1、A probabilistic method to predict fatigue crack initiationSALIL. S. KULKARNI, L. SUN, B. MORAN, S. KRISHNASWAMY andJ.D. ACHENBACHDepartment of Mechanical Engineering, Northwestern University, Evanston, IL-60208, USAAuthor for Correspondence. (E-mail: sailnorthwestern.edu)Received 8 August 2005; acce
2、pted in revised form 6 September 2005Abstract. A probabilistic method to predict macrocrack initiation due to fatigue damage is presented in this paper. Acoustic non-linearity is used to quantify pre-macrocrack initiation damage. This data is then used in a probabilistic analysis of fatigue damage.
3、The probabilistic fatigue damage analy- sis consists of a suitably chosen damage evolution equation to model accumulated damage coupled with a procedure to calculate the probability of macrocrack initiation. The probability of macrocrack initiation is evaluated using the Monte Carlo Method with Impo
4、rtance Sampling. Numerical results for the probabilistic assessment of fatigue damage for a sample problem are presented and compared with experimental results.Key words: Acoustic non-linearity, crack initiation, damage evolution, fatigue, probabilistic method, struc- tural health monitoring.1. Intr
5、oductionConventional procedures for life prediction of components subjected to fatigue are generally based on the safe-life approach (see e.g. Suresh, 1991), coupled with Palmgren (see Palmgren, 1924) and Miner (see Miner, 1945) rules of linear cumu- lative damage. In the safe-life approach for meta
6、l fatigue, life prediction is based on data from fatigue testing of components. Components of a structure are replaced when the probability of failure reaches a prescribed (often small) value, even though some of them may have a signicant remaining life. Hence it is a conservative approach with an e
7、conomic penalty. To avoid this penalty, the damage-tolerant approach is often a suitable alternative for life predictions. This approach is espe- cially useful when the rate of damage accumulated is well understood and can be monitored with a technique of quantitative non-destructive evaluation. How
8、ever, in certain materials, such as high strength steels, like those used for drive trains of rotor- craft, critical damage in the form of a crack of detectable but very small length, often occurs late in the lifetime of a component. When a detectable crack has developed out of microscopic damage pr
9、ocesses, it grows to an unacceptable length in a time that is short as compared to the total lifetime of the component. Periodic monitor- ing by a condition monitoring system can, however, signicantly improve the safety of the damage tolerance approach. Particularly, if pre-crack damage can be moni-
10、 tored and related to crack formation by an analytical fatigue damage procedure, sub- stantial safety and cost benets can be gained. With this objective, a methodology toProbabilistic method to predict fatigue crack initiation 17calculate the probability of macrocrack initiation based on periodic in
11、 situ measure- ments is presented in this paper. The methodology essentially consists of two parts: A structural health monitoring system to monitor the fatigue process. In the pres-ent approach, acoustic second harmonic generation (see Section 2) is used to mon- itor the damage accumulated during t
12、he fatigue process. A probabilistic fatigue damage procedure which takes the data from the healthmonitoring system as its input and calculates the probability of macrocrack initia- tion as its output. The probabilistic damage procedure consists of a suitably cho- sen damage evolution equation to mod
13、el accumulated damage (see Section 3) and a procedure to calculate the probability of macrocrack initiation (see Section 4). The procedure to calculate the probability of macrocrack initiation is capable of updating its forecast based on the latest inspection data from the monitoring sys- tem.Using
14、this methodology, the probability of macrocrack initiation is calculated for a sample problem taken from the literature, and the results are presented in Section 5.2. Acoustic second harmonic generationTo quantify the damage accumulation in a component undergoing fatigue, it is rst necessary to rela
15、te the accumulated damage to an observable variable. The accumu- lated damage is caused by changes in the microstructure of the component which in turn introduce material non-linearity in the specimen. To characterize the material non-linearity, a single frequency ultrasonic wave generated by a tran
16、sducer (gener- ator) is transmitted through the specimen and the signal received by the receiving transducer is analyzed. The material non-linearity distorts the single frequency wave and leads to generation of second and higher harmonics. As a result, the signal received at the receiver not only consists of a component at
