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.     

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.     

Behavior of graphite/epoxy plates with holes under biaxial loading

An experimental investigation was conducted to study the behavior under biaxial tensile loading of quasiisotropic 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.) laminates of [0/±45/90] _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. Equal biaxial loading was introduced by means fo four whiffle-tree grip linkages and controlled with a servohyraulic system. Initially, the circumferential strain is uniform around the boundary of the hole. Subsequently, with increasing load, regions of high strain concentration with nonlinear response develop at eight characteristic locations 22.5 deg off the fiber axes. Failure in the form of cracking and delamination initiates at these points. Maximum strains at failure on the hole boundary reach values up to twice the ultimate strain of the unnotched laminate. The effect of hole diameter on strength was described satisfactorily using an average biaxial-stress criterion. Good correlation was also obtained with theoretical predictions based on a tensor-polynomial failure criterion for the lamina and a progressive degradation model.     

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.     

Influence of stacking sequence and interlaminar layer on stress singularities at free edge of composite laminates

Summary The topic concerning the singularity in the state of stress existing at the free edges of plane composite laminates with resin interlaminar layer, has been dealth with. The problem has been studied by means of a F.E. approach, founded on a method able to determine the free edge state of stress without aprioristical hypotheses about the presence of a singularity. Then the singularity itself has been studied through a linear-logarithmic formulation which enables, for the stacking sequences considered — all belonging to the [°/°–90°] _s family — and for all meaningful stress components, to compute the power of the singularity and the boundary layer stress intensity factor (or free edge stress intensity factor). Taking into account these parameters, various laminations and stacking sequences have been compared, in order to provide a practical measure of the severity of the singular stress field and its influence on failure modes.Then a comparative analysis has been worked out, in order to evaluate the effects due to the thickness of the resin interlaminar layer between two fiber layers.

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Sommario Si prende in considerazione il problema connesso con l'esistenza di singolarità nel campo di sforzo presente ai bordi liberi di laminati piani in materialxe composito, in presenza di uno strato di resina interlaminare.La questione viene affrontata tramite un approccio numerico agli elementi finiti, basato su di un metodo in grado di determinare il campo di sforzo al bordo libero senza assumere aprioristicamente la presenza di singolarità. La eventuale singolarità viene poi studiata mediante una trattazione logaritmico-lineare che consente di calcolare, per tutte le laminazioni prese in considerazione, (appartenenti alla famiglia [°/°–90°] _s )e per le componenti di sforzo più significative, il valore della potenza della singolarità e quello che viene definito fattore d'intensità degli sforzi al bordo libero. Sulla scorta di tali valori si confrontano le varie laminazioni e sequenze di impaccamento.Per tuttii questi aspetti viene inoltre condotta un'indagine comparativa, per valutare l'effetto dovuto allo spessore dello strato di resina interlaminare.

     

Behavior of Pin-loaded Laminated Composites

In this study, an investigation was carried out to determine the effects of joint geometry and fiber orientation on the failure strength and failure mode in a pinned joint laminated composite plate. Behavior of pin-loaded laminated composites with different stacking sequence and different dimensions has been observed experimentally. E/glass–epoxy composites were manufactured to fabricate the specimens. Mechanical properties of the composites were characterized under tension, compression and in-plane shear in static loading conditions. Laminated composites were loaded through pins. Single-hole pin-loaded specimens were tested for their tensile response and width-to-hole diameter (W/D) and edge distance-to-hole diameter (E/D) ratios evaluated. A series of experiments was performed with six different material configurations ([0/±45]_s–[90/±45]_s, [0/90/0]_s–[90/0/90]_s and [90/0]_2s–[±45]_2s), in all, over 120 specimens. E/D ratios and W/D ratios of plates were changed from 1 to 5 and 2 to 5, respectively. Failure propagation and failure type were observed on the specimens. The influence of the joint geometry on the strength of the pin-loaded composites was assessed. When laminated composite plates were loaded to final failure, three basic failure modes consisting of net-tension, shear out and bearing failure were observed for the different geometric dimensions. All the connections tested showed that the fiber orientations have a definite influence on the position around hole circumference at which failure initiated. Net-tension failure occurred for specimens that had small width and large end distance. When the width was increased, the specimens which had small end distances failed in the shear-out modes. When the end distance was increased, bearing failure developed in addition to shear-out failure. The experimental results showed that the ultimate load capacities of E/glass–epoxy laminate plates with pin connection were increased by increasing W and E. However, increasing the E/D and W/D ratios beyond a critical value has an insignificant effect on the ultimate load capacity of the connection.     

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.     

Measurement of fatigue damage in composite materials

Numerical results for the stress state around a circular hole in a [0/±45/0]_s boron-epoxy plate under tensile loading are presented. This serves as a model for the initial stress state around the hole during fatigue loading. Comparison is drawn with experimental results for a fatigued specimen obtained from thermography and radiography. Using these results, an interpretation of the effects of the initial stress state on the thermal behavior and on failure initiation is given. This interpretation shows that the circumferential normal stresses are responsible for the initial heat generation and failure initiation in the fatigued specimen.     

Experimental study of a metal-matrix composite

A metal-matrix specimen was investigated using moiré interferometry with 2400 ℓ/mm (60,960 ℓ/in.). The specimen was a 6-ply [0/±45] _s boron-aluminum tensile coupon with a central slot. The unequal deformations in fibers and matrix were evident. Special attention was given to a plastic slip zone in the matrix. Normal and shear strains were calculated in the slip zone; the shear-strain concentration factor rose dramatically with the onset of plastic slip and continued to rise gradually with load to 95 percent of the failure load. The precipitous change from maximum tensile strain in one fiber to zero tensile strain in the neighboring fiber was accommodated by the very high shear strain in the matrix in the slip zone. Experimental considerations are discussed: shear strains are independent of rigid-body rotations; simplified strain calculations are justified; averaging across the narrow slip region and the influence of finite thickness of the specimen grating contribute to underestimation of peak strains. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

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.     

The Development of a High Rate Tensile Testing System for Micro Scaled Single Crystal Silicon Specimens

Structures have been built at micro scales with unique failure mechanisms that are not yet understood, in particular, under high-rate loading conditions. Consequently, microelectromechanical systems (MEMS) devices can suffer from inconsistent performance and insufficient reliability. This research aims to understand the failure mechanisms in micro-scaled specimens deforming at high rates. Single-crystal silicon (SCS) micro specimens that are 4 μm thick are subjected to tensile loading at an average strain rate of 92 s^?1 using a miniature Hopkinson tension bar. A capacitance displacement system and piezoelectric load cell are incorporated to directly measure the strain and stress of the silicon micro specimens. The average dynamic elastic modulus of the silicon micro specimens is measured to be 226.8?±?18.50 GPa and the average dynamic tensile strength of the silicon is measured to be 1.26?±?0.310 GPa. High-speed images show that extensive fragmentation of the specimens occurs during tensile failure.     

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.     

Photoelasto-plastic studies on brittle fracture of high-polymer solids

The mechanism of brittle fracture of high-polymer solids is experimentally investigated under one-or two-dimensional stress states by a new photoelastoplastic method suggested by the author. The application of the photoelasto-plastic method on the brittle-fracture problem is based on the principle that breaking stress can be computed in brittle fracture by the measurement of the fringe orderN _B of isochromatic lines at fracture point. Bending under three-point and four-point loads, and the plane problems, some having stress concentration and others being under contacting load, are examined by using rigid polyester cast resin containing styrol as a model specimen; and, in conclusion, the brittle fracture of high-polymer solids under one- or two-dimensional stress states is decided by the constant tensile stress, whose magnitude depends only upon the material used as a model specimen, and is larger than its ultimate tensile strength. Many kinds of factors in fracture are defined, and stress-concentration factors in fracture are compared with stress-concentration factors in elasticity. A new photoelasto-plastic simple method for the determination of stress-concentration factors in elasticity is suggested by utilization of the experimental results on this brittle fracture of high-polymer solids and is examined on the perforated plane problem having finite width under tension in comparison with theoretical analysis and the experimental results by other measuring methods.     

Brittle-material failures as indicators of stress-concentration factors

The objective of this paper is the study of the possibility of using the amount of load producing failure in brittle-material models to compute stress-concentration factors. Several correlations between brittle-failure loads and stress-concentration factors were investigated. For their tests, the authors developed a plaster-silica mortar and studied the influence of twelve variables on its ultimate tensile strength. Included were physical and processing variables, and loading and stress conditions. Some applications of the method are shown.     

Layup optimization with GA for tapered laminates with internal plydrops

Layup optimization of the maximum strength of laminated composites with internal ply-drops is performed by genetic algorithm (GA). Interlaminar stresses are considered in estimating the strength of laminates and calculated by the stress function based complementary virtual work principle. Out-of-plane stress functions are expanded in terms of harmonic series through the thickness direction and initially satisfied the traction free boundary conditions of laminates automatically. As the number of expansion terms is increased, stress concentration near the dropped plies is predicted with better accuracy. Since the proposed analysis is relatively simple and efficient in the prediction of interlaminar stress concentration near the ply-drops, the layup optimization of composite laminates with dropped plies considering interlaminar strength can be easily performed by GA. In the formulation of genetic algorithm, a repair strategy is adopted to satisfy given constraints and multiple elitism scheme is implemented to efficiently find multiple global optima or near-optima.     

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.     

褶皱与晶界耦合作用对石墨烯断裂行为的影响

由CVD方法制备的石墨烯含有大量的晶界,通常还带有许多褶皱,本文通过分子动力学方法研究了具有褶皱和晶界的石墨烯 平面拉伸断裂行为,结果显示,在垂直晶界方向,褶皱能够显著提高小角度双晶石墨烯的断裂应力,断裂应力增幅最 大约为50%,褶皱对断裂应力的影响随晶界角的增大减弱,导致双晶石墨烯断裂应力对晶界角不敏感,只略低于单晶石墨 烯,和实验结果完全吻合;在沿晶界方向,褶皱对双晶石墨烯断裂应力影响不明显. 另外,褶皱可以显著提高双晶石墨烯的断 裂应变,增幅最大约为100%. 增强机制归纳主要如下:通过面外变形,褶皱可以部分释放晶界5-7环中C---C键的预拉伸变形, 提高双晶石墨烯的断裂应力;褶皱可以降低相邻5-7环之间相互作用,导致断裂应力对晶界角不敏感;在拉伸作用下,褶皱被部分 拉平,这可以显著降低C---C键面内拉伸变形,导致断裂应变显著增大. 本研究为准确理解多晶石墨烯断裂行为提供重要帮助.      

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.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.