Damage in composite laminates: Effects of transverse cracks

Two different methods of solution are used to study the effects of transverse cracks in cross-ply composite laminates. The results of an approximate analytical solution are compared with those obtained using a finite element analysis in order to study the effects of transverse cracks on the degradation of elastic and thermal coefficients as well as stress distributions. In particular, it is shown that transverse cracks cause significant degradation of the Poisson's ratio and shear modulus of the laminates, and also affect some stress distributions in a peculiar manner. Theoretical results are compared with existing experimental results where appropriate.     

Overall moduli and natural frequencies of composite laminates containing multiple interlaminar transverse cracks

In this paper, the overall tensile modulus of a composite laminate containing embedded multiple interlaminar transverse cracks is studied. The modulus is calculated based upon an energy method and the crack opening displacement which is obtained by solving a boundary-value problem. Numerical computation is applied to fibre-reinforced composite laminates following the theoretical analysis. The theoretical prediction is compared with the experimental data, and good agreement is found. The solution is then used to examine the natural frequencies of two representative cross-ply beams with multiple matrix cracks in some of the outer transverse layers. The difference between the natural frequencies of the intact and the damaged cross-ply beams is presented. It is found that for a graphite/epoxy composite, the multiple transverse cracks only have a minor influence on the frequency, whereas for a glass/epoxy composite, the multiple cracks may have a significant influence on the frequency when the cracks reach the saturation level in a relatively large area of a beam.     

Analysis of the transverse cracking in hybrid cross-ply composite laminates

A modified shear-lag analysis, taking into account the concept of interlaminar shear stress, is employed to evaluate the effect of transverse cracks on the stiffness reductions in different glass/epoxy and graphite/epoxy hybrid cross-ply laminates. The modified shear-lag model is proposed that assumes interlaminar adhesive layer between two neighbouring layers transferring not only interlaminar shear stress but also normal stress. The stress distribution is solved by the used model which rigorously satisfies the stress equilibrium equations, boundary conditions and the traction continuity at interfaces between layers.     

Engineering expressions for thermo-elastic constants of laminates with high density of transverse cracks

Thermo-elastic constants of symmetric and balanced laminates with intralaminar cracks in 90-layers depend on the opening displacement (COD) of the crack. The COD dependence on the interaction between cracks in the same layer is studied using FEM. The COD dependence on crack density is described by interaction function in form of tanh(). This interaction function multiplied with COD of non-interactive crack is the input parameter in analytical model for thermo-elastic properties of damaged symmetric and balanced laminates. Predictions performed for cross-ply laminates with cracks in inside and in surface layers and for quasi-isotropic laminates with different position of the 90-layer are in a very good agreement with direct FEM calculations.     

Lamb wave evaluation and localization of transverse cracks in cross-ply laminates

This paper investigates the effect of transverse cracks on the S ₀ mode velocity in GFRP and CFRP cross-ply laminates, and proposes a new AE source location method that considers the change in the S ₀ mode velocity due to the transverse cracks. We found experimentally that the stiffness and the velocity decreased as the transverse crack density increased. Analytical predictions deduced from the combination of the complete parabolic shear-lag analysis, the classical plate theory and the laminated plate theory are in good agreement with the experimental results. Utilizing this relationship between the velocity and the mechanical damage, we located AE sources of transverse cracks in cross-ply laminates with the calculated in situ velocity. We were able to show that highly accurate source location requires the reduction of the in situ value of the velocity. The present method is simple but quantitative and useful in health-monitoring for detecting and localizing the damage in composite structures.     

基于Puck理论的复合材料层合板横向剪切失效分析

针对复合材料层合板三维失效分析问题,建立了一种基于Puck失效准则的分析模型。针对Puck失效理论中的基体失效,分别采用遍历法和分区黄金分割法（PGSS）的一维搜索算法预测了不同应力状态下基体失效的断裂面角度,并对比分析了两种算法的计算精度和计算效率。研究表明,PGSS具有较高的搜索精度和搜索效率。在ABAQUS有限元分析平台下,编写了基于Puck失效准则的VUMAT显式用户自定义材料子程序,对复合材料层合板横向（G₂₃）剪切性能进行了数值预测和渐进失效分析,并与试验载荷-位移曲线、DIC测得的应变场及破坏模式进行了对比。分析结果表明:当前的分析模型能较好地预测复合材料层合板G₂₃剪切试验的力学响应和破坏模式。      

Stress distribution in damaged composite laminates under transverse impact

Studies on damage in composite laminates subjected to central and normal impact are conducted by a 3-D finite element analysis. The stress analysis is carried out by developing a constitutive equation of composite laminates coupled with the damage. Effects of the damage on the stress distribution in the laminates are investigated in details. The obtained contact force history correlates well with the results reported in literatures. Stress distributions across the thickness of the elastic non-damaged laminate show a probable distribution of delamination. The simulated result for delamination is coincided with the observation of experiments. Stress distributions for the damaged laminates show that the damage releases strain energy and lessens stress concentration.     

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

Fractographic study of transverse cracks in a fibre composite

Transverse fracture of unidirectional fibre composites was studied in a model glass/epoxy composite in which 1 mm-diameter rods had been used in place of fibres. The fracture surface resulting from transverse cracking in this model system was studied by scanning electron microscopy (SEM). The interaction of the crack with the epoxy matrix resin and the glass rods was the following: Cracks in the resin appeared to have effected a debonding at the glassmatrix interface before reaching the glass. The debonding then propagated along the interface and induced secondary cracks ahead of the primary debonding crack. The confluence of the secondary and primary cracks resulted in sharp ridges being formed on the matrix resin surface, produced by plastic deformation of the rigid epoxy resin. These appeared as a field of parabolic marks. Considering the brittleness of the resin, the amount of plastic deformation indicated by the ridges was astonishing. As the debonding continued around the glass rod, a transverse corrugated texture developed on the resin surface, again produced by plastic deformation. Finally, the cracks reentered the matrix from small patches of polymer adhering especially strongly to the glass surface. The overall fracture energy of transverse cracking of unidirectional fibre composites is suggested to consist, therefore, of the following elements in addition to crack propagation in the matrix resin: (a) the glass-resin debonding before the incoming cracks reach the glass, (b) the initiation of secondary cracks or debonds at the interface, (c) the plastic deformation in generating the ridges on the rigid resin surface, appearing both as the paraboloids and the transverse corrugation, and (d) cracking of the matrix reinitiated at the opposite side of the glass. The use of an enlarged glass reinforcement in this study provided a more direct observation of the properties of transverse crack propagation in composite materials than would have been possible with the small, roughly 10m fibres.     

Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model to estimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loads varied with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracture toughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, the fracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantly at cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.     

Damage characterization in thin-ply composite laminates under out-of-plane transverse loadings

Composite laminates with thin-ply layers are expected to exhibit superior damage resistance to the standard composite laminates. This study investigated the damage characteristics of carbon fiber/toughened epoxy thin-ply laminates subjected to transverse loadings. Quasi-isotropic laminates were prepared using both standard prepregs and thin-ply prepregs in order to examine the effect of ply thickness on the damage accumulation processes. Clear difference on damage accumulation process between standard laminates and thin-ply laminates was identified; fiber fractures were susceptible to formation in thin-ply laminates. Finally, the reason of the difference on damage process was investigated using finite element analyses, and it was clarified that the accumulated delamination position has a significant effect on the fiber fractures during the indentation.     

Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates

In previous papers the microscopic failure process of (0/90_n/0) (n = 4,8,12) cross-ply laminates was investigated. Progressive damage parameters, such as the transverse crack density and the delamination ratio, were measured. A simple modified shear-lag analysis including the thermal residual strains was conducted to predict the transverse crack density and the delamination length. The analysis did not consider the interaction between the transverse cracks and the delamination. In the present paper, a prediction is presented for the transverse crack density including the effect of delamination growth. The prediction shows better agreement with the experimental results, especially for laminates with thicker 90 ° plies in which extensive delamination occurs.

Loading/unloading tests have also been performed to obtain the Young's modulus reduction and the permanent strain as functions of the damage state. The shear-lag predictions of the Young's modulus reduction and the permanent strain are compared with the experimental data. Better agreement is obtained when the interaction between transverse cracks and delamination is considered.     

Effects of damage thresholds on stresses in composite laminates under transverse impact

Studies on stresses and damage in fiber reinforced polymeric matrix composite laminates subjected to transverse impact are conducted by a 3D finite element analysis. The stress analysis is carried out by developing a constitutive equation including damage variables, therefore, effects of damage and damage thresholds on the stresses in the laminates can be investigated. Effects of damage threshold of matrix materials on stresses suggest suitable matrix materials for composite laminates, which could improve damage tolerance of the composite laminates, and resistance of the composite laminates to impact could be improved significantly by increasing the damage threshold.     

Dynamics of anisotropic composite cantilevers weakened by multiple transverse open cracks

In this paper an exact solution methodology, based on Laplace transform technique enabling one to analyze the bending free vibration of cantilevered laminated composite beams weakened by multiple non-propagating part-through surface cracks is presented. Toward determining the local flexibility characteristics induced by the individual cracks, the concept of the massless rotational spring is applied. The governing equations of the composite beam with open cracks as used in this paper have been derived via Hamilton's variational principle in conjunction with Timoshenko's beam model. As a result, transverse shear and rotatory inertia effects are included in the model. The effects of various parameters such as the ply-angle, fiber volume fraction, crack number, position and depth on the beam free vibration are highlighted. The extensive numerical results show that the existence of multiple cracks in anisotropic composite beams affects the free vibration response in a more complex fashion than in the case of beam counterparts weakened by a single crack. It should be mentioned that to the best of the authors' knowledge, with the exception of the present study, the problem of free vibration of composite beams weakened by multiple open cracks was not yet investigated.