Thermoelastic analysis of the asymmetries of interfacial embedded delamination characteristics in laminated FRP composites

This paper presents two sets of full three-dimensional thermoelastic finite element analyses of superimposed thermo-mechanically loaded FRP composite laminates with embedded interfacial elliptical delaminations, emphasizing the influence of residual thermal stresses and material anisotropy on the delamination fracture behavior characteristics. Modified crack closure integral (MCCI) methods based on the concepts of linear elastic fracture mechanics (LEFM) have been used as a meaningful tool to calculate the individual modes of strain energy release rates from the thermoelastic stress and displacement fields due to a combined thermal and a quasi-static impact loading. Residual stresses developed due to the thermoelastic anisotropy of the laminae are found to strongly influence the delamination onset and propagation characteristics, which have been reflected by the asymmetries in the nature of energy release rate plots and their significant variation along the delamination front.     

含分层损伤大层数复合材料层合板层间热效应分析

在机械载荷和热载下对含分层损伤大层数复合材料层合板采用三维有限元法分析其后屈曲行为。这种有限元的特点是每个单元可包含多个具有不同铺设角、不同组分材料的铺层。在分析中引入接触元来防止层间的闭合接触效应,并进一步分析了分层前缘的能量释放率。结果表明温度对于复合材料层合板的层间破坏有重要影响。     

Effect of delamination face overlapping on strain energy release rate calculations

The strain energy release rate is often used as a fracture mechanics parameter to describe delamination propagation and onset in composites, and is conveniently evaluated using finite element analysis. A common problem encountered in analysis is overlapping (interpenetration) of the delamination faces if these faces are not constrained. This paper examines the effect of overlapping on strain energy release rate calculated using the virtual crack closure method in conjunction with 3-dimensional anisotropic finite element analysis. A bilinear gap element was used between the delamination faces to prevent these faces from overlapping. Three problems were studied: (1) laminates with an embedded crack and embedded delaminations; (2) laminates with free edge delaminations; and (3) end-notched flexure specimens. The results of this investigation indicated that overlapping has a significant effect on the component values of G_I and G_II as well as on the total strain energy release rate. It was also found that end effects can create non-uniform energy release rates along the crack front in edge delamination problems due to twisting of the sublaminate with unsymmetrical lay-up, so that 3-dimensional finite element analysis is required.     

Mode III fatigue delamination growth of glass fiber reinforced polymer woven laminates at cryogenic temperatures

This paper investigates the cryogenic fatigue delamination behavior of glass fiber reinforced polymer woven laminates under Mode III loading. Fatigue delamination tests were conducted using split cantilever beam specimens at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). A finite element analysis was also employed to calculate the energy release rate. The temperature dependence of the fatigue delamination growth rate vs. energy release rate range is discussed. Fracture surfaces were examined by scanning electron microscopy to identify the delamination mechanisms under fatigue loading. The important conclusion we reach is that the Mode III fatigue delamination growth rates of woven laminates at cryogenic temperatures are lower than that at room temperature.     

Cryogenic Interlaminar Fracture Properties of Woven Glass/Epoxy Composite Laminates Under Mixed-Mode I/III Loading Conditions

We characterize the combined Mode I and Mode III delamination fracture behavior of woven glass fiber reinforced polymer (GFRP) composite laminates at cryogenic temperatures. The eight-point bending plate (8PBP) tests were conducted at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K) using a new test fixture. A three-dimensional finite element analysis was also performed to calculate the energy release rate distribution along the delamination front, and the delamination fracture toughnesses were evaluated for various mixed-mode I/III ratios. Furthermore, the microscopic examinations of the fracture surfaces were carried out with scanning electron microscopy (SEM), and the mixed-mode I/III delamination fracture mechanisms in the woven GFRP laminates at cryogenic temperatures were assessed. The fracture properties were then correlated with the observed characteristics.     

Delamination growth mechanisms in woven glass fiber reinforced polymer composites under Mode II fatigue loading at cryogenic temperatures

The purpose of this research is to characterize the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates subjected to Mode II fatigue loading. Mode II fatigue delamination tests were performed at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K) using the four-point bend end-notched flexure (4ENF) test method, and the delamination growth rate data for the woven GFRP laminates were obtained. The energy release rate range was determined by the finite element method. Microscopic examinations of the specimen sections and fracture surfaces were also carried out. The present results are discussed to obtain an understanding of the fatigue delamination growth mechanisms in the woven GFRP laminates under Mode II loading at cryogenic temperatures.     

带脱层复合材料层板的低速冲击响应

研究了含脱层损伤的复合材料层板在低速冲击下的瞬态响应问题。首先,用基于Mindlin板理论的有限元法来描述层板的运动和变形,并同时考虑了层板大变形的影响。另外,用一种修正的Hertzian压痕法则来计算层板和刚球间的冲击力。同时为了有效地处理脱层间的动态接触问题,采用了由笔者以前提出的一种修正的Lagrange multiplier乘子法来提高计算精度和效率;为了研究脱层的扩展机理,提出了一种基于Mindlin板模型的应变能释放率的计算方法,用于计算脱层前沿的应变能释放率的分布。最后,算例研究了刚球的初始冲击速度、脱层面积和脱层位置对计算结果的影响,算例中提供的信息为人们更好地理解脱层损伤的扩展机理和它对复合材料层板的低速冲击响应的影响提供了依据。     

Mode III Interlaminar Fracture Behavior of Glass Fiber Reinforced Polymer Woven Laminates at 293 to 4 K

This paper deals with mode III delamination properties of glass fiber reinforced polymer woven laminates at room temperature (293 K), liquid nitrogen temperature (77 K), gas helium temperature (20 K), and liquid helium temperature (4 K). In order to evaluate these properties, the Split Cantilever Beam (SCB) fracture test is performed. The load is applied to a test specimen through a set of identical grips in order to reduce (in some degree) the mode II loading at the free edges. A three-dimensional finite element analysis is used to study the stress and strain state of the specimens and to interpret the experimental measurements. The strain energy release rate is calculated by using the virtual crack closure technique. It is found that the strain energy release rate is dominated by the mode III component. A non-uniform distribution of the strain energy release rate along the delamination front is obtained with mode III component having maximum at the center of the delamination front, while mode II component increases towards the free edges. The strain energy release rate is also determined using the crack closure technique. A finite element analysis is also carried out to calculate the stress intensity factors for the SCB specimens. The fracture surfaces are examined by scanning electron microscopy to identify the fracture mechanisms. The most important conclusion from the present study is that at temperature lowering from 293 to 20 K the mode III fracture toughness increases, further cooling to 4 K produces a toughness decrease.     

Characterization of the interlaminar fracture toughness of a laminated carbon/epoxy composite

Delamination between layers is an important problem in applications of fiber reinforced composite laminates. Tests were carried out to determine the interlaminar fracture toughness of AS4/3501-6 (carbon/epoxy) composite laminates using mixed-mode bending tests. Analysis of the test specimens in terms of mode I and mode II energy release rates showed good agreement between methods based on beam equations, compliance measurements, and detailed finite element analyses. The results showed that the critical mode I energy release rate for delamination decreased monotonically with increasing mode II loading. This is in contrast to some results in the literature. Various analytic representations of the mode interaction from the literature were compared, and shown to fit the data with reasonable accuracy.     

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.     

Delamination vs matrix cracking in layered composites subjected to transverse loading

An algorithm is presented to compute the distribution of the strain energy release rate along the crack front of a penny-shaped delamination in a layered orthotropic body. The method applies a finite element recently proposed for three-dimensional analysis of layered orthotropic circular plates. The algorithm is economical even though it treats a full three-dimensional state of stress. The method requires only a single virtual crack extension to accurately compute the strain energy release rate at a point along the crack front. The method is applied to the study of delamination crack growth in a nine layer cross-ply laminate. The variation of strain energy release rate, G, along the crack front, is determined. The significance of the plate aspect ratio, as well as length scale, on the fracture process is studied. The establishment of a loading case where a distributed transverse compressive loading causes delamination growth is given.     

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.     

Fatigue delamination growth in woven glass/epoxy composite laminates under mixed-mode II/III loading conditions at cryogenic temperatures

We investigate the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode II/III fatigue loading. Fatigue delamination tests were conducted with six-point bending plate (6PBP) specimens at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), and the delamination growth rate data for various mixed-mode ratios of Modes II and III were obtained. The energy release rate was evaluated using the three-dimensional finite element method. In addition, the fatigue delamination growth mechanisms were characterized by scanning electron microscopic observations of the specimen fracture surfaces.     

Ranking of laminates for edge delamination resistance

Edge delamination is a problem of some concern in laminated fibre composites. In the present study, energy release rates for potential edge delamination propagation are calculated using finite element techniques, for various stacking sequences of quasi-isotropic laminates under tension loading. Gap elements are included in the calculations to prevent non-physical material interpenetration that can occur in calculations. The results permit a ranking of stacking sequences based on minimizing the energy release rate. Experiments show that the newer, high toughness resin systems are effective in reducing strength loss associated with edge delamination under monotonic loading.     

Effect of damage levels and curing stresses on delamination growth behaviour emanating from circular holes in laminated FRP composites

This paper deals with the study of the effect of drilling induced delamination damage levels and residual thermal stresses (developed during manufacturing process of cooling the laminate form curing temperature to room temperature) on delamination growth behaviour emanating form circular holes in graphite/epoxy laminated FRP composites. Two sets of full three dimensional finite element analyses (one with the residual thermal stresses developed while curing the laminate and the other without residual thermal stresses i.e. with mechanical loading only) have been performed to calculate the displacements and interlaminar stresses along the delaminated interfaces responsible for the delamination onset and propagation. Modified crack closure integral (MCCI) techniques based on the concepts of linear elastic fracture mechanics (LEFM) have been used to calculate the distribution of individual modes of strain energy release rates (SERR) to investigate the interlaminar delamination initiation and propagation characteristics. Asymmetric variations of SERR obtained along the delamination front are caused by the overlapping stress fields due to the coupling effect of thermal and mechanical loadings. It is found that parameters such as ply orientation, drilling induced damage levels and material heterogeneity at the delaminated interface dictate the interlaminar fracture behaviour of laminated FRP composites.     

Crack-tip force method for computing energy release rate in delaminated plates

A new method called the crack-tip force method (CTFM) is derived for computing the energy release rate in delaminated beams and plates. In this method the delaminated plate is divided into two laminates on either side of the plane of delamination. The interaction forces, called crack-tip forces, between the sub-laminates at the crack-tip are computed. The energy release rate is expressed as a quadratic function of the crack-tip forces and the plate compliance coefficients. The CTFM is compared to the virtual crack closure technique (VCCT) as well as to a previously derived method called the strain energy density method using double cantilevered beam specimens as examples. The CTFM is found to be very efficient as the crack-tip forces are part of the solution of finite element analysis of delaminated plates, and they can be readily used to compute the point-wise energy release rate along the delamination front.     

The influence of ply sequence and thermoelastic stress field on asymmetric delamination crack growth behavior of embedded elliptical delaminations in laminated FRP composites

The influence of ply lay up and the interaction of residual thermal stresses and mechanical loading on the interlaminar asymmetric embedded delamination crack growth behavior have been investigated. Two sets of full three-dimensional thermo-elastic finite element analyses have been performed for the interlaminar elliptical delaminations, which may be due to manufacturing defects or other reasons and are located symmetrically with respect to the midplane in a quasi-isotropic FRP composite laminate lay up. Depending upon the through-the-thickness location of the embedded elliptical delaminations, four different laminate configurations have been considered. Strain energy release rate (SERR) procedures have been employed to assess the delamination crack growth characteristics at the interfaces. It is found that the individual fracture modes exhibit asymmetric and non self-similar crack growth behavior along the delamination front depending upon the location of the interfacial delaminations; ply sequence and orientation and thermo-elastic anisotropy of the laminae.     

吸湿后复合材料层合板快速加热分层扩展数值模拟

为研究复合材料层合板吸湿后的分层现象,首先建立了吸湿后复合材料层合板快速加热导致分层损伤的有限元模型,并对ABAQUS有限元软件进行二次开发,通过UAMP子程序模拟吸湿后复合材料快速加热时水分汽化引起的局部高压载荷作用下层合板分层扩展与载荷施加过程;然后,采用该模型预测了饱和吸湿T650-35/HFPE-II-52碳纤维聚酰亚胺复合材料层合板快速加热至310 ℃时产生的分层现象,并将数值模拟与文献实验结果对比;最后,运用该模型分析了树脂吸湿量和富脂区树脂聚集体积对层合板分层损伤面积的影响。结果表明:建立的有限元模型有效;快速加热后,层合板的分层损伤面积随树脂吸湿量的增加而增加;当富脂区树脂聚集体积较小时,其对层合板快速加热后分层损伤面积影响较小,但当富脂区树脂聚集体积增加到一定值后,层合板分层损伤面积随富脂区树脂聚集体积的增加而显著增加。所得结论表明,使用ABAQUS的UAMP子程序建立的有限元模型可以有效分析吸湿后复合材料层合板快速加热导致的分层现象。      

A generalized micromechanical approach for the analysis of transverse crack and induced delamination in composite laminates

The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90]_s, [45/−45]_s, [30/−30]_s and [90/45/0/−45]_s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed.     

TENSILE IMPACT DELAMINATION OF A CROSS-PLY INTERFACE STUDIED BY MOIRÉ PHOTOGRAPHY

Abstract Impact induced delamination along a cross-ply interface in carbon fiber/epoxy laminates is studied by high resolution moiré photography. The specimens were loaded in a tensile split-Hopkinson bar giving mode I dominated fracture, and a high speed camera captures images during loading and delamination. The resulting moiré fringes are analysed to produce full field displacement maps of the area around the loaded and propagating crack tips. The displacement map prior to failure shows good agreement with numerical solutions, calculated using a 3D self-adaptive p-version of the finite element method. The calibrated finite element solutions are then used to give further information about the matrix cracking zone size around the crack tip and the energy release rate. In comparison to quasi-static loading, tensile impact loading was found to increase the failure load and the resulting energy release rates; some physical explanations for this behaviour are discussed. It was concluded that the procedures presented have good potential for further determination of rate dependent material properties in carbon/fiber epoxy composites.