A New Higher Order Displacement Discontinuity Method Based on the Joint Element for Analysis of Close-Spacing Planar Fractures

Summary The 2D displacement discontinuity method (DDM) has been widely used to characterize the hydraulic fracture geometry and the induced in-situ stresses in the oil and gas industry owing to its simplicity and accuracy. As smaller fracture spacing is used by multistage fracturing, the constant DDM (CDDM) loses its accuracy in predicting the fracture behaviors, especially for the inner fractures in a stage where they are subjected to the strong stress shadowing effect. In this paper, the 2D higher order DDM (HDDM) based on the joint elements was developed to overcome this limitation. The higher order displacement discontinuity intensively increases the accuracy of CDDM but maintains the same amount of computation time by using patched-element pattern. The joint elements are introduced to simultaneously determine the opening, shearing, and closing of each fracture element based on the stress boundary condition, which can avoid the “negative width” of the inner fractures given by CDDM which are mechanically closed under the strong stress shadowing effect. The developed 2D joint element HDDM (JE-HDDM) gives the same results with the CDDM when the fracture spacing is relatively large, but shows its outperformance in both efficiency and accuracy over the CDDM in predicting the displacement discontinuities and induced in-situ stresses in close fracture-spacing case.

Investigation of Systems Weakened by Kinked Cracks

Прочность летательных аппаратов любых типов — важнейший вопрос безопасности полетов. Наличие скрытых дефектов в материале существенно влияет на прочность при различных нагрузках. Важными характеристиками прочности материалов с дефектами являются скорость и направление роста трещины, а также величина критической нагрузки (коэффициента интенсивности напряжений), при которой начинается рост трещины. В данной работе исследуется трехмерная упругая среда, ослабленная системой плоских трещин и одной трещиной с изгибом. В качестве численного метода был выбран метод граничных элементов, а именно метод разрывных перемещений. Код реализован на C++. Было проведено сравнение с известными аналитическими результатами. Изучено поведение трещин при изгибе при различных нагрузках. Structural strength of aircraft is a key aspect of flight safety. Hidden defects in the material significantly affect its strength under various loads. The crack growth rate and direction, and the crack growth threshold load (stress intensity factor) affect the strength of the damaged material. This study investigates a 3D elastic structure weakened by a system of flat cracks and a kinked crack. The numerical method used was the boundary element method, specifically, the displacement discontinuity method. The code was developed with C++. The results were compared against the available analytic results. The behavior of cracks under bending and a range of loading conditions was studied.