of both materials increases by more than two orders of magnitude and the dier- ence in the fatigue life of ABP silicon nitride (14,000 cycles) and CBP silicon nitride (12,000 cy- cles) was found to be relatively less signi®cant. The observed signi®cant dierences in the fatigue lives between 400 and 0.01/s strain-rates was accredited to the dierences in the energy loss, which is given by the enclosed area within the axial stress±strain curve, in a typical compression fatigue cycle. The energy loss per cycle, in samples from both materi- als, at a strain-rate of 0.01/s was observed to be Mechanics of Materials 29 (1998) 253±273 * Corresponding author. E-mail: ceam@ames.ucsd.edu. 0167-6636/98/$ ± see front matter Ó 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 6 3 6 ( 9 8 ) 0 0 0 2 4 - 6