On the use of crack-tip-opening displacement to predict the fracture strength of notched graphite/epoxy laminates

The fracture strength and crack-opening displacement of notched graphite/epoxy laminates were measured experimentally using the center-cracked tension-specimen geometry. Four replicate tests were conducted for a variety of laminate stacking sequences, thicknesses, and notch lengths. Most laminates exhibited extensive notch-tip damage prior to fracture. Values of crack-tip-opening displacement (CTOD) at fracture were estimated from values of crack-opening displacement measured at the crack center line. CTOD was independent of specimen crack length for the [0/±45/90] _s , [0/±45/90]_15s , [0/±45] _s , [0/±45/]_15s , and [0/90]_24s laminates. In addition, notched laminate strength was accurately predicted using a Dugdale-type model along with the estimated CTOD.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Thermal residual stresses in thick graphite/epoxy composite laminates—Uniaxial approach

Thermal residual stresses have been known to be very large in laminates of continuous-fiber-reinforced polymer composites. When the thickness of the laminate is large, however, the measurement of the residual stresses raises questions on the accuracy of the conventional methods. A novel concept of layer separation is developed to measure quantitatively and precisely the tensile residual stresses in thick plates with layered distribution of residual stresses. It is applied to thick [O₂/9O₄]_13s, AS/3501-6 graphite/epoxy laminates. The test specimens were mechanically modeled into the thin strips for the application of the new concept of layer separation. The tensile residual stresses measured in the 90-deg layers of these laminates are nonuniform throughout the specimen, and vary from 55.6 MPa to 71.4 MPa. It is very interesting to compare these values with the transverse strengthF ₂ ^tu of AS/3501-6 unidirectional composites, which is 65.4 MPa.     

Experimental and analytical comparisons of failure in thermoplastic composite laminates

Failure characteristics of Gr/PEEK were studied, using an experimental investigation and a fully nonlinear ply-by-ply finite-element technique. The stacking sequence of the laminates (with centrally located holes) investigated were: 0, 90, ±45 deg, (0/45/90/−45 deg)_2s and (0±45/90 deg)_2s. The [0 deg] laminate failure was characterized by splitting at the extremities of the hole and along the fibers. The [90 deg] laminates failed in the transverse direction, whereas the [±45 deg] laminates exhibited considerable elongation to failure. In the case of the quasi-isotropic laminates, the failure progression appeared to be due dominantly to matrix cracking followed by fiber failure. Analytical predictions of the failure process showed reasonably good correlation with the experimentally determined data.     

Effect of laminate construction on residual stresses in graphite/polyimide composites

The influence of ply-stacking sequence and ply orientation on the magnitude of lamination residual stresses in graphite/polyimide angle-ply laminates was investigated. The effect of stacking sequence was investigated with laminates of [0₂/±45]_s, [±45/0₂]_s, [0/+45/0/?45]_s and [+45/0₂/?45]_s layup. The effect of ply orientation was evaluated with additional specimens of [0₂/±15]_s and [0₂/90₂]_s layup. Thermal strains were measured using embedded-gage techniques. Residual strains were determined by comparing thermal strains in the angle-ply laminates with those of a unidirectional laminate. The ply-stacking sequence did not have an influence on the magnitude of residual strains. The highest residual strains occur in the [0₂/90₂]_s laminate and the lowest, approximately one-fourth in magnitude, occur in the [0₂/±15]_s laminate. The maximum residual strains in the [0₂/±45]_s group are slightly lower than those in the [0₂/90₂]_s laminate. Residual stress computations show that, at room temperature, the transverse-to-the-fibers stresses in all plies, except those of the [0₂/±15]_s laminate, exceed the transverse tensile strength of the unidirectional material.     

Fracture of composite laminates containing cracks due to shear loading

The responses of graphite/epoxy [0/90/±45] _s , [±45]_2s , [0/90]_2s and [0/±45]_2s composite laminates with and without center cracks were studied under shear loading using the three-rail shear test. The shear stress/strain relationship, the failure mechanisms and the notched strength were analyzed. Substantial amounts of local buckling were observed in some of the laminates. The present paper shows that shear modulus can be determined accurately using the three-rail shear test with proper interpretation of data. Using the minimum strength model, only one characteristic length was needed to predict accurately the notched strength of a composite laminate under shear and tensile loadings.Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.     

The effect of stacking sequence on the impact-induced damage in cross-ply E-glass/epoxy composite plates

The aim of this study is to determine the damage mechanisms of unidirectional E-glass/epoxy laminated composites under localized impacts. The projectile velocities at low ranges (0.54–3.10 m/s) have been considered to establish a parametric analysis of clamped laminated composite responses. The used circular plates are symmetrical laminates which are composed of ten plies and have three different cross-ply stacking sequences: [0₂/90₆/0₂], [0₃/90₄/0₃] and [0₄/90₂/0₄]. They are subjected at their centers to an impact of an aluminum projectile which is applied in the transverse direction by using a drop weight machine. The time histories of the impactor acceleration, the projectile displacement and the plate deflection were measured. The analysis of the nature of the damage mechanisms and its relation to the structural responses has been performed. The identification of the matrix cracks and the delamination at the interfaces has allowed to determine the initiation and extension criteria of the damage.     

STUDY ON DRILLING CHARACTERISTICS AND MECHANICAL PROPERTIES OF CFRP COMPOSITES

Stacking plates of CFRP composite materials are increasingly used because of their unique characteristics. However, unlike other materials used in metallurgy they have a disadvantage of uneven quality and anisotropy when combined with other composites. Hence, specimens of CFRP stacking plates are manufactured by changing orientation angles throughout three quasiisotropic plies （0°/45°/90°/-45°）68, （03°/453°/903°/-453°）2s, and （06°/456°/906°/-456°）s and throughout three cross plies （0°/90°/0°/90°）68, （03 °/903 °/03°/903°）2s, and （06 °/906 °/06°/906°）8 In this study 3-point bending tests and transverse bending tests have been carried out in order to find out mechanical characteristics according to orientation angles by stacking in 6 different types along with the change of stacking composition method of a CFRP composite.     

Stress resultants and moments around holes in unsymmetrical composite laminates subjected to remote uniform loading

Stress resultants and moments around the holes of infinite unsymmetrical composite laminates under remote uniform loading are analyzed using the complex potential approach developed by Chen and Shen [Mech. Res. Commun. 28 (4) (2001) 423; 28 (5) (2001) 513]. In the analysis, the authors’ previous work has been modified to determine the complex constants B_k appeared in the complex potential functions of Chen and Shen [Mech. Res. Commun. 28 (5) (2001) 513]. Herein B_k are the unknown quantities related to the remote loading conditions. The effect of bending extension coupling has been discussed for several laminates such as [0/90]_T, [45/−45]_T and [0/90/45/−45]_nT. Results indicates that the coupling between bending and extension significantly affects the stresses around the hole of an unsymmetrical laminate containing one sub-laminate only. Such the effect rapidly decreases as the number of the sub-laminates increases. The results confirm the validity of the developed complex potential approach.     

Three dimensional K-T z stress fields around the embedded center elliptical crack front in elastic plates

Through detailed three-dimensional (3D) finite element (FE) calculations, the out-of-plane constraints T_z along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of T_z are obtained near the crack front with aspect ratios (a/c) of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. T_z decreases from an approximate value of Poisson ratio ν at the crack tip to zero with increasing normalized radial distances (r/a) in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle ϕ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, T_z is getting nearly independent of ϕ and is only related to r/a. Based on the present FE calculations for T_z, empirical formulas for T_z are obtained to describe the 3D distribution of T_z for embedded center-elliptical cracks using the least squares method in the range of 0.2≤a/c≤1.0. These T_z results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded center-elliptical crack front field, and a two-parameter K-T_z principle is proposed. The project supported by the National Natural Science Foundation of China (50275073) The English text was polished by Keren Wang.     

复合材料正交叠层板最终拉伸强度的细观统计分析

本文对复合材料正交叠层板［０／９０／０］的最终拉伸破坏行为进行了研究．首先，提出一种修正的剪滞分析方法，求解叠层中由９０°层的基体开裂和０°层的部分纤维断裂相互作用所导致的应力重新分布；然后，采用随机临界核统计模型，对叠层板的最终破坏进行了细观统计分析．对［Ｏ＿２／９０＿ｍ］＿ｓ、［Ｏ＿４／９０＿ｍ］＿ｓ碳／环氧和［Ｏ＿４／９０＿ｍ］＿ｓ玻璃／环氧的计算结果表明，估计的最终拉伸强度与现有的实验结果有较好的符合．     

Delaminations induced by constrained transverse cracking in symmetric composite laminates

Transverse ply cracking and its induced delaminations at the φ/90° interfaces in [. . . /φ_i/φ_m/90_n] _s laminates are theoretically investigated. Three cracked and delaminated model laminates, one five-layer model (FLM) laminate [S^L/φ_m/90_2n/φ_m/S^R] _T and two three-layer model (TLM) laminates I and II, [φ_m/90_2n/φ_m] _T and [S′^L/90_2n/S′^R] _T, are designed to examine constraining mechanisms of the constraining plies of the center 90°-ply group on transverse crack induced delaminations, where S^L, S^R, S′^L and S′^R are sublaminates [. . ./φ_i] _T, [φ_i/. . .] _T, [. . ./φ_i/φ_m] _T and [φ_m/φ_i/. . .] _T, respectively. A sublaminate-wise first-order shear laminate theory is used to analyze stress and strain fields in the three cracked and delaminated laminates loaded in tension. The extension stiffness reduction of the constrained 90°-plies and the strain energy release rate for a local delamination normalized by the square of the laminate strain are calculated as a function of delamination length and transverse crack spacing. The constraining effects of the immediate neighboring plies and the remote plies are identified by conducting comparisons between the three model laminates. It is seen for the examined laminates that the nearest neighboring ply group of the 90°-plies primarily affects the stiffness reduction and also the normalized strain energy release rate, whereas the influences of the remote constraining layers are negligible.     

Dynamic compressive behavior of thick composite materials

The effect of strain rate on the compressive behavior of thick carbon/epoxy composite materials was investigated. Falling weight impact and split Hopkinson pressure bar systems were developed for dynamic characterization of composite materials in compression at strain rates up to 2000 s^–1. Strain rates below 10 s^–1 were generated using a servohydraulic testing machine. Strain rates between 10 s^–1 and 500 s^–1 were generated using the drop tower apparatus. Strain rates above 500 s^–1 were generated using the split Hopkinson pressure bar. Unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions, and cross-ply laminates were characterized. The 90-deg properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The 0-deg and cross-ply laminates show higher strength and ultimte strain values as the strain rate increases, whereas the modulus increnases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases, the dynamic stress-strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal direction and highest in the transverse direction.     

An experimental investigation on the tensile moduli and strengths of graphite/epoxy laminates

The results of a series of tensile tests on graphite/epoxy [0°]_8S and [0°/±30°/0°]_2S laminates at rates varying from 0.002 in/min to 2 in./min are reported. The loads are applied at various angles to the fiber directions in each case. The rate-dependent behavior of the stress-strain response is assessed. Evidence is presented to indicate that failure first occurs on inner plies. Also, evidence is presented to indicate that, in some cases, moduli increase with increased stress or strain level. Lamination theory is used to predict moduli and comparisons with experiment are given. This theory is also used in conjunction with three failure theories to predict ultimate strengths with varying degrees of success. Further, two approaches to ply unloading after first-ply failure are used and discussed. One is a standard method found in the literature while the other is a proposed ‘strength-of-materials’ type of technique which is computationally much simpler.     

Heat-transfer characteristics of the top heat mode closed-loop oscillating heat pipe with a check valve (THMCLOHP/CV)

The aim of this study is to investigate the heat-transfer characteristics of a top heat mode closed-loop oscillating heat pipe with a check valve (THMCLOHP/CV). Water and ethanol are used as the working fluids at various working temperatures. The results show that the specific heat flux increases significantly when the working temperature increases and when the aspect ratio of the evaporator length L _e to the pipe diameter d decreases for the pipe filling ratio varying from 30 to 80%. The maximum specific heat flux equal to 786.34 W/m² is reached with the use of ethanol as the working fluid at L _e /d = 25, angle of inclination to the horizontal axis 90°, and filling ratio of 80%.     

Stress state characterization of delamination cracks in [0/90] symmetric laminates by BEM

The presence in a laminate of plies oriented at 90° with respect to the preferred direction of load generates almost immediately the appearance in these plies of cracks transverse to the load (parallel to the fibres in the lamina). These cracks reach the interface with the neighbouring ply, which in this paper will be considered oriented 0° with respect to the direction of the load. This may cause the bifurcation of the crack, which now appears propagating as a delamination crack between the two plies. The objective of this study is to characterize the stress state at the tip of both, the transverse crack in the 90° ply reaching the interface with the 0° ply, and the delamination crack for different lengths of the debonding. The analysis is performed by means of the Boundary Element Method allowing contact, without or with friction, to take place between the faces of the crack. The plies are considered as equivalent homogeneous bodies under a generalized plane strain state. The results are compared with those predicted by the open and contact models of Interfacial Fracture Mechanics. Accurate knowledge of the stress state at the neighbourhood of the tips of the cracks studied is necessary to generate failure criteria based on Fracture Mechanics parameters to predict the appearance and growth of the type of damage described.     

CONSTITUTIVE RELATION AND STIFFNESS DEGRADATION OF CRACKED ANISOTROPIC COMPOSITE LAMINATES(II)─DETERMINATION OF RESOLVED STIFFNESS AND INVESTIGATION OF STIFFNESS DEGRADATION

The study on properly degradation of damaged,.onlj,osile laminates is extendedto anisotropic laminates with matrix cracking. In (II) of the paper, a solution forpartitioned stiffness is given to complete the constitutive relations developed in (I) Thestiffness degradation in (θ_m/90_n)_s cracked laminates is calculated and the results arediscussed.     

Effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates

A modified shear-lag analysis, taking into account the concept of stress perturbation function, is developed and applied to evaluate the effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates. Effects of number of 90° layers and number of θ° layers in the outer angle-ply laminates on the reduction of the effective axial coefficient of thermal expansion have also been studied. The results of this paper represent well the dependence of the reduction of the effective axial coefficient of thermal expansion on the hygrothermal conditions, the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of un-cracked outer θ° layers in laminate.     

Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium

A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical properties (ρ, μ and c _p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and mixed convection. Temperature and velocity profiles are also presented.     

The Effect of Sweep-Angle Variation on the Turbulence Structure in a Separated,Three-Dimensional Flow

A three-dimensional separated flow behind a swept, backward-facing step is investigated by means of DNS for Re _H = C _∞ H/ν = 3000 with the purpose to identify changes in the statistical turbulence structure due to a variation of the sweep angle α from 0° up to 60°. With increasing sweep angle, the near-wall turbulence structure inside the separation bubble and downstream of reattachment changes due to the presence of an edge-parallel mean flow component W. Turbulence production due to the spanwise shear ∂W/∂y at the wall becomes significant and competes with the processes caused by impingement of the separated shear-layer. Changes due to a sweep angle variation can be interpreted in terms of two competing velocity scales which control the global budget of turbulent kinetic energy: the step-normal component U _∞ = C _∞cosα throughout the separated flow region and the velocity difference C _∞ across the entire shear-layer downstream of reattachment. As a consequence, the significance of history effects for the development into a two-dimensional boundary layer decreases with increasing sweep angle. For α ≥50°, near-wall streaks tend to form inside the separated flow region. Received 7 November 2000 and accepted 9 July 2002 Published online 3 December 2002 RID="*" ID="*" Part of this work was funded by the Deutsche Forschungsgemeinschaft within Sfb 557. Computer time was provided by the Konrad-Zuse Zentrum (ZIB), Berlin. Communicated by R.D. Moser     

Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers

In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 × 10⁴ < Ra < 5 × 10⁵) for different annulus gap widths (L/D _o = 0.23, 0.3, and 0.37) and different inclination of the annulus (α = 0°, 30° and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and (3) increasing Ra increases the heat transfer rate for any L/D _o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D _o and α. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.