Prediction of Process-Induced Distortions in L-Shaped Composite Profiles Using Path-Dependent Constitutive Law

In this paper, the corner spring-in angles of AS4/8552 L-shaped composite profiles with different thicknesses are predicted using path-dependent constitutive law with the consideration of material properties variation due to phase change during curing. The prediction accuracy mainly depends on the properties in the rubbery and glassy states obtained by homogenization method rather than experimental measurements. Both analytical and finite element (FE) homogenization methods are applied to predict the overall properties of AS4/8552 composite. The effect of fiber volume fraction on the properties is investigated for both rubbery and glassy states using both methods. And the predicted results are compared with experimental measurements for the glassy state. Good agreement is achieved between the predicted results and available experimental data, showing the reliability of the homogenization method. Furthermore, the corner spring-in angles of L-shaped composite profiles are measured experimentally and the reliability of path-dependent constitutive law is validated as well as the properties prediction by FE homogenization method.     

Prediction of processing-induced distortion of curved flanged composite laminates

It is well known that angles in composite parts contract as they are cooled down from the curing temperature, this is often referred to as spring-in. It is caused mainly by the significantly different thermal contractions and cure shrinkage's experienced between the fibre direction and the through-thickness direction during the manufacturing process. A number of works have reported on the spring-in of straight angle composite parts. However, little has been done to investigate the distortion of curved flanged composite parts, which will distort differently owing to the introduction of the additional curvature, thus constraint.

In the present work, the distortion of the circularly curved flanged laminates is studied numerically. The finite element method is used to predict the processing-induced distortion of the part with two different approaches. In the first approach, the shear angles of the composite plies are predicted by a draping analysis. The effect of the fibre shearing on the mechanical properties of the laminates is considered in the model used to predict the distortion. The second simplified approach assumes that the in-plane properties of the laminates are isotropic. The results obtained by these two approaches are compared with those obtained experimentally.     

Investigation on the spring-in phenomenon of carbon nanofiber-glass fiber/polyester composites manufactured with vacuum assisted resin transfer molding

Process-induced residual stress arises in polymer composites as a result of mismatched resin contraction and fiber contraction during the cure stage. When a curved shell-like composite part is de-molded, the residual stress causes the spring-in phenomenon, in which the enclosed angle of the part becomes smaller than the angle of its mold. In this paper, a new approach is presented to control and reduce the spring-in angle by infusing a small amount of carbon nanofibers (CNFs) together with liquid resin into the glass fiber preform using vacuum assisted resin transfer molding (VARTM) process. The experimental results showed that the spring-in angles of the L-shaped composite specimens were effectively restrained by the CNFs. An analytical model and a 3-D FEA model were developed to predict the spring-in phenomenon and to understand the role of CNFs in reducing the spring-in angle. The models agreed with the experimental results reasonably well. Furthermore, the analytical model explains how the CNF-enhanced dimensional tolerance control is accomplished through the reductions in the matrix’s equivalent coefficient of thermal expansion and linear crosslinking shrinkage.     

A linear finite element model to predict processing-induced distortion in FRP laminates

Manufacturing processes for laminated composites often produce parts whose dimensions do not match the mold from which they were made. This distortion is commonly referred to as ‘spring-in’. The amount of spring-in can depend on many factors including the manufacturing process (cure temperature, resin bleed, and applied pressure), the part (geometry, material, thickness, cure shrinkage, thermal expansion and layup sequence), and the tool (surface, thickness and thermal expansion). Much of the current work devoted to spring-in relies on extensive resin characterization. While this approach has been reasonably successful, it does little to assist the designer using material systems that have not been fully characterized (which is not always possible or feasible). This study considers the ability of a linear elastic finite element model to describe and quantify many of the factors contributing to spring-in. The aim of this study is to show that spring-in can be accurately predicted without a complete resin characterization. Numerical predictions based on relatively simple mechanical tests were observed to compare favorably with experimental measurements. Spring-in was dominated by thickness shrinkage, which contributed approximately 3/4 of the measured distortion. The mold stretching contribution diminished with thickness and was negligible for parts thicker than 2.5 mm (0.1 in.). While the material system at hand did not exhibit a fiber volume fraction gradient, its effects were included in the formulation of the model. For materials that have reported a gradient, it was found to account for approximately 10% of the part spring-in.     

结构参数对复合材料V型构件固化变形影响试验及解析分析

为研究结构参数对复合材料V型构件固化变形的影响,完成了针对V型构件厚度、拐角半径、拐角角度及铺层等结构参数的变形影响研究试验。基于剪力滞后理论和弯曲理论,利用解析法建立了考虑结构参数影响的复合材料V型构件固化变形预测模型,利用模型预测了V型构件的回弹变形并分析了不同结构参数对V型构件回弹变形的影响机制。结果表明:回弹变形随着厚度的增大而减小,厚度为1~3mm之间,角度回弹变形差异最大在30%左右;回弹变形与拐角角度的补角呈约为0.014的比例;拐角半径的不同导致变形的差异不超过5%;准各向同性铺层试验件展现了最大回弹变形,0°铺层的变形减小了23.5%,90°铺层几乎不发生变形。模型分析结果表明,厚度主要通过弯曲刚度和剪切变形两方面影响回弹变形;铺层引起的力学性能和泊松效应的变化是使回弹变形有较大区别的主要原因;V型构件直边变形最大为0.20°,对回弹变形影响较大。变形预测结果与试验结果对比验证了解析法模型的准确性。     

纤维体积含量和富树脂对复合材料V型结构固化变形的影响

为研究模具因素对复合材料纤维体积含量、富树脂以及固化变形的影响,利用热压罐工艺完成了T700/QY9611复合材料V型结构成型试验,对其纤维体积含量、富树脂厚度以及回弹变形进行测量与研究。建立了考虑热载荷、树脂收缩载荷、模具接触、纤维体积含量以及富树脂等因素的复合材料回弹变形预测三维有限元分析模型,定量分析了纤维体积含量梯度和富树脂对回弹变形的影响。研究结果表明：使用阴模模具产生10.0%的纤维体积含量梯度和2.2 mm的富树脂,拐角半径增大后分别减小为6.8%和1.2 mm,模具材料的影响较小;使用阴模成型试验件变形增大21.0%,使用拐角半径较大的阴模,变形减小了9.6%,阴模模具主要通过纤维体积含量和富树脂影响回弹变形;模拟结果表明：V型构件的变形与纤维体积含量梯度和富树脂厚度呈正比例,10%的纤维体积含量梯度导致13.5%的变形差异,3.0 mm厚的富树脂会产生45.8%的变形差异。模拟结果与实验结果对比验证了模型的准确性。     

Development of spring-in angle during cure of a thermosetting composite

The development of spring-in angle during cure of AS4/8552 thermosetting composite is investigated by using a cure quench technique. C-shaped preforms are cured on the inner wall of an aluminium tube. The cure is interrupted at various points during the Manufacturer's Recommended Cure Cycle (MRCC) by quenching the tool tube into water. The diameters of the specimens cured in this way are measured and the spring-in angles for a 90° arc of the specimens are calculated. The test data show that the samples quenched at earlier stages of cure exhibit a larger spring-in and the spring-in angle reduces as the specimen is further cured.

A cure kinetics simulation is performed to understand the development of cure throughout the MRCC. It has been found that the vitrification of the specimen occurs approximately 45 min after the start of the 180 °C dwell period, and the specimens quenched before vitrification are observed to have larger spring-in.

An explanation of this observation is the fact that, before vitrification the specimen is in the rubbery state during the temperature range between the cure temperature and the instantaneous glass transition temperature, and in this state it has a larger thermal expansion coefficient compared to that in the glassy state, causing more contraction in the through-the-thickness direction, hence more spring-in.

The cure quench experiment provides an insight into the relative importance of the thermal contraction above and below the glass transition temperature and the cure shrinkage.     

Experimental investigation into the thermoelastic spring-in of curved sandwich panels

An investigation into the thermoelastic spring-in of curved sandwich panels has been conducted. Sandwich panels incorporating solid foam cores and biaxial glass–epoxy skins were manufactured and spring-in measured. The major contributors to spring-in were found to be the thermal expansion and Poisson’s ratio of the foam which were subsequently characterised. Also important was the development of resin rich regions on the surface of the panel. Experimental findings were implemented into a finite element (FE) model developed using 3-dimensional elements in ANSYS. The investigation was extended to panels including a core with machined slots. A refined FE model highlighted the influence of in-plane restraint reduction within the core, as well as the effect of a much thicker resin rich region caused by core segmentation. Results showed good agreement with experiment and provided a good basis for shape prediction of sandwich panels.     

Effect of Spring-in Deviation on Fatigue Life of Composite Elevator Assembly

The spring-in deviation results in the extra stresses around the joints of the composite C-beam and metallic parts when they are assembled together. These extra stresses affect the composite elevator’s fatigue life, which should be explored with the fatigue experimentation. The paper presents the experimental investigation on the effect of spring-in deviation on the fatigue life of the composite elevator assembly. The investigation seeks to build the relationship between the spring-in and the fatigue life in order to determine the spring-in threshold during the course of assembling. The phenomenological model of the composite C-beam is constructed to predict the stresses around the joints. Based on the predicted spring-in induced stresses around the joints, pre-stresses are precisely added to the fatigue specimen when conducting the fatigue experiment. At last, the relationship curve of the spring-in on the composite C-beam’s fatigue life is obtained from the experimental data. Giving the fatigue life accepting limits, the maximum accepting spring-in deviation during the course of assembling could be obtained from the relationship curve. The reported work will enhance the understanding of assembling the composites with spring-in deviation in the civil aircraft industry.     

Three-dimensional computational micro-mechanical model for woven fabric composites

This work presents a computational material model for plain-woven fabric composite for use in finite element analysis. The material model utilizes the micro-mechanical approach and the homogenization technique. The micro-mechanical model consists of four sub-cells, however, because of the existing anti-symmetry only two sub-cells have to be homogenized for prediction of the elastic material properties. This makes the model computationally very efficient and suitable for large-scale finite element analysis. The model allows the warp and fill yarns not to be orthogonal in the plane of the composite ply. This gives the opportunity to model complex-shaped composite structures with different braid angles. General homogenization procedure is employed with two levels of property homogenization. The model is programmed in MATLAB software and the predicted material properties of different composite materials are compared and presented. The material model shows good capability to predict elastic material properties of composites and very good computational efficiency.     

Investigation of the dimensional stability of carbon epoxy cylinders manufactured by resin transfer moulding

The prediction of process-induced dimensional variability and residual stresses occurring during the manufacturing of composite structures is critical to produce parts where tight tolerances are required. Therefore, the development of material constitutive models and processing properties, and the validation of these models, are two essential steps in order to accurately simulate the behaviour of the materials involved. In this paper, the material constitutive models of a one-part epoxy resin were implemented in a three-dimensional finite element software based on the ABAQUS/COMPRO platform to investigate the dimensional stability of a composite structure manufactured by resin transfer moulding (RTM). A simplified geometry was used as a representative structural component with different layup configurations. Both heat transfer analysis and stress analysis were conducted. Contact interactions were implemented in the stress analysis to simulate the tool–part interaction. The presented analysis predicted the angle variation and the composite debonding caused by the coefficient of thermal expansion mismatch between the mould and the composite part and the resin volumetric chemical shrinkage.     

双随机分布细观分析模型与复合材料性能预报

发展了一种细观力学有限元分析方法——拟真实的参数化双随机分布模型, 该模型综合考虑了纤维增强树脂基复合材料的真实微结构特点和纤维单丝综合力学性能测试结果的离散性特征, 模拟了复合材料中纤维排列和强度分布的随机性。借助移动窗口法研究了该参数化双随机分布模型的可靠性, 确定了其代表性体积单元的尺寸。基于能量法原理推导了单向复合材料的弹性模量预测公式, 结合能量法和渐进失效分析方法, 利用该细观力学有限元方法分别预测了单向纤维增强树脂基复合材料T300/5228的弹性模量和强度性能。数值模拟结果和大部分试验结果吻合良好, 表明发展的细观力学有限元方法能够较好地预测复合材料的力学性能。      

吸湿后复合材料层合板快速加热分层扩展数值模拟

为研究复合材料层合板吸湿后的分层现象,首先建立了吸湿后复合材料层合板快速加热导致分层损伤的有限元模型,并对ABAQUS有限元软件进行二次开发,通过UAMP子程序模拟吸湿后复合材料快速加热时水分汽化引起的局部高压载荷作用下层合板分层扩展与载荷施加过程;然后,采用该模型预测了饱和吸湿T650-35/HFPE-II-52碳纤维聚酰亚胺复合材料层合板快速加热至310 ℃时产生的分层现象,并将数值模拟与文献实验结果对比;最后,运用该模型分析了树脂吸湿量和富脂区树脂聚集体积对层合板分层损伤面积的影响。结果表明:建立的有限元模型有效;快速加热后,层合板的分层损伤面积随树脂吸湿量的增加而增加;当富脂区树脂聚集体积较小时,其对层合板快速加热后分层损伤面积影响较小,但当富脂区树脂聚集体积增加到一定值后,层合板分层损伤面积随富脂区树脂聚集体积的增加而显著增加。所得结论表明,使用ABAQUS的UAMP子程序建立的有限元模型可以有效分析吸湿后复合材料层合板快速加热导致的分层现象。      

Modeling the process-induced dimensional variations of general curved composite components and assemblies

Dimensional variations are induced during the processing of composite materials. General curved components are commonly used in composite structures. Their performance is affected by the dimensional variations associated with the manufacturing process. This paper presents a piece-wise approach for predicting the dimensional variations of general curved composite components and assemblies. For a general curved composite component, it is first divided into a number of pieces of simple geometry. For each piece, the dimensional variation, i.e. spring-in, is calculated using the effective coefficients of thermal expansion. Based on the dimensional variation of each piece, the dimensional variations of the general curved component are calculated sequentially. This approach was validated against the finite element analysis. It shows that it offers excellent accuracy while avoiding time-consuming numerical computations. Besides general curved components, this approach can also be applied to composite assemblies. It provides the foundation for the tolerance analysis/synthesis of composites.     

高温复合材料舵面研制与试验验证

设计了一种蒙皮骨架结构高温复合材料舵面,并采用模压工艺制备了舵面,最后完成了舵面自由状态和固支状态下的固有模态测试,同时进行了静强度试验。采用三维实体单元,建立了舵面固有模态有限元分析模型,该模型分析的舵面固有模态与试验结果吻合良好,验证了有限元模型的有效性;并基于该模型研究了舵面在弯曲载荷下的破坏模式。试验结果表明: 舵面首先在根部树脂连接区发生树脂脱粘破坏,进而引起复合材料蒙皮与钛合金骨架的层间分层,从而导致整个舵面失效。有限元分析结果表明: 传感器质量分布对舵面的频率影响很大,但对其振型影响不大。应力分析结果表明: 根部树脂连接区的拉伸正应力导致此处树脂脱粘,有限元预测的破坏位置与试验结果一致。     

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.     

A parametric study on the process-induced deformation of composite T-stiffener structures

A parametric study on the process-induced deformation of composite stiffener structures is presented in this paper. The deformation was calculated numerically by Finite element analysis (FEA). The results suggest that the overall deformation of the structure can be characterized by the spring-in of the skin. Based on FEA, a parametric study and sensitivity analysis was conducted, from which it is shown that: (1) the spring-in decreases with the fiber volume fraction; (2) the spring-in linearly increases with the radius–thickness ratio; (3) the spring-in vs. the bonding length is a power increasing function; (4) the spring-in is most sensitive to the laminate fiber volume fraction, followed by the radius–thickness ratio and the bond length, and least sensitive to the noodle fiber volume fraction; and (5) at higher fiber volume fractions, the spring-in is more sensitive to the fiber volume fraction.     

Hierarchical modelling of a polymer matrix composite

A hierarchical modelling scheme to predict the properties of a polymer matrix composite is introduced. The stress–strain curves of amine-cured tetraglycidyl 4,4′-diaminodiphenylmethane (TGDDM) cured have been predicted using group interaction modelling (GIM). The GIM method, originally applied primarily to linear polymers, has been significantly extended to give accurate, consistent results for TGDDM, a highly crosslinked two-component matrix. The model predicts a complete range of temperature-dependent properties, from fundamental energy contributions, through engineering moduli to full stress–strain curves through yield. The predicted properties compare very well with experiment. Using the GIM-predicted TGDDM stress–strain curve, a 3D finite element model is used to obtain strain concentration factors (SCF) of fibres adjacent to a fibre break in a unidirectional (UD) composite. The strain distribution among the intact neighbouring fibres is clearly affected by the yielding mechanism in the resin matrix. A Monte Carlo simulation is carried out to predict the tensile failure strain of a single composite layer with the thickness equal to the fibre ineffective length. The effect of matrix shear yielding is introduced to the model through the SCF of surviving fibres adjacent to the fibre-break. The tensile failure strain of the composite is then predicted using a statistical model of a chain of composite layers.     

Three Phase Composite Cylinder Assemblage Model for Analyzing the Elastic Behavior of MWCNT-Reinforced Polymers

Evolution of computational modeling and simulation has given more emphasis on the research activities related to carbon nanotube (CNT) reinforced polymer composites recently. This paper presents the composite cylinder assemblage (CCA) approach based on continuum mechanics for investigating the elastic properties of a polymer resin reinforced by multi-walled carbon nanotubes (MWCNTs). A three-phase cylindrical representative volume element (RVE) model is employed based on CCA technique to elucidate the effects of inter layers, chirality, interspacing, volume fraction of MWCNT, interphase properties and temperature conditions on the elastic modulus of the composite. The interface region between CNT and polymer matrix is modeled as the third phase with varying material properties. The constitutive relations for each material system have been derived based on solid mechanics and proper interfacial traction continuity conditions are imposed. The predicted results from the CCA approach are in well agreement with RVE-based finite element model. The outcomes reveal that temperature softening effect becomes more pronounced at higher volume fractions of CNTs.     

Influence of the constitutive characteristics of resins on the composite materials delamination

This paper discusses the problem of interlaminar delamination in composite materials, with particular attention focused on the important role played by the resin properties. A Double Cantilever Beam (DCB) specimen has been modelled for finite element analysis assuming that the crack is situated inside a thin pure resin layer, similarly to the models proposed by Ozdil and Crews. A test program on the epoxy resin EPON 828, a typical resin commonly used for advanced composite systems for aerospace applications, has been carried out, in order to evaluate the mechanical properties; the results have shown a non-linear elastic behaviour without hysteresis effect. The non-linear relationship has been introduced in the bidimensional finite element model for the DCB specimen analysis. The stress and strain fields are used for the evaluation of the Energy Release Rate by means of a numerical model, based on an energetic approach such as the J-integral of Rice. The results show a considerable dependence on the constitutive relationship and give the opportunity of a more accurate evaluation of the toughness for experimental results from DCB specimen.