Simulation of Distributed Co-Crack Propagation in Cellular Automata by Time Warp Synchronization

Abstract

Damage tolerance design is a philosophy used to refine fail safe design, especially for the aircraft design field. This design concept predicts structural failure, assuming that cracks exist and will grow large enough to produce failures. Calculation of crack propagation in global aspect as like wing requires a solution of complex system by considering crack opening or crack closure. When analyzing multiple cracks, this behavior becomes more complex. In this paper, the aircraft wing is modeled based NASA Common Research Model (CRM) and simulations are performed to observe the multiple crack propagation that are almost impossible to examine in real environmental tests because of its cost and complexity. The Structural Common Research Model (SCRM) is developed by creating internal structures from the CRM for the simulation. The simulation is performed with two level hierarchical models. At the macro level, the SCRM is used as a general finite element model to get static stress and analyzed with strain-life approach as crack initiation analysis (CIA). If a crack is initialized in a certain element, then the element is considered as a base model to build the micro level environment. This micro level analysis is performed by Linear Elastic Fracture Mechanics (LEFM) to calculate crack propagation using Cellular Automata (CA). CA is an effective way to solve a complex system by working without central control and performing with simple local rules of operation. CA local rule is employed that a cell is regarded as a dead cell if the residual strength calculated based on LEFM approaches a critical factor. Dead cells become acting cavities in the model and induce a reduction in strength for neighboring cells. The cellular model acts automatically following cyclic load from the history spectrum. Transport Wing Standard spectrum (TWIST) is selected to represent the test loading spectrum in order to simulate the transport aircraft wing. Crack propagation at the micro level is performed by independent calculations for each CA model which is originally from SCRM. So they can be easily distributed in parallel computing given that each crack propagation process is treated as a logical process. But, a synchronization algorithm is required to consider interaction effects when two cracks get close enough. The Time Warp algorithm was selected for the synchronization manager. Since Time Warp allows violation of local causality constraint mechanism, the parallel analysis of distributed crack propagation can be achieved more optimistic way. In result, CIA is accomplished and generated initial crack cycle information for every element in macro wing model. Crack propagation analysis is performed following local rule, neighboring cells rule, and updating rule of CA. This result makes it possible to estimate the design safety withhold accounting for in-service or manufacturing defects. This simulation method also raises up the possibility of evaluation the safety of complex system for both macro and micromechanical aspects.