Cohesive Zone Model Modification Techniques According to the Mesh Size in Finite Element Models of Stiffened Panels with Debonding

When catastrophic failure phenomena in aircraft structures, such as debonding, are numerically analyzed during their design process in the frame of “Damage Tolerance” philosophy, extreme requirements in terms of time and computational resources arise. Here, a decrease in these requirements is achieved by developing a numerical model that efficiently treats the debonding phenomena that occur due to the buckling behavior of composite stiffened panels under compressive loads. The Finite Element (FE) models developed in the ANSYS© software (Canonsburg, PA, USA) are calibrated and validated by using published experimental and numerical results of single-stringer compression specimens (SSCS). Different model features, such as the type of the element used (solid and solid shell) and Cohesive Zone Modeling (CZM) parameters are examined for their impact on the efficiency of the model regarding the accuracy versus computational cost. It is proved that a significant reduction in computational time is achieved, and the accuracy is not compromised when the proposed FE model is adopted. The outcome of the present work leads to guidelines for the development of FE models of stiffened panels, accurately predicting the buckling and post-buckling behavior leading to debonding phenomena, with minimized computational and time cost. The methodology is proved to be a tool for the generation of a universal parametric numerical model for the analysis of debonding phenomena of any stiffened panel configuration by modifying the corresponding geometric, material and damage properties.

The Impacts of Increased Ductility in Organic-Rich Shale on Fracture Network Growth by Hydraulic Fracturing

The difficulty of hydraulic fracturing in organic-rich shale caused by the increased ductility has not been well interpreted quantitatively, although it is well perceived that the increased shale ductility can impede the propagation of hydraulic fractures and enhance the healing of created fractures upon injection shutdown. This study aims to quantitatively study the impacts of increased ductility on the stimulated reservoir volume (SRV) using an advanced XFEM-based simulator. To achieve this goal, a modified cohesive zone model has been integrated into an in-house fully coupled poroelastic XFEM framework. The study continues by extending the functionality of the numerical framework to simulating multiple interacting fractures. The utilization of the object-oriented programming paradigm in the development of the framework makes it an easy extension to include the multi-fracture network by creating more instances of crack segments. A main hydraulic fracture with an arbitrary number of intersected branches can thus be modeled. A series of parametric studies will be conducted to investigate the impacts of increased ductility on the induced SRV by varying four involved material parameters individually. The modified cohesive zone model, which is essentially a traction-separation law (TSL), is characterized by four parameters: the initial tensile strength Tini, ultimate tensile strength Tkrg, the critical separation Dc, and the final crack separation Dmax. It can flexibly model different crack opening scenarios and simulate more realistically the increased shale ductility. The fully coupled poroelastic XFEM framework has been comprehensively verified against the latest semi-analytical solutions on the four well-known propagation regimes. The numerical results show that the shape of TSL does affect the main hydraulic fracture growth as well as the evolvement of the fracture network, given the same cohesive crack energy and tensile strength. It infers that ductility is not only controlled by cohesive crack energy and tensile strength, which further indicates the necessity of the newly proposed cohesive zone model. The magnitude of the initial tensile strength, controlling when the cohesive crack starts propagating, is found to have the greatest impacts on the fracture length, and SRV, among all four TSL parameters. The novelty of this study is two-fold. First, the newly modified cohesive zone model can more realistically represent the increased shale ductility. Second, the advanced XFEM framework that enables the simulation of a fracture network can study the impacts of increased ductility on the whole SRV but not a single crack.

Domain discretizations for numerical solution of fracture problems

В работе для численного моделирования хрупкого разрушения с целью повышения эффективности громоздких расчетов предлагается использовать двухуровневую процедуру построения сетки дискретизации. На верхнем уровне генерируется сетка фрагментов - локусов задаваемых размеров и произвольной случайной формы, по границам которых может происходить разрушение. На нижнем уровне каждый локус разбивается на сетку конечных элементов. Разрыв связей между конечными элементами по траектории разрушение между локусами реализуется с помощью процедуры сцепляющей среды. Для построения сетки дискретизации верхнего уровня использована диаграмма Воронова. Разработан алгоритм процедуры создания локусов на телах произвольной формы в двумерной и трехмерной постановках. Процедура реализована на языке APDL, для использования в программном комплексе ANSYS. Алгоритм протестирован при различных значениях задаваемых параметров и на объектах разнообразной формы. Численное решение задачи о разрушении цилиндрического образца из хрупкого материала по бразильскому тесту определения прочностных характеристик материала на растяжение продемонстрировало хорошее согласование полученной картины разрушения с реальной. In this paper, for numerical modeling of brittle fracture in order to increase the efficiency of complex calculations, it is proposed to use a two-level procedure for generating a discretization network. At the upper level, a network of fragments – locus’s, of specified sizes and arbitrary random shape, is generated. At the lower level, each locus is meshed by FE. The breaking of connections between finite elements along the trajectory of destruction between locus is realized using the cohesive zone procedure. The properties of the Voronov diagram are used to generate the upper-level discretization network. The algorithm of the procedure for creating locus on bodies of arbitrary shape in two-dimensional and three-dimensional formulations is developed. The procedure is implemented in the APDL, for use in the ANSYS. The algorithm is tested at various values of the specified parameters and on objects of various shapes. The numerical solution of the problem of the destruction of a cylindrical sample made of brittle material according to the Brazilian test for determining the tensile strength characteristics of the material demonstrated a good agreement of the obtained fracture pattern with the real one.