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.     

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.     

Alleviation of the stress concentration with analogue reinforcement

In order to reduce the stress concentration around a hole in a plate, new, “analogue” reinforcements instead of reinforcing rings were used in this investigation. In two of these specimens, reinforcements with different volume fractions were arranged to coincide with the stress trajectories for an infinite plate with a hole under uniaxial tension. Two other specimens containing straight rectangular-grid-type reinforcements were made by using a photofabrication method. Specimens were then prepared by sandwiching these reinforcements between two epoxy-resin plates. Plane specimens, i.e., without reinforcement, were also made of the same epoxy resin for comparison. The stress concentrations at the edge of the hole under uniaxial tension were determined by photoelastic techniques. The measured stress-concentration factors were compared with well-known values for an infinite, isotropic, homogeneous plate containing a hole. Results were also compared with published data on [90/0/90/0]_s 7-ply laminated composite plates, and on plates strengthened with reinforcing rings. A definite reduction in stress concentration was observed on specimens containing analogue reinforcement.     

Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of [15/0/±10/0/−15] _s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearities at the ply level and first-ply failure loads with the help of an analytical model. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of [15/0/±10/0/−15] _s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearities at the ply level and first-ply failure loads with the help of an analytical model. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

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.     

Out-of-plane deflections of metallic and composite pin-loaded coupons

The projection shadow moiré technique was employed to determine an out-of-plane contouring history of aluminum, [(+45/–45)]_3S , [(0/90₃,0] _S and [(0/90/+45/–45)]_2S fiberglass epoxy pin-loaded specimens experimentally. The contouring interval was limited to 0.0254 mm by experimental concerns. Qualification of the projection shadow moiré optical arrangement was initially accomplished by the out-of-plane contouring of a clamped, centrally loaded, circular aluminum plate. Experimental results indicate significant out-of-plane displacements in the bearing region of the coupon at load levels well below ultimate. Effects of material anisotropy could be seen in the fiber-oriented shape of the displacement contours. Comparisons with three-dimensional finite-element results indicate that experimental out-of-plane contours were significantly larger than their finite-element counterparts in the region above the pin for the [(+45/–45)]_3S , [(0/90)₃, 0] _S laminates. These deviations increased with increasing pin-load level. These variations could be attributed to linear-elastic through-thickness moduli assumptions as well as through-thickness finite-element mesh coarseness.     

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.     

Biaxial testing of [O2/±45] s graphite/epoxy plates with holes

An experimental investigation was conducted to study the behavior under biaxial-tensile loading of [O₂/±45] _s graphite/epoxy plates with circular holes and to determine the influence of hole diameter on failure. The specimens were 40-cm×40-cm (16-in.×16-in.) graphite/epoxy plates of [O₂/±45] _s layup. Four hole diameters, 2.54 cm (1.00 in.), 1.91 cm (0.75 in.), 1.27 cm (0.50 in.) and 0.64 cm (0.25 in.), were investigated. Deformations and strains were measured using strain gages and birefringent coatings. Biaxial tension in a 2∶1 ratio was applied by means of four whiffle-tree grip linkages and controlled with a servohydraulic system. Stress and strain redistributions occur around the hole at a stress level corresponding to localized failure around the 67.5-deg location and nonlinear strain response at the 0-deg location. Maximum measured strains at failure on the hole boundary are higher (approximately 0.016) than the highest ultimate strain of the unnotched laminate (0.010). Two basic patterns of failure were observed: (a) horizontal cracking initiating at points off the horizontal axis and accompanied by extensive delamination of the subsurface ±45 deg plies, and (b) vertical cracking along vertical tangents to the hole and accompanied by delamination of the outer 0-deg plies. The strength reduction ratios are lower than corresponding values for uniaxial loading by approximately 16 percent, although the stress-concentration factor under biaxial loading is lower.     

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.     

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.     

Strain and stress concentrations in composite laminates containing a hole

The strain concentrations of orthotropic composite laminates containing a circular hole and subject to tensile loading were measured experimentally using strain gages. Then the stress concentrations were calculated using the strain distributions in the initial region of the stress-strain curve before any microdamages were developed. The graphite/epoxy AS4/3502 [O₂/±45]_2s and [45]_4s were chosen to represent fiber-dominated and matrix-dominated laminates, respectively. Several combinations of hole-diameter/plate-width ratio were designed to show the width effect. The conditions of the laminates, after the holes were drilled, were examined using X-ray techniques. Good correlation was obtained between theory and experimental result using specimens in good condition (without machining damages). A procedure for accurately determining the strain and stress concentrations is given. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics, held in Cambridge, MA on May 29–June 1.     

Residual surface stresses in laminated cross-ply fiber-epoxy composite materials

Residual (curing) stresses in a cross-ply laminated plate are related to the strains released when individual plies are separated. Released displacements are determined using high-sensitivity moiré interferometry and linearized strain-displacement equations are used to determine residual strains. Elastic orthotropic stress-strain relations are used to calculate residual stresses remote from free-edges of a [90₂₀/0₂₀/90₂₀] graphite-epoxy cross-ply panel. The measured strains compare favorably with those predicted by laminated plate theory. In a second example, the circumferential and radial residual strains and stresses at the end-section of a thick-walled cross-ply graphite-epoxy cylinder are determined. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas NV on June 8–11.     

Effects of material and stacking sequence on behavior of composite plates with holes

Strain distributions to failure, tensile and compressive strain-concentration factors, and strength-reduction factors were determined for glass-, boron-, and graphite-epoxy plates with holes loaded in tension. Strain gages, photoelastic coatings and moiré techniques were used. Ten variations of layup and stacking sequence were studied. The boron-epoxy composite was found to be the stiffest and strongest of the three. The graphite laminate with the highest stress concentration and the most linear strain response exhibited the highest strength-reduction factor. In all cases, the maximum strain at failure on the hole boundary was higher than the ultimate tensile-coupon strain. In general, it was found that, the higher the stress-concentration factor, the higher the strength-reduction factor. Thus, the [0/90/0/90]_s layup with a stress-concentration factor of 4.82 had a strength-reduction factor of 3.18. At the other extreme, the most flexible layup [±45/±45]_s with the lowest stress-concentration factor of 2.06 had the lowest strength-reduction factor of 1.10. Stacking sequences associated with the tensile interlaminar normal stress or high interlaminar shear stress near the boundary, resulted in laminates 10 to 20 percent weaker than corresponding alternate stacking sequences. Furthermore, it was found that stacking-sequence variations can alter the mode of failure from catastrophic to noncatastrophic.     

Effects of deformed volume, volume fraction and particle size on the deformation behaviour of W/Cu composites

Tungsten/copper (W/Cu) particle reinforced composites were used to investigate the scaling effects on the deformation and fracture behaviour. The effects of the volume fraction and the particle size of the reinforcement (tungsten particles) were studied. W/Cu-80/20, 70/30 and 60/40 wt.% each with tungsten particle size of 10 μm and 30 μm were tested under compression and shear loading. Cylindrical compression specimens with different volumes (D_S = H) were investigated with strain rates between 0.001 s⁻¹ and about 5750 s⁻¹ at temperatures from 20 °C to 800 °C. Axis-symmetric hat-shaped shear specimens with different shear zone widths were examined at different strain rates as well. A clear dependence of the flow stress on the deformed volume and the particle size was found under compression and shear loading. Metallographic investigation was carried out to show a relation between the deformation of the tungsten particles and the global deformation of the specimens. The size of the deformed zone under either compression or shear loading has shown a clear size effect on the fracture of the hat-shaped specimens.The quasi-static flow curves were described with the material law from Swift. The parameters of the material law were presented as a function of the temperature and the specimen size. The mechanical behaviour of the composite materials were numerically computed for an idealized axis-symmetric hat-shaped specimen to verify the determined material law.     

Predictions of first-ply failure load of laminated composite shafts

The failure strengths of laminated composite shafts subjected to static bending load and/or torque are studied using both theoretical and experimental approaches. We investigate optimal angle-ply orientations of laminated composite shafts with the design of symmetric main fiber lay-ups [θ/−θ/...] _S and anti-symmetric reinforcing fiber lay-ups [α/−α/...]_−S for maximum stiffness. Different analytical methods, together with various failure criteria, are used to predict the first-ply failure strengths of the composite shafts. A hand lay-up and pressure bag technique was used to manufacture the composite shafts, which includes the stacking of pieces of prepreg in the desired orientations and the curing process. The first-ply failure loads of laminated composite shafts were determined using acoustic emission. The failure modes of the shafts are studied and experimental results are used to verify the theoretical predictions. The experimental results have been proven to be efficient and effective in the theoretical prediction of first-ply failure loads of laminated composite shafts.     

Mode III fracture behavior of laminated composite with edge crack in torsion

A three-dimensional (3-D) finite element analysis was performed on a [90,(+45/−45)_n,(−45/+45)_n,90]_s class of laminated composites under the edge crack torsion (ECT) test configuration. Finite element delamination models were established and formulas for calculating the Mode III fracture toughness from 3-D finite element models were developed. The relations between the interlaminar fracture behavior and various configuration parameters were investigated and the effects of point loads, ends, geometry, Mode II interference, and friction were evaluated. Results showed that with proper selection of ECT specimen configuration and layup, the delamination could grow in pure Mode III in the middle region of the specimen. Specimen end effect played an important role in the ECT test. A Mode II component occurred in the end regions but it did not interfere significantly with the Mode III delamination state. Specimen dimension ratio, layup, and crack length exhibited significant effect on the interlaminar fracture behavior and the calculated strain energy release rates. However, friction between crackfaces was found to have negligible effect on the interlaminar properties.     

Component-wise analysis of laminated anisotropic composites

This paper proposes a one-dimensional (1D) refined formulation for the analysis of laminated composites which can model single fibers and related matrices, layers and multilayers. Models built by means of an arbitrary combination of these four components lead to a component-wise analysis. Different scales can be used in different portions of the structure and this leads to a global–local approach. In this work, computational models were developed in the framework of finite element approximations. The 1D FE formulation used has hierarchical features, that is, 3D stress/strain fields can be detected by increasing the order of the 1D model used. The Carrera Unified Formulation (CUF) was exploited to obtain advanced displacement-based theories where the order of the unknown variables over the cross-section is a free parameter of the formulation. Taylor- and Lagrange-type polynomials were used to interpolate the displacement field over the element cross-section. Lagrange polynomials permitted the use of only pure displacements as unknown variables. The related finite element led straightforwardly to the assembly of the stiffness matrices at the structural element interfaces (matrix-to-fiber, matrix-to-layer, layer-to-layer etc). Preliminary assessments with solid model results are proposed in this paper; various numerical examples were carried out on cross-ply symmetrical fiber-reinforced laminates [0/90/0] and a more complex composite C-shaped model. The examples show that the proposed models can analyze laminated structures by combining fibers, matrices, layers and multilayers and by referring to a unique structural finite element formulation.     

Transient responses of magnetostrictive plates by using the GDQ method

We used the generalized differential quadrature (GDQ) method to compute the transient response of thermal stresses and center displacement in laminated magnetostrictive plates under thermal vibration. We obtained the GDQ solutions in a three-layer (0°^m/90°/0) and a 10-layer (0°^m/90°/0°/90°/0)_s laminated magnetostrictive plate with four simply supported edges. We presented the transient responses of thermal stress and center displacement with and without velocity feedback control, respectively. The advantage of the GDQ method used provide us with an efficient method to compute the results including shear deformation effect with a few grid points. These GDQ results had its potential that could be used and considered as basic data in the future magnetostrictive laminate studies.