Meso-Scale Progressive Damage Behavior Characterization of Triaxial Braided Composites under Quasi-Static Tensile Load

Based on continuum damage mechanics (CDM), a sophisticated 3D meso-scale finite element (FE) model is proposed to characterize the progressive damage behavior of 2D Triaxial Braided Composites (2DTBC) with 60° braiding angle under quasi-static tensile load. The modified Von Mises strength criterion and 3D Hashin failure criterion are used to predict the damage initiation of the pure matrix and fiber tows. A combining interface damage and friction constitutive model is applied to predict the interface damage behavior. Murakami-Ohno stiffness degradation scheme is employed to predict the damage evolution process of each constituent. Coupling with the ordinary and translational symmetry boundary conditions, the tensile elastic response including tensile strength and failure strain of 2DTBC are in good agreement with the available experiment data. The numerical results show that the main failure modes of the composites under axial tensile load are pure matrix cracking, fiber and matrix tension failure in bias fiber tows, matrix tension failure in axial fiber tows and interface debonding; the main failure modes of the composites subjected to transverse tensile load are free-edge effect, matrix tension failure in bias fiber tows and interface debonding.     

Characterisation of mechanical behaviour and damage analysis of 2D woven composites under bending

In this paper, flexural loading of woven carbon fabric-reinforced polymer laminates is studied using a combination of experimental material characterisation, microscopic damage analysis and numerical simulations. Mechanical behaviour of these materials was quantified by carrying out tensile and large-deflection bending tests. A substantial difference was found between the materials' tensile and flexural properties due to a size effect and stress stiffening of thin laminates. A digital image-correlation technique capable of full-field strain-measurement was used to determine in-plane shear properties of the studied materials. Optical microscopy and micro-computed tomography were employed to investigate deformation and damage mechanisms in the specimens fractured in bending. Various damage modes such as matrix cracking, delaminations, tow debonding and fibre fracture were observed in these microstructural studies. A two-dimensional finite-element (FE) model was developed to analyse the onset and propagation of inter-ply delamination and intra-ply fabric fracture as well as their coupling in the fractured specimen. The developed FE model provided a correct prediction of the material's flexural response and successfully simulated the sequence and interaction of damage modes observed experimentally.     

Braided textile composites under compressive loads: Modeling the response, strength and degradation

This paper discusses the results of a finite element (FE) based micromechanics study of the compressive damage development mechanisms of 2D triaxial braided carbon fiber composites (2DTBC). The micromechanics based study was carried out on a Representative Unit Cell (RUC) size 3D FE model. The uniaxial compressive response was established using an arc-length method in conjunction with the ABAQUS commercial FE code. In this work, explicit account of the braid microstructure (geometry and packing) and the measured inelastic properties of the matrix (the in situ properties) are accounted for via the use of the FE method. This enables accounting for the different length scales that are present in a 2DTBC. This detail is necessary for developing a mechanism based damage prediction capability. The computational model provides a means to assess the compressive strength of 2DTBC and its dependence on various microstructural parameters. In particular, the dependence of compressive strength on the axial fiber tow properties and axial tow geometrical imperfections is discussed and shown to be significant in capturing the mechanism of damage development.     

碳纤维编织复合材料层合板抗侵彻性能研究

通过弹道冲击实验开展了碳纤维编织复合材料层合板的抗侵彻性能研究,进行了动态响应分析和损伤模式分析。建立了基于Hashin失效和Yeh分层失效准则的渐进损伤模型,运用ABAQUS有限元软件模拟了碳纤维编织复合材料层合板的侵彻失效过程,采用Lambert-Jonas公式拟合了柱状弹侵彻层合板弹道极限曲线,对比分析了碳纤维编织复合材料层合板侵彻实验与数值模拟的弹道极限速度及损伤形貌。结果表明,层合板侵彻损伤模式主要为分层、纤维断裂和基体开裂失效,弹道极限速度数值模拟结果与实验结果吻合较好。     

A Discrete Model for Simulation of Composites Plate Impact Including Coupled Intra- and Inter-ply Failure

Laminated composites can undergo complex damage mechanisms when subjected to transverse impact. For unidirectional laminates it is well recognized that delamination failure usually initiates via intra-ply shear cracks that run parallel to the fibres. These cracks extend to the interface of adjacent orthogonal plies, where they are either stopped, or propagate further as inter-ply delamination cracks. These mechanisms largely determine impact energy absorption and post-delamination bending stiffness of the laminate. Important load transfer mechanisms will occur that may lead to fibre failure and ultimate rupture of the laminate. In recent years most Finite Element (FE) models to predict delamination usually stack layers of ply elements with interface elements to represent inter-ply stiffness and treat possible delamination. The approach is computationally efficient and does give some estimate of delamination zones and damaged laminate bending stiffness. However, these models do not properly account for coupled intra-ply shear failure and delamination crack growth, and therefore cannot provide accurate results on crack initiation and propagation. An alternative discrete meso-scale FE model is presented that accounts for this coupling, which is validated against common delamination tests and impact delamination from the Compression After Impact (CAI) test. Ongoing research is using damage prediction from the CAI simulation as a basis for residual strength analysis, which will be the published in future work.     

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.     

Interaction of Matrix Cracking and Delamination in Cross-ply Laminates: Simulations with Stochastic Cohesive Zone Elements

Two main damage mechanisms of laminates—matrix cracking and inter-ply delaminationare closely linked together (Joshi and Sun 1). This paper is focussed on interaction between matrix cracking and delamination failure mechanisms in CFRP cross-ply laminates under quasi-static tensile loading. In the first part of the work, a transverse crack is introduced in 90o layers of the cross-ply laminate [01/904/01], and the stresses and strains that arise due to tensile loading are analyzed. In the second part, the cohesive zone modelling approach where the constitutive behaviour of the cohesive elements is governed by traction-displacement relationship is employed to deal with the problem of delamination initiation from the matrix crack introduced in the 90o layers of the laminate specimen. Additionally, the effect of microstructural randomness, exhibited by CFRP laminates on the damage behaviour of these laminates is also accounted for in simulations. This effect is studied in numerical finite-element simulations by introducing stochastic cohesive zone elements. The proposed damage modelling effectively simulated the interaction between the matrix crack and delamination and the variations in the stresses, damage and crack lengths of the laminate specimen due to the microstructural randomness.     

Ballistic impact behaviour of woven fabric composites: Formulation

Resistance to high velocity impact is an important requirement for high performance structural materials. Even though, polymer matrix composites are characterized by high specific stiffness and high specific strength, they are susceptible to impact loading. For the effective use of such materials in structural applications, their behaviour under high velocity impact should be clearly understood. In the present study, investigations on the ballistic impact behaviour of two-dimensional woven fabric composites have been presented. Ballistic impact is generally a low-mass high velocity impact caused by a propelling source. The analytical method presented is based on wave theory. Different damage and energy absorbing mechanisms during ballistic impact have been identified. These are: cone formation on the back face of the target, tension in primary yarns, deformation of secondary yarns, delamination, matrix cracking, shear plugging and friction during penetration. Analytical formulation has been presented for each energy absorbing mechanism. Energy absorbed during each time interval and the corresponding reduction in velocity of the projectile has been determined. The solution is based on the target material properties at high strain rate and the geometry and the projectile parameters. Using the analytical formulation, ballistic limit, contact duration at ballistic limit, surface radius of the cone formed and the radius of the damaged zone have been predicted for typical woven fabric composites. The analytical predictions have been compared with the experimental results. A good correlation has been observed.     

含界面相三维全五向编织复合材料拉伸行为模拟及失效机制研究

基于三维全五向（Q5D）编织复合材料的细观结构模型,通过引入界面相单元,建立了含界面相Q5D编织复合材料单轴拉伸损伤失效分析模型。应用Python语言实现对ABAQUS的二次开发,将Linde等提出的失效准则和Von-Mises应力准则分别用于纱线和基体的渐进损伤判断,并确定材料的整体失效模式;对于界面相,采用Quads准则进行损伤判断。利用周期性位移边界条件,对含界面相Q5D编织复合材料的纵向拉伸应力-应变行为进行了渐进损伤数值模拟,详细讨论了在纵向拉伸载荷作用下材料的细观损伤起始、扩展和最终失效的演化过程,分析了材料的细观损伤失效机制,预测了材料的极限破坏强度,并研究了界面相性能对材料整体力学行为的影响规律。研究结果表明,数值模拟结果与实验值吻合较好,验证了渐进损伤模型的有效性,为该类材料的力学分析和优化设计奠定了基础。     

Parametric analyses of stitched composite T-joints by the finite element method

Numerical methods were employed to perform a detailed parametric study on composite T-joints with transverse stitching using the finite element method. This analysis was accomplished to discern the effects of key joint parameters including fiber insertion tow modulus, fiber insertion filament count, fiber insertion depth, and resin-rich interface zone thickness on T-joint displacement and damage initiation load. T-joint load conditions included flexure, tension, and shear. Significant results of the parametric finite element analysis indicate that under flexural loading, increasing the fiber insertion tow modulus and tow filament count increases the T-joint damage initiation load; increasing the fiber insertion depth reduces T-joint deflection; and reducing the web-to-flange interface thickness reduces the T-joint deflection. Fiber insertion tow filament count and modulus have a negligible effect on T-joint deflection under tension and initial damage load under shear.     

纤维增强复合材料层合板缺口尺寸及形状效应数值模拟

通过考虑基体裂纹、纤维断裂、层内劈裂和层间脱层等破坏形式,建立三维有限元模型研究含中心圆孔和中心裂缝的准各向同性复合材料层合板([45/0/-45/90]_(2S))在拉伸载荷下的缺口尺寸效应及缺口形状效应。模拟结果显示:随着缺口尺寸的增大,层合板的破坏强度逐渐降低,然而,在本文研究范围内含中心裂缝的层合板破坏强度始终高于对应的含中心圆孔的层合板破坏强度。进一步分析有限元模拟结果表明,含中心裂缝的层合板亚临界损伤发生得更早,并且亚临界损伤范围更大,亚临界损伤会大大缓解缺口尖端的应力集中,从而使含中心裂缝层合板表现出更高的破坏强度。     

Delamination of beams: an application to the DCB specimen

This paper deals with the problem of the delamination of laminated beams. A model based on adhesion theory is adopted. The laminate is modeled as two beams in adhesion, with an initial defect in part of the interface. Adhesion is governed by two state variables: the relative displacement of the points belonging to the two beams and lying at the interface, and a damage parameter. This model is governed by a nonsmooth functional. Then, a simple regularized model is derived for the interface. The corresponding differential equations are given and the closed form solution is provided. Both the perfect nonsmooth and the regularized proposed models are used to study the classical double cantilever beam (DCB) specimen. In particular, a simple theory is developed to predict the external loads leading to delamination for pure mode I or pure mode II. Numerical computations, developed for both the nonsmooth and the smooth proposed models, are compared with results available in the literature.     

GLARE层板挤压渐进损伤分析

对GLARE36/5层板进行挤压性能试验研究,采用超声C扫描、断口微距拍摄和扫描电子显微镜等方法观测GLARE层板挤压渐进损伤过程和最终破坏模式。结果表明:GLARE层板挤压起始损伤为铝合金塑性变形;损伤扩展阶段,0°纤维主要承受挤压正应力,铝合金塑性变形增大,铺层间分层起始并扩展;0°纤维屈曲折断后层内纤维基体损伤和分层损伤急剧扩展,层板最终发生挤压破坏。将GLARE层板挤压失效分为层内失效和层间失效,采用应变描述的Hashin准则和界面单元方法并引入金属塑性建立GLARE层板挤压渐进损伤数值模型,数值模型对层板损伤起始位置、分层产生位置、损伤演化过程、最终破坏模式及破坏载荷进行了预测,计算结果与试验结果吻合较好,说明该计算方法能够有效模拟GLARE层板挤压渐进损伤性能。      

跨尺度预测非屈曲织物增强复合材料的刚度和强度

为了预测非屈曲织物增强复合材料的力学性能, 建立了纤维束的正六边形单胞和非屈曲织物复合材料的长方形单胞, 并重点推导了正六边单胞的方程边界条件。通过跨尺度逐级计算这两个单胞的有效弹性常数, 得到了非屈曲碳纤维织物增强环氧树脂基复合材料的宏观有效弹性性能和强度。对该非屈曲织物复合材料在拉伸载荷下的累计失效进行了有限元损伤分析。结果表明: 初始损伤发生在富树脂区或横向纤维束, 损伤在富树脂区与横向纤维束内逐步扩展, 最后向纵向纤维束扩展并迅速导致整体失效; 非屈曲织物增强复合材料的面内拉伸模量的计算预测值非常接近实验值, 面内拉伸强度计算值略小于实验值。     

缝合式三维编织C/SiC复合材料拉伸加卸载力学行为

本文通过开展缝合式三维编织C/SiC复合材料的准静态单轴拉伸及循环加卸载试验,研究加卸载行为对复合材料的损伤及材料内部能量耗散的影响。通过对材料的断口分析,探究加卸载对材料破坏强度的影响规律。结果表明,加卸载行为会消耗材料内部的能量,对纤维束与基体之间的界面造成损伤,进而降低材料的承载能力;材料滞回曲线的面积随着卸载点应力的增大而增大;材料的整体失效属于脆性破坏,复合材料断口表现出明显的分层现象,且单轴拉伸时断口相对于循环加卸载更整齐。      

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.     

强度失配对铝合金板焊接接头抗弹性能影响的有限元分析

通过建立7.62mm穿甲弹侵彻铝合金板的模型,采用Johnson-Cook材料模型模拟研究了焊接接头的强度失配对铝合金板抗弹性能的影响。研究结果表明：当子弹侵彻铝合金焊接接头附近时,由于材料的不均匀变形,子弹会改变侵彻方向,其方向角的改变大小与子弹速度、侵入位置、弹头形状、强度失配比、靶板厚度有关;当子弹以低速侵彻铝合金板中间的软焊缝材料时,由于变形局部化,出现材料的抗弹性能低于纯焊缝材料的情况;由于子弹侵彻方向的改变,出现部分区域的抗弹性能高于铝合金基体材料的情况。研究结果为不均匀材料的抗弹性能研究提供参考。     

Multi-Scale Progressive Damage Model for Analyzing the Failure Mechanisms of 2D Triaxially Braided Composite under Uniaxial Compression Loads

Based on continuum damage mechanics (CDM), a multi-scale progressive damage model (PDM) is developed to analyze the uniaxial compression failure mechanisms of 2D triaxially braided composite (2DTBC). The multi-scale PDM starts from the micro-scale analysis which obtains the stiffness and strength properties of fiber tows by a representative unit cell (RUC) model. Meso-scale progressive damage analysis is conducted subsequently to predict the compression failure behaviors of the composite using the results of micro-scale analysis as inputs. To research the free-edge effect on the local failure mechanisms, meso-scale models of different widths are also established. The stress-strain curves obtained by numerical analysis are verified with the experimental data. Results show that fiber and matrix compression failure inside the fiber tows are the major failure modes of the composite under axial compression. For transverse compression, the dominated failure modes are recorded for matrix compression failure inside the fiber tows. It is also presented that the free-edge effect plays an important role in the transverse mechanical response of the composite, and the failure behaviors of the internal fiber tows are strongly influenced as well.     

Energy absorption and damage propagation in 2D triaxially braided carbon fiber composites: effects of in situ matrix properties

Results from an experimental program to investigate the propagation of damage and energy dissipation in 2D triaxially braided carbon fiber textile composites (2DTBC) under static conditions are reported. A methodology is presented in which classical concepts from fracture mechanics are generalized to address damage growth in an orthotropic and heterogeneous structural material. Along with results from the experimental program, a novel numerical technique that employs ideas from cohesive zone modeling, and implemented through the use of finite-element analysis, is also presented. The inputs that are required for the discrete cohesive zone model (DCZM) are identified. Compact tension specimen fracture tests and double notched tension tests were carried out to measure the fracture energy (G _Ic), and the maximum cohesive strength (σ _c), of the 2DTBC. The DCZM modeling strategy was independently verified by conducting single edge notched three-point bend tests using a modified three-point bend test fixture. The experimental and numerical analyses were carried out for two different types of 2DTBC made from the same textile architecture but infused with two different resin systems to validate the proposed methodology.