基于界面单元的复合材料Ⅱ型层间损伤分析

为了研究复合材料层间损伤, 建立了一种新型零厚度界面单元模型, 可以准确地预测复合材料Ⅱ型层间分层扩展。模型包括本构关系建立、损伤准则和损伤演化引入, 并在大型商用有限元软件ABAQUS用户单元子程序(VUEL)中实现, 采用显示积分方法求解, 不存在收敛性问题。将该模型应用于国产碳纤维增强树脂基复合材料CCF300/5428端部缺口弯曲试验(ENF)模拟分析中, 结果表明, 此界面单元模型能够准确模拟复合材料层板Ⅱ型裂纹扩展, 为复合材料层间损伤分析提供了一种有效的方法。     

基于界面单元的复合材料层间损伤分析方法

为了研究复合材料层间损伤, 建立了一种新型零厚度界面单元模型, 可以准确地预测复合材料 Ⅰ 型层间裂纹扩展。模型包括本构关系建立、损伤准则和损伤演化引入, 并在大型商用有限元软件ABAQUS用户单元子程序VUEL中实现, 采用显示积分方法求解, 不存在收敛性问题, 同时允许使用较粗的有限元网格。最后将该模型应用于国产碳纤维增强树脂基复合材料(CCF300/5428)双悬臂梁试验(DCB)模拟分析中, 结果表明, 此界面单元模型能够准确模拟复合材料层板 Ⅰ 型裂纹扩展, 为复合材料层间损伤分析提供了一种有效的方法。     

CRTS Ⅱ型轨道板/CA砂浆界面内聚力模型研究

轨道板与CA砂浆层间离缝是CRTS Ⅱ型板式无砟轨道结构的主要病害之一。为描述轨道板-CA砂浆层间界面本构行为、揭示层间离缝机理,该文提出了一种改进指数型界面内聚力模型,并基于理论分析和试验数据确定了改进模型的参数取值。该模型为含有指数系数的分段函数,可以表征层间界面拉力-位移关系的非线性特征。研究结果表明:改进指数型内聚力模型可以高效计算轨道板-CA砂浆界面内聚强度、损伤萌生时界面相对位移和界面临界断裂能,结果与试验值基本一致;改进指数型模型可以较为准确地模拟轨道板-CA砂浆界面的法向和切向开裂行为。     

基于组合单元的层压复合材料三维应力分析

为了分析层压复合材料层间特性,推导了将刚性元-弹簧元相结合的离散型界面单元的刚度矩阵。建立了层压板的准三维模型,即将Mindlin板单元应用于层压板的各子层,层间作用则利用上述界面单元来模拟。通过弯曲板元计算子层面内应力,通过界面单元的弹簧力确定层间应力。对受面内拉伸的多向层压板条进行了应力分析,与使用商业软件三维实体模型计算得到的层间和面内应力对比,结果表明准三维模型的计算结果合理。这种新型界面单元的优点是可用来表征层间损伤,并且能通过对弹簧刚度的消减来模拟分层损伤的演变。     

基于DPC-CZM混合模型的金属粉末压坯裂纹三维数值模拟

消除和控制金属粉末压坯裂纹对生产高质量粉末冶金零件具有指导作用。本工作将修正的Drucker-Prager Cap(DPC)模型与内聚力模型(CZM)相结合,分别定义金属粉末压坯实体单元与零厚度内聚力单元的力学行为。通过巴西圆盘和单轴压缩试验获取压坯断裂性能参数,编写Python程序在实体单元中批量插入零厚度内聚力单元,模拟金属粉末压坯在外载荷作用下的拉伸和剪切裂纹以及裂纹扩展过程,并与实验结果进行对比分析。研究结果表明,采用指数型内聚力本构模型与DPC模型混合,可更准确地描述压坯裂纹损伤区的变化,与零厚度内聚力单元相关的裂纹扩展过程与实验结果更为一致。     

层压复合材料分层扩展分析的虚拟裂纹闭合技术及其应用

提出一种基于虚拟裂纹闭合技术的界面元模型,用以模拟复合材料的分层破坏和预测结构的承载能力。界面元被嵌入在模型分层扩展路径上,计算结构的能量释放率,结合幂指数破坏准则,模拟复合材料的分层扩展。对由于裂尖单元长度不同所带来的分析误差进行了适当的修正,以降低网格粗细变化所带来的不利影响。为了检验该界面元的可靠性,分别将其应用于对双悬臂梁(DCB) 模型、端边切口(ENF) 模型和混合模式弯曲(MMB) 模型的分层扩展分析中。计算结果与解析解基本吻合,从而验证了采用该界面元模拟复合材料分层破坏的可行性。用该方法对3个含有不同初始损伤复合材料T型接头的界面拉脱分层破坏进行数值模拟,计算结果与试验数据吻合良好。      

复合材料疲劳分层的界面单元模型

提出一种三维黏聚力界面损伤模型,可以描述单调和交变载荷下层合复合材料混合型的分层损伤。损伤用界面所经历过的最大位移间断来定义,交变荷载下一个周期的加、卸载过程均考虑有损伤积累,模型还考虑了单调和疲劳损伤的门槛效应和交变载荷下裂纹的闭合效应。建立了包含该界面损伤模型的初始无厚度八节点等参界面单元,并引入加速损伤的算法,用一次计算循环代替若干次实际循环,提高计算效率。用该单元模型对某复合材料动部件疲劳分层裂纹的形成和扩展进行了模拟,得到了分层裂纹前沿界面局部损伤和结构疲劳分层的发展规律,模型预测的裂纹长度-荷载循环次数对数(a-log N)曲线和结构剩余刚度与试验数据吻合。     

一种改进的内聚力损伤模型在复合材料层合板低速冲击损伤模拟中的应用

针对传统内聚力损伤模型(CZM)无法考虑层内裂纹对界面分层影响的缺点,提出了一种改进的适用于复合材料层合板低速冲击损伤模拟的CZM。通过对界面单元内聚力本构模型中的损伤起始准则进行修正,考虑了界面层相邻铺层内基体、纤维的损伤状态及应力分布对层间强度和分层扩展的影响。基于ABAQUS用户子程序VUMAT,结合本文模型及层合板失效判据,建立了模拟复合材料层合板在低速冲击作用下的渐进损伤过程的有限元模型,计算了不同铺层角度和材料属性的层合板在低速冲击作用下的损伤状态。通过数值模拟与试验结果的对比,验证了本文方法的精度及合理性。     

缝线增强层合板混合模式弯曲试验的数值模拟

对缝线在复合材料层合板中的桥联作用进行参数分析,结果显示缝线的直径和拉伸强度,缝合角度,层合板厚度和挤压强度均会对缝线的桥联曲线以及断裂能产生影响,甚至改变缝线的破坏模式。以计算所得的桥联曲线作为输入参数,分别用连接器(Connector)和离散内聚力单元(Cohesive单元)的方法建立有限元模型,模拟缝线增强复合材料层合板的混合模式弯曲(MMB,Mix-Mode Bending)试验。两种方法的有限元计算结果具有较好的一致性,且均能够与文献中的试验数据较好吻合。相比离散Cohesive单元模型,Connector模型的计算效率更高,需要的输入参数更少,且建模更为简便。     

胶层网格尺寸与性能参数相关性的反演研究

在使用内聚力模型对复合材料胶层进行有限元失效分析时,为了保证计算结果的准确性和收敛性,胶层网格尺寸应小于1 mm。然而当使用内聚力模型对飞机上的大型复合材料结构进行有限元分析时,模型将会产生上百万的有限元单元,这将耗费大量的计算资源。本文在研究胶层参数对胶层失效分析影响的基础上,通过对不同网格尺寸下胶层参数进行反演,提出了一种修改胶层参数的方法以适用于不同网格尺寸下胶层失效分析。使用此方法对不同网格尺寸的混合型弯曲(MMB)有限元模型和复合材料圆壳模型进行了有限元仿真。结果表明:所提出的方法能够大幅降低模型的网格数量,减小计算规模,快速准确地计算出混合加载条件下胶层损伤演化和破坏情况。      

短纤维增强橡胶密封复合材料界面疲劳损伤行为

依据广义自洽方法,建立了包含芳纶纤维、界面相、橡胶基体和等效介质的代表性体积单元(RVE)模型。采用自定义材料子程序对内聚力疲劳累积损伤模型进行编译,分别在基体/界面相的界面和纤维/界面相的界面设置内聚力单元,研究界面相性能参数对纤维增强橡胶密封复合材料(SFRC)界面疲劳损伤行为的影响。探讨了界面相厚度和模量的确定方法,获得了不同界面相厚度和模量下SFRC界面脱粘起始位置以及脱粘起始疲劳次数。结果表明,较低的界面相模量能够抑制界面脱粘的产生;随着界面相厚度的增加,界面脱粘的起始疲劳次数增加,SFRC抗疲劳损伤能力得到提高。     

Discrete cohesive zone model for mixed-mode fracture using finite element analysis

The discrete cohesive zone model (DCZM) is implemented using the finite element (FE) method to simulate fracture initiation and subsequent growth when material non-linear effects are significant. Different from the widely used continuum cohesive zone model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses rod type elements and applies the cohesive law as the rod internal force vs. nodal separation (or rod elongation). These rod elements have the provision of being represented as spring type elements and this is what is considered in the present paper. A series of 1D interface elements was placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes were introduced within the interface element to extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations were examined. For pure mode I, the double cantilever beam configuration, using both uniform and biased meshes were analyzed and the results show that the DCZM is not sensitive to the mesh size. Results also show that DCZM is not sensitive to the loading increment, either. Next, the end notched flexure for pure mode II and, the mixed-mode bending were studied to further investigate the approach. No convergence difficulty was encountered during the crack growth analyses. Therefore, the proposed DCZM approach is a simple but promising tool in analyzing very general two-dimensional crack growth problems. This approach has been implemented in the commercial FEA software ABAQUS^® using a user defined subroutine and should be very useful in performing structural integrity analysis of cracked structures by engineers using ABAQUS^®.     

Cohesive zone criterion for cracking along the Cu/Si interface in nanoscale components

Crack initiation and propagation along the Cu/Si interface in multilayered films (Si/Cu/SiN) with different thicknesses of the Cu layer (20 and 200 nm) are experimentally investigated using a nano-cantilever and millimeter-sized four-point bending specimens. To examine the cohesive zone model (CZM) criterion for interfacial delamination along the Cu/Si interface in nanoscale stress concentration, an exponential type of CZM is utilized to simulate the observed delamination processes using the finite element method. After the CZM parameters for the Cu/Si interface are calibrated by experiment, interface cracking in other experiments is predicted. This indicates that the CZM criterion is universally applicable for describing cracking along the interface regardless of specimen dimensions and film thickness which include the differences in plastic behavior and residual stress. The CZM criterion can also predict interfacial cracking along Cu/Si interfaces with different stress singularities.     

Analysis of a rotation‐free 4‐node shell element

In this paper, a shell element for small and large deformations is presented based on the extension of the methodology to derive triangular shell element without rotational degrees of freedom (so‐called rotation‐free). As in our original triangular S3 element, the curvatures are computed resorting to the surrounding elements. However, the extension to a quadrilateral element requires internal curvatures in order to avoid singular bending stiffness. The quadrilateral area co‐ordinates interpolation is used to establish the required expressions between the rigid‐body modes of normal nodal translations and the normal through thickness bending strains at mid‐side. In order to propose an attractive low‐cost shell element, the one‐point quadrature is achieved at the centre for the membrane strains, which are superposed to the bending strains in the centred co‐rotational local frame. The membrane hourglass control is obtained by the perturbation stabilization procedure. Free, simply supported and clamped edges are considered without introducing virtual nodes or elements. Several numerical examples with regular and irregular meshes are performed to show the convergence, accuracy and the reasonable little sensitivity to geometric distortion. Based on an updated Lagrangian formulation and Newton iterations, the large displacements of the pinched hemispherical shell show the effectiveness of the proposed simplified element (S4). Finally, the deep drawing of a square box including large plastic strains with contact and friction completes the ability of the rotation‐free quadrilateral element for sheet‐metal‐forming simulations. Copyright © 2005 John Wiley & Sons, Ltd.     

A FLAT TRIANGULAR SHELL ELEMENT WITH LOOF NODES

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiencies are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal configuration of the element is similar to the SemiLoof element, and the formulation is an improvement of a previous formulation. The element is used for both linear statics, linear buckling and geometrical non-linear analysis, and numerical examples are presented to show the robustness, accuracy and quick convergence of the element.     

A consistent partly cracked XFEM element for cohesive crack growth

Present extended finite element method (XFEM) elements for cohesive crack growth may often not be able to model equal stresses on both sides of the discontinuity when acting as a crack‐tip element. The authors have developed a new partly cracked XFEM element for cohesive crack growth with extra enrichments to the cracked elements. The extra enrichments are element side local and were developed by superposition of the standard nodal shape functions for the element and standard nodal shape functions for a sub‐triangle of the cracked element. With the extra enrichments, the crack‐tip element becomes capable of modelling variations in the discontinuous displacement field on both sides of the crack and hence also capable of modelling the case where equal stresses are present on each side of the crack. The enrichment was implemented for the 3‐node constant strain triangle (CST) and a standard algorithm was used to solve the non‐linear equations. The performance of the element is illustrated by modelling fracture mechanical benchmark tests. Investigations were carried out on the performance of the element for different crack lengths within one element. The results are compared with previously obtained XFEM results applying fully cracked XFEM elements, with computational results achieved using standard cohesive interface elements in a commercial code, and with experimental results. The suggested element performed well in the tests. Copyright © 2007 John Wiley & Sons, Ltd.     

附加约束阻尼层的复合材料梁单元建模分析

复合材料空心圆截面梁是桁架和刚架结构中大量采用的常用构件，而实践证明约束阻尼层能有效改善复合材料空心圆截面梁的动力学特性，但传统的约束阻尼层结构有限元计算方法需要大量的单元，这给大型复杂结构的计算带来了巨大的困难。本文采用Timoshenko梁假定。建立了一类附加约束阻尼层复合材料空心圆截面梁弯曲的数学模型。应用Hamilton原理。采用三节点高次梁单元对构件进行离散化。建立了附加约束阻尼层复合材料空心圆截面梁的梁单元。同传统的锥壳单元相比，该方法极大地减少了计算时间。用实验验证了本文计算结果的正确性。同时也分析了约束层厚度对损耗因子的影响。     

Roughness of a mode I in-plane crack front propagating along a heterogeneous cohesive interface

The roughness of the crack front of an interfacial crack propagating along a weak plane in a heterogeneous disordered medium has been repeatedly studied both experimentally and numerically. For an interfacial toughness varying randomly on the interface, the front is self-affine. Quite often, however, the calculated roughness exponent differs from the experimental estimate. Several theoretical models have been employed up to now in the numerical simulations (elastic line depinning, random fuse and spring or beam models). In this paper we present finite element simulations (FEA) of the macroscopic mode-I static propagation of a crack front along a planar interface of an elastic or elastic-plastic coating adhered to a rigid substrate. The interfacial elements separate obeying a cohesive law, their toughness spatially fluctuating at random. The cohesive elements here employed allow for taking into account local I + II + III mixed-opening mode, i.e., allow for mode mixity at the local level. Our results indicate that for a given macroscopic toughness the crack front roughness is strongly sensitive to both the local cohesive law and the local fracture criterion.     

A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates

This is the first paper of a pair which together discuss the development of a class of overlapping hinged bending finite elements which are suitable for the analysis of thin-shell, plate and beam structures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based on quadratic overlapping assumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher-order nodal variables. In this paper the hinged bending element concept is introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements are formulated. In paper II these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin-shell structures.     

A fracture framework for Euler–Bernoulli beams based on a full discontinuous Galerkin formulation/extrinsic cohesive law combination

A new full Discontinuous Galerkin discretization of Euler–Bernoulli beam is presented. The main interest of this framework is its ability to simulate fracture problems by inserting a cohesive zone model in the formulation. With a classical Continuous Galerkin method, the use of the cohesive zone model is difficult because inserting a cohesive element between bulk elements is not straightforward. On one hand if the cohesive element is inserted at the beginning of the simulation, there is a modification of the structure stiffness and on the other hand inserting the cohesive element during the simulation requires modification of the mesh during computation. These drawbacks are avoided with the presented formulation as the structure is discretized in a stable and consistent way with full discontinuous elements and inserting cohesive elements during the simulation becomes straightforward. A new cohesive law based on the resultant stresses (bending moment and membrane) of the thin structure discretization is also presented. This model allows propagating fracture while avoiding through‐the‐thickness integration of the cohesive law. Tests are performed to show that the proposed model releases, during the fracture process, an energy quantity equal to the fracture energy for any combination of tension‐bending loadings. Copyright © 2010 John Wiley & Sons, Ltd.