Experimental and three-dimensional global-local finite element analysis of a composite component including degradation process at the interfaces

A specimen is studied in order to analyse the stringer runout effect in a specific design. An experimental test was carried out in several stages until specimen collapse, allowing the damaged regions and their characteristic geometric dimensions to be identified by ultrasound inspections. Several numerical analyses based on finite element method of the component were performed using the commercial software ABAQUS. These numerical analyses aimed to study in detail the onset and propagation of damage in the skin-stringer joint during the load procedure. Due to the high computational cost that this kind of procedure usually requires, a global–local approach was performed, comparing the two techniques offered by the software ABAQUS: Submodeling and Shell-to-Solid Coupling. Shell element typology was used in both cases for the global model. In order to estimate the extension of the critical zone in the specimen, the adhesive layer was modeled by means of solid elements. With reference to the local analysis, laminate continuum elements were selected to discretize the skin and the stringer, whereas the adhesive was represented by interface cohesive elements to take the damage evolution into account. A final correlation was carried out between numerical predictions and experimental results of the damaged regions in the component at several load levels.     

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).     

Numerical shape optimization of cold forging tools by means of FEM/BEM simulation

The procedure of a numerical shape optimization of the cold forging tool geometry allows for a reduction and a homogenization of tool load stresses. This procedure considers the workpiece-tool-machine interaction by means of the FEM/BEM coupling. The coupling requires modifications to insure accurate integration in TOSCA software for further shape optimization. The resulting distribution of the nodal displacements and changes of tool geometry are discussed and analyzed. Additionally, the numerical validation of the results by means of mechanical simulation of the optimized geometry with the extended FEM/BEM model is given. The equivalent stresses distribution at the end of lateral extrusion in the tool and in workpiece is presented. The numerical shape optimization leads to the maximum equivalent stress value reduction on the press shoulder on 856 MPa, corresponding to a percentage decrease of 24.3 % in comparison with the initial geometry. The approach for the compensation of load induced workpiece deviations, involving the described optimization procedure, is presented as well.     

Progressive damage and failure of mechanically fastened joints in CFRP laminates – Part II: Failure prediction of an industrial junction

In part II of this study, a methodology is presented to compute the failure of large-scale bolted joints in composite structures. This methodology is based both on a multilevel calculation strategy and on virtual testing. At the global level, coarse FE modelling of the structure is used to assess the load distribution between the fasteners. The most loaded fasteners are identified and the loads issued from the global calculation are used as boundary conditions for the local failure analysis, based on fast semi-empirical models. Nevertheless, in this work, instead of using experimental data, prevision of failure is achieved by fully numerical means. The parameters of the semi-empirical models are evaluated by virtual testing, using the refined FE model proposed in part I of this paper.     

Collapse load of composite laminates: Lower bound evaluation by stress field analytical approximation

The paper proposes a limit analysis approach to define the ultimate load capacity of orthotropic composite laminates under biaxial loading and plane stress conditions. A lower bound to the collapse load multiplier is computed by solving a maximization nonlinear problem, according to the static theorem of limit analysis. To set up the optimization problem a stress field distribution is hypothesized at lamina level, moreover inter-lamina stresses are also considered. The effectiveness and validity of the proposed approach is shown by comparing the obtained numerical predictions both with available experimental data and with other numerical results carried out by means of a different numerical lower bound approach.     

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.     

Combination of finite element analysis and analytical crack tip solution for mixed mode fracture

A finite element program was developed which combines the analytical crack tip solution with a conventional finite element analysis and evaluates various crack tip parameters as part of the solution. This program was used to analyze cracked specimens subjected to mixed mode loading. The importance of retaining the second term of the series expansion for local stress, a contribution which is independent of the distance from the crack tip, was demonstrated. It was first shown analytically that the presence of a load applied parallel to the crack reveals itself only through this constant second term, which vanishes only for specific loading conditions. The results of the numerical analysis demonstrate that the stress intensity factor K_I is independent of the load applied parallel to the crack only when this term is included in the analytical crack tip solutions. Failure to include the constant term has the effect that K_I varies with the horizontal load. The parameter K₁₁ is independent of this load in both cases. This indicatesonce again that it is this constant term which accounts solely and entirely for the presence of a load applied parallel to the crack.     

一种基于复合材料加筋板结构效率的稳定性优化方法

提出一种以承载效率最高作为目标的新设计方法, 对复合材料加筋板的承载能力进行优化。讨论了不同压缩与弯曲刚度的匹配模式与加筋板临界失稳载荷的关系。将全局失稳载荷、局部失稳载荷与静载荷的接近程度作为结构承载效率的量化标准, 通过静载荷的控制, 使结构的稳定性向着效率最高的方向优化。以宏观的加筋板压缩与弯曲刚度参数作为设计变量, 构建了一种可用于结构效率优化的代理模型, 避免了局部最优点的出现, 更便于数值寻优。通过有限元分析验证, 优化后壁板的临界失稳载荷与所施加的静载荷基本一致, 反映出较高的效率, 从而验证了该方法的可靠性。      

Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

含预裂缝复合材料缠绕圆柱壳轴压承载特性分析

为探究穿透裂缝对复合材料缠绕圆柱壳承载能力及失效模式的影响,首先开展不同壁厚含预裂缝复合材料缠绕圆柱壳轴向压缩试验。对于A系列厚壁圆柱壳,裂缝导致承载能力下降53.96%,失效模式由局部屈曲转化为裂缝扩展、脆性断裂;而B系列薄壁圆柱壳均发生局部屈曲,裂缝使承载能力下降12.59%。其次,采用有限元软件ABAQUS 6.14,基于非线性RIKS算法,建立轴压作用下含预裂缝复合材料圆柱壳极限承载能力计算模型,通过引入Hashin失效准则及损伤演化判据,预测结构渐进破坏模式及极限荷载。数值结果与试验数据吻合良好,最大误差为7.01%,验证了数值算法的可靠性。在此基础上,探讨裂缝方向、缠绕角度对含预裂缝复合材料圆柱壳极限承载的影响,可知:对于±55°螺旋铺层复合材料圆柱壳,随裂缝角度α增加,极限承载能力先升高再降低,当α=45°时,具备最大承载能力;对于含开缝角α=15°、45°、55°缠绕圆柱壳,随缠绕角θ增加,其承载能力呈先上升后下降趋势。且开缝角越小,缠绕角度对极限荷载的影响越大,当缠绕角θ=30°时,达到最大承载能力。     

A 3D anisotropic elastoplastic‐damage model using discontinuous displacement fields

This paper is concerned with the development of constitutive equations for finite element formulations based on discontinuous displacement fields. For this purpose, an elastoplastic continuum model (stress–strain relation) as well as an anisotropic damage model (stress–strain relation) are projected onto a surface leading to traction separation laws. The coupling of both continuum models and, subsequently, the derivation of the corresponding constitutive interface law are described in detail. For a simple calibration of the proposed model, the fracture energy resulting from the coupled elastoplastic‐damage traction separation law is computed. By this, the softening evolution is linearly dependent on the fracture energy. The second part of the present paper deals with the numerical implementation. Based on a local and incompatible additive split of the displacement field into a continuous and a discontinuous part, the parameters specifying the jump of the displacement field are condensed out at the material level without employing the standard static condensation technique. To reduce locking effects, a rotating localization zone formulation is applied. The applicability and the performance of the proposed numerical implementation is investigated by means of a re‐analysis of a two‐dimensional L‐shaped slab as well as by means of a three‐dimensional ultimate load analysis of a steel anchor embedded in a concrete block. Copyright © 2004 John Wiley & Sons, Ltd.     

Enhanced solution control for physically and geometrically non‐linear problems. Part I—the subplane control approach

Geometrically or physically non‐linear problems are often characterized by the presence of critical points with snapping behaviour in the structural response. These structural or material instabilities usually lead to inefficiency of standard numerical solution techniques. Special numerical procedures are therefore required to pass critical points. This paper presents a solution technique which is based on a constraint equation that is defined on a subplane of the degrees‐of‐freedom (dof's) hyperspace or a hyperspace constructed from specific functions of the degrees‐of‐freedom. This unified approach includes many existing methods which have been proposed by various authors. The entire computational process is driven from only one control function which is either a function of a number of degrees‐of‐freedom (local subplane method) or a single automatically weighted function that incorporates all dof's directly or indirectly (weighted subplane method). The control function is generally computed in many points of the structure, which can be related to the finite element discretization. Each point corresponds to one subplane. In the local subplane method, the subplane with the control function that drives the load adaptation is selected automatically during the deformation process. Part I of this two‐part series of papers fully elaborates the proposed solution strategy, including a fully automatic load control, i.e. load estimation, adaptation and correction. Part II presents a comparative analysis in which several choices for the control function in the subplane method are confronted with classical update algorithms. The comparison is carried out by means of a number of geometrically and physically non‐linear examples. General conclusions are drawn with respect to the efficiency and applicability of the subplane solution control method for the numerical analysis of engineering problems. Copyright © 1999 John Wiley & Sons Ltd.     

A methodology to measure the interface shear strength by means of the fiber push-in test

A methodology is presented to measure the fiber/matrix interface shear strength in composites. The strategy is based on performing a fiber push-in test at the central fiber of highly-packed fiber clusters with hexagonal symmetry which are often found in unidirectional composites with a high volume fraction of fibers. The mechanics of this test was analyzed in detail by means of three-dimensional finite element simulations. In particular, the influence of different parameters (interface shear strength, toughness and friction as well as fiber longitudinal elastic modulus and curing stresses) on the critical load at the onset of debonding was established. From the results of the numerical simulations, a simple relationship between the critical load and the interface shear strength is proposed. The methodology was validated in an unidirectional C/epoxy composite and the advantages and limitations of the proposed methodology are indicated.     

Improved nonlinear buckling analysis of structures

The theory of structural stability is both an important and a difficult subject, whose main field of application is found in the design of thin wall lightweight structures and shells. It is unavoidable to employ nonlinear model and to use finite element numerical method in order to obtain the critical load under the action of which the instability of structures will occur. Thus, it becomes very important how to simplify such a nonlinear problem that appears in instability analysis. In this paper, an improvement on previous nonlinear buckling analysis is proposed, in which the emphasis is on the shortcut of calculation of pre-buckling fundamental path. The nonlinear equation used to solve the displacement vector is translated into the linear one to solve the load factor by means of the concept of energy conservation. The detailed procedure to calculate the nonlinear buckling load is presented and two simple examples are also shown as the application of suggested method. The theoretical analysing and numerical examples show that the suggested method is valid for predicting the nonlinear critical loads of structures.     

Numerical Simulations of Inter-laminar Damage Evolution in a Composite Wing Box

In this paper, a numerical study has been carried out on skin delamination and skin-stringer debonding growth in a composite wing-box under compressive loading conditions. The adopted numerical models use the Virtual Crack Closure Technique to simulate the inter-laminar damage evolution and the numerical analyses have been performed by means of the FEM code ABAQUS and B2000++. The obtained numerical results have been assessed and compared each other in terms of delaminated area evolution, delamination growth initiation load and strain distributions. In order to investigate the effectiveness of the adopted numerical platforms in predicting the evolution of inter-laminar damages, comparisons with experimental data, in terms of load displacement curves and strains in the debonding area, have been also introduced.     

The constant stress term

The importance of retaining the second, constant stress term of the series expansion for local stress is demonstrated both analytically and numerically. It is shown how the standard singular expressions for the stress and displacement field in the vicinity of the crack tip need to be corrected. A load applied parallel to the crack shows up solely and entirely in this constant term. Omitting this term not only denies the physical presence of such a load and hence violates the principle of the uniqueness of the solution of boundary value problems of linear elasticity, but also misleads one into thinking that load biaxiality does not influence fracture behavior. It is shown analytically and numerically that the standard expressions are correct only for equal tension-tension loading. The numerical results show that K_I is independent of a horizontal load only when the constant stress term is included.     

Failure Analysis of Two-Dimensional Carbon-Epoxy Composite Plate Pinned Joint

The aim of this study is to investigate failure strength and failure mode of a mechanically fastened carbon-epoxy composite plate of arbitrary orientation. The failure load and the failure mode are analyzed numerically and experimentally. The numerical method includes two steps. First, the stress distribution in the plate is calculated by the use of finite-element method. Second, the failure load and the failure mode are predicted by means of Tsai-Hill and fiber tensile-compressive failure criteria. A computer program was developed which can be used to calculate the failure load, the failure mode, and the propagation of failure. The distance-to-diameter, E/D , and width-to-diameter, W/D , ratios in the plate are changed from 1 to 5 and 2 to 5, respectively. It is found that full bearing strength is developed when E/D and W/D ratios are equal to or greater than 4.     

钢-预应力混凝土组合梁滑移规律分析及连接件局部加强设计

为了对预加力阶段组合梁剪力连接件的局部加强设计提供理论依据,采用能量变分法,考虑翼板剪力滞效应和钢梁与混凝土板之间相对滑移的影响,推导了钢-混凝土预应力组合梁在预加轴力作用下荷载效应的解析解,计算结果与试验结果吻合较好,并在解析解基础上分析了预加轴力作用下组合梁结合面的相对滑移规律.分析表明:组合梁在预应力锚固区的界面...     

Effect of shear deformation on post-buckling behaviour of columns

The post-buckling behaviour of a cantilever column of variable moment of inertia with tip load is studied by means of a simple numerical iterative scheme. The governing equation of equilibrium is formulated using the axial and transverse displacement quantities, and applying linear constitutive and nonlinear kinematic relations. Numerical results obtained by numerical iterative procedure are presented in the form of curves showing the relation between non-dimensional tip-deflection and non-dimensional load for different values of shear correction factors and taper ratios.     

深水爆炸载荷数值仿真研究

为了更好地研究水下爆炸载荷的特点,应用AUTODYN有限元程序,通过数值仿真得出深水水下爆炸冲击波载荷、气泡脉动载荷以及冲量,并与经验公式计算结果比较,同时分析了近场水下爆炸条件下圆形壳体结构的损伤。数值模拟得到的二次脉动压力、气泡大小、脉动周期等均与经验值接近,水下冲击波和气泡脉动的冲量大小相当,表明应用AUTODYN是研究水下爆炸现象的有效手段之一。