Numerical investigation of onset and evolution of LVI damages in Carbon–Epoxy plates

In order to study the onset and the evolution of low velocity impact damages in Carbon–Epoxy plates, a numerical investigation has been led. A detailed finite element model has been created by using the finite element code Abaqus® which, thanks to the different implemented algorithms, allowed considering both intra-laminar and inter-laminar failure criteria.In particular, the numerical modelling technique of such failure criteria allowed predicting delamination growth, by using special purpose-elements (cohesive elements) and fiber and matrix failure, by using Hashin criteria.Moreover, with the aim to reduce the required CPU time, a global/local finite element modelling approach has been proposed.For validation purpose, numerical results have been compared with data from two sessions of experimental impact tests. The considered impact energy values are 6 J, 10 J and 13 J respectively.     

缝合复合材料层板低速冲击损伤数值模拟

建立了缝合复合材料层板在低速冲击载荷下的渐进损伤分析模型。模型中采用空间杆单元模拟缝线的作用;采用三维实体单元模拟缝合层板,通过基于应变描述的Hashin准则,结合相应的材料性能退化方案模拟层板的损伤和演化;采用界面单元模拟层间界面,结合传统的应力失效判据和断裂力学中的应变能释放率准则判断分层的起始和扩展规律。通过对碳800环氧树脂复合材料（T800/5228）层板的数值仿真结果和试验结果相比较,验证了模型的正确性,同时讨论了不同冲击能量下缝合层板的损伤规律。研究结果表明：缝线能够有效地抑制层板的分层损伤扩展;相同冲击能量下缝合与未缝合层板的基体损伤和纤维损伤在厚度分布上相似,缝合层板的损伤都要小于未缝合层板。     

低速冲击作用下碳纤维复合材料铺层板的损伤分析

建立了一个有效计算模型, 以分析碳纤维复合材料层合板在低速冲击作用下的层内和层间失效行为。针对铺层板的层内损伤, 在基于应变描述的Hashin 失效准则的基础上, 建立了单层板的逐渐累积损伤分析模型;针对铺层板的脱层损伤, 建立了各向同性脱层损伤模型, 通过结合传统的应力失效准则和断裂力学中的能量释放率准则定义了界面损伤演化规律, 并在潜在产生脱层的区域模拟为粘结接触, 并将脱层损伤模型作为界面的接触行为。该计算模型通过商用有限元软件ABAQUS/ Explicit 的用户子程序实现。使用该计算模型对碳纤维增强环氧树脂复合材料层合板在横向低速冲击作用下的损伤和变形行为进行预测分析。数值仿真的结果与试验结果进行了比较, 取得了满意的结果, 验证了该模型的正确性。      

Modelling of chip separation in machining unidirectional FRP composites by stiffness degradation concept

Progressive failure of unidirectional glass fiber-reinforced polymer composites (FRP) was studied using finite element analysis in orthogonal machining. Chip formation process and damage modes such as matrix cracking, fiber–matrix debonding and fiber breaking were modelled by degrading the material properties. Damage analysis was carried out using Hashin, Maximum stress and Hoffman failure criteria. After damage was detected, selective stiffness degradation was applied to the workpiece material. The objective of this study is to better understand the chip formation process and to analyse the cutting-induced damage from initiation stage until complete chip formation. The effect of the fiber orientation on cutting forces and sub-surface damage was investigated with different failure criteria. The results were addressed in terms of cutting forces evolution and damage progression in the composite structure during machining. It was demonstrated that the use of the stiffness degradation concept with the appropriate failure criterion responds potentially in a predictable fashion to changes in chip formation process for machining of FRPs.     

含分层复合材料层板的压缩性能

使用商用有限元软件建立了含分层复合材料层板的有限元模型,采用Hashin失效准则对层板内单元进行损伤判断,并编写程序对失效单元进行刚度折减,使用cohesive单元模拟层间区域,并对缺陷区域进行弱化处理,利用应力失效判据和能量释放准则判断层板内起始分层与分层的扩展。对完好以及含分层缺陷复合材料单向层板试验件进行压缩实验研究,实验结果给出了分层位置和尺寸及对材料压缩性能的影响。研究表明,有限元模拟结果与实验结果具有良好的一致性。     

Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach

The subject of this paper is numerical prediction of bird strike induced damage in real aeronautical structures using highly detailed finite element models and modern numerical approaches. Due to the complexity of today’s aeronautical structures, numerical damage prediction methods have to be able to take into account various failure and degradation models of different materials. A continuum damage mechanics approach has been employed to simulate failure initiation and damage evolution in unidirectional composite laminates. Hashin’s failure initiation criteria have been employed in order to be able to distinct between four ply failure modes. The problem of soft body impacts has been tackled by applying the Coupled Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. This improvement in impactor deformation modelling resulted in a more realistic behaviour of bird material during impact. Numerical geometrical and material nonlinear transient dynamic analyses have been performed using Abaqus/Explicit. The main focus of the work presented in this paper is the application of the damage prediction procedure in damage assessment of bird impact on a typical large airliner inboard flap structure. Due to the high cost of gas-gun testing of aircraft components, experimental testing on the real flap structure could not have been performed. In order to evaluate the accuracy of the presented method, the bird and composite damage model have been validated against experimental data available in the literature.     

Stacking Sequence Effects on Fatigue Intra-laminar Damage Progression in Composite Joints

In this paper the effects of the stacking sequence on the fatigue intra-laminar damage accumulation in pinned composite joints is investigated. A fatigue damage propagation numerical model based on gradual material degradation rules and Hashin fatigue failure criteria is formulated, implemented in a finite element platform and then used to simulate the intra-laminar fatigue damage evolution in the analysed composite joints. The model has been preliminary validated against literature experimental data in terms of s-n curves providing confirmation of its effectiveness in predicting the joints fatigue life. Different stacking sequences: zero-dominated, quasi-isotropic, cross-ply with different 0 ° and 90 ° plies distributions, have been considered when investigating the influence of the stacking sequence on the fatigue behaviour of the joints. The simulation of the joints’ fatigue life provided detailed information on the intra-laminar damage mechanisms on-set and evolution related to fatigue gradual degradation of material stiffness and strength for different values of the applied maximum stresses.     

Finite Element Simulation of Low Velocity Impact Damage on an Aeronautical Carbon Composite Structure

Low velocity barely visible impact damage (BVID) in laminated carbon composite structures has a major importance for aeronautical industries. This contribution leads with the development of finite element models to simulate the initiation and the propagation of internal damage inside a carbon composite structure due by a low velocity impact. Composite plates made from liquid resin infusion process (LRI) have been subjected to low energy impacts (around 25 J) using a drop weight machine. In the experimental procedure, the internal damage is evaluated using an infrared thermographic camera while the indentation depth of the face is measured by optical measurement technique. In a first time we developed a robust model using homogenised shells based on degenerated tri-dimensional brick elements and in a second time we decided to modelize the whole stacking sequence of homogeneous layers and cohesive interlaminar interfaces in order to compare and validate the obtained results. Both layer and interface damage initiation and propagation models based on the Hashin and the Benzeggagh-Kenane criteria have been used for the numerical simulations. Comparison of numerical results and experiments has shown the accuracy of the proposed models.     

Numerical/experimental impact events on filament wound composite pressure vessel

Impacts on pressure vessels, produced by winding glass fibre with vinyl ester resin over a polyethylene liner, were numerically and experimentally investigated in the current work.Pressure vessels were experimentally tested under low velocity impact loads. Different locations and incident energies were tested in order to evaluate the induced damage and the capability of the developed numerical model.An advanced 3-D FE model was used for simulating the impact events. It is based on the combined use of interlaminar and intralaminar damage models. Puck and Hashin failure theories were used to evaluate the intralaminar damages (matrix cracking and fibre failure). Cohesive zone theory, by mean of cohesive elements, was used for modelling delamination onset and propagation.The experimental impact curves were accurately predicted by the numerical model for the different impact locations and energies. The overall damages, both intralaminar and interlaminar, were instead slightly over predicted for all the configurations.The model capabilities to simulate the low velocity impact events on the full scale composite structures were proved.     

Numerical simulation of ballistic impact on composite laminates

The paper reports experimental and numerical simulation of ballistic impact problems on thin composite laminated plates reinforced with Kevlar 29. Ballistic impact was imparted with simulated fragments designed in accordance with STANAG-2920 on plates of different thickness. Numerical modelling was developed and used to obtain an estimate for the limit perforation velocity (V₅₀) and simulate failure modes and damage. Computations were carried out using a commercial code based on finite differences and values obtained are compared with the experimental data to evaluate the performance of the simulation. Good correlation between computational simulation and experimental results was achieved, both in terms of deformation and damage of the laminates. Future work is advanced to include the interposition of an outer ceramic layer as well as examining the influence of dry-wet and temperature cycles on the mechanical strength of the plates and their temporal evolution under accelerated ageing.     

复合材料加筋板低速冲击损伤的数值模拟

建立了复合材料加筋板在横向低速冲击载荷作用下的渐进损伤有限元模型。该模型考虑了复合材料加筋板受低速冲击时的纤维断裂、基体开裂及分层脱粘等五种典型的损伤形式, 在层内采用应变描述的失效判据, 结合相应的材料性能退化方案, 通过编写VUMAT用户自定义子程序以实现相应损伤类型的判断和演化。在层间以及筋条与层板间加入界面元, 模拟层间区域的情况, 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判断分层损伤的起始和演化规律。通过对数值模拟结果与实验数据的比较, 验证了模型的合理性和有效性。同时探讨了不同位置、不同冲击能量以及含初始损伤(脱粘)等因素对复合材料加筋板低速冲击性能的影响。     

Finite element model for compression after impact behaviour of stitched composites

A finite element (FE) model using coupling continuum shell elements and cohesive elements is proposed to simulate the compression after impact (CAI) behaviour and predict the CAI strength of stitched composites. Continuum shell elements with Hashin failure criterion exhibit the composite laminate damage behaviour; whilst cohesive elements using traction-separation law characterise the laminate interfaces. Impact-induced delamination is explicitly modelled by reducing material properties of damaged cohesive elements. Computational results have demonstrated the trend of increasing CAI strength with decreasing impact-induced delamination area. Spring elements are introduced into the model to represent through-thickness stitch thread in the composite laminates. Results in this study validate experimental finding that CAI strength is improved when stitching is incorporated into the composite structure. The proposed FE model reveals good CAI strength predictions and indicates good agreement with experimental results, making it a valuable tool for CAI strength prediction of stitched composites.     

Damage-based failure theory and its application to 2D-C/SiC composites

Damage evolution is of great importance to determine the final failure of ceramic matrix composites (CMCs). In order to characterize the damage coupling behavior and its effect on failure strength of CMCs, a new methodology for damage coupling analysis was formulated. And, new kind of damage-based failure criteria were established under plane stress state, including maximum damage criterion and quadratic damage criterion. Both the criteria require investigation upon the damage evolution laws. The proposed failure theory was applied to predict the coupled damage behavior and the off-axis strength of a 2D C/SiC composite. The theoretical results agree well with the experimental data.     

复合材料层合板低速冲击的接触力和能量响应仿真

以连续介质损伤力学（CDM）为基础,提出了一个有效的数值分析模型来模拟碳纤维增强复合材料（CFRP）层合板低速冲击的接触力响应和能量响应。该模型考虑了不同的失效模式,引入了不可逆的损伤变量和新的刚度折减方式以考虑损伤造成的刚度变化,定义了耗散能的计算方式以考虑损伤造成的能量变化。通过在Abaqus/Explicit平台上编写VUMAT子程序具体实现模型,数值仿真与试验结果吻合较好,验证了该模型的有效性。此外,还综合考虑了Hashin准则与LaRC04准则各自的优缺点,用Hashin和LaRC04相混合得到的准则对低速冲击进行了模拟。结果表明：在冲击外载作用下当CFRP层合板中存在较多基体压缩失效时,采用混合的失效准则模拟得到的接触力响应和能量响应结果更接近试验结果,而使用纯Hashin准则得到的预测结果偏保守。     

Failure analysis of woven kevlar fiber reinforced epoxy composites pinned joints

An investigation was performed to determine the failure mode and the failure load of mechanically fastened joints in woven kevlar epoxy composite plates. Two-dimensional finite element code is developed to predict damage initiation, progression and strength of joints. Hashin, Hoffman and Maximum Stress criteria were used in this failure analysis. Experiments were performed to find the failure load and to predict the failure mode. Parametric studies were also carried out to evaluate the effect of joint geometry on this analysis. The obtained results were compared each other and comparison showed good agreement between numerical and experimental methods.     

An efficient approach for damage quantification in quasi-isotropic composite laminates under low speed impact

An efficient method to determine the type, size, and location of damage in impacted quasi-isotropic composite laminates is presented. The method uses the peak force during impact obtained from energy balance, a Hertzian contact formulation and energy minimization to determine the complete state of stress in the laminate. Comparisons of the analytical predictions to limiting cases of infinite thickness plates or to detailed finite element models for finite thickness plates shows the predicted stresses to be in excellent agreement with other methods. The stresses are then modified to account for the creation of damage and used in out-of-plane and in-plane failure criteria to predict delamination sizes, matrix failure and fiber failure. The predicted damage states are then compared to published test results for two different materials, eight different stacking sequences, and a range of impact energies from 5 to 50 J. Very good agreement of the predicted damage sizes with the experimentally measured values is observed for a wide range of energy levels but, for two laminates, the discrepancies are significant. Possible improvements of the method are discussed briefly. This method is very promising and can be used in preliminary design allowing extensive trade studies and, eventually, layup optimization. It can also form the beginning of an efficient methodology to predict compression after impact strength of quasi-isotropic laminates.     

缝合泡沫夹层复合材料低速冲击数值模拟及实验

在ABAQUS分析平台中建立了缝合泡沫夹层复合材料在低速冲击下的动力学有限元模型,采用杆单元模拟缝线树脂柱的作用,基于Hashin破坏准则模拟层板面内损伤,通过各向同性硬化本构模型利用等效塑性变形模拟泡沫夹芯损伤演化。针对相同铺层的缝合和未缝合泡沫夹层结构,模拟了相同冲击能量下的低速冲击响应过程及面板、泡沫的损伤情况,数值结果与实验结果吻合较好,证明了该方法的有效性和准确性。研究结果表明,在低速冲击下,泡沫夹层结构引入缝线后虽然降低了泡沫缓冲吸能的作用,使得面板表面受到较大的冲击破坏,但增强了整体刚度,增大了面板抵抗弯曲变形的能力,减小了内部面板的损伤,使其在改善复合材料面板易分层缺陷的同时还依然拥有优良的面内性能。     

The Influence of the Boundary Conditions on Low‐Velocity Impact Composite Damage

Abstract: The objective of this work was to study the influence of the boundary conditions on low‐velocity impact behaviour of carbon‐epoxy composite plates. Experimental work and numerical analysis were performed on [0₄,90₄]_s laminates. The influence of different boundary conditions on the impacted plates was analysed considering rectangular and square plates. The X‐radiography was used as a non‐destructive technique to evaluate the internal damage caused by impact loading. A three‐dimensional numerical analysis was also performed considering progressive damage modelling. The model includes three‐dimensional solid elements and interface finite elements including a cohesive mixed‐mode damage model, which allows simulating delamination between different oriented layers. It was verified that plate’s boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of the delamination was obtained.     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.