Mechanisms of Internal Damage and Their Effect on the Behavior and Properties of Cross-Ply Composite Laminates

This paper is a review of experimental and theoretical studies into the damage mechanisms in glass/epoxy and carbon/epoxy cross-ply composite laminates subjected to static or cyclic loading and their influence on the behavior and stiffness properties of such laminates. How the equivalent-constraint model is applied to the analysis of cross-ply laminates with transverse and longitudinal matrix cracks and crack-tip delaminations is shown and discussed.     

基体开裂的正交复合材料对称层合板的粘弹性力学行为

本文讨论了含有均匀基体裂纹的正交复合材料对称层合板的线性粘弹性力学行为.采用二维剪切滞后模型并对其层间剪应力在厚度方向进行线性假设分布,求得层合板的平均应力应变的线弹性解,利用等效约束模型和经典层合理论可得到层合板因为含有基体裂纹而所引起的刚度退化现象.在弹性-粘弹性对应原理的基础上对其层合板的线粘弹性进行了讨论和研究.结果表明:层合板的松弛模量和蠕变泊松比随着时间的增加而减少,到达稳态后其值基本上是恒值.并跟Zocher的解析解和有限元数值解作了比较,发现结果非常吻合.     

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.     

复合材料刚度性能表征的协同损伤力学模型

针对复合材料层合板的弥散型损伤,提出一个刚度性能表征的协同损伤力学模型. 该模型兼顾了微观物理损伤响应和宏观材料刚度性能表征. 从微观角度,建立细观RVE 模型求解裂纹表面张开位移和滑开位移,以此定义损伤张量,并在宏观上通过对材料应变和损伤表面位移进行均匀化处理,建立单向板或层合板的损伤刚度矩阵和损伤张量之间的联系. 以基体裂纹为例,详细分析并建立了横向裂纹和纵向裂纹的损伤本构. 计算了[±θ/90₄]_S 铺层层合板中基体横向裂纹对刚度性能的影响,结果表明该方法能够准确地预测复合材料层合板由损伤导致的刚度性能衰减.      

Effects of Environmental Degradation on Flexural Failure Strength of Fiber Reinforced Composites

Fiber-reinforced composite laminates are often used in harsh environments that may affect their long-term durability as well as residual strength. In general, environmental degradation is observed as matrix cracking and erosion that leads to deterioration of matrix-dominated properties. In this work, cross-ply laminates of carbon fiber reinforced epoxy were subjected to environmental degradation using controlled ultraviolet radiation (UV) and moisture condensation and the post-exposure mechanical properties were evaluated through elastic modulus and failure strength measurements. Additionally, both degraded and undegraded were subjected to cyclic fatigue loading to investigate possible synergistic effects between environmental degradation and mechanical fatigue. Experimental results show that the degradation results in reduced failure strength. Greater effects of degradation are observed when the materials are tested under flexural as opposed to uniaxial loading. Based on strength measurements and scanning electron microscopy, we identified various damage modes resulting from exposure to UV radiation and moisture condensation, and cyclic loading. The principal mechanisms that lead to reduction in mechanical properties are the loss of fiber confinement due to matrix erosion, due to UV radiation and moisture condensation, and weakened/cracked ply interfaces due to mechanical fatigue. An empirical relationship was established to quantify the specific influence of different damage mechanisms and to clarify the effects of various degradation conditions.     

A novel technique for time-resolved detection and tracking of interfacial and matrix fracture in layered materials

A novel experimental technique is developed for time-resolved detection and tracking of damage in the forms of delamination and matrix cracking in layered materials such as composite laminates. The technique is non-contact in nature and uses dual or quadruple laser interferometers for high temporal resolution. Simultaneous measurements of differential displacement and velocity at individual locations are obtained to analyze the initiation and progression of interfacial fracture and/or matrix cracking/delamination in a polymer matrix composite laminate system reinforced by graphite fibers. The measurements at multiple locations allow the speeds at which interfacial crack front (mode-I) or matrix cracking/delamination front (mode-II dominated) propagates to be determined. Experiments carried out use three-point bend configurations. Impact loading is achieved using a modified Kolsky bar apparatus with a complete set of diagnostics for load, deformation, deformation rate, and input energy measurement. This technique is used to characterize the full process of damage initiation and growth. The experiments also focused on the quantification of the speed at which delamination or damage propagates under primarily mode-I and mode-II conditions. The results show that the speed of delamination (mode-I) or the speed of matrix cracking/delamination (primarily mode-II) increases linearly with impact velocity. Furthermore, speeds of matrix failure/delamination under primarily mode-II conditions are much higher than the speeds of mode-I crack induced delamination under mode-I conditions.     

Matrix crack initiation and progression in compositelaminatessubjected to bending and extension

An experimental investigation of matrix crack initiation and progression inglass/epoxy laminates of differentstacking sequences is presented. The laminates have beenloaded in extension and bending, and the degree ofdamage as function of the load has beenrecorded. The changes in certain elastic properties caused by the damagewere also measured, andare compared to results from a previously developed approximate analytic model. Anenergyrelease rate resistance curve is adopted in an attempt to describe the initiation and progression ofmatrixcracks in the laminates. The amount of cracking is also viewed in relation to the straintransverse to the fibres inthe ply under consideration, and the ply stresses at the onset of crackingare calculated. The different damageevolution criteria are compared to the experimental results,and their validity and reliability are discussed. By use ofthe ply strain transverse to the fibres as acritical parameter for damage evolution, the load–deformation curves ofthe tested laminates aresimulated taking damage progression into account.     

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.     

Mixed-mode failure of composite laminates with cracks

The behavior of quasi-isotropic graphite/epoxy laminates with cracks subjected to various biaxial-stress fields was studied experimentally. This was accomplished by uniaxial tensile loading of specimens with cracks of various orientations with the loading axis. It was found that the critical stress-intensity factor, based on a projected crack length increased by a characteristic damage dimension, is nearly constant with stress biaxiality and initial crack length. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

PREDICTIVE APPROACH TO FAILURE OF COMPOSITE LAMINATES WITH EQUIVALENT CONSTRAINT MODEL

<正>This work established a new analytical model based upon the equivalent constraint model(ECM)to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading,by taking into account the effect of matrix cracking.The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate.Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates,is introduced for the construction of the failure criterion. The effects of lamina properties,lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper.A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems.The theory predictions demonstrated great match with the experimental observations investigated in this study.     

Experimental and analytical comparisons of failure in thermoplastic composite laminates

Failure characteristics of Gr/PEEK were studied, using an experimental investigation and a fully nonlinear ply-by-ply finite-element technique. The stacking sequence of the laminates (with centrally located holes) investigated were: 0, 90, ±45 deg, (0/45/90/−45 deg)_2s and (0±45/90 deg)_2s. The [0 deg] laminate failure was characterized by splitting at the extremities of the hole and along the fibers. The [90 deg] laminates failed in the transverse direction, whereas the [±45 deg] laminates exhibited considerable elongation to failure. In the case of the quasi-isotropic laminates, the failure progression appeared to be due dominantly to matrix cracking followed by fiber failure. Analytical predictions of the failure process showed reasonably good correlation with the experimentally determined data.     

Modelling matrix damage and fibre–matrix interfacial decohesion in composite laminates via a multi-fibre multi-layer representative volume element (MRVE)

A three-dimensional multi-fibre multi-layer micromechanical finite element model was developed for the prediction of mechanical behaviour and damage response of composite laminates. Material response and micro-scale damage mechanism of cross-ply, [0/90]_ns, and angle-ply, [±45]_ns, glass-fibre/epoxy laminates were captured using multi-scale modelling via computational micromechanics. The framework of the homogenization theory for periodic media was used for the analysis of the proposed ‘multi-fibre multi-layer representative volume element’ (M²RVE). Each layer in M²RVE was represented by a unit cube with multiple randomly distributed, but longitudinally aligned, fibres of equal diameter and with a volume fraction corresponding to that of each lamina (equal in the present case). Periodic boundary conditions were applied to all the faces of the M²RVE. The non-homogeneous stress–strain fields within the M²RVE were related to the average stresses and strains by using Gauss’ theorem in conjunction with the Hill–Mandal strain energy equivalence principle. The global material response predicted by the M²RVE was found to be in good agreement with experimental results for both laminates. The model was used to study effect of matrix friction angle and cohesive strength of the fibre–matrix interface on the global material response. In addition, the M²RVE was also used to predict initiation and propagation of fibre–matrix interfacial decohesion and propagation at every point in the laminae.     

On the description of anisotropic damage in composite laminates

A general anisotropic damage theory of cracked laminates is formulated here. The deformation of composite laminates is composed of matrix elastic strains, pseudo-elastic damage strains due to cracking and permanent damage strains due to interlaminar slip. The surface of damage initiation is constructed according to the concept of linear elastic fracture mechanics for the virgin material. After the initial damage, a pesudo-elastic damage can be used to describe the damage behaviour if interlaminar slip is negligible. Damage evolution, load induced anisotropy and interlaminar intralaminar interaction for composite laminates are examined; the latter can perturb the normality structure of damage strain rate. Explicit expressions are given for pseudo-elastic (or secant) moduli of the damaging composite laminates, under a non-interacting assumption imposed on the cracks between different families.     

用改进的揭层技术研究含表面裂纹层压板的损伤

本文对揭层技术进行了改进,作为标记溶液的氯化金乙醚溶液用硝酸铜酒精溶液代替,并改进了标记溶液的渗透方法,采用改进了的揭层技术,对含表面裂缝正交铺层玻璃纤维/环氧层压板的损伤形貌进行了检测,并分别对表面裂缝的裂缝面形状和深度对损伤形貌的影响进行了探讨。结果表面,新的揭层枝术是方便而有效的,同时所得结果是有意义的。     

纤维/金属网增强层板低速冲击损伤机理和演化

本文首先通过落锤低速冲击实验测试了纯玻璃纤维增强环氧树脂复合材料和304不锈钢丝网(SSWM)/玻璃纤维混杂复合材料的力学性能,探究了SSWM嵌入数量对混杂复合材料抗冲击性能的影响．随后采用Abaqus有限元软件建立了混杂复合材料的低速冲击模型,分别采用三维Hashin失效准则和Jason-Cook破坏准则模拟了纤维/基体和SSWM的损伤;建立了基于表面接触的内聚力模型来模拟界面分层;编写了VUMAT用户子程序定义混杂复合材料层合板的渐进失效过程．结果表明：相较于纯玻璃纤维增强环氧树脂层合板,SSWM/玻璃纤维混杂增强环氧树脂层合板的抗冲击性能更优,其中铺层形式为铺层III的混杂复合材料抗冲击性能最佳．通过对比发现有限元仿真结果与实验结果吻合良好,表明建立的模型适用于SSWM/玻璃纤维混杂增强环氧树脂复合材料低速冲击损伤的评估．通过分析仿真结果发现混杂复合材料的低速冲击损伤主要是冲击区域的纤维断裂、基体破坏和层间分层;SSWM通过吸收和传递冲击能量从而提升了混杂复合材料的抗冲击性能．     

充液弯管连续/离散模型振动的动刚度解法

由充液弯管三维振动模型切入,应用动刚度法构建了弯管及直管单元的振动求解方法,进而用于组装求解充液管系的振动,可同时适用于含弯管单元的连续模型或只含直管单元的离散模型;通过算例对比,证明动刚度法比传递矩阵法和有限元法在计算效率和精度上有所提升;与充液L型管道振动实验测得的加速度频响曲线对比,验证了本文对于管道组装的计算方法的有效性,此外还分析了连续模型和离散模型的区别及适用范围。     

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.     

Interlaminar fracture toughness of graphite/epoxy composite under mixed-mode deformations

An antisymmetric test fixture is employed to investigate interlaminar fracture behavior in graphite/epoxy composite material under mixed-mode deformations. Finite correction factors for the graphite/epoxy fracture specimen with various crack lengths are used to determine the interlaminar fracture toughness by finite-element stress analysis. Interlaminar fracture characteristics of graphite/epoxy composite material under mode-I, mode-II and mixed-mode deformations are evaluated experimentally. A mixed-mode fracture criterion is also investigated to obtain information on mixedmode interlaminar fracture behavior of graphite/epoxy composite material.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Strength or toughness? A criterion for crack onset at a notch

Both energy and stress criteria are necessary conditions for fracture but neither one nor the other are sufficient. Experiments by Parvizi et al. on transverse cracking in cross-ply laminates corroborate this assumption. Thanks to the singularity at the tip of the notch, the incremental form of the energy criterion gives a lower bound of admissible crack lengths. On the contrary, the stress criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation. It enjoys the desirable property of coinciding with the usual Griffith criterion to study the crack growth and with the stress criterion for the uniform traction along a straight edge. Comparisons with experiments carried out on homogeneous notched materials and on bimaterial structures show a good agreement.