Determination of fracture energy and tensile cohesive strength in Mode I delamination of angle-ply laminated composites

The energy release rate in delamination of angle-ply laminated double cantilever composite beam specimens was calculated using the compliance equation, and interlaminar cohesive strengths were obtained. Instead of the traditional approach of a beam on an elastic foundation, a second-order shear-thickness deformation beam theory (SSTDBT) was considered. The equilibrium equations were obtained using the principle of minimum total potential energy and the system of ordinary differential equations were solved analytically. The problem was solved for [0°]₆ , [±30°]₅, and [±45°]₅ laminates with mid-plane delaminations and the results were verified using experimental evidence available in the literature.     

Experimental and theoretical investigations on stiffened and unstiffened composite panels under uniform transverse loading

An experimental investigation on fibre-reinforced stiffened and unstiffened panels under transverse uniform pressure has been carried out. The deflections and strains measured inside the laminate are compared with a finite element analysis. The effect of one or two stiffeners within the panel is small since the stiffener fail at small loads. In contrary to this, the effect of a different lay-up is big, because the angle-ply panels [+45°/−45°]₂ carried higher loads than the cross-ply panels [0°/90°]₂. The failure of the panels near the centre of the long edge at the clamping is correctly predicted by the FEA. In addition, calculated and predicted stresses are close to each other.     

An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity

The failure characteristic of graphite polyetheretherketone (Gr/PEEK) under compression with a centrally located circular discontinuity was investigated through experimentation and a nonlinear ply-by-ply finite element technique. The stacking sequence of the laminates investigated were: [0 °₁₆], [90 °₁₆], [±45 °]_4S [0 °/90 °]_4S, and [0 °/ ± 45 0°/90 °]_2S. In the experimentation, [90 °]₁₆, [0 °/90 °]_4S, and [0 °/ ±45 °/90 °]_2S laminates, as well as three of the [0 °]₁₆, failed due to a crack that was normal to the loading direction and initiated from the edge of the hole progressing to the outer edges of the specimen. The [±45 °]_4S specimens failed to support the load due to an internal crack that originated from the hole's edge and then traveled at an angle of about 42% to the direction of loading. The finite element method used to analytically model the failure of Gr/PEEK accurately modeled the response of the specimens tested experimentally.     

Nonlinear analysis of interlaminar stress in graphite/epoxy laminates with and without delamination cracks

A quasi three-dimensional yield function, which is quadratic in stresses except for σ₁₁, is proposed for graphite/epoxy composites. The elastic-plastic interlaminar stress response near a free edge in the [90/0]_s, [0/90]_s, and [45/−45]_s laminates with and without delamination cracks was investigated using the pseudo three-dimensional finite element technique. The plasticity model was evaluated by comparison with off-axis experimental data. Since shear response is the key element for nonlinear stress-strain behavior of graphite/epoxy composites, the plasticity theory predicts interlaminar stresses in the [45/−45]_s laminate significantly different from linear elasticity. Moreover, the existence of a delamination crack caused more plasticity effects on interlaminar stresses.     

Analysis of stiffness reduction of cracked cross-ply laminates

Stiffness reduction of cracked [0°_m/90°_n]_s laminates is analyzed by variational methods on the basis of the principle of minimum complementary energy. For this purpose admissible stress systems are constructed which satisfy equilibrium and all boundary and interface conditions. The optimal stress field is then determined by minimization of complementary energy. The analysis allows for crack interaction and random crack distribution. Results are given for Young's modulus, shear modulus and Poisson's ratio. Young's modulus results are in excellent agreement with experimental data for [[0°/90°₃]]_s glass/epoxy laminate.     

Measurement of the static compressive strength of carbon-fibre/epoxy laminates

This paper describes an experimental study of the compressive failure of T800/924C carbon-fibre/efoxy composite laminates. Undirectional laminates loaded parallel to the fibres have compressive strengths that are 70% of the tensile strength and fail by fibre-microbuckling. During microbuckling the fibre debonds from the matrix, and the fibres break in bending. Multidirectional [(±45/0₂)₃]_sm laminates were also tested in compression, and the critical failure mechanism observed was microbuckling of the 0° plies. The failure strain was almost the same as for the undirectional laminate, The failure strain was almost the same as for the unidirectional laminate, which indicated that the ±45° plies have no significant influence on the failure strength of the 0° plies.     

Strength of carbon/epoxy laminates with countersunk hole

The aim of this study is to predict the static strength of carbon/epoxy laminates with countersunk hole. Also, three-point bend (TPB) specimens with the same lay-up were analysed. For this purpose, the notched strength of the laminates was analysed by a damage zone model (DZM), where damage around the notch is represented by an ‘equivalent crack’ with cohesive forces acting between the crack surfaces. The DZM requiring only basic properties of the laminate such as unnotched tensile strength, δ₀, fracture energy, G_c^*, and stiffnesses of the laminate. However, the complex geometry around the countersunk hole implies that both δ₀ and G_c^* will vary in this area, and in order to avoid this problem an approximate geometry of the countersunk hole is used in the DZM-calculations. With this approximation, good agreement between experimental and calculated strength was observed for the laminates with countersunk hole. This was also the case for the TPB specimens.     

An investigation of non-linear elastic behavior of CFRP laminates and strain measurement using Lamb waves

This paper investigates the non-linear elastic behavior of unidirectional and cross-ply CFRP laminates and proposes a new method to measure tensile strain using Lamb waves. Young’s modulus was measured as a function of strain in situ using Lamb wave velocity during a tensile test. The stiffening effect of the carbon fibers on [0]₈ specimens and the softening effect of the epoxy matrix on [90]₈ specimens were accurately evaluated. Young’s modulus of the 0° ply was obtained as a quadratic function of strain. Using the function and the rule of mixture, the dependence of Young’s modulus on strain was accurately predicted for cross-ply laminates. Based on the results, the tensile strain was quantitatively correlated with the corresponding arrival time of the Lamb waves. The strains obtained from the proposed method agreed well with those from the strain gauge. Finally, the effect of transverse cracks on the in situ Young’s modulus of the cross-ply laminate under a tensile load was investigated. This method clearly detected even a small decrease in the Young’s modulus due to the transverse cracks in stiffening cross-ply laminate.     

A study on the low-velocity impact response of laminates for composite railway bodyshells

This paper presents a study on the low-velocity impact response of woven fabric laminates for the composite bodyshell of a tilting railway vehicle. In this study, low-velocity impact tests for the three laminates with size of 100 mm × 100 mm were conducted at three impact energy levels of 2.4 J, 2.7 J and 4.2 J. Based on these tests, the impact force, the absorbed energy and the damaged area were investigated according to different energy levels and stacking sequences. The damage area was evaluated by visual inspection and C-scan measurement. The test results showed that the absorbed energy of [fill]₈ laminate was highest whereas [fill₂/warp₂]_s laminate was lowest. The [fill]₈ laminate had the largest delamination area because of the highest impact energy absorption.     

The relation between compressive strength of carbon/epoxy fabrics and micro-tow geometry with various bias angles

In this paper compressive tests of carbon/epoxy (plain weave, 3k) fabric composites were performed to investigate the relation between compressive strength and various bias angles and shear angles. Compressive properties such as chord modulus and maximum strength of the fabric composite materials are essential to analyze the drape behaviour and estimate the quality of the final products. Various specimens with different bias and shear angles which were fabricated by using autoclave de-gassing moulding process were prepared to estimate the strength and chord modulus with respect to the bias and shear angle variations. The stacking sequences of the compressive test specimens are [0]_10T, [15]_10T, [30]_10T and [45]_10T for bias specimens and [±37]_10T, [±32]_10T, [±28]_10T, [±22]_10T for sheared specimens. Micro-tow structures were observed to correlate the fabric compressive strength with crimp angle. Anti-buckling rig was involved to prevent specimens from buckling during the compressive tests. The compressive test was performed with 1.3 mm/min strain rates. Compressive test results were compared with calculation results. Facture modes which were classified in two different modes were analyzed using microscopic observation.     

基于断裂韧性预报复合材料层合板的开孔拉伸强度

开孔层合板的强度预报往往取决于孔边的临界长度,它不仅与材料性能,而且与铺层、孔径都有关。本文基于线弹性断裂力学,提出了一种预报对称铺层层合板开孔拉伸强度的新方法,只需提供正交层合板的断裂韧性和无缺口层合板的拉伸强度,显著降低对实验数据的依赖性。首先,将临界长度表作为层合板断裂韧性和无缺口拉伸强度的函数,再通过正交层合板[90/0]_8s的紧凑拉伸试验和虚拟裂纹闭合技术,确定出0°层断裂韧性,进而计算得到任意对称铺层层合板的断裂韧性。本文测试了T300/7901层合板[0/±45/90]_2s和[0/±30/±60/90]_s的开孔拉伸强度,孔径分别为3 mm、6 mm和9 mm。理论预报结果与试验值吻合较好,最大误差为15.2%,满足工程应用需求。      

Matrix cracking behavior of K3B/IM7 composite laminates subject to static and fatigue loading

The matrix cracking behavior of a new high-performance thermoplastic composite material, K3B/IM7, was systematically investigated. Laminates in various grouped thickness and ply stacking sequences, [0₂/90₂/0₂], [0₂/90₄/0₂], and a quasi-isotropic laminate [+45/0/−45/90]_s were tested under static and tension–tension fatigue loading. Depending on the stacking sequence of the laminates and the type of loading, various matrix cracking behavior were found. Under static loading, the matrix cracks were mainly close to the specimen edges. A few cracks were found to penetrate the specimen width, even when the load was large enough to break the specimen. However, under fatigue cyclic load, the edge initiated cracks propagated fully across the specimen width. Combined with the fatigue Paris Rule and considering the ply thickness and stacking sequence, the energy release rate method was applied to predict the relations between the loading strain amplitude and fatigue cycles for matrix cracking failure.     

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ₄/90)_s and (0/ ± ₂/90)_s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/90₅)_s cross-ply laminates.     

Microdebonding investigation of the effects of thermal residual stress on the bond strength of a graphite/polymide composite

The microdebonding test was used to investigate the effects of thermal residual stresses resulting from different lay-ups in fabrication on the fiber/matrix bond strength of a graphite-fiber-reinforced polyimide composite. This was accomplished by comparing the results of a cross-plied laminate with those of a unidirectional laminate. The results indicated that the measured interfacial bond strength of the unidirectional composites was greater than that of the cross-plied laminate. The thermal radial stress distribution around the fiber for the unidirectional and the [0₂, 90₂]_s laminates were estimated, to explain this reduction of the interfacial bond strength.     

High strain rate compressional behavior of stitched and unstitched composite laminates with radial constraint

This paper is concerned with the high strain rate compressional behaviour of glass/epoxy (Hy-E 9134B, Fiberite, USA) composite laminates with or without stitching reinforcement by untwisted Kevlar-49 threads (1140 denier). The split Hopkinson pressure bar (SHPB) apparatus is used in performing the high strain rate tests. Test data are analyzed in a manner similar to that reported by Hauser Exp. Mech., 6 (1966) 395. Specimens are tested at strain rates up to 10⁴ s⁻¹. Unidirectional laminated parallelepiped samples are impacted along their fiber direction. Their high velocity compressive ductility is observed. Both [0°]₂₄ and [(0°/90°)₆]_S glass/epoxy circular specimens with disc diameters of 10 and 50·8 mm are transversely impacted by an input bar in order to study their high strain rate behavior. Moreover, two sets of stitched circular specimens with disc diameters of 10 and 50·8 mm are also examined. The effect of strain rate and radial constraint on the dynamic properties of stitched and unstitched GFRP laminated specimens and their associated damage patterns are described.     

Double cantilever beam testing of multidirectional laminates

Several difficulties in the double cantilever beam (DCB) tests of multidirectional laminates often prevent valid measurements of the mode I critical strain energy release rate G_Ic. In this paper, several DCB specimens were analysed with 3D finite element models. The results showed that the undesired effects of residual stresses and of mode-mixity can be minimised. An interlaminar stress based fracture criterion predicts that the G_Ic of multidirectional specimens is typically 10–40% higher than the G_Ic of unidirectional [0°]_n laminates. This agrees with the few valid experimental data available.     

Growth of delamination cracks due to bending in a [905/05/905] laminate

A study of the growth of delamination due to bending in a [90₅/0₅/90₅] graphite/epoxy laminate is presented. A plane strain finite element analysis is used to determine the strain energy release rate during delamination in a three-point-bend specimen. A closed form expression for energy release rate is obtained from classical lamination theory and Timoshenko beam theory and is compared with the finite element analysis result. These results combined with the experimentally determined critical load, P_crit, are used to calculate the critical strain energy release rate, G_C. The critical energy release rate is also determined experimentally by the compliance method.     

Effects of temperature on impact damages in CFRP composite laminates

In this paper, the effect of temperature variations (low and high temperatures) was studied experimentally on impact damage to CFRP laminates. The composite laminates used in this experiment were CF/EPOXY orthotropic laminated plates with lay-up [0₆/90₆]_s and [0₄/90₄]_s, and CF/PEEK orthotropic laminated plates with a lay-up of [0₆/90₆]_s. A steel ball launched by the air gun was used to generate the CFRP laminate impact damage. For impact-damaged specimens, nondestructive evaluation (NDE), such as a scanning acoustic microscopy (SAM) was performed on the delamination-damaged samples to characterize damage growth at different temperatures.

Therefore, this study was undertaken to experimentally determine the interrelations between impact energy and impact damage (i.e. the delamination area and matrix) of CFRP laminates (CF/EPOXY and CF/PEEK) subjected to foreign object damages (FOD) at low and high temperatures.     

Damage detection of surface cracks in composite laminates using modal analysis and strain energy method

This paper presents an approach to detect surface cracks in various composite laminates. Carbon/epoxy composite AS4/PEEK was used to fabricate laminated plates, [0]₁₆, [90]₁₆, [(0/90)₄]_S and [±45/0/90]_2S. Surface crack damage was created on one side of the plate using a laser cutting machine. Modal analysis was performed to obtain the mode shapes from both experimental and finite element analysis results. The mode shapes were then used to calculate strain energy using the differential quadrature method (DQM). Consequently, the strain energies of laminated plates before and after damaged were used to define a damage index which successfully identified the surface crack location.     

Chemical vapor deposition of copper–cobalt binary films

Chemical vapor co-deposition of Cu–Co films has been demonstrated using (1,1,1,5,5,5-hexafluoro-2,4-pentanedionato)Cu(II) [Cu(hfac)₂] [hfac=hexafluoroacetylacetonate] and (acetylacetonate)Co(II) [Co(acac)₂] [acac=acetylacetonate] as precursors. The deposition was performed at the substrate temperature of 270°C in a warm-wall impinging jet type reactor. The precursor Co(acac)₂ was sublimed at 140°C to achieve reasonable precursor delivery rates and avoid decomposition of precursor in the sublimator. Films with varying Cu content from 17 wt.% to 98 wt.% were deposited by subliming Cu(hfac)₂ in the temperature range of 40–100°C with a fixed Co(acac)₂ delivery rate. The morphologies and crystallinities of the binary films were strongly dependent on the film stoichiometry. Overall, this study provides insights into the mechanism of Cu–Co binary film formation by CVD.