Composite delamination modelling using a multi-layered solid element

This paper focuses on the latest development of a solid hexahedron element for composite delamination analysis. The 8-node solid is derived from a 20-node hexahedron. It is transformed into two physical independent 4-node shell elements according to the propagation of delamination process within the element.     

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.     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.     

Accuracy assessment of a three-dimensional,crack tip element based approach for predicting delamination growth in stiffened-skin geometries

Experimental observations of delamination growth in two stiffened-skin geometries are compared to predictions made using a three-dimensional crack tip element based approach. Each geometry consists of a six-ply graphite/epoxy skin co-cured to a six-ply, hat-shaped stiffener containing a preimplanted teflon delamination between the skin and stiffener at the stiffener termination point. One stiffened-skin geometry was loaded in three-point bending and the other had in-plane tension loads applied to the skin. To predict delamination growth, a three-dimensional crack tip element analysis was first performed on each geometry in order to determine the total energy release rate, G, as well as its mode I, II and III components, G_I, G_II and G_III, respectively. These results were used to define a mode mix at each point along the delamination front, G_s/G, where G_s=G_II + G_III. To obtain the delamination toughness, G_c, it was assumed that G_c exhibits the same dependence on G_s/G as on G_II/G, where the results for G_c versus G_II/G were taken from an earlier experimental study. Next, a comparison of the energy release rate to the toughness at each position along the delamination front was performed, and these results were scaled appropriately in order to predict the sequence of loads and corresponding locations at which the delamination will advance. The predictions were then compared to experimental results that included c-scan images of the test specimens taken at each increment of observed growth, and very good quantitative and qualitative correlations were obtained for both geometries. These results indicate the practicality of, and considerable computational savings that may be achieved by, employing crack tip element analyses for delamination growth predictions in realistic structural geometries.     

An interface element for the simulation of delamination in unidirectional fiber-reinforced composite laminates

Unidirectional fiber-reinforced composite laminates are widely used in aerospace industry for a great variety of structural parts. In order to enhance the exploitation of material reserves, there is a need for the integration of progressive damage scenarios in the design phase. Due to their hazardous effects on the load-carrying capacity of composite structures, this work focusses on the simulation of delaminations. A finite element based on a cohesive zone approach is developed. Two constitutive laws are proposed. One is characterized by linear degradation after delamination onset, the other is governed by exponential softening response. The damage process is history-dependent leading to an irreversible stiffness degradation in damaged zones. The practicability of the proposed model and the assets and drawbacks of the two material laws are shown by some numerical examples.     

A damage model for simulation of mixed-mode delamination growth

An interface element capable of modelling delamination progression under mixed-mode loading is presented. The kinematics of the element are based on the concept of regularised displacement discontinuity. This concept allows the interfacial constitutive equations to be formulated in terms of the traction vector of the interface and the corresponding displacement discontinuity. The decohesion within the interface, corresponding to delamination progression, is accomplished by assigning a non-associative perfectly plastic material model including isotropic damage to the interface element. All parameters of the model can be determined from experimental material data. Damage initiation is calibrated against the interlaminar fracture stresses whereas the evolution of damage is calibrated against the mixed-mode fracture toughness. The interface element has been implemented in a finite element code and results for simulations of standard fracture toughness tests are shown. The results display the applicability of the proposed model and the calibration procedure.     

Formulation and assessment of an enhanced finite element procedure for the analysis of delamination growth phenomena in composite structures

An existing procedure based on the combined use of the Virtual Crack Closure Technique and of a fail release approach for the analysis of delamination growth phenomena in composite structures has been enhanced with a front-tracing algorithm and suitable expressions for the evaluation of the Strain Energy Release Rate when dealing with non-smoothed delamination fronts. The enhanced procedure has been implemented into a commercial finite element software by means of user subroutines and applied to the analysis of a composite stiffened panel with an embedded delamination under compressive load. The effectiveness and robustness of the enhanced procedure have been assessed by comparing literature experimental data and numerical results obtained by using different mesh densities in the damaged area (global/local approach).     

Effect of delamination failure in crashworthiness analysis of hybrid composite box structures

In the present paper the effects of delamination failure of hybrid composite box structures on their crashworthy behaviour will be studied and also their performance will be compared with non-hybrid ones. The combination of twill-weave and unidirectional CFRP composite materials are used to laminate the composite boxes. Delamination study in Mode-I and Mode-II with the same lay-ups was carried out to investigate the effect of delamination crack growth on energy absorption of hybrid composite box structures. The end-loaded split (ELS) and double-cantilever beam (DCB) standard test methods were chosen for delamination studies. In all hybrid composite boxes the lamina bending crushing mode was observed. Regarding the delamination study of hybrid DCB and ELS the variation of the specific energy absorption (SEA) versus summation of G_IC and G_IIC were plotted to combine the effect of Mode-I and Mode-II interlaminar fracture toughness on the SEA. From this relationship it was found the hybrid laminate designs which showed higher fracture toughness in Mode-I and Mode-II delamination tests, will absorb more energy as a hybrid composite box in crushing process. The crushing process of hybrid composite boxes was also simulated by finite element software LS-DYNA and the results were verified with the relevant experimental result.     

Diffusion-induced stress and delamination of layered electrode plates with composition-gradient

Diffusion-induced stress can result in failure of layered electrodes in lithium-ion batteries during the process of fast lithiation and delithiation. Recent studies have demonstrated that the electro-chemo-mechanical properties of compositions-gradient nanoparticles are superior to those of homogeneous ones. In light of this aspect, we develop a theoretical model to probe the effects of composition-gradient on the stress evolution in layered electrodes. Our analysis concludes that, compared with the corresponding homogeneous structure, symmetrical negative-exponent gradient active plates or positive-exponent gradient bilayer electrodes can significantly reduce the maximum compressive stress and the stress drop at the electrode–collector interface, while the energy release rate of interface delamination is slightly weakened by it. These results, again, show that the composition-gradient could improve the mechanical performance of electrodes in lithium-ion batteries, and are instrumental to the design of electrode structures.     

Hybrid spectral/finite element analysis of dynamic delamination of patterned thin films

A combined spectral and finite element analysis is performed to investigate the dynamic edge delamination of patterned thin films from a substrate. The analysis is motivated by an emerging experimental technique in which high-amplitude laser-induced stress waves initiate progressive interfacial debonding of thin film interfaces. The numerical method relies on the spectral representation of the elastodynamic solutions for the substrate and the finite element model for the thin film. A cohesive model is introduced along the interface of the bimaterial system to capture the decohesion process. The important role of the film inertia on the crack extension and the appearance of the mixed-mode failure are demonstrated by observing the traction stress evolution at various points along the bond line. Parametric studies on the effect of film thickness, interface fracture toughness, loading pulse shape and amplitude on the debonding process are performed. A semi-analytical investigation on the inertial effect is carried out to predict the final crack length as a function of the film thickness and pulse amplitude.     

Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM).A finite element model considering solid elements of the ABAQUS^® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.     

Decohesion finite element with enriched basis functions for delamination

In order to address the stringent mesh size requirement of the cohesive element, currently 0.5 mm or less, the mixed-mode interface finite element is enriched with the analytical solution of an idealized beam on elastic foundation. Both the interface and the solid continuum elements are enriched; the partition of unity (PU) method is utilized to obtain the enhanced interpolation, implemented with two user elements (UEL) in the commercial package ABAQUS/Standard. The new formulation yields predictions in excellent agreement with theoretical and experimental results for a typical mode I delamination benchmark, with elements 5 mm in size.     

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。     

Delamination buckling growth in laminated composites using layerwise-interface element

In this paper, a numerical investigation on the buckling of composite laminates containing delamination, under in-plane compressive loads, is presented. For this purpose, delamination propagation is modeled using the softening behavior of interface elements. The full layerwise plate theory is applied for approximating the displacement field of laminates and the interface elements are considered as a numerical layer between any two adjacent layers where the delamination is expected to propagate. A non-linear computer code was developed to handle the numerical procedure of delamination buckling growth in composite laminates using layerwise-interface elements. The load/displacement behavior and the contours of embedded and through-the-width delamination propagation for composite laminates are presented. It is shown that delamination growth can be well predicted using this layerwise-interface elements with decohesive law.     

Comparison of continuous and discontinuous finite element methods for parabolic differential equations employing implicit time integration

This article compares the computational cost, stability, and accuracy of continuous and discontinuous Galerkin Finite Element Methods (GFEM) for various parabolic differential equations including the advection–diffusion equation, viscous Burgers’ equation, and Turing pattern formation equation system. The results show that, for implicit time integration, the continuous GFEM is typically 5–20 times less computationally expensive than the discontinuous GFEM using the same finite element mesh and element order. However, the discontinuous GFEM is significantly more stable than the continuous GFEM for advection dominated problems and is able to obtain accurate approximate solutions for cases where the classic, un-stabilized continuous GFEM fails.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

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。     

Numerical analysis of delamination buckling and growth in slender laminated composite using cohesive element method

In this article, the finite element method (FEM) using cohesive element is applied to predict the delamination buckling and growth in slender laminated composite with embedded delamination under compressive load. In particular, the study is focused on the significant effects of delamination buckling for various parameters in slender composite laminate, such as model length–width ratio, delamination shape, delamination size, and delamination depth position. Furthermore, the delamination growth is assessed to investigate the influence of some key parameters (delamination size and delamination depth position) on the delamination growth load, growth shape and direction.