Research on coalescence and probabilistic failure physics modeling of coplanar semiellipse cracks

Abstract

Abstract. Multiple fatigue cracks, causing transient fatigue fracture and resulting in great loss of life and property, are very commen in engineering structures. In order to predict the fatigue life of engineering alloys more accurately, the interaction and coalescence of adjacent cracks was investigated and the four stages of cracks growth were discussed in this paper. The SIF(stress intensity factor) value was found to growth rapidly in the ligament failure, and simulation method was used to find out the coalescence point. Then, the Paris' law was chosen to discribe the crack growth process. Taking random factors like structure size, material properties, environment stress parameter into account, the probability physical of failure model of alloys can predict the failure life more accurate. Accordingly, the uncertain parameters of the Paris' law were updated via Bayesian update method. The posterior distributions of uncertain parameters were obtained by the MCMC-Gibbs sampling. Finally, the probabilistic failure life models before and after coalescence were established by Monte Carlo simulation method. The probabilistic modeling method, which can greatly reduces the historical data or experimental data needed for the reliability evaluation of small sample products, can also be applied to other aspect of physic of failure , effectively saving time and cost. IntroducitionFatigue failures, which occures at stress below the tensile strength or yield strength of alloys is hard to be detected. Since most engineering components are or similarly are subjected to alternating stress. Multiple fatigue cracks causing transient fatigue fracture and resulting in great loss of life and property, are very commen in engineering structures. Crack mainly initiats in localized areas of stress concentratin or material defects [1,2]. Then these initial cracks grow together by interacting with each other, meanwhile shortening the fatigue life with an accelerated crack growth rate [3]. Interaction and coalescence processes of adjacent cracks is the key issue in the study of coplanar fatigue cracks.Various theories have been propounded to assess the growth of adjacent surface cracks growth. The British Standard Institution[4] proposed a prediction method assuming cracks to be indepentend. However this idealize simple model mainly considering the geometric condition of cracks, turned out to be too conservative [5]. Iida [6] assumed that when the cracks touch, a semi-elliptical crack immediately drawn through the outer tips of the two adjucent cracks and through the deepest point of the deeper crack. The study neglected the interaction in calculation between adjucent cracks(the interaction factors γA to F =1) and proposed a simple realistic prediction method. However the a Corresponding