BEM solution of delamination problems using an interface damage and plasticity model

The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer surface are studied. The energy amounts dissipated in fracture Mode I (opening) and Mode II (shear) at an interface may be different. A concept of internal parameters is used here on the delaminating interfaces, involving a couple of scalar damage variable and a plastic tangential slip with kinematic-type hardening. The so-called energetic solution concept is employed. An inelastic process at an interface is devised in such a way that the dissipated energy depends only on the rates of internal parameters and therefore the model is associative. A fully implicit time discretization is combined with a spatial discretization of elastic bodies by the BEM to solve the delamination problem. The BEM is used in the solution of the respective boundary value problems, for each subdomain separately, to compute the corresponding total potential energy. Sample problems are analysed by a collocation BEM code to illustrate the capabilities of the numerical procedure developed.     

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.     

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.     

直升机桨叶蒙皮大梁粘结面分层裂纹端部场分析

针对直升机桨叶受离心力、挥舞和摆振弯曲、扭矩等载荷特性, 采用非线性桨叶结构模型, 推导了复合材料桨叶蒙皮的广义二维位移方程。在此基础上, 基于Stroh 理论, 应用各向异性界面断裂力学给出桨叶蒙皮大梁粘结面分层裂纹端部的应力与位移通解的渐近表达式。联合其特解, 采用边界配置法计算了离心力作用下桨叶蒙皮与大梁之间存在分层裂纹时裂尖的奇异应力及应力强度因子, 与采用界面元法计算的结果接近, 表明本文方法可有效地分析复合材料桨叶蒙皮大梁间的分层破坏, 为研究桨叶分层失效提供依据。      

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.     

Fracture mechanics weight functions in three dimensions: Subtraction of fundamental fields

A new procedure is presented for the determination of the fracture mechanics weight functions that are required for the evaluation of stress intensity factors in cracked solids. The procedure can be used with a standard three-dimensional boundary element code. The weight functions are proportional to the displacements on the boundary of the solid when the only loading is a pair of self-equilibrated point forces at the crack front. In previous work, the highly singular crack-tip fields that this loading produces have been modelled by replacing the crack front by a cylindrical cavity with appropriate displacement boundary conditions on the cavity walls. It is shown here that results are dependent on the cavity radius and that convergence of the results cannot be guaranteed. An alternative procedure, based on the substraction of fundamental fields (SFF), is demonstrated herein. The high-order singularities are removed from the field before the reduced problem is solved numerically using a standard boundary element method. Since the reduced problem is equivalent to an unloaded crack in a solìd subjected to boundary tractions, the usual quarter-point displacement elements and quarter-point traction singular elements can be used to improve the accuracy. Weight functions, so obtained, are used to evaluate stress intensity factors as a function of position on the crack front for a straight-fronted crack in a rectangular bar subjected to various loadings. Both edge and central cracks are considered and the validity of the technique is demonstrated by comparing the results with previously published values.     

Finite element analysis of contact induced adhesion failure in multilayer coatings with weak interfaces

Experimental work reveals that the Ag/ZnO interface in the multilayer solar control coatings is weakest and most likely to fail during contact. In this study, a cohesive zone model embedded in a finite element code was used to model delamination in multilayer stack consisting of ZnO/Ag/ZnO on glass during contact. It shows that delamination occurs at the upper ZnO/Ag interface during loading when penetration exceeds a critical value, while, the double pinned buckling delamination failure occurs at the lower Ag/ZnO interface during the unloading cycle. Furthermore, it reveals the model based on mechanism of lateral crack at interface yields reasonably accurate values of interfacial toughness when tensile stress induced delamination occurs during unloading.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

含非对称矩形分层的复合材料层合板状态分解-片条合成能量解法

根据叠加原理将横向载荷作用下的含有非对称矩形内部分层的层板进行状态分解,从而将分层问题归结为分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析,并据此建立一个仅包含分层区的简单的力学模型。进而在分层区中切取平行于边界的无限小的切片,将切片视为含分层的层合梁,其位移模态以相应的层合梁的附加位移模态表示。在此基础上构造层板分层区内满足位移边界条件的位移模态,最后用最小势能原理确定位移幅值的闭合解并且分析了分层区的应力场和能量释放率。      

Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part II: Sensitivity study on modeling details

The interface element and VCCT process described in Part I of this two-part paper, developed to compute strain energy release rates of an arbitrary delamination front using non-orthogonal finite element meshes, are further investigated in this paper for robustness and ease of use in tracking delamination growth. Standard 3-D elements are used in conjunction with the interface elements. No special singularity elements are required. Stationary meshes that are independent of the shape of the delamination front can be used. Three cases having different initial delamination shapes are examined. The process is shown to be insensitive to the values used for the interfacial spring stiffness, the orientation of the interface element, or even the mesh pattern if the mesh has a reasonable degree of refinement. Therefore, the method can be used with ease and confidence in general-purpose delamination growth analysis for engineering applications.     

含矩形内部分层的复合材料层板的 状态分解-片条合成能量解法

根据叠加原理将含有矩形内部分层的层板在横向载荷作用下的受力状态进行分解, 从而 将分层问题归结为在分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析, 并据此 建立了一个仅包含分层区的力学模型。进而在层板分层区中切取平行于边界的切片, 将切片视为 含分层的层合梁, 其位移模态以相应层合梁的附加位移模态来表示。这样, 可构造层板分层区内满 足位移边界条件的位移场。最后, 应用最小势能原理确定位移幅值的闭合解。计算结果表明, 挠度 幅值远远大于中面位移幅值, 且与由双三角级数能量解法所得挠度幅值吻合很好。      

A shell element for the prediction of residual load-carrying capacities due to delamination

This paper deals with layered plates and shells subjected to static loading. The kinematic assumptions are extended by a jump function in dependence of a damage parameter. Additionally, an intermediate layer is arranged at any position of the laminate. This allows numerical simulation of onset and growth of delaminations. The equations of the boundary value problem include besides the equilibrium in terms of stress resultants, the local equilibrium in terms of stresses, the geometric field equations, the constitutive equations, and a constraint which enforces the correct shape of a superposed displacement field through the thickness as well as boundary conditions. The weak form of the boundary value problem and the associated finite element formulation for quadrilaterals is derived. The developed shell element possesses the usual 5 or 6 degrees of freedom at the nodes. This is an essential feature since standard geometrical boundary conditions can be applied and the elements are applicable to shell intersection problems. With the developed model, residual load-carrying capacities of layered shells due to delamination failure are computed.     

Finite element study of a penny-shaped crack along the interface in a bi-material cylinder

A contemporary approach to the analysis of interface cracks in bi-material cylinders using finite elements is presented. From results obtained with a commercial finite element code using regular and singular isoparametric elements, three fracture mechanics techniques are considered to study the interface crack problem and are presented in a fundamental manner. These are the stress intensity factor evaluation by the crack opening displacement method, the strain energy release rate evaluation using the modified crack closure integral method, and the J-integral evaluation using the virtual crack extension technique. Only the finite element results in the vicinity of the crack are then needed. The accuracy of the proposed approach is assessed by solving standard test problems with known solutions. In particular, the mode I problem of a penny-shaped crack in a homogeneous isotropic cylinder under remote tension loading is used as a standard test case. Finally, the mixed-mode (I and II) problem of a penny-shaped crack along the interface in a bi-material cylinder under three loading conditions is studied in detail. Numerical results are presented to quantify the combined effects of geometry and material discontinuities on the strain energy release rate.     

热载荷下轴对称回转复合材料层合壳体的边界效应

本文采用有限单元法研究轴对称回转复合材料层合壳体在热荷载作用下壳体内的温度场和热应力场的分布, 并以算例讨论了温度场的分布、铺层次序、壳厚对层合壳体热应力(包括层间应力)的影响。      

Modeling of delamination using a discretized cohesive zone and damage formulation

Delamination initiation and growth are analyzed by using a discrete cohesive crack model. The delamination is constrained to grow along a tied interface. The model is derived by postulating the existence of a maximum load surface which limits the adhesive forces in the process zone of the crack. The size of this maximum load surface is made dependent on the amount of dissipated crack opening work, such that the maximum load surface shrinks to zero as a predefined amount of work is consumed. A damage formulation is used to reduce the adhesive forces. Mode I, II and III loading or any combined loading is possible. An analytical solution is obtained for a single mode opening and the implications of this result on the governing equations is discussed. The delamination model is implemented in the finite element code LS-DYNA and simulation results are shown to be in agreement with experimental results.     

反平面载荷作用下带界面裂纹的不同正交异性层板的应力分析

本文对含有边缘界面裂纹的不同正交各向异性平板在反平面载荷作用下的位移场与应力场进行了分析,得到了满足所有基本方程以及裂纹面边界条件与交界面连续条件的位移场与应力场展开式,本文进一步应用变分原理决定应力场展开式中奇异项系数—应力强度因子,计算结果表明,应力强度因子的收敛性是令人非常满意的.      

Buckling and Delamination Growth Analysis of Composite Laminates Containing Embedded Delaminations

The objective of this work is to study the post buckling behavior of composite laminates, containing embedded delamination, under uniaxial compression loading. For this purpose, delamination initiation and propagation is modeled using the softening behavior of interface elements. The full layer-wise plate theory is also employed for approximating the displacement field of laminates and the interface elements are considered as a numerical layer between any two adjacent layers which delamination is expected to propagate. A finite element program was developed and the geometric non-linearity in the von karman sense is incorporated to the strain/displacement relations, to obtain the buckling behavior. It will be shown that, the buckling load, delamination growth process and buckling mode of the composite plates depends on the size of delamination and stacking sequence of the laminates.     

An extended layerwise/solid-element method of stiffened composite plates with delaminations and transverse crack

The stiffened composite plates with the transverse crack and delamination were studied in this paper, and an extended layerwise/solid-element (XLW/SE) method was developed. In the proposed method, the governing equations of composite plates and stiffeners were established based on the extended layerwise method and 3D solid elements, respectively. The final governing equation of stiffened composite plates is assembled by using the compatibility conditions and internal force equilibrium conditions at the joint interface between the plates and stiffeners. For the stiffened composite plates with damages, the XLW/SE method can obtain the local stress and displacement fields accurately and simulate the in-plane transverse cracks and delaminations simultaneously, considering complicated stiffeners without any assumptions. In the numerical examples, the results obtained by the proposed method are compared with those obtained by the 3D elastic models developed in the general finite element code, and the good agreements were achieved for the stiffened composite plates with/without delaminations and/or transverse crack.     

Thermal fatigue failure induced by delamination in thermal barrier coating

The paper presents the experimental and theoretical investigation on the thermal fatigue failure induced by delamination in thermal barrier coating system. Laser heating method was used to simulate the operating state of TBC (thermal barrier coating) system. The non-destructive evaluation such as acoustic emission (AE) detect was used to study the evolution of TBC system damage. Micro-observation and AE detect both revealed that fatigue crack was in two forms: surface crack and interface delamination. It was found that interface delamination took place in the period of cooling or heating. Heating or cooling rate and temperature gradient had an important effect on interface delamination cracking propagation. A theoretical model on interface delamination cracking in TBC system at operating state is proposed. In the model, a membrane stress P and a bending moment M are designated the thermal loads of the thermal stress and temperature gradient in TBC system. In this case, the coupled effect of plastic deformation, creep of ceramic coating as well as thermal growth oxidation (TGO) and temperature gradient in TBC system was considered in the model. The thermal stress intensity factors (TSIFs) in non-FGM (functional gradient material) thermal barrier coating system is analytical obtained. The numerical results of TSIFs reveal some same results as obtained in experimental test. The model is based on fracture mechanics theory about heterogeneous materials and it gives a rigorous explanation of delaminations in TBC system loaded by thermal fatigue. Both theoretical analysis and experimental observation reveal an important fact: delaminations are fatigue cracks which grow during thermal shocks due to compressive stresses in the loading, this loads the delaminations cracks in mixed I and II mode.