Simulation and analysis of shape memory alloy fiber reinforced composite based on cohesive zone model

Shape memory alloy (SMA) composite has been wildly used in engineering fields as a smart structure. The interface between SMA fiber and matrix plays an important role in determining the effective response of the composites, since it is the medium through which stress transfer occurs. Therefore, it is necessary to investigate how the variation of interfacial properties affects the overall behavior of the composites. In this paper, the interfacial shear strength and ultimate strength of composites are evaluated based on pull-out tests and uniaxial tensile tests, respectively. An algorithm for the automatic generation of unidirectional random distribution short-fiber reinforced composites is developed by using Monte-Carlo method and boundary condition control equation via ANSYS Parameter Design Language (APDL). Cohesive zone model (CZM) approach is used to characterize the interfacial traction separation relationships. Uniaxial tensile test is simulated using finite element method to study the overall macroscopic behavior of the composite through varying fiber ratios and ambient temperatures. The effects of interfacial debonding process, fiber ratios and ambient temperatures on the response of composites are discussed under the same fiber volume fraction.     

基于内聚力模型的形状记忆合金短纤维增强树脂基复合材料的模拟分析

通过单纤维拔出实验和单轴拉伸实验, 测定了形状记忆合金(SMA)增强树脂基复合材料的界面脱粘剪切强度和单向随机分布SMA短纤维增强复合材料的拉伸强度。根据蒙特卡罗法和边界条件控制方程, 编写了适于软件调用的单向随机分布短纤维增强复合材料的APDL语言生成程序, 建立数值模拟模型。基于指数型内聚力模型, 对SMA纤维与环氧树脂基体界面分离(即界面脱粘)过程进行了有限元模拟。结果表明: 相同纤维体积分数下, 随着纤维长细比的减小, 复合材料整体弹性模量逐渐降低; 温度驱使SMA纤维弹性模量发生变化, 可以有效提高复合材料整体弹性模量。     

基于粘聚区模型的含填充区复合材料接头失效数值模拟

建立了Ⅰ型与Ⅱ型失效模式耦合的粘聚单元本构模型, 并通过模拟双悬臂梁实验进行了验证。将粘聚单元插入填充区任何2 个实体单元之间, 预测填充区的随机裂纹, 模拟了接头在拉伸载荷下的失效。计算了复合材料基体、界面胶膜、填充物3 者不同强度、填充区半径、填充物刚度等多种情况下接头的拉伸失效。计算结果表明: 复合材料基体、界面胶膜、填充物3 者的强度显著影响接头的承载能力与失效模式; 随着填充区半径增大, 结构承载能力也随之提高。试验结果验证了模拟结果。      

Finite element simulation of delamination growth in composite materials using LS-DYNA

In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (η) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.     

Application of cohesive zone model in crack propagation analysis in multiphase composite materials

A nonlinear cohesive stress distribution function is employed by relating the cohesive stress to the cohesive zone size (CZS) and the distance from the crack tip to investigate the elastic-plastic fracture behaviors. A crack-inclusion interaction problem is taken as an example to explore the fracture process in the cohesive zone area. The CZS and crack surface opening displacement are evaluated numerically. It is found that for different cohesive parameter combinations, the normalized CZS and crack surface opening displacements change drastically. By reducing the current model to the famous Dugdale model, the results obtained match well with the existing ones.     

基于小波内聚力模型的界面裂纹扩展

利用区间B样条小波良好的局部化性能,将内聚力模型（CZM）引入小波有限元法（WFEM）数值分析中,以区间B样条小波尺度函数作为插值函数,构造小波内聚力界面单元,推导了小波内聚力界面单元刚度矩阵,基于虚拟裂纹闭合技术（VCCT）计算界面裂纹应变能释放率（SERR）,采用β-Κ断裂准则,实现界面裂纹扩展准静态分析。将WFEM和传统有限元法（CFEM） 的SERR数值分析结果与理论解进行比较,结果表明:采用WFEM和CFEM计算的SERR分别为96.60 J/m2 和 101.43 J/m2,2种方法的SERR数值解与理论解相对误差分别为1.85%和3.06%,这明确表明WFEM在计算界面裂纹扩展方面能用较少单元和节点数获得较高的计算精度和效率。在此基础上,探讨了界面裂纹初始长度和双材料弹性模量比对界面裂纹扩展的影响,分析结果表明:界面裂纹尖端等效应力随界面裂纹初始长度的增加而增加;双材料弹性模量比相差越大,界面裂纹越易于扩展,且裂纹扩展长度也越大,因此可通过调节双材料弹性模量比来延缓界面裂纹扩展。      

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.     

Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods

In conventional cohesive zone models the traction-separation law starts from zero load, so that the model cannot be applied to predict mixed-mode cracking. In the present work the cohesive zone model with a threshold is introduced and applied for simulating different mixed-mode cracks in combining with the extended finite element method. Computational results of cracked specimens show that the crack initiation and propagation under mixed-mode loading conditions can be characterized by the cohesive zone model for normal stress failure. The contribution of the shear stress is negligible. The maximum principal stress predicts crack direction accurately. Computations based on XFEM agree with known experiments very well. The shear stress becomes, however, important for uncracked specimens to catch the correct crack initiation angle. To study mixed-mode cracks one has to introduce a threshold into the cohesive law and to implement the new cohesive zone based on the fracture criterion. In monotonic loading cases it can be easily realized in the extended finite element formulation. For cyclic loading cases convergence of the inelastic computations can be critical.     

Finite element analysis of viscoelastic composite structures based on a micromechanical material model

The stress and creep analysis of structures made of micro-heterogeneous composite materials is treated as a two-scale problem, defined as a mechanical investigation on different length scales. Reinforced composites show by definition a heterogeneous texture on the microlevel, determined by the constitutive behaviour of the matrix material and the embedded fibres as well as the characteristics of the bonding properties in the interphase. All these heterogeneities are neglected by the finite element analysis of structural elements on the macroscale, since a ficticious and homogeneous continuum with averaged properties is assumed. Therefore, the constitutive equations of the substitute material should well reflect the mechanical behaviour of the existing micro-heterogeneous composite in an average sense.The paper at hand starts with the brief outline of a micromechanical model, named generalized method of cells (GMC), which provides the macrostress responses due to macrostrain processes as well as the homogenised constitutive tensor of the substitute material. The macroscopic stresses and strains are obtained as volume averages of the corresponding microfields within a representative volume element. The effective material tensor constitutes the mapping between the macro-strains and the macro-stresses. The cells method is used for the homogenisation of the unidirectionally reinforced single layers of laminates made of viscoelastic resins and flexibly embedded elastic fibres. The algorithm for the homogenisation of the constitutive properties runs simultaneously to the finite element analysis at each point of numerical integration and provides the macro-stresses and the homogenised constitutive properties. The validity of the proposed two-scale simulation is investigated by solving boundary value problems and comparing the numerical results for the structures to the experimental data of creep and relaxation tests or analytical solutions.     

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。     

Finite element analysis of damaged woven fabric composite materials

Since fiber reinforced composite materials have been used in main parts of structures, an accurate evaluation of their mechanical characteristics becomes very important. Due to their anisotropic nature and complicated architecture, it is very difficult to reveal the damage mechanisms of these materials from the results of mechanical tests. Therefore, there is a need to conduct reliable simulations and analytical evaluations. In this paper, the damage behavior of FRP is simulated by finite element analysis using an anisotropic damage model based on damage mechanics. The proposed procedure is applied to an example; the finite element analysis of microscopic damage propagation in woven fabric composites. Experimental tests have been conducted to evaluate the validity of the proposed method. It is recognized that there is a good agreement between the computational and experimental results, and that the proposed simulation method is very useful for the evaluation of damage mechanisms.     

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^®.     

扩展有限元方法与内聚力模型耦合下斜接修补复合材料的胶层损伤和缺陷

将扩展有限元方法（XFEM）与内聚力模型（CZM）耦合用于斜接修补复合材料的胶层分析,实现了对复合材料与修补胶层之间的脱粘以及胶层内部裂纹扩展现象的描述,模拟得到的结构强度与试验结果吻合较好。对复合材料与胶层的界面缺陷和胶层内部缺陷展开分析,讨论了缺陷长度和缺陷位置对结构强度的影响。结果表明：在相同条件下,结构具有界面缺陷比具有胶层内部缺陷更加危险;结构强度受缺陷长度和与缺陷尖端相邻复合材料铺层角度的共同影响,随着缺陷长度的增加而降低,降低速率大于缺陷长度增长比例;当缺陷位置不同时,结构强度主要与缺陷对应位置的平均剪应力水平相关。最后,通过参数分析讨论了界面剪切强度的影响。     

Assessment of debond simulation and cohesive zone length in a bonded composite joint

Finite element methods combined with cohesive elements were used to simulate progressive failure behaviour in a bonded double cantilever beam configuration. The introduced cohesive zone was represented by three cases. Responses of both global load–displacement and local cohesive traction–separation were investigated. An unexpected finding was that the overall cohesive traction stiffness was much less than the assumed input value. In addition, the local nodal separation moment was identified. Consequently, correct cohesive zone lengths were obtained using the extracted traction profile along the cohesive zone path at this moment. Information of the global load–displacement profile, traction stiffness, and cohesive zone length induced by the three zone cases was explored. Moreover, the study can explain why very small cohesive zone lengths are generated numerically, as compared to theoretical solutions. Recommendations on the application of the numerical model with cohesive elements to practical experimental analysis were suggested.     

复合材料层合板低速冲击损伤的有限元模拟

建立了用于预测复合材料层合板在低速冲击作用下损伤的3D有限元模型。采用应变描述的失效判据来判断铺层层内的各类损伤, 如纤维断裂、 纤维挤压、 基体开裂、 基体挤裂, 并结合相应的刚度折减方案对失效单元进行刚度折减。使用界面元模拟层间区域, 结合传统的应力失效判据和断裂力学中的能量释放率准则来定义分层损伤的起始和演化规律, 提出了一种界面元损伤起始强度沿厚度方向的分布函数。通过对数值仿真结果和实验结果的比较, 验证了模型的合理性和准确性。      

Finite element modelling of bridging micro-mechanics in through-thickness reinforced composite laminates

Delamination and debonding are the major failure modes in laminated composites, which significantly reduce the performance of a structure under compressive or bending loads. To overcome this problem, new composites with through-thickness reinforcement (TTR) have been used to improve the interlaminar strength and damage tolerance of laminated composites [Freitas G, Fusco T, Campbell T, Harris J, Rosenberg S. Z-fiber^TM technology and products for enhancing composite design. In: 83rd Meeting of AGARD SMP, 1996, CP-590; Farley GL, Dickinson LC. Mechanical response of composite materials with through-the-thickness reinforcement. NASA CR-14753, 1993. p. 123–43; Cartié DDR, Partridge IK. Delamination behaviour of Z-pinned laminates In: Williams JG, Pavan A. editors, Proceedings of second ESIS TC4 conference, Les Diablerets, Switzerland, 13–15 September 1999, ESIS Publication, 2000. ISBN 008 043710-9; Greenhalgh E, Hiley M. The assessment of novel materials and processes for the impact tolerant design of stiffened composite aerospace structures. Comp Part A: Appl Sci Manuf 2003;34(2):151–61. [1], [2], [3] and [4]]. Although the TTR can change the structural elastic response of a composite laminate [Stringer LG, Hiley MJ. Through-thickness reinforcement of composites: Z-pinning, Stitching, and 3D weaving. In: 14th International conference for composite materials, ICCM14, 11–14 July, San Diego, CA, 2003; Mouritz AP, Leong KH, Herszberg I. A review of the effect of stitching on the in-plane mechanical properties of fibre-reinforced polymer composites. Composites Part A 1999;28A:979–91; Grassi M, Zhang X, Meo M. Prediction of stiffness and stresses in z-fibre reinforced composite laminates. Comp Part A: Appl Sci Manuf 2002;33(12):1653–64; Patridge IK, Cartié DDR, Troulis M, grassi, M, Zhang X. Evaluating the mechanical effectiveness of Z-pinning. In: Proceedings of SAMPE/Dayton technical conference, 2003. [5], [6], [7] and [8]] they start working only when delamination propagates in their field, which provides non-linear bridging closure forces that shield the delamination crack from the full delaminating force and moment of the applied loads [Grassi M, Zhang X. Finite element analyses of mode I interlaminar delamination in z-fibre reinforced composite laminates. Comp Sci Technol 2003;63(12):1815–32; Robinson P, Das S. Mode I DCB testing of composite laminates reinforced with z-direction pins: a simple model for the investigation of data reduction strategies. Eng Fract Mech 2004;71(3):345–64. [9] and [10]].Fiber pull-out test has been developed in order to study the micro-mechanics of the TTR bridging a crack under Mode I loading conditions [Cartié DDR, Cox BN, Fleck NA. Mechanisms of crack bridging by composite and metallic rods. Comp Part A: Appl Sci Manuf 2004;35(11):1325–36. [11]], and several analytical models have been developed to analyze these phenomena [Cox B. A constitutive model for through-thickness reinforcement bridging a delamination crack. Adv Comp Lett 1999;8(5):249–56; Jain LK, Mai YW. On the effect of the stitching on Mode I delamination toughness of laminated composites. Comp Sci Technol 1994;51:331–45; Allegri G, Xiang Z. Private communications, 2004. [12], [13] and [14]]. In terms of energy the TTR fiber pull-out can be accompanied by significant amount of energy dissipation due to the frictional work at interface; this process absorbs part of the energy that would otherwise be placed at the delamination front of the structure.The basic objective of this research project was to develop an efficient and accurate finite-element-based numerical tool to simulate the spontaneous propagation of a single TTR pull-out under quasi-static conditions and in the presence of frictional contact between the fiber/matrix interface. The pull-out phenomenon was studied assuming a constant friction coefficient at the interface along the TTR axial direction and using improved contact-elements to solve the frictional contact problem. Load/displacement bridging curves of the fiber pull-out process, which includes elastic deformation with a fully/partially bonded interface plus frictional sliding, were calculated. Moreover, the effect of friction model was also investigated. Numerical results were validated by experimental observations of debonding and frictional sliding of a fiber in steady-state pull-out tests under pure Mode I loading conditions.     

An irreversible cohesive zone model for interface fatigue crack growth simulation

Fatigue crack growth (FCG) along an interface is studied. Instead of using the Paris equation, the actual process of material separation during FCG is described by the use of an irreversible constitutive equation for the cyclic interface traction-separation behavior within the cohesive zone model (CZM) approach. In contrast to past development of CZMs, the traction-separation behavior does not follows a predefined path. The model definition, its predicted cyclic material separation behavior and application to a numerical study of interface FCG in double-cantilever beam, end-loaded split and mixed-mode beam specimens are reported.     

The proper generalized decomposition for the simulation of delamination using cohesive zone model

The use of cohesive zone models is an efficient way to treat the damage especially when the crack path is known a priori. It is the case in the modeling of delamination in composite laminates. However, the simulations using cohesive zone models are expensive in a computational point of view. When using implicit time integration or when solving static problems, the non‐linearity related to the cohesive model requires many iteration before reaching convergence. In explicit approaches, an important number of iterations are also needed because of the time step stability condition. In this article, a new approach based on a separated representation of the solution is proposed. The proper generalized decomposition is used to build the solution. This technique coupled with a cohesive zone model allows a significant reduction of the computational cost. The results approximated with the proper generalized decomposition are very close the ones obtained using the classical finite element approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Homogenization of glass/alumina two-phase materials using a cohesive zone model

This paper is devoted to glass/alumina materials which can exhibit important damages at the interface in the case of a difference of the coefficients of thermal expansion between the matrix and the inclusions. One of the key-issue for this type of materials use is to determine and quantify this damage. This paper presents numerical and experimental approaches for this purpose. A numerical model is used and coupled to a homogenization procedure to evaluate damages provoked by the difference of the coefficients of thermal expansion. Cohesive elements have been introduced in the FE model so as to simulate the interface damage. Some thermal tests have been done on two-phase specimens. Experimental and numerical results are compared and analyzed.