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Abstract
In the context of the predicted growth in air transportation, the additional attention will be paid to the organization of the competitive maintenance and repair operations for the commercial airplanes. The implementation of new technological processes for airframe repairs and the application of modern information technologies during the development of the repair procedures can be a significant advantage in the expanding market of post-production support of the commercial air fleet. Airframe adhesive repairs allow using lifting abilities of the materials more intensively, but application of the adhesive joints technology requires more complicated strength calculation procedure. It is advisable to utilize the modern finite element software packages to perform the reliable calculation. The capabilities of these software packages allow obtaining adequate computational results for adhesive repair joint parameters subjected to cyclic loads. This paper is concentrated on application of the finite element methods to simulate the crack growth in isotropic material and on methods for accelerated calculation of the mechanical response of cracked structures. Crack growth simulation is performed based on XFEM methods where the created finite element model is complemented with asymptotic imitation function of crack tip and with discontinuous jump function across the crack surfaces. Fatigue properties of the repair joint are modelled in accordance with direct cyclic approach, where a Fourier series approximation with time integration of the nonlinear material behavior is applied. After that, the result of integration at each point of the load history is used for the prediction of the material fatigue properties degradation at the next step of computation; this allows us to evaluate the material damage growth rate. Based on calculation results, a conclusion was made that the received numerical data match the full-scale test results; the time spent for calculation with the usage of accelerated computational methods was evaluated.
Highlights
It is advisable to utilize the modern finite element software packages to perform the reliable calculation. The capabilities of these software packages allow obtaining adequate computational results for adhesive repair joint parameters subjected to cyclic loads
This paper is concentrated on application of the finite element methods to simulate the crack growth in isotropic material and on methods for accelerated calculation of the mechanical response of cracked structures
Crack growth simulation is performed based on XFEM methods where the created finite element model is complemented with asymptotic imitation function of crack tip and with discontinuous jump function across the crack surfaces
Summary
Метод XFEM (Extended finite element method) применяется для моделирования разрывов сплошности материала (трещин) и позволяет искать решения уравнений в частных производных для разрывных функций [24]. Конечно-элементная аппроксимация решения приведенного участка модели будет выражаться: uh (x) Ni (x) ui , i 1 где Ni – функция формы для i-го узла, ui – вектор перемещений i-го узла, x – вектор координат узла сетки. Для моделирования сингулярности в вершине трещины вводится дополнительная асимптотическая функция ψ в ячейках, прилегающих к трещине Где u I – вектор перемещений узлов, a I – вектор степеней свободы узлов сетки, совместно с функцией скачка. – вектор степеней свободы узлов сетки, совместно с функцией вершины трещины i (x) представляющий сингулярность в материале. Для изотропного упругого материала (каким в данном случае можно считать алюминиевый сплав 7075-Т6) функция вершины трещины представляется в виде [26]. Для расчета развития существующей трещины задаются характеристики трещинностойкости материала и производится вычисление действующей интенсивности напряжений в вершине трещины. После нахождения численными методами значения J-интеграла (Abaqus предлагает такую возможность) можно определить КИН в вершине трещины и получить облако точек для построения зависимости скорости прироста трещины от КИН и провести сравнение результатов КЭ-расчета с данными натурных испытаний
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