A variational multiscale method to model crack propagation at finite strains

This contribution presents a hierarchical variational multiscale framework to model propagating discontinuities at finite strains. Thereby the deformation map is decomposed into coarse‐scale and fine‐scale displacements, which results in a decoupled system of coarse‐scale and fine‐scale equations. Both are solved numerically by means of the finite element method whereby crack propagation is taken into account at the fine scale. Growing cracks are numerically handled by the introduction of discontinuous elements. A locality assumption on the fine‐scale solution and an adaptive scheme to resize the fine‐scale domain are introduced and demonstrated to increase the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling crack propagation in reinforced concrete using a hybrid finite element–scaled boundary finite element method

A previously developed hybrid finite element–scaled boundary finite element method (FEM–SBFEM) is extended to model multiple cohesive crack propagation in reinforced concrete. This hybrid method can efficiently extract accurate stress intensity factors from the semi-analytical solutions of SBFEM and is also flexible in remeshing multiple cracks. Crack propagation in the concrete bulk is modelled by automatically inserted cohesive interface elements with nonlinear softening laws. The concrete–reinforcement interaction is also modelled by cohesive interface elements. The bond shear stress–slip relation of CEB-FIP Model Code 90 and an empirical confining stress–crack opening relation are used to characterise slip and split failure at the concrete–reinforcement interface, respectively. Three RC beams were simulated. The numerical results agreed well with both experimental and numerical results available in the literature. Parametric studies demonstrated the importance of modelling both slip and split failure mechanisms at the concrete–reinforcement interface.     

Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams

This paper presents a finite element (FE) model for fully automatic simulation of multiple discrete crack propagation in reinforced concrete (RC) beams. The discrete cracks are modelled based on the cohesive/fictitious crack concept using nonlinear interface elements with a bilinear tensile softening constitutive law. The model comprises an energy-based crack propagation criterion, a simple remeshing procedure to accommodate crack propagations, two state variable mapping methods to transfer structural responses from one FE mesh to another, and a local arc-length algorithm to solve system equations characterised by material softening. The bond-slip behaviour between reinforcing bars and surrounding concrete is modelled by a tension-softening element. An example RC beam with well-documented test data is simulated. The model is found capable of automatically modelling multiple crack propagation. The predicted cracking process and distributed crack pattern are in close agreement with experimental observations. The load-deflection relations are accurately predicted up to a point when compressive cracking becomes dominant. The effects of bond-slip modelling and the efficiency and effectiveness of the numerical algorithms, together with the limitations of the current model, are also discussed.     

Application of viscoelastic fracture criteria to progressive crack propagation in polymer matrix composites

With the view of comparing local and global viscoelastic fracture criteria, an extension of Christensen's criterion to composite materials with stiff elastic fibers is proposed. Several versions of this criterion are compared with Schapery's local approach of the same phenomenon. The asymptotic version of Christensen's criterion for rapid crack propagation is found suitable for the material investigated, at room temperature. Dissipation in the specimen has two main sources: the undamaged material on one hand, and the damaged material inside the `failure zone' close to the crack tip on the other. The respective roles of these two kinds of dissipation are assessed.     

Mesh superposition-based multiscale stress analysis of composites using homogenization theory and re-localization technique considering fiber location variation

In this article, the accuracy of multiscale stress analysis of heterogeneous materials (unidirectional fiber-reinforced composite) was improved by considering microscopic geometrical variation using the mesh superposition method. When analyzing the stress distribution in a composite with the finite element method considering the variation of the fiber location, updating the mesh significantly is necessary; however, generating an appropriate mesh for a large geometrical variation is difficult. Therefore, we focused on the mesh superposition method, which can easily generate a numerical FE model, even if the internal structure is complex, because the matrix and inclusion can be expressed by the global mesh and local mesh independently. However, in the original mesh superposition method, the analysis accuracy may be degraded owing to the mesh overlap conditions. Therefore, an improved method was applied to the homogenization theory-based analysis. In this article, the effectiveness of the proposed approach was discussed by comparing the numerical results of this method with those of conventional mesh superposition method and standard finite element method. From the numerical results, accuracy improvement by the proposed approach for the multiscale stochastic stress analysis is confirmed.     

基于相移光纤光栅传感器的碳纤维增强树脂复合材料基体裂纹超声探伤

复合材料内部的微小裂纹常会引起后续严重的破坏,因此需要对其进行检测。然而超声探伤复合材料基体裂纹非常困难。本文搭建了一个具有高灵敏度、大带宽的相移光纤光栅超声传感系统,利用此系统探测了在正交铺层碳纤维增强树脂复合材料板中传播的Lamb波。对Lamb波进行数据处理发现,随着三点弯曲实验产生的基体裂纹个数增加,Lamb波的幅值和频谱峰值线性减少。通过和传统压电传感器比较表明,相移光纤光栅传感器测得的Lamb波信号随复合材料基体裂纹数的增加其幅值具有更高的下降速率,表明相移光纤光栅传感器更适合于复合材料基体裂纹的超声探伤。研究表明,新开发的传感系统能够探测到中心频率为300 kHz的微弱超声信号,并能够对碳纤维增强树脂复合材料板中微小基体裂纹个数进行精确评估。      

Numerical investigation of matrix cracking propagation in cross‐ply laminated composites subjected to three‐point bending load using concurrent multiscale model

The purpose of the present study is to analyze fiber‐matrix debonding and induced matrix cracking formation as two major micromechanical damage modes in cross‐ply composite laminates using a two‐dimensional numerical approach. To this aim, the cross‐ply laminates containing 90‐degree layers are modeled, where the fibers are arranged randomly in transverse plies. Damage modes in this numerical model are simulated by the cohesive surface method. The performed analyses reveal that in the laminates with 90‐degree layers located in the outer positions, the primary micro damage mode is micro matrix cracking which is initiated from the fiber‐matrix debonding damage mode and will be followed by matrix cracking. The main benefit of the present study in comparison to other numerical methods is proposing a virtual test method for damage analysis of different cross‐ply laminates in which, the matrix cracking formation will emerge physically in a random and antisymmetric pattern similar to the experimental observations.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

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。      

连续石墨纤维增强铝基复合材料准静态拉伸损伤演化与断裂力学行为

针对连续石墨纤维增强铝基(CF/Al)复合材料,采用三种纤维排布方式的代表体积单元(RVE)建立了其细观力学有限元模型,采用准静态拉伸试验与数值模拟结合的方法,研究了其在轴向拉伸载荷下的渐进损伤与断裂力学行为。结果表明,采用基体合金和纤维原位力学性能建立的细观力学有限元模型,对轴向拉伸弹性模量和极限强度的计算结果与实验结果吻合良好,而断裂应变计算值较实验结果偏低。轴向拉伸变形中首先出现界面和基体合金损伤现象,随应变增加界面发生失效并诱发基体合金的局部失效,最后复合材料因纤维发生失效而破坏,从而出现界面脱粘后纤维拔出与基体合金撕裂共存的微观形貌。细观力学有限元分析结果表明,在复合材料制备后纤维性能衰减而强度较低条件下,改变界面强度和刚度对复合材料轴向拉伸弹塑性力学行为的影响较小,复合材料中纤维强度水平是决定该复合材料轴向拉伸力学性能的主要因素。     

Dual boundary element method and finite element method for mixed‐mode crack propagation simulations in a cracked hollow shaft

Three‐dimensional mixed‐mode crack propagation simulations were performed by means of the dual boundary element method code BEASY and 2 finite element method‐based crack propagation codes: ZENCRACK (ZC) and CRACKTRACER3D (CT3D). The stress intensity factors (SIFs) along the front of an initial semielliptical crack, initiated from the external surface of a shaft, were calculated for 4 different load cases: bending, press fit, shear, and torsion. The methods used for the SIF assessment along the crack front were the J‐integral for BEASY and ZC and the quarter point element stress method for CT3D. Subsequently, crack propagation simulations were performed, with the crack growth rate evaluated by using Paris' law, calibrated for the material at stake (American Society for Testing and Materials A469 steel). The kink angles were evaluated by using the minimum strain energy density and maximum tangential stress criteria for BEASY, the maximum energy release rate and maximum tangential stress for ZC, and the maximum principal asymptotic stress for CT3D. The results obtained in terms of SIFs and crack propagation life show very good agreement among the 3 codes. Also, the shape of the propagated crack, which is significantly out‐of‐plane for the shear and torsion loading, matched very well.     

Delamination buckling and propagation analysis of honeycomb panels using a cohesive element approach

The cohesive element approach is proposed as a tool for simulating delamination propagation between a facesheet and a core in a honeycomb core composite panel. To determine the critical energy release rate (G _c) of the cohesive model, Double Cantilever Beam (DCB) fracture tests were performed. The peak strength (_c) of the cohesive model was determined from Flatwise Tension (FWT) tests. The DCB coupon test was simulated using the measured fracture parameters, and sensitivity studies on the parameters for the cohesive model of the interface element were performed. The cohesive model determined from DCB tests was then applied to a full-scale, 914×914 mm (36×36 in.) debond panel under edge compression loading, and results were compared with an experiment. It is concluded that the cohesive element approach can predict delamination propagation of a honeycomb panel with reasonable accuracy.     

Stochastic XFEM fracture and crack propagation behavior of an isotropic plate with hole emanating radial cracks subjected to various in-plane loadings

In this article, the statistics of fracture response in terms of the mean and coefficient of variation of mixed mode stress intensity factor (SIF) of an isotropic plate with hole emanating radial cracks and crack growth subjected to in-plane mechanical tensile, shear, and combined loading is evaluated. The random system parameters, such as normalized crack length, crack angle, and normalized radius of hole, are assumed as uncorrelated random variables. The basic formulation is based on the extended finite-element method with level set method combined with second-order perturbation method. The effects of the normalized radius of the hole, normalized crack length, crack angles, different positions of the hole with cracks, and in-plane loadings on the statistics of mixed mode SIF with input random system parameters are analyzed.     

An exact reanalysis algorithm using incremental Cholesky factorization and its application to crack growth modeling

In this paper, an exact reanalysis algorithm based on an incremental Cholesky factorization is presented, which can solve a linear system of equations when a small portion of the coefficient matrix is modified. The efficiency of the proposed algorithm is demonstrated by modeling quasi‐static crack growth in the extended finite element method. The example presented shows that a 60% to 70% reduction in computational time is achievable by using the reanalysis approach for solving crack growth problems. It is shown that the reanalysis approach has increasing benefits as the mesh density increases. Copyright © 2012 John Wiley & Sons, Ltd.     

Control of interfacial adhesion in continuous carbon and kevlar fiber reinforced polymer composites

Carbon fiber surfaces were treated by cold plasmas of oxygen, nitrogen, argon, ammonia, and propylene. A two-component bismaleimide, an epoxy, and a model thermoplastic resin polypropylene were used as the matrices for composites. The effectiveness of various plasmas in improving the interfacial adhesion between carbon fibers and matrix resins was demonstrated. Predominant adhesion promotion mechanisms as influenced by various plasma treatments were determined. Oxygen and argon plasmas were found to promote mechanical keying by increasing the level of fiber surface roughness and porosity. The wettability of carbon fiber surface by the matrix resin was also enhanced by oxygen plasmas and argon plasmas (to a lesser extent), as evidenced by the increased total surface energies and their polar components. These surface energy increases are mainly due to the various oxygen-containing functional groups observed on the oxygen plasma-treated surface. For the cases of ammonia and combined ammonia/argon plasma treatments, possible chemical bonding between bismaleimide and the plasma-deposited amine groups is one important promoter of interfacial bonding. In these cases increased wettability was also observed. Ammonia and ammonia/argon plasmas appear to be the more appropriate treatments for carbon-fiber/thermoset resin composites considering that they generally do not induce any appreciable reduction in fiber strength. In contrast, excessively prolonged exposure of carbon fibers to oxygen, nitrogen or argon plasma could lead to a significant reduction in fiber strength. The plasma-polymerized polypropylene deposited on the fiber surface was capable of improving the compatibility and adhesion between the fiber and the polypropylene matrix.     

Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium

The mechanism of mixed‐mode fatigue crack propagation was investigated in pure aluminum. Push‐pull fatigue tests were performed using two types of specimens. One was a round bar specimen having a blind hole, one was a plate specimen having a slit. The slit direction cut in the specimen was perpendicular or inclined 45 degrees relative to the centre of the specimen axis. In both cases, cracks propagated by mode I or by the mixed mode combining mode I and shear mode, depending on the testing conditions. In these cases the crack propagation rate was evaluated with a modified effective stress intensity factor range. Crack propagation retardation was observed in some specimens. However, it was found that the crack propagation rate could also be evaluated by the effective stress intensity factor range independent of the crack propagation mode.     

The effects of volume percent and aspect ratio of carbon fiber on fracture toughness of reinforced aluminum matrix composites

Carbon fiber reinforced aluminum matrix composites are used as advanced materials in aerospace and electronic industries. In order to investigate role of aspect ratio of carbon fiber on fracture toughness of aluminum matrix composite, the composite was produced using stir casting. Al–8.5%Si–5%Mg selected as a matrix. The samples were prepared with three volume fractions (1, 2 and 3) and three aspect ratios (300, 500 and 800). Three-point bending test was performed on the specimens to evaluate the fracture toughness of the materials. The results showed that the fracture toughness of composites depends on both fiber volume fraction and aspect ratio. Scanning electron microscopy (SEM) was employed to elucidate the fracture behavior and crack deflection of composites. The study also, showed that the toughening mechanism depends strongly on fiber volume fraction, aspect ratio and the degree of wetting between fiber and matrix.     

纤维增强复合材料界面脱层和基体裂纹的模拟分析

基于Ghosh提出的Voronoi单元有限元方法,构造能同时反映纤维增强复合材料界面脱层和基体裂纹扩展的单元(X-VCFEM单元);应用界面力学理论和断裂力学理论,建立界面脱层、界面裂纹扩展方向和基体裂纹扩展的判断准则;结合网格重划分技术,模拟分析了只含有一个夹杂时界面脱层和基体裂纹扩展的过程,并通过与传统有限元计算结果的比较,验证X-VCFEM单元的可靠性和有效性;同时,模拟分析含任意随机分布夹杂的纤维增强复合材料界面脱层和基体裂纹的产生和扩展过程。结果表明：应用该方法模拟复杂多相复合材料裂纹问题具有计算速度快和精度高的优越性。     

汉麻纤维表面改性对其增强聚丙烯复合材料性能及挥发性有机化合物释放影响

通过非织造-热压工艺制备了汉麻纤维增强聚丙烯（HF/PP）复合材料。采用热重-质谱联用仪（TG-MS）研究了HF/PP复合材料的挥发性有机化合物（Volatile organic compounds,VOC）释放来源及汉麻经聚乙烯醇（PVA）改性和尿素改性对HF/PP复合材料VOC释放的影响,同时研究了两种改性方法对HF/PP复合材料热学性能和力学性能的影响。结果表明：HF/PP复合材料中的VOC主要来源于汉麻纤维,改性后的HF/PP复合材料力学性能相比未处理的均有不同程度的提升,尿素改性后,HF/PP复合材料的拉伸强度和弯曲强度达到最大值,较未处理时分别提升了19.32%和15.04%。PVA改性后,HF/PP复合材料的拉伸模量、弯曲模量和剪切强度达到最大值,相比未改性时分别提升了17.72%、15.94%和24.72%。改性后HF/PP复合材料热稳定性能和VOC释放相较未处理时均得到了优化：PVA改性后HF/PP复合材料热稳定性最优,三个阶段总活化能较未处理时提高了121.99%,达到了392.56 kJ·mol^-1,并且HF/PP复合材料热稳定性与界面性能密切相关;尿素及PVA改性后HF/PP复合材料的总VOC（TVOC）释放量相较未处理时均降低。