A Unit‐Cell Approach of Finite Element Analysis for Transverse Impact Damage of 3‐D Biaxial Spacer Weft‐Knitted Composite

Abstract: This paper evaluates the transverse impact damage of a 3‐D biaxial spacer weft‐knitted composite using experimental results and complimentary finite element analysis. The load–displacement curves and damage morphologies during impact loading were obtained to analyse energy absorption and impact damage mechanisms of the knitted composite. A unit‐cell model based on the microstructure of the 3‐D knitted composite was established to calculate the deformation and damage evolution when the composite is impacted by a hemisphere‐ended steel rod. An elastoplastic constitutive equation is incorporated into the unit‐cell model and the critical damage area failure theory developed by Hahn and Tsai has been implemented as a user‐defined material law (VUMAT) for commercial available finite element code ABAQUS/Explicit. The load–displacement curves, impact damages and impact energy absorption obtained from ABAQUS/Explicit are compared with those FROM experiments. The good agreement of the comparisons supports the validity of the unit‐cell model and user‐defined subroutine VUMAT. The unit‐cell model can also be extended to evaluate the impact crashworthiness of engineering structures made out of the 3‐D knitted composites.     

Impact Damage of 3D Orthogonal Woven Composite Circular Plates

The damages of 3D orthogonal woven composite circular plate under quasi-static indentation and transverse impact were tested with Materials Test System (MTS) and modified split Hopkinson bar (SHPB) apparatus. The load vs. displacement curves during quasi-static penetration and impact were obtained to study the energy absorption of the composite plate. The fluctuation of the impact stress waves has been unveiled. Differences of the load-displacement curves between the quasi-static and impact loading are discussed. This work also aims at establishing a unit-cell model to analyze the damage of composites. A user material subroutine which named VUMAT for characterizing the constitutive relationship of the 3-D orthogonal woven composite and the damage evolution is incorporated with a finite element code ABAQUS/Explicit to simulate the impact damage process of the composite plates. From the comparison of the load-displacement curves and energy absorption curves of the composite plate between experimental and FEM simulation, it is shown that the unit-cell model of the 3D woven composite and the VUMAT combined with the ABAQUS/Explicit can calculate the impact responses of the circular plate precisely. Furthermore, the model can also be extended to simulate the impact behavior of the 3D woven composite structures.     

Finite element analyses on transverse impact behaviors of 3-D circular braided composite tubes with different braiding angles

This paper presents finite element analyses (FEA) on the transverse impact responses of 3-D circular braided composite tubes with the braiding angles of 15°, 30° and 45°. A finite element model of the braided composite tube was established at microstructure level to analyze the transverse impact behaviors. From the FEA results, the impact damage, deformation and stress distribution were obtained to analyze the damage mechanism. Stress propagation in lower braiding angle tubes was faster than that of the higher braiding angle. The impact responses of the braided composite tubes were also tested to obtain load–displacement curves and energy absorption for the comparisons with the FEA results. The impact damage and fracture morphology obtained from the FEA were in good agreement with the experimental results, which demonstrated the feasibility of the FEA model for the design of the braided tube.     

A unit cell approach of finite element calculation of ballistic impact damage of 3-D orthogonal woven composite

This paper presents ballistic impact damages of 3-D orthogonal woven composite in finite element analysis (FEA) and experimental. A unit-cell model of the 3-D woven composite was developed to define the material behavior and failure evolution. A user-defined subroutine VUAMT was compiled and connected with commercial available FEA code ABAQUS/Explicit to calculate the ballistic penetration. Ballistic impact tests were conducted to investigate impact damage of 3-D kevlar/glass hybrid woven composite. Residual velocities of conically-cylindrical steel projectiles (Type 56 in China Military Standard) and impact damage of the composite targets after ballistic perforation were compared both in theoretical and experimental. The reasonable agreements between FEA results and experimental results prove the validity of the unit-cell model in ballistic limit prediction of the 3-D woven composite. We believe such an effort could be extended to bulletproof armor design with the 3-D woven composite.     

In-plane Compressive Behaviors of 3-D Textile Composites at Various Strain Rates

The in-plane compressive behaviors of 3-D textile composites, which including 3-D woven composite, multi-axial multi-layer warp knitted (MMWK) composite and 3-D braided composite, were studied at quasi-static and high strain rate compression loading. The compression behaviors at high strain rates (600∼2,500/s) were tested with split Hopkinson pressure bar (SHPB). The quasi-static compressive tests were conducted on a MTS 810.23 tester and compared with the results at high strain rates. The comparisons indicate that the compression stiffness, failure stress and failure strain for the three kinds of 3-D textile composites are sensitive to strain rate. The MMWK composite has higher failure stress than the 3-D woven composite and 3-D braided composite at the same strain rate; however, the failure strain of the 3-D braided composites is higher than that of the 3-D woven composite and 3-D knitted composite at quasi-static compression because of the quasi-isotropic structure feature in the 3-D braided composite. The compressive failure modes of the 3-D woven composite, MMWK composite and 3-D braided composite are totally different because of the different preform structure.     

Low-Velocity Impact Response and Finite Element Analysis of Four-Step 3-D Braided Composites

The low-velocity impact characters of 3-D braided carbon/epoxy composites were investigated from experimental and finite element simulation approaches. The quasi-static tests were carried out at a constant velocity of 2 mm/min on MTS 810.23 material tester system to obtain the indentation load–displacement curves and indentation damages. The low-velocity tests were conducted at the velocities from 1 m/s to 6 m/s (corresponding to the impact energy from 3.22 J to 116 J) on Instron Dynatup 9250 impact tester. The peak force, energy for peak force, time to peak force, and total energy absorption were obtained to determine the impact responses of 3-D braided composites. A unit cell model was established according to the microstructure of 3-D braided composites to derive the constitutive equation. Based on the model, a user-defined material subroutine (VUMAT) has been compiled by FORTRAN and connected with commercial finite element code ABAQUS/Explicit to calculate the impact damage. The unit cell model successfully predicted the impact response of 3-D braided composites. Furthermore, the stress wave propagation and failure mechanisms have been revealed from the finite element simulation results and ultimate damage morphologies of specimens.     

Tensile properties and meso-scale mechanism of weft knitted textile composites for energy absorption

The investigation on large deformation tensile properties and the relevant meso-scale mechanisms of weft knitted textile composites is presented. The correlation between fabric structure (e.g. loop height and width, number of wale or course per unit length, etc.), matrix damage and material properties are described. Weft knitted fabrics with 1×1 interlock structure were used as the preform for the composites. The materials studied include knitted nylon fabric/unsaturated polyester resin and co-knitted polyethylene terephthalate (PET)/polypropylene (PP) textile composites. The results show that all the nylon/polyester thermoset textile composites samples displayed an ideal bi-linear character in their tensile stress–strain curves, whilst the tensile curves of PET/PP co-knitted thermoplastic samples along the wale, course and 45° directions are all significantly non-linear. The tensile behavior is superior in the wale direction to those in the course and 45° directions. The deformation mechanisms in meso-scale were identified experimentally by in-situ observation of large deformation process for both thermoset matrix and thermoplastic matrix textile composites. For the nylon/polyester composite samples, the non-linear properties mainly come from the change in the configuration of the fabric structure during extension. For the PET/PP co-knitted textile composite samples, the inelastic properties are attributed to the damage evolution in the matrix, interface damage between fiber bundle and matrix, sliding between the wales of the knitted fabric, as well as the change in the configuration of the fabric structure during loading.     

三维四向编织复合材料界面损伤机理数值分析

考虑界面脱粘表面压应力下摩擦力对材料界面力学性能的影响,建立损伤-摩擦相结合的界面本构模型,编写用户材料子程序VUMAT,实现其在有限元软件ABAQUS中的嵌入。基于周期性胞元分析思想,在单胞模型中纤维束/基体、纤维束/纤维束分界面引入界面单元,结合损伤-摩擦相结合的界面本构模型,建立含界面相三维四向编织复合材料的细观有限元模型。模拟典型载荷下界面损伤的起始和扩展过程,分析界面应力传递和界面破坏机理,研究界面性能对复合材料宏细观力学性能的影响规律,为实现三维四向编织复合材料界面性能优化设计和控制提供参考。      

单向纤维增强聚合物复合材料压缩渐进破坏单向纤维增强聚合物复合材料压缩渐进破坏

复合材料结构在承压时破坏如何演化,是其强度破坏分析的基础和核心任务。本文提出了基于连续介质损伤力学（CDM）的单向纤维增强聚合物复合材料压缩破坏渐进损伤分析（PDA）模型。建模中考虑了材料非线性行为、失效判断及损伤演化中材料性能退化等基本问题,分别对应于拉压不对称弹塑性本构关系、Puck准则、LaRC05准则及考虑破坏面方向的刚度退化方法。该模型通过用户材料子程序接口VUMAT引入到有限元软件ABAQUS中实现了有限元求解。对文献中提供的纵向、横向及偏轴压缩案例进行了数值计算并与试验数据对比。数值分析结果与试验数据吻合较好,证明了该方法的合理性和有效性,对开展多向层合板压缩破坏分析富有参考价值。      

不同结构UHMWPE纤维纬编针织复合材料压缩性能

针对高性能超高分子量聚乙烯（UHMWPE）纤维的特性,成功编织出纬平针、罗纹、畦编3种针织物。采用真空辅助树脂传递模塑成型（VARTM）技术,分别制备出6层纬平针、6层罗纹以及6层畦编织物复合材料板。对3种结构复合材料进行压缩试验,并比较分析了比压缩强度-应变曲线、比压缩能量-应变曲线、比压缩能量-应变拟合曲线,分析了压缩过程中的能量吸收情况及材料的破坏形式。结果表明:纬平针结构复合材料的比压缩强度和比压缩能量均最大,其次是罗纹,畦编最小;且3种结构复合材料的压缩破坏过程均不属于脆性破坏;由于材料表现出较好的柔韧性,试样的比压缩能量与压缩应变呈线性相关;相同结构复合材料纵、横向比压缩强度-应变曲线和比压缩能量-应变曲线几乎重合。基体沿增强结构呈分层现象的破坏和树脂的塑性变形是材料的主要破坏形式。      

A damage model for knitted fabric composites

A progressive damage model is presented for the prediction of the overall non-linear tensile behaviour of knitted fabric composites. The model is an extension of a recently developed inclusion method for textile composites, taking into account the major damage modes of knitted fabric composites simultaneously. Matrix non-linearities, playing an important role in the behaviour of knitted fabric composites, are implemented using the secant stiffness method. Whereas, non-linearities can be attributed to different sources, depending upon the resin toughness, only some limited yielding was currently investigated. Yarn/matrix debonding, predominantly responsible for the knee behaviour of knitted fabric composites, is investigated using a simple interfacial failure criterion. A selective degradation scheme based upon a finite set of interfacial damage state variables is employed in the reduction of the inclusion stiffness. Finally, a Hoffman criterion is used for yarn failure. The model was used to simulate the tensile behaviour of knitted fabric E-glass/epoxy composites, showing the ability to predict the material response with reasonable accuracy in the region before ultimate failure.     

The effects of deforming knitted glass fabrics on the basic composite mechanical properties

The effects of deforming knitted fabrics on the tensile and compressive properties of their composites have been investigated for the weft-knit Milano rib fibre architecture. The properties have been studied for both the course and wale directions for composites with fabrics deformed in either of the two directions. It was found that any change in the mechanical properties of the deformed composites with respect to their undeformed counterpart is strongly related to the changes in the knit structure brought about by the induced deformation to the knitted fabric. Deformation in the knitted fabric also affects the tensile fracture mode whereby increased deformation, be it wale- or course-wise, transforms transverse fracture to shear fracture in either loading axis. On the contrary, the compressive fracture mode is insensitive to fabric deformation. Fractographic studies using stereo-optical and scanning electron microscopy have further revealed that tensile failure is caused by fibre breakages occurring at two locations of the knitted loops—one, at the leg components and, two, at fibre crossover points, whilst compression failure is controlled by Euler buckling of the looped fibres of the knitted composite. All these characteristics were revealed to be related to the microstructure of the knitted composite laminates.     

A study of damage development in a weft knitted fabric reinforced composite. Part 2: Stress–strain and early cyclic behaviour of composite laminates with realistic fabric layups

The mechanical behaviour of knitted fabric composites, consisting of four or five layers of weft knitted glass fabric in a Derakane vinyl ester matrix, has been investigated under simple tensile loading and in cyclic tests at increasing peak strains for a range of loading angles with respect to the wale direction of the knitted fabric. Stress–strain curves are non-linear from very low strains for all loading angles and they exhibit a rapidly reducing tangent modulus with increasing strain. Acoustic emission results and the results of the cyclic loading, together with comparisons with the results on the model specimens in Part 1, suggest the following sequence of damage development: damage develops initially between yarns at the loop cross-over points in the knitted fabric structure, progresses to the development of matrix cracking damage from these initiation sites at weak planes in the composite due to the fabric architecture, and then to the pulling out of loops across matrix cracks. The pulling out of loops across matrix cracks, together with matrix non-linearity, gives rise to a stress–strain curve with a very low tangent modulus at high strains and to hysteresis loops which do not close on unloading and reloading.     

Layerwise modeling of progressive damage in fiber-reinforced composite laminates

This paper investigates the effects of discrete layer transverse shear strain and discrete layer transverse normal strain on the predicted progressive damage response and global failure of fiber-reinforced composite laminates. These effects are isolated using a hierarchical, displacement-based 2-D finite element model that includes the first-order shear deformation model (FSD), type-I layerwise models (LW1) and type-II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C ⁰ continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C ⁰ continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics (CDM) model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the homogenized composite material ply. In modeling laminates that exhibit either widespread or localized transverse shear deformation, the results obtained in this study clearly show that the inclusion of discrete layer kinematics significantly increases the rate of local damage accumulation and significantly reduces the predicted global failure load compared to solutions obtained from first-order shear deformable models. The source of this effect can be traced to the improved resolution of local interlaminar shear stress concentrations, which results in faster local damage evolution and earlier cascading of localized failures into widespread global failure.     

The effect of tube end constraining on the axial crushing behavior of an aluminum tube

The effect of various types of end constraining on the deformation and load–displacement behavior of a 3003-H14 Al tube were experimentally and numerically studied. No effect of single-end constraining of tubes was found. Few conditions of double-end constraining tended to revert the deformation mode to mixed and/or diamond mode of deformation. Double-end constraining of tube ends further resulted in an increase in initial drop-load values, widening the initial overshot region in average load–displacement curves. The agreement between numerical and experimental results showed the capabilities of the used numerical model in order to predict end-condition effects in tubular structures.     

三维编织复合材料弹道侵彻准细观层次有限元计算

三维编织复合材料相比于层合复合材料有较高的层间剪切强度和断裂韧性,因而具有更高的冲击损伤容限。用钢芯弹对三维编织复合材料作弹道贯穿测试,得到弹体的入射速度和剩余速度,并考察侵彻破坏模式。目前对三维编织复合材料弹道侵彻性能计算主要建立在连续介质假设上,从真实细观结构计算三维编织复合材料弹道冲击性能尚有一定难度,用三维结构复合材料的纤维倾斜模型在准细观结构层次上分解三维编织复合材料,就其中的一块倾斜单向板作弹道侵彻有限元计算,由弹体动能损失得到贯穿整个复合材料靶体后弹体的剩余速度。有限元计算及与弹道测试结果的比较证明在准细观层次上计算三维编织复合材料弹道冲击性能的有效性。      

Numerical simulation of the impact behaviors of shear thickening fluid impregnated warp-knitted spacer fabric

The impact behavior of warp-knitted spacer fabrics (WKSFs) impregnated with shear thickening fluid (STF) under low-velocity impact loadings have been investigated from experimental and finite element analyses (FEA) approaches. From the experimental approach, the impact load–displacement curves have been obtained. It was observed that the WKSF impregnated with the STF composite material (the WKSF/STF composite) shows a higher stiffness and lower peak force than those of the WKSF under the same impact loadings. In FEA approach, the geometrical models of the WKSF and the WKSF/STF composite material were established based on the WKSF fabric architectures. The dynamic responses including the impact load–displacement curves and impact deformation of the samples were predicted based on finite element analyses at the microstructure level. It was found that the STF and the coupling effect between the STF fluid and fiber tows are the key factors which influence the cushioning behaviors of the composite. The energy absorption mechanisms include the buckling of the spacer finer tows and the thickening effect of the STF under impact loading. The WKSF/STF composite could be expected as a damping or energy-absorptive materials under impact loading.     

Strength prediction in CFRP woven laminate bolted double-lap joints under quasi-static loading using XFEM

The current paper is concerned with modelling damage and fracture in woven fabric composite double-lap bolted joints that fail by net-tension. A 3-D finite element model is used, which incorporates bolt clamp-up, to model a range of CFRP bolted joints, which were also tested experimentally. The effects of laminate lay-up, joint geometry, hole size and bolt clamp-up torque were considered. An Extended Finite Element (XFEM) approach is used to simulate damage growth, with traction–separation parameters that are based on previously reported, independent experimental measurements for the strength and toughness of the woven fabric materials under investigation. Good agreement between the predicted and measured bearing stress at failure was obtained.     

Modelling and simulation of earthquake resistant 3D woven textile structural concrete composites

Concrete is a composite material composed of water, sand, coarse granular material called aggregate and cement that fills the space among the aggregate particles and glues them together. Conventional building structures are made up of steel skeleton with concrete impregnation. These are very heavy weight structures with steel vulnerable to corrosion. The conventional concrete structures tend to undergo large deformations in the event of a strong earthquake. Mechanical simulation of various textile structural concretes is carried out successfully for their ductility behaviour. 3D woven reinforced concretes display superior ductile character showing ray of hope to develop seismic resistant building. Simulation of three 3D woven fabrics and their composites was carried to predict ductility and strengths of fabric reinforced concrete structures. Maximum deformation was observed for beam reinforced with orthogonal interlock fabric under the same load and minimum deformation was observed for plain concrete. Maximum equivalent stress was observed to be highest for plain concrete followed by beam reinforced with angle interlock fabric followed by orthogonal fabric and warp interlock fabric under similar loading conditions. From the results it was clear that 3D fabric reinforced structures are more ductile than the traditional steel reinforced structures. Hence 3D fabric reinforced concrete structures are much better in strength and ductility as compared to conventional construction materials. Among the three 3D fabric, orthogonal fabric reinforced composites are most ductile and are also less stiff. They can deform more than the other two fabric composites. Hence, orthogonal fabric reinforced composites can undergo higher deformations without collapsing. These composites can be more elastic under earthquake shaking.     

Meso-Scale Damage Simulation of 3D Braided Composites under Quasi-Static Axial Tension

The microstructure of 3D braided composites is composed of three phases: braiding yarn, matrix and interface. In this paper, a representative unit-cell (RUC) model including these three phases is established. Coupling with the periodical boundary condition, the damage behavior of 3D braided composites under quasi-static axial tension is simulated by using finite element method based on this RUC model. An anisotropic damage model based on Murakami damage theory is proposed to predict the damage evolution of yarns and matrix; a damage-friction combination interface constitutive model is adopted to predict the interface debonding behavior. A user material subroutine (VUMAT) involving these damage models is developed and implemented in the finite element software ABAQUS/Explicit. The whole process of damage evolution of 3D braided composites under quasi-static axial tension with typical braiding angles is simulated, and the damage mechanisms are revealed in detail in the simulation process. The tensile strength properties of the braided composites are predicted from the calculated stress-strain curves. Numerical results agree with the available experiment data and thus validates the proposed damage analysis model. The effects of certain material parameters on the predicted stress-strain responses are also discussed by numerical parameter study.