Three-dimensional microscopic interlaminar analysis of cross-ply laminates based on a homogenization theory

In this study, a method for three-dimensional microscopic interlaminar analysis of cross-ply laminates is developed based on a homogenization theory to analyze microscopic interactions between unidirectional long fiber-reinforced laminae. For this, a unit cell of a cross-ply laminate, which includes interlaminar areas, is defined under the assumption that each lamina in the laminate has a transversely square fiber array. Then, showing that the laminate has a point-symmetric internal structure, the symmetry is utilized to introduce half of the unit cell as the domain of analysis. Moreover, the domain of analysis is divided into substructures using a substructure method combined with the homogenization theory, significantly reducing the computational costs. The present method is then applied to the analysis of interlaminar stress distributions in a carbon fiber/epoxy cross-ply laminate subjected to in-plane uniaxial tension. It is shown that microscopic shear stress noticeably occurs at the interface between the 0°- and 90°-plies. It is also shown that the microscopic interaction between the two plies is observed only in the vicinity of the interface.     

Residual surface stresses in laminated cross-ply fiber-epoxy composite materials

Residual (curing) stresses in a cross-ply laminated plate are related to the strains released when individual plies are separated. Released displacements are determined using high-sensitivity moiré interferometry and linearized strain-displacement equations are used to determine residual strains. Elastic orthotropic stress-strain relations are used to calculate residual stresses remote from free-edges of a [90₂₀/0₂₀/90₂₀] graphite-epoxy cross-ply panel. The measured strains compare favorably with those predicted by laminated plate theory. In a second example, the circumferential and radial residual strains and stresses at the end-section of a thick-walled cross-ply graphite-epoxy cylinder are determined. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas NV on June 8–11.     

Progressive fracture of laminated composite stiffened plate

Laminated fiber-reinforced composite stiffened plate with [0/90/±45]_S plies made of S-Glass/epoxy are evaluated via computational simulation to study damage and fracture progression. The loads are pressure and temperature which varies from 21 to 65.5 °C (case I) and from 143.3 to 21 °C (case II). An integrated computer code is used for the simulation of the damage progression. Results show that damage initiation begins at low load level, with matrix cracking at the 0° (bottom and top) plies, fiber fracture at the bottom (0°) ply and interply delamination at the top (0°) ply. Increasing the applied pressure, the damage growth is expended resulting in fracture through the thickness of the structure. At this stage, 90% of the plies damage at applied pressure 15.306 MPa for the case I and 15.036 MPa for the case II. After this stage, the cracks propagate rapidly and the structure collapses.     

Deformation of Cross-Ply Composite Laminates with Cracked Ceramic Matrix

The deformation of cross-ply ceramic-matrix composite laminates under biaxial loading is studied theoretically. Experimentally, microscopic damage evolution in cross-ply ceramic-matrix composite laminates has not been well characterized yet, mainly due to the difficulties involved in testing of anisotropic plates under biaxial loading. It is assumed that the initial damage mechanism observed in ceramic-matrix composite laminates is the formation of tunneling macrocracks both in the 90°- and 0°-plies. The paper addresses the stiffness-deterioration behavior of cross-ply ceramic-matrix laminates with transverse and longitudinal macrocracks. The analysis is based on the equivalent-constraint model of a damaged laminate. Numerical results for SiC/CAS cross-ply laminates of various lay-ups are presented and discussed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 37–46, January 2005.     

纤维增强陶瓷基复合材料疲劳迟滞回线模型研究

纤维增强陶瓷基复合材料初始加载到疲劳峰值应力时, 基体出现裂纹, 纤维/基体界面发生脱粘. 在疲劳载荷作用下, 纤维相对基体在界面脱粘区往复滑移使得陶瓷基复合材料出现疲劳迟滞现象. 建立了纤维陶瓷基复合材料疲劳迟滞回线细观力学模型, 采用断裂力学方法确定了初始加载纤维/基体界面脱粘长度、卸载界面反向滑移长度与重新加载新界面滑移长度, 分析了4种不同界面滑移情况的疲劳迟滞回线. 假设正交铺设与编织陶瓷基复合材料疲劳迟滞回线主要受0°铺层、轴向纱线内纤维/基体界面滑移的影响, 预测了单向、正交铺设与编织陶瓷基复合材料在不同峰值应力与不同循环的疲劳迟滞回线, 与试验结果吻合.      

Spherical indentation of composite laminates with controlled gradients in elastic anisotropy

Three-dimensional elastic analyses and experiments of indentation of thick laminated plates of carbon fiber reinforced epoxy are presented. Pointwise, the material is characterized as a linear elastic orthotropic material. The in-plane orientation of the carbon fibers is systematically varied as a function of depth. The influence of fiber orientation as a function of depth on the indentation response is considered along with the relationship between the indenter force vs depth. The fiber orientation profiles considered are those of a continuous linear variation between 90° at the outer surfaces and 0° at the center plane of the laminate, and a cross ply laminate involving alternating 90° and 0° layers through thickness. Experimentally, it is found that for the case of a cross-ply laminate, the indentation produces delaminations localized at the interfaces that separate planes of dissimilar orientation. For this case, stress concentrations at interfaces between plies of dissimilar orientation coincide with the observed sites of delamination. For the graded case, evidence of enhanced nonlinear deformation is found, without the nucleation of cracks. Computations show that for the graded material, tensile stresses perpendicular to fibers are suppressed significantly, possibly explaining the absence of matrix cracks in this material. Measured and computed indenter force-depth variations were found to be in good agreement. Experiments and computations also reveal that the orientation-graded material is more compliant when subjected to indentation than the conventional cross-ply laminate.     

INVESTIGATION ON FATIGUE HYSTERESIS LOOPS MODELS OF FIBRE-REINFORCED CERAMIC-MATRIX COMPOSITES

纤维增强陶瓷基复合材料初始加载到疲劳峰值应力时, 基体出现裂纹, 纤维/基体界面发生脱粘. 在疲劳载荷作用下, 纤维相对基体在界面脱粘区往复滑移使得陶瓷基复合材料出现疲劳迟滞现象. 建立了纤维陶瓷基复合材料疲劳迟滞回线细观力学模型, 采用断裂力学方法确定了初始加载纤维/基体界面脱粘长度、卸载界面反向滑移长度与重新加载新界面滑移长度, 分析了4种不同界面滑移情况的疲劳迟滞回线. 假设正交铺设与编织陶瓷基复合材料疲劳迟滞回线主要受0°铺层、轴向纱线内纤维/基体界面滑移的影响, 预测了单向、正交铺设与编织陶瓷基复合材料在不同峰值应力与不同循环的疲劳迟滞回线, 与试验结果吻合.     

An experimental and analytical treatment of matrix cracking in cross-ply laminates

The development of damage in cross-ply Hercules AS4/3502 graphite/epoxy laminates has been investigated. Specific endeavors were to identify the mechanisms for initiation and growth of matrix cracks and to determine the effect of matrix cracking on the stiffness loss in cross-ply laminates. Two types of matrix cracks were identified. These include both straight and curved cracks. The experimental study of matrix crack damage revealed that the curved cracks formed after the straight cracks and followed a repeatable pattern of location and orientation relative to the straight cracks. Therefore, it was postulated that the growth mechanism for curved cracks is driven by the stress state resulting from the formation of the straight cracks. This phenomenon was analytically investigated by a finite-element model of straight cracks in a cross-ply laminate. The finite-element results provide supporting evidence for the postulated growth mechanism. The experimental study also revealed that the number of curved cracks increased with the number of consecutive 90-deg plies. Finally, experimental results show as much as 10-percent degradation in axial stiffness due to matrix cracking in cross-ply graphite/epoxy laminates.     

Dynamic compressive behavior of thick composite materials

The effect of strain rate on the compressive behavior of thick carbon/epoxy composite materials was investigated. Falling weight impact and split Hopkinson pressure bar systems were developed for dynamic characterization of composite materials in compression at strain rates up to 2000 s^–1. Strain rates below 10 s^–1 were generated using a servohydraulic testing machine. Strain rates between 10 s^–1 and 500 s^–1 were generated using the drop tower apparatus. Strain rates above 500 s^–1 were generated using the split Hopkinson pressure bar. Unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions, and cross-ply laminates were characterized. The 90-deg properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The 0-deg and cross-ply laminates show higher strength and ultimte strain values as the strain rate increases, whereas the modulus increnases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases, the dynamic stress-strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal direction and highest in the transverse direction.     

Interlaminar edge stress analysis of composite cross-ply flat specimens

Summary Interlaminar stresses in composite flat specimens are analysed by a method previously presented, apt to compute inertial and elastic properties of anisotropic beam. This method is based on the Virtual Work Principle (V. W.P.), and develops a finite element displacement formulation, extending the De Saint Vénant approach to anisotropic beams. In the present paper symmetric four cross ply flat laminates under uniaxial extension are considered, and the important role of the resin layer between two fibre plies is pointed out by means of a detailed stress analysis of interlaminar regions. Through the use of increasingly refined meshes the possible existence of singularities in the stress trend at the free edge is examined. The results obtained are shown to be in good accordance with those already available in the literature; furthermore the modellization of the interlaminar layer shifts the possible presence of a free edge singularity to the fibre ply/interlamina interface, showing on the contrary a non singular trend in stress field inside the interlaminar ply. This is important especially in view of the fact that, through this approach, natural boundary conditions are enforced at convergence by the V.W.P., without any a priori assumption.

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Sommario Si analizzano gli sforzi interlaminari di bordo in provini piani di materiale composito. Il metodo utilizzato si basa sul Principio dei Lavori Virtuali e sviluppa una formulazione ad elementi flniti, estendendo approccio di De Saint Vénant alle travi anisotrope. Si prendono in considerazione laminati piani simmetrici cross-ply a quattro strati sottoposti a estensione uniassiale e si mette in rilievo importante ruolo svolto dal sottile strato interlaminare di resina posto tra due stati di flbra. L'eventuale esistenza di singolarità nell'andamento degli sforzi al bordo libero viene esaminata attraverso I'uso di schematizzazioni via via più dettagliate. I risultati sembrano indicare la presenza di tali singolarità solo all'interno dello strato interlaminare limitatamente alla zona di interfaccia con lo strato di fibre a 90°. Infine si mostra come i risultati ottenuti siano in buon accordo con quelli ricavati da altri autori.

     

A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation

The present work focuses on the development of a physically-based model for large deformation stress-strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic-viscoplastic model of [Boyce et al., 1988] and [Boyce et al., 2000]. The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic-viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core-hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress-strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.     

Numerical simulation of interlaminar damage propagation in CFRP cross-ply laminates under transverse loading

This paper proposes a numerical simulation of interlaminar damage propagation in FRP laminates under transverse loading, using the finite element method. First, we conducted drop-weight impact tests on CFRP cross-ply laminates. A ply crack was generated at the center of the lowermost ply, and then a butterfly-shaped interlaminar delamination was propagated at the 90/0 ply interface. Based on these experimental observations, we present a numerical simulation of interlaminar damage propagation, using a cohesive zone model to address the energy-based criterion for damage propagation. This simulation can address the interlaminar delamination with high accuracy by locating a fine mesh near the damage process zone, while maintaining computational efficiency with the use of automatic mesh generation. The simulated results of interlaminar delamination agreed well with the experiment results. Moreover, we demonstrated that the proposed method reduces the computational cost of the simulation.     

The effect of stacking sequence on the impact-induced damage in cross-ply E-glass/epoxy composite plates

The aim of this study is to determine the damage mechanisms of unidirectional E-glass/epoxy laminated composites under localized impacts. The projectile velocities at low ranges (0.54–3.10 m/s) have been considered to establish a parametric analysis of clamped laminated composite responses. The used circular plates are symmetrical laminates which are composed of ten plies and have three different cross-ply stacking sequences: [0₂/90₆/0₂], [0₃/90₄/0₃] and [0₄/90₂/0₄]. They are subjected at their centers to an impact of an aluminum projectile which is applied in the transverse direction by using a drop weight machine. The time histories of the impactor acceleration, the projectile displacement and the plate deflection were measured. The analysis of the nature of the damage mechanisms and its relation to the structural responses has been performed. The identification of the matrix cracks and the delamination at the interfaces has allowed to determine the initiation and extension criteria of the damage.     

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题．针对金属－陶瓷功能梯度圆板,考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况,应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性振动微分方程．考虑周边夹支边界条件,利用伽辽金法得到了横向非线性固有振动方程,并确定了静载荷引起的静挠度．用改进的多尺度法求解强非线性方程,得出非线性固有频率表达式．通过算例,分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况．结果表明,非线性固有频率随金属含量的增加而降低;随转速和圆板厚度的增大而升高;随功能梯度圆板表面温度的升高而降低．     

2D编织陶瓷基复合材料应力-应变行为的试验研究和模拟

本文对2D编织陶瓷基复合材料拉伸应力-应变行为进行了试验研究和理论模拟。将2D编织结构简化为：正交铺层结构和纤维束波动结构。基于基体随机开裂、纤维随机断裂的统计分布理论,得到正交铺层结构的应力-应变关系;基于体积平均方法,将纤维束波动部分分割为若干子单元;由于纤维束的波动使各子单元材料方向与加载方向不一致,因此考虑了各子单元的线性行为和非线性行为对材料响应的影响,同时引入强度分析模型,得到纤维束波动部分的应力-应变关系。结合正交铺层部分和纤维束波动部分的应力-应变关系,得到2D编织结构的应力-应变行为,理论与试验吻合较好。     

二维编织陶瓷基复合材料应力-应变行为

对二维编织陶瓷基复合材料拉伸应力-应变行为进行了试验研究和理论模拟. 将二维 编织结构简化为：正交铺层结构和纤维束波动结构. 基于基体随机开裂、纤维随机断裂分布 理论,得到正交铺层结构的应力-应变关系;基于体积平均方法,将纤维束波动部分进行分割, 引入强度分析模型,得到纤维束波动部分的应力-应变关系. 结合正交铺层部分和纤维束波动 部分的应力-应变关系,得到二维编织结构的应力-应变行为,理论与试验吻合较好.     

Influence of Interlayer Defects on the Effective Elastic Properties of Cross-Ply Composites*

International Applied Mechanics - The problem of the effective elastic properties of a fiber-reinforced cross-ply composite material and imperfect contact between plies with orthogonal fiber...     

Discrete dislocation dynamics modelling of mechanical deformation of nickel-based single crystal superalloys

Discrete dislocation dynamics (DDD) has been used to model the deformation of nickel-based single crystal superalloys with a high volume fraction of precipitates at high temperature. A representative volume cell (RVC), comprising of both the precipitate and the matrix phase, was employed in the simulation where a periodic boundary condition was applied. The dislocation Frank-Read sources were randomly assigned with an initial density on the 12 octahedral slip systems in the matrix channel. Precipitate shearing by superdislocations was modelled using a back force model, and the coherency stress was considered by applying an initial internal stress field. Strain-controlled loading was applied to the RVC in the [0 0 1] direction. In addition to dislocation structure and density evolution, global stress-strain responses were also modelled considering the influence of precipitate shearing, precipitate morphology, internal microstructure scale (channel width and precipitate size) and coherency stress. A three-stage stress-strain response observed in the experiments was modelled when precipitate shearing by superdislocations was considered. The polarised dislocation structure deposited on the precipitate/matrix interface was found to be the dominant strain hardening mechanism. Internal microstructure size, precipitate shape and arrangement can significantly affect the deformation of the single crystal superalloy by changing the constraint effect and dislocation mobility. The coherency stress field has a negligible influence on the stress-strain response, at least for cuboidal precipitates considered in the simulation. Preliminary work was also carried out to simulate the cyclic deformation in a single crystal Ni-based superalloy using the DDD model, although no cyclic hardening or softening was captured due to the lack of precipitate shearing and dislocation cross slip for the applied strain considered.     

Shear strains in a graphite/PEEK beam by moiré interferometry with carrier fringes

A multispan quasi-isotropic graphite-PEEK beam exhibited dramatic shear strains in the interlaminar region between plies. Shear strains in the plies themselves varied in basic accord with fiber direction. The large anomalous shear strains were developed near the center of the beam height, where shear stresses were large. High-sensitivity moiré interferometry with 2400l/mm (60,960l/in.) was used. A new technique of data extraction was developed, using carrier fringes to transform the pattern to one in which fringe slopes are proportional to derivatives of displacement. This technique enhanced detection and measurement of highly localized shear-strain gradients. Paper was presented at the 1986 SEM Fall Conference on Experimental Mechanics held in Keystone, CO on Nov. 2–5.     

Interlaminar hygrothermal stresses in laminated plates

Within the elasticity formulation the most general displacement field for hygrothermal problems of long laminated composite plates is presented. The equivalent single-layer theories are then employed to determine the global deformation parameters appearing in the displacement fields of general cross-ply, symmetric, and antisymmetric angle-ply laminates under thermal and hygroscopic loadings. Reddy’s layerwise theory is subsequently used to determine the local deformation parameters of various displacement fields. An elasticity solution is also developed in order to validate the efficiency and accuracy of the layerwise theory in predicting the interlaminar normal and shear stress distributions. Finally, various numerical results are presented for edge-effect problems of several cross-ply, symmetric, and antisymmetric angle-ply laminates subjected to uniform hygrothermal loads. All results indicate high stress gradients of interlaminar normal and shear stresses near the edges of laminates.