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.     

中等应变率下单向玻璃纤维增强环氧树脂基复合材料的剪切本构关系

采用真空辅助成型工艺制备单向玻璃纤维增强环氧树脂基的[±45°]_8s复合材料试样,通过专用试验设备开展恒定应变率下的面内剪切性能研究,应变率范围为3×10^-4~128.4 s^-1。以Khan-Huang本构关系模型表达形式为基础,考虑应变率效应,建立了一种单向玻璃纤维增强环氧树脂基复合材料在中等应变率下的剪切本构模型,通过最小二乘法和遗传算法获得了最优本构参数。结果表明,单向玻璃纤维增强环氧树脂基复合材料的剪切性能具有应变率敏感性,剪切强度随着应变率的提高逐渐增大,在128.4s^-1时极限强度提高了35.5%。建立的本构关系模型能够准确反映剪切性能与应变率的关系,可用于中等应变率条件下的剪切性能预测。     

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.     

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.     

Beam analysis of angle-ply laminate end-notched flexure specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0]₆, [±30]₅ and [±45]₅ laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle θ at the ±θ interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.     

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.     

Mechanical behaviour of glass and carbon fibre reinforced composites at varying strain rates

The choice of composite materials as a substitute for metallic materials in technological applications is becoming more pronounced especially due to the great weight savings these materials offer. In many of these practical situations, the structures are prone to high impact loads. Material and structural response vary significantly under impact loading conditions as compared to quasi-static loading. The strain rate sensitivity of both carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) are studied by testing a single laminate configuration, viz. cross-ply [0°/90°] polymer matrix composites (PMC) at strain rates of 10⁻³ and 450 s⁻¹. The compressive material properties are determined by testing both laminate systems, viz. CFRP and GFRP at low to high strain rates. The laminates were fabricated from 48 layers of cross-ply carbon fibre and glass fibre epoxy. Dynamic test results were compared with static compression test carried out on specimens with the same dimensions. Preliminary compressive stress–strain vs. strain rates data obtained show that the dynamic material strength for GFRP increases with increasing strain rates. The strain to failure for both CFRP and GFRP is seen to decrease with increasing strain rate.     

Effect of stitching and weave architecture on the high strain rate compression response of affordable woven carbon/epoxy composites

In this study, experimental investigations on stitched and unstitched woven carbon/epoxy laminates under high strain rate compression loading are discussed. Stitched/unstitched laminates are fabricated with aerospace grade plain and satin weave fabrics with room temperature curing SC-15 epoxy resin using affordable vacuum assisted resin infusion molding process. The samples are subjected to high strain rate loading using modified compression split Hopkinson’s pressure bar at three different strain rates ranging from 320 to 1149 s⁻¹. Results are discussed in terms of unstitched/stitched configuration, fabric type and loading directions. Dynamic compression properties are compared with those of static loading. Failure mechanisms are characterized through optical and scanning microscopy.     

Influence of in-plane fibre orientation on mode I interlaminar fracture toughness of stitched glass/polyester composites

The influence of in-plane fibre orientation on the mode I interlaminar fracture toughness, G_Ic of unstitched and stitched glass/polyester composites is investigated in this paper. The G_Ic of planar specimens depends on the fibre orientation, θ in the layers adjacent to the fracture plane, in addition to the property of matrix material. The mode I fracture toughness and fracture behavior of unstitched and stitched 0/0, 30/−30, 45/−45, 60/−60, 90/90 and 0/90 interfaces of unidirectional fibre mats (UD) and 30/−30, 45/−45 and 90/90 interfaces of woven roving mats (WRM) are studied. WRM layer orientation is represented by the direction of warp fibres. Stitching is done by untwisted Kevlar fibre roving of Tex 175 g/km at the stitch densities (number of stitches per unit area) of 10.24 and 20.48 stitches/inch². The specimens having same stitch density, but different stitch distributions are prepared, and the influence of stitch distribution on G_Ic is studied. Double cantilever beam (DCB) tests are carried out and the G_Ic is determined using modified beam theory. The G_Ic of both unstitched and stitched specimens increases with increase in orientation angle, θ upto 45° above which it decreases. The G_Ic values of unstitched 45/−45 delamination interface is around 2.4 times that of the unstitched 0/0 interfaces. The influence of fibre orientation on G_Ic is clearly observed in unstitched specimens, whereas in the stitched specimens, stitching plays an important role in improving the G_Ic and suppresses the influence of fibre orientation; degree of suppression increases with increasing stitch density. When the value of θ is above 45°, transverse cracks are observed in the delamination interface surrounded by UD layers; while in the delamination interface surrounded by WRM layers, transverse cracks are not initiated irrespective of the fibre orientation angle.     

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.     

Fatigue damage mechanics of composite materials Part III: Prediction of post-fatigue strength

A damage-based model for post-fatigue notch strength is presented. The model is an extension of a method developed previously to predict the notch strength of laminated composites. A simple finite element representation of the notch tip damage zone is used to obtain the localized damage-modified stress distribution. A uniaxial tensile stress failure criterion is applied to the 0° plies from which the laminate strength is evaluated. In conjunction with the fatigue damage growth law described in Part II, residual strength is calculated as a function of the applied loading conditions, specimen geometry and lay-up for (90/0)_s, (90/0)_2s and (90₂/0₂)_s T300/914C carbon-fibre/epoxy laminates subjected to tension-tension fatigue cycling.     

Determination of the fracture toughness of fabric reinforced composites by the J-integral approach

The fracture behaviour of a glass-fabric-reinforced epoxy composite has been investigated experimentally. Load-displacement curves for single-edge-notched specimens were obtained on an MTS system and the J-integral evaluated through its energy rate interpretation. J_c, the critical value of the J-integral, obtained directly for a₀/w > 0·4 and that obtained through an extrapolation procedure for a₀/w < 0·4 compare quite well. J_c appears to be independent of crack length for specimen widths between 15 and 45 mm. J_c for ±45° specimens is less than half that for 0/90 specimens.     

Effect of strain rate on interlaminar shear properties of carbon/epoxy composites

In this paper, the effect of strain rate on interlaminar shear properties of laminates is studied. The material tested was a T300/5208 carbon/epoxy composite, and the range of strain rates explored was about 10⁻³ − 10³ s⁻¹. The specimens used were designed and optimized by finite element analysis, and the calculations are presented here. One of the specimens permitted the determination of the interlaminar shear modulus, G₁₃, and the other permitted the determination of the interlaminar shear strength, S₁₃. No influence of testing speed on interlaminar properties was observed at low, intermediate and high strain rates. Fracture surfaces were studied by scanning electron microscopy: a slight difference was observed between specimens tested at low and high strain rates.     

Formation of Transparent and Photo Conducting Films by High Temperature Chemical Conversion of Solution Grown Precursor Films

The formation of photoconducting ZnO and transparent conducting CdO films by high temperature oxidation and thermal decomposition of chemically deposited ZnS and Cd(OH)₂ precursor films respectively is reported. The ZnS to ZnO and Cd(OH)₂ to CdO conversions were confirmed by x-ray diffraction (XRD)₂ electrical and optoelectronic studies. As deposited ZnS and Cd(OH)₂ films exhibited very low dark conductivity and no photoconductivity. Air oxidation of ZnS films at about 400°C for at least 15 minutes converted them to ZnO films with higher dark and photoconductivity. Cd(OH)₂ to CdO conversion occurred at about 300°C. CdO films exhibited a dark conductivity of the order of 10³ (Ωcm)^-1 and an optical transmittance in the range of 90%. These characteristics of ZnO and CdO films make them suitable candidates for the development of low cost photoconductors and solar cell structures.     

Al2O3 formation on Si by catalytic chemical vapor deposition

Catalytic chemical vapor deposition (Cat-CVD) has been developed to deposit alumina (Al₂O₃) thin films on silicon (Si) crystals using N₂ bubbled tri-methyl aluminum [Al(CH₃)₃, TMA] and molecular oxygen (O₂) as source species and tungsten wires as a catalyzer. The catalyzer dissociated TMA at approximately 600 °C. The maximum deposition rate was 18 nm min⁻¹ at a catalyzer temperature of 1000 °C and substrate temperature of 800 °C. Metal oxide semiconductor (MOS) diodes were fabricated using gates composed of 32.5-nm-thick alumina film deposited at a substrate temperature of 400 °C. The capacitance measurements resulted in a relative dielectric constant of 7.4, fixed charge density of 1.74×10¹² cm⁻², small hysteresis voltage of 0.12 V, and very few interface trapping charges. The leakage current was 5.01×10⁻⁷ A cm⁻² at a gate bias of 1 V.     

Fracture behavior of cross-ply graphite/ epoxy laminates

Fracture behavior of cross-ply (0/90)_4s, (0/90)_10s, (0₂/90₂)_2s and (0₄/90₈/0₄)_T laminates of T300/934 graphite/epoxy material was studied using compact tension specimens of several widths and thicknesses, center notched tension and three point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.     

Direct liquid injection metal-organic chemical vapor deposition of HfO2 thin films using Hf(dimethylaminoethoxide)4

Hf(OCH₂CH₂NMe₂)₄, [Hf(dmae)₄] (dmae=dimethylaminoethoxide) was synthesized and used as a chemical vapor deposition precursor for depositing Hf oxide (HfO₂). Hf(dmae)₄ is a liquid at room temperature and has a moderate vapor pressure (4.5 Torr at 80 °C). It was found that HfO₂ film could be deposited as low as 150 °C with carbon level not detected by X-ray photoelectron spectroscopy. As deposited film was amorphous but when the deposition temperature was raised to 400 °C, X-ray diffraction pattern showed that the film was polycrystalline with weak peak of monoclinic (020). Scanning electron microscope analysis indicated that the grain size was not significantly changed with the increase of the annealing temperature. Capacitance–voltage measurement showed that with the increase of annealing temperature, the effective dielectric constant was increased, but above 900 °C, the effective dielectric constant was decreased due to the formation of interface oxide. For 500 Å thin film, the dielectric constant of HfO₂ film annealed at 800 °C was 20.1 and the current–voltage measurements showed that the leakage current density of the HfO₂ thin film annealed at 800 °C was 2.2×10⁻⁶ A/cm² at 5 V.     

Behavior of notched and unnotched [0/±30/±60/90]s GFR/EPOXY composites under static and fatigue loads

The main objective of the present paper is to study the bending behavior of notched and unnotched angle-ply, [0/±30/±60/90]_s, glass fiber reinforced epoxy (GFRE) composites under static and fatigue loads. Static and fatigue bending properties have been determined for notched and unnotched angle-ply specimens. For this purpose different circular notch sizes (2, 4.5, 7, 9 mm) were drilled at the specimen center. Constant-deflection bending fatigue tests were performed at zero mean stress and 25 Hz. A 15% reduction of the initial applied moment was taken as a failure criterion. S–N diagrams for notched GFRE specimens have been constructed based on gross and net cross-section area. The results show that the ultimate bending strength of notched GFRE specimens decreased linearly with increasing notch diameter. Based on gross-section the fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. On the other hand, the S–N diagrams based on net-section indicate the insensitivity of angle-ply composites to the notch size. This is considered to be a peculiar phenomenon to composite materials. The results also show that the S–N diagrams have not any fatigue limit rigorous within 10⁷ cycles.     

Fracture strength testing of δ-alumina fibres with variable diameters and lengths

Tensile tests were performed on individual δ-alumina fibres (Saffil, RF grade). The results revealed a large scatter in strengths and a clear dependence of the fracture strength on the specimen volume. The tests were evaluated on the basis of the Weibull probability function, a special modification of the Weibull analysis being developed that successfully copes with the problem of testing fibres with various diameters and test lengths. For the sample studied the Weibull modulus, m, was found to be 2·2, with a scaling constant δ₀ = 6·0 MPa (units of volume mm³; i.e. V₀ = 1 mm³).     

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.