Mode I DCB testing of composite laminates reinforced with z-direction pins: a simple model for the investigation of data reduction strategies

The applicability of standard composite mode I interlaminar toughness data reduction schemes is investigated for composites reinforced by inserting straight pins in the z-direction. A simple model of a z-pinned mode I test is used to generate load, displacement and crack length data. Data reduction schemes are applied to the model data and the resulting toughness is compared to the true toughness. These schemes are shown to be inaccurate for the initial stage of crack growth, during which the zone bridged by z-pins is developing and an improved scheme is proposed. Beyond this stage, the toughness is most accurately predicted if the ‘developing’ data is omitted.     

Dynamic crack propagation and arrest in orthotropic DCB fiber composite specimens

An orthotropic double cantilever beam (DCB) model is used to study dynamic crack propagation and arrest in 90° unidirectional Hercules AS/3501-6 graphite fiber epoxy composites. The dynamic fracture toughness of the composite is determined from tests performed on the long-strip specimen and DCB crack arrest experiments are conducted. By using the dynamic fracture toughness in a finite-difference solution of the DCB governing partial differential equations, a numerical solution of the crack propagation and arrest events is computed. Excellent agreement between the experimental and numerical crack arrest results are obtained.     

Effect of delamination failure in crashworthiness analysis of hybrid composite box structures

In the present paper the effects of delamination failure of hybrid composite box structures on their crashworthy behaviour will be studied and also their performance will be compared with non-hybrid ones. The combination of twill-weave and unidirectional CFRP composite materials are used to laminate the composite boxes. Delamination study in Mode-I and Mode-II with the same lay-ups was carried out to investigate the effect of delamination crack growth on energy absorption of hybrid composite box structures. The end-loaded split (ELS) and double-cantilever beam (DCB) standard test methods were chosen for delamination studies. In all hybrid composite boxes the lamina bending crushing mode was observed. Regarding the delamination study of hybrid DCB and ELS the variation of the specific energy absorption (SEA) versus summation of G_IC and G_IIC were plotted to combine the effect of Mode-I and Mode-II interlaminar fracture toughness on the SEA. From this relationship it was found the hybrid laminate designs which showed higher fracture toughness in Mode-I and Mode-II delamination tests, will absorb more energy as a hybrid composite box in crushing process. The crushing process of hybrid composite boxes was also simulated by finite element software LS-DYNA and the results were verified with the relevant experimental result.     

Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests.The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens.The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.     

Effect of natural stitched composites on the crashworthiness of box structures

In the present paper the effects of stitching on the energy absorption and crashworthy behaviour of composite box structures will be studied. The combination of unidirectional carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP) composite materials are used to laminate the composite boxes. Delamination study in Mode-I with the same lay-up was carried out to investigate the effect of stitching on delamination crack growth on energy absorption of stitched and non-stitched composite box structures. The double cantilever beam (DCB) standard test method was chosen for delamination studies. For non-stitched and stitched composite boxes the lamina bending and brittle fracture crushing modes were observed. It was found that the stitched composite boxes which show higher fracture toughness in Mode-I delamination tests, are not necessarily able to absorb more crushing energy in comparison with non-stitched composite boxes. It was also observed that the position of stitched area can affect the crushing mode and consequently energy absorption capability of composite box structures. The main reason can be related to other mechanisms such as bending, friction and bundle fracture which significantly contribute to energy absorption. The analytical model based on energy balance approach is proposed to estimate the mean crushing force, F_m, in axial crushing of square composite box.     

An asymptotic approach to size effect on fracture toughness and fracture energy of composites

Size effect on fracture toughness and fracture energy of composites is investigated by a simple asymptotic approach. This asymptotic analysis based on the elastic/plastic fracture transition of a large plate with a small edge crack is extended to study fracture of composite. A reference crack length, a^*, is used in the model, which indicates an ideal elastic/plastic fracture transition defined by the yield strength and plane strain fracture toughness criteria. Experimental results of cementitious materials available in literature are analyzed and compared. It is shown that the common K_R-curves can also be obtained by the current asymptotic model. Furthermore, a local fracture energy distribution concept is also discussed and compared with the present asymptotic approach.     

低温环境下测试复合材料Ⅰ型层间断裂韧性的简易方法

目前ASTM复合材料Ⅰ型层间断裂韧性测试标准需不断观测裂纹扩展长度。然而在低温环境下,裂纹扩展长度不易测量且过程繁琐。为克服这一缺陷,本文采用双柔度法测试复合材料低温环境下Ⅰ型层间断裂韧性,该方法的步骤与ASTM标准基本相同,但不需观测裂纹扩展长度便能获得低温下Ⅰ型层间断裂韧性。为了验证该方法的可靠性和精度,采用5件碳纤维增强环氧树脂基复合材料双悬臂梁（DCB）试样在-10℃环境下进行Ⅰ型层间裂纹扩展实验,应用ASTM标准所推荐的三种方法及本文的双柔度法进行数据处理获得复合材料Ⅰ型层间断裂韧性。结果表明:ASTM标准的三种方法与双柔度法得到的Ⅰ型层间断裂韧性结果一致,相对差别小于5%,而本文的双柔度法不需测量裂纹扩展长度,因此更简单,为测试低温环境下Ⅰ型层间断裂韧性提供了一种准确、简单的新方法。      

Crack growth resistance of a gray cast iron

Gray cast iron exhibits a discontinuous crack growth process. No definite crack front is observed but fracture is induced by the progression and extension of a damaged zone whose extremities remain ill-defined. It was demonstrated, in an earlier study, that the crack resistance of a grey cast iron is therefore strongly dependent on the length of the cracked zone. In order to otbain a meaningful toughness value, i.e. a measurement of the resistance to crack propagation, it is necessary to use a specimen configuration in which the size and position of the damaged zone remain unaffected by the crack propagation. Such measurements have been made on a continuously cooled gray cast iron by using DCB specimens with circular side grooves. After the fracture had initially progressed to a relatively large extent, the loading points were moved forward and a new loading sequence was applied. Crack resistance was measured during successive loading sequences, applied after displacement of the loading points. Compliance measurements were used to evaluate the crack increase and an equivalent R-curve was drawn for each loading sequence. Except for the initial sequence the successive R-curves remained fairly identical. Moreover, a constant R-value was observed for a relatively large range of crack extensions. This demonstrates that stationary fracture conditions have been obtained. From these results it may be concluded that by using this particular procedure applied to a DCB specimen, a resistance to fracture propagation has been measured which is independent of the size of the cracked zone and which is representative of the microstructure.     

Alternative test method for interlaminar fracture toughness of composites

Two methods of determining the mode I interlaminar fracture toughness for fiber-reinforced polymer matrix (FRPM) composites using a double cantilever beam (DCB) test are compared. The standard method of determining G _IC is based in linear-elastic fracture mechanics theory and requires a visual measurement of the crack length, presenting data acquisition and analysis difficulties. The proposed method makes use of elastic–plastic fracture mechanics theory and an analytical closed form solution to the J-integral to relate the fracture toughness J _IC , load, and angular displacement at the load application points. This method has the advantage of replacing visually acquired data with data easily obtained using inexpensive transducers as well as being applicable to a broader class of materials.     

Interlaminar and intralaminar fracture modes in 0/90 cross-ply glass/epoxy laminate

Delamination of a cross-ply 0/90 glass fibre-reinforced composite laminate with an epoxy-phenol matrix was studied using a double cantilever beam test. Fracture toughness was determined by measurement of bend angle of the cantilever beams. Results obtained with this method were in agreement with those from conventional compliance and area methods. Two different fracture modes were observed: interlaminar and intralaminar. In the interlaminar fracture mode, crack jumps in the space between two neighbouring 0° and 90° plies were observed. With the interlaminar fracture mode, during crack initiation G_Ic decreased with crack length. Intralaminar fracture mode consisted of the gradual growth of a crack through a 0° ply. Fibres bridging the opposite sides of the crack were observed in this case, and fracture toughness G_Ic did not change with crack length. G_Ic (420 J m⁻²) at intralaminar fracture mode was approximately twice that at interlaminar fracture mode (220 J m⁻²). The difference in fracture toughness was explained by the dissipation of energy by fibres bridging the opposite sides of the crack at intralaminar fracture mode.     

The effect of initial notch shape of compact specimen on fatigue pre-cracking and fracture toughness testing

The circular notched compact specimens, along with standard specimens having straight or chevron notch are provided for fatigue and fracture toughness testings in order to study the crack observation capability during fatigue pre-cracking, skewness of the crack front, and the resulting fracture toughness K_Q. The test results indicated that circular notched specimens significantly facilitate the crack observation during fatigue testing as the cracks initiate on both surfaces of the specimen. No remarkable differences were observed on geometries of the fatigue crack front obtained and the resulting fracture toughness among these three types of specimen. The macroscopic observation of beach marks on the fracture surfaces revealed that, in the present material Ti-6Al-4V (ELI), the advance of only 1.3% of the whole crack length corresponded to the load level at which fracture toughness K_Q was evaluated.     

Influence of silane coupling agents on interlaminar fracture in glass fibre fabric reinforced unsaturated polyester laminates

The relationship between the adhesive properties of the interphase of glass fibre/resin and the resultant composite Mode I delamination fracture toughness in glass fibre fabric laminate (GFFL) was studied. The Mode I interlaminar fracture toughness of GFFL was obtained by using a double cantilever beam (DCB) specimen. The delamination resistance of GFFLs which have two silane coupling agents and three concentration finishes is discussed on the basis of interlaminar fracture toughness. The crack propagation behaviour of DCB testing was mainly divided into stable and unstable manners. The fracture toughness and the crack propagation behaviour were dependent on the types and concentration of silane coupling agents.     

Fracture toughness of foams with tetrakaidecahedral unit cells using finite element based micromechanics

Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.     

Design and analysis of the crack rail shear specimen for mode III interlaminar fracture

The crack rail shear (CRS) specimen is a proposed test method to characterize the Mode III interlaminar fracture toughness of continuous-fiber-reinforced composite materials. The specimen utilizes the two-rail shear test fixture, and contains embedded Kapton film placed symmetrically about the midplane to provide starter cracks for subsequent characterization. Otherwise, specimen length and width are identical to the ASTM shear test specimen geometry. An analytical expression for the strain energy release rate is developed based on a strength of materials approach. The model illustrates the important material and geometric parameters of the test, and provides a simple data reduction scheme for experiments. A quasi three-dimensional, linear elastic finite element code, CCMQ3D, is employed to verify the pure Mode III fracture state and to determine admissible crack lengths. Deformation of the model shows that only the out-of-plane displacement is non-zero, indicating that a pure Mode III fracture state does indeed exist within the constraints of the Q3D assumption. Compliance and strain energy release rate predictions are in good agreement with the strength of materials model over the range of crack lengths, 0·15<a/w<0·85. A fully three-dimensional, linear elastic finite element analysis of the CRS is employed to quantify the effect of finite length on the fracture state. Only intermediate crack lengths are investigated. Crack closure techniques are utilized to determine the components of the strain energy release rate present. Results indicate that a small boundary layer of mixed mode behavior exists at the free edges that diminishes to a pure Mode III fracture state. Compliance and strain energy release rate predictions by the 3D model show good agreement with the Q3D and strength of materials models.     

PBO纤维增强环氧树脂复合材料层间Ⅰ型断裂韧性的DIC技术测量

Ⅰ型双悬臂梁(DCB)试验通常用于单向复合材料的层间抗拉性能研究,目标是测量Ⅰ型层间断裂韧性,其可作为复合材料分层扩展及失效机制研究的重要输入参数。在DCB试验中必须经常暂停试验以实现多次测量裂纹长度,这不仅会对裂纹传播产生潜在影响,造成测量误差且多次反复试验的时效性较差。数字图像相关(DIC)测试技术应用于裂纹扩展长度测量具有实时跟踪、精确定位的优点,可有效提高Ⅰ型断裂韧性试验的测量效率,但应用于非连续变形行为仍存在局限性,且易受到图像噪声的干扰,产生测量误差。本文发展了一种基于DIC测试技术的实时获取裂纹长度的检测方法,通过图像匹配算法获取试件的非连续变形位移场,并提出一种根据全局横向位移离散程度的辨别方法,实现了裂纹尖端的实时捕捉。再通过DCB试验,与传统测量方式对比,裂纹长度的测量误差平均不超过2.76%,验证了该方法的准确性和高效性,同时也克服了聚对苯撑苯并双噁唑(PBO)/环氧树脂复合材料侧表面毛糙、散斑质量较差及纤维桥接对测量结果的干扰,最终获取了有效的Ⅰ型层间断裂韧性初始值及稳态扩展值。     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

Z-pin增强复合材料Ⅰ型断裂韧性数值分析

采用细观力学方法以及虚拟裂纹闭合法(VCCT)对含有Z-pin增强复合材料双悬臂梁(DCB)结构Ⅰ型断裂韧性进行了研究。利用有限元法建立了结构模型,采用实体单元模拟复合材料层压板结构和非线性弹簧元模拟Z-pin。通过计算应变能释放率对含有不同体积分数Z-pin的复合材料层压板Ⅰ型断裂韧性与不含Z-pin的复合材料层压板Ⅰ型断裂韧性进行了对比分析。研究表明,含有Z-pin增强复合材料双悬臂梁(DCB)结构Ⅰ型断裂韧性在裂纹扩展过程中受到Z-pin桥联作用的影响而显著增强,且其增强效果与Z-pin的体积分数、处在桥联区的Z-pin数目均相关,这表明Z-pin增强方法能够有效提高复合材料层压板的分层扩展阻力。     

Studies of the effect of metal particles on the fracture toughness of ceramic matrix composites

The purpose of this study was to describe the influence of metal particles on the fracture toughness of ceramic matrix composites. Here, alumina matrix composites with molybdenum particles have been investigated. The results presented show that the change of fracture toughness of a ceramic–metal composite can be controlled by the volume fraction of metallic phase and size of metal particles.

The model proposed in this paper describes the change of crack length and as a consequence, the change of K_IC value. The results of modelling calculations have been compared with experimentally measured K_IC values. This model is useful for simulation of crack length changes in the composites and to design a material with an optimum fracture toughness.     

Fracture mechanics of plastic-fiber composites

The concept of fracture mechanics is introduced to characterize the toughness of fiber-reinforced composites which should be distinguished from tensile strength. A material may have a high tensile strength but a low toughness meaning that it has a low resistance to crack extension. Depending on the analytical model used, the same experimental data may report different fracture toughness values. In general, the combination of crack propagation in directions parallel and perpendicular to the fibers makes the composite problem very difficult to analyze.Composites with well-aligned fibers are more susceptible to crack propagation parallel than perpendicular to the fibers and can be analyzed with a reasonable degree of accuracy by using the existing K_c or S_c-theory in fracture mechanics. The K_c-theory is used primarily in laboratory testing where the load is aligned normal to the crack plane whereas the S_c-theory is not subjected to such a restriction. The K_c or S_c values for several composites are reported and applied to solve various example problems illustrating the advantage of fiber reinforcement.