Micro-Mechanical Analysis About Kink Band in Carbon Fiber/Epoxy Composites Under Longitudinal Compression

Kink band is a typical phenomenon for composites under longitudinal compression. In this paper, theoretical analysis and finite element simulation were conducted to analyze kink angle as well as compressive strength of composites. Kink angle was considered to be an important character throughout longitudinal compression process. Three factors including plastic matrix, initial fiber misalignment and rotation due to loading were considered for theoretical analysis. Besides, the relationship between kink angle and fiber volume fraction was improved and optimized by theoretical derivation. In addition, finite element models considering fiber stochastic strength and Drucker-Prager constitutive model for matrix were conducted in ABAQUS to analyze kink band formation process, which corresponded with the experimental results. Through simulation, the loading and failure procedure can be evidently divided into three stages: elastic stage, softening stage, and fiber break stage. It also shows that kink band is a result of fiber misalignment and plastic matrix. Different values of initial fiber misalignment angle, wavelength and fiber volume fraction were considered to explore the effects on compressive strength and kink angle. Results show that compressive strength increases with the decreasing of initial fiber misalignment angle, the decreasing of initial fiber misalignment wavelength and the increasing of fiber volume fraction, while kink angle decreases in these situations. Orthogonal array in statistics was also built to distinguish the effect degree of these factors. It indicates that initial fiber misalignment angle has the largest impact on compressive strength and kink angle.     

The development of compression damage zones in fibrous composites

Recent experimental work (Narayanan S, Schadler LS. Mechanisms of kink band formation in graphite/epoxy compsites: a micromechanical experimental study. Comp Sci Technol 1999; 59:2201-13) suggests that kink bands in unidirectional continuous carbon fiber reinforced polymer composites initiate from damage zones formed under axial compressive loads. A damage zone consists of a cluster of locally crushed fibers and broken fibers, that are often fractured at an angle, θ > 0°, normal to the fiber axis. Typically, under compressive loads, fiber breaks in damage zones form roughly along a plane at an angle φ, normal to the fiber axis. These damage zones produce stress concentrations which can lead to instabilities in the nearby fiber and matrix and initiate microbuckling and kink bands. This paper extends a micromechanical influence function technique based on earlier shear lag fiber composite models. Our modified technique calculates the fiber axial and matrix shear stress concentrations due to multiple angled and crushed fibers in arbitrary configurations. Modeling reveals that angled or ‘shear’ breaks (θ > 0°) can lead to higher shear stress concentrations in the matrix than transverse breaks (θ=0°). Also we find that the damage zone is more likely to form at an angle φ, which is greater than that of its individual fiber breaks, θ. When φ is slightly greater than θ, the shear stress in the surrounding matrix regions within the damage zone achieves a maximum, potentially weakening the matrix and interface and consequently leading to kink band formation. Monte Carlo simulations incorporating this stress analysis predict that the initiation and propagation of crushed and angled breaks progress roughly along an angle, φ ≈ 17° in a linear elastic system. When possible, our model results are compared to strain measurements of fiber composites under compression obtained by Narayanan and Schadler using micro-Raman spectroscopy (MRS).     

Compressive strength of unidirectional fiber composites with matrix non-linearity

A study has been made of the effect of fiber misalignment and non-linear behavior of the matrix on fiber microbuckling and the compressive strength of a unidirectional fiber composite. The initial fiber misalignment constituted the combined axial and shear stress state in the matrix, and the state of stress just prior to the buckling was considered to be the initial state of stress in bifurcation analysis. The expression for the critical microbuckling stress was found to be the same as that for the elastic shear-mode microbuckling stress except that the matrix elastic shear modulus was replaced by the matrix elastic-plastic shear modulus. Incremental theory of plasticity and deformation theory of plasticity were used to model the matrix non-linearity. The analysis results showed reasonable correlation with available experimental data for AS4/3501-6 and AS4/PEEK graphite composites with 2° to 4° range of initial fiber misalignment.     

Impact properties of laminated angle ply composites

The impact properties of laminated composites have been studied as a function of fiber orientation angle, lamination configuration and specimen geometry. The energy absorbing mechanisms havebeen identified. The impact properties of laminated composites are influenced significantly by the fiber orientation angle, lamination configuration and specimen geometry. All off-axis composites (0° < θ < 90°) fail by brittle inter-fiber cleavage mode with little or no interlayer delamination. The longitudinal composites (θ = 0°), both unidirectional and crossplied, fail by a combination of failure modes which take place in a sequential manner—fiber failure and interfacial splitting followed by a layer-to-layer delamination. The presence of 0° layer(s) in transverse composite (θ ±90°) improves their impact performance.     

Transformation zones, crack shielding, and crack-growth resistance of Ce-TZP/alumina composite in mode II and combined mode II and mode I loading

Crack-tip transformation zones, crack shielding and crack-growth-resistance (R-curve) behaviors of a transformation-toughened ceria-partially stabilized zirconia–alumina (Ce-TZP/alumina) composite were studied in mode II and combined mode I and mode II loading using compact-tension-shear (CTS) specimens. The mode II and mode I stress intensities for both the initial straight cracks and the subsequent kinked cracks were assessed by the method of caustics using geometrically equivalent specimens of polymethyl methacrylate (PMMA). The angle of formation of the transformation zones as well as of extension of the cracks increased systematically with increasing ratio of the mode II and the mode I stress intensities and approached a value of θ^*=−72° in pure mode II loading. This angle was close to the angle for maximum hoop tension in the stress field of a mode II crack (θ^*=−70.5°). A crack-initiation toughness envelope was constructed on a K_I–K_II diagram using the critical loads for incremental crack extension. The crack-initiation toughness in pure mode II loading was less than the corresponding toughness in mode I loading. This result was consistent with calculations that indicated no shielding from the asymmetric and elongated zones developed in mode II loading. The fracture toughness measured for the kinked cracks at long kink lengths approached the maximum fracture toughness measured for a mode I crack.     

Lattice rotation and stability of 22.5° ND rotated cube orientation in cold rolled polycrystalline AA 5182 aluminum alloy

AA 5182 aluminum alloy with a strong cube texture was cold rolled to different reductions at an angle of 22.5° to the prior rolling direction. The texture evolution at this new rolling direction was investigated by X-ray diffraction. The rotation paths and stability of the 22.5° ND rotated cube orientation were determined based on the variation in the three-dimensional orientation distribution function (ODF) with rolling reduction. The results show that most of the grains with the 22.5° ND rotated cube orientation are directly rotated to the β fiber along different rotation paths, but there are a few grains moving through the cube orientation to the β fiber. The {0 0 1}<1 1 0> oriented grains possess the lowest stability during rolling, and the stability increases as the initial orientation changes from the {0 0 1}<1 1 0> orientation to the {0 0 1}<1 0 0> orientation along the ₁ axis.     

The effect of hydrostatic pressure and loading rate on compressive failure of fiber-reinforced ceramic-matrix composites

The influence of hydrostatic confinement on compressive strength and corresponding failure mechanisms is explored for SiC-reinforced glass-ceramics tested at different strain rates. Two composite architectures (0° and 0°/90°) are studied, and their behavior is compared with that of monolithic glass-ceramic tested under similar conditions. Composite confined pressure results are interpreted in terms of fiber buckling under quasi-static conditions and fiber kinking at high pressures, and compared with monolithic (non-composite) microfracture coalescence at low pressures and shear band formation under more intense confinement. In particular, dilatational fracture within the matrix dominates composite failure at low pressures, while high pressures cause a transition to shear-dominated mechanisms based on fiber kinking.     

Compressive response of Kevlar-epoxy composites: experimental verification

The initial misalignment of Kevlar fibres in Kevlar-epoxy composites is quantitatively investigated. This misalignment has been found to be one of the most important factors for determining the compressive response of these composites. A theoretical model, which considers initial fibre misalignment and assumes that the compressive response of Kevlar-epoxy composites is dominated by kink band failure, is in good agreement with experimental results. In addition, photomicrographs of the failure surfaces suggest that kink band formation is the predominant failure mode in this composite system.     

Influence of Compression and Shear on the Strength of Composite Laminates with Z-Pinned Reinforcement

The influence of compression and shear loads on the strength of composite laminates with z-pins is evaluated parametrically using a 2D Finite Element Code (FLASH) based on Cosserat couple stress theory. Meshes were generated for three unique combinations of z-pin diameter and density. A laminated plate theory analysis was performed on several layups to determine the bi-axial stresses in the zero degree plies. These stresses, in turn, were used to determine the magnitude of the relative load steps prescribed in the FLASH analyses. Results indicated that increasing pin density was more detrimental to in-plane compression strength than increasing pin diameter. Compression strengths of lamina without z-pins agreed well with a closed form expression derived by Budiansky and Fleck. FLASH results for lamina with z-pins were consistent with the closed form results, and FLASH results without z-pins, if the initial fiber waviness due to z-pin insertion was added to the fiber waviness in the material to yield a total misalignment. Addition of 10% shear to the compression loading significantly reduced the lamina strength compared to pure compression loading. Addition of 50% shear to the compression indicated shear yielding rather than kink band formation as the likely failure mode. Two different stiffener reinforced skin configurations with z-pins, one quasi-isotropic and one orthotropic, were also analyzed. Six unique loading cases ranging from pure compression to compression plus 50% shear were analyzed assuming material fiber waviness misalignment angles of 0, 1, and 2°. Compression strength decreased with increased shear loading for both configurations, with the quasi-isotropic configuration yielding lower strengths than the orthotropic configuration.     

Micromechanical modeling of damage and failure mechanisms in C/C–SiC

This paper deals with modeling of damage and failure mechanisms observed in 2D C/C–SiC composite samples loaded by tension, shear and compression. In a specimen subjected to tension, the early stage of damage is characterized by transverse cracking. Further load increase induces fiber failure in the longitudinal plies, which leads to fracture. Shear loading gives origin to cracks oriented at 0°/90° and 45° to the fiber axes, the latter causing fracture. Specimens loaded in compression exhibit catastrophic failure due to microbuckling of fiber bundles. Micromechanical models are formulated for the discussed mechanisms. Results of numerical simulations show good agreement with experiments and the ability of the model to describe more complex loadings.     

考虑纤维初始位错的复合材料轴向压缩性能

通过试验及模拟对复合材料的轴向压缩失效过程进行了研究。试验中,采用高速摄像机对失效过程进行捕捉,并对最终破坏模式进行光学显微镜分析。基于纤维初始位错、纤维随机强度及基体Ducker-Prager塑性本构,通过有限元软件ABAQUS建立了复合材料轴向压缩的有限元模型,并对比分析剪切型及拉伸型两种不同初始位错模型的模拟结果。研究结果表明,复合材料轴向压缩包含弹性变形及塑性变形阶段,离散的纤维基体二维有限元模型能够有效模拟压缩的渐进损伤过程,且模拟结果与试验结果相吻合。复合材料轴向压缩强度是纤维初始位错及塑性基体剪切屈服共同作用的结果,其随着纤维初始位错幅值的减小、波长的增加及纤维体积分数的增加而增加。     

Measurement of small angle fiber misalignments in continuous fiber composites

In aligned, continuous fiber composites the fibers actually wander with small angular misalignments about the mean direction. These misalignments are suspected of having a significant influence on several mechanical properties, such as longitudinal compression strength and tensile modulus. A technique is presented for measuring the volume fraction distribution of fiber misalignment angle in the range of ±10°, with an estimated resolution of ±0·25°. The method can provide a full bivariate distribution, which includes both in-plane and out-of-plane misalignments. Data from a carbon fiber composite, APC-2, are given as an illustration. Misalignment distributions for prepreg, a 0/90 laminate, and a unidirectional laminate are given. It is found that the distribution in the prepreg is axially symmetric, but changes upon laminations, the changes depending on stacking sequence. In this particular material most of the fibers are found to lie within ±3° of the mean fiber direction. Distribution standard deviations range from 0·693 to 1·936 degrees.     

Improvement of the mode II interface fracture toughness of glass fiber reinforced plastics/aluminum laminates through vapor grown carbon fiber interleaves

The effects of acid treatment, vapor grown carbon fiber (VGCF) interlayer and the angle, i.e., 0° and 90°, between the rolling stripes of an aluminum (Al) plate and the fiber direction of glass fiber reinforced plastics (GFRP) on the mode II interlaminar mechanical properties of GFRP/Al laminates were investigated. The experimental results of an end notched flexure test demonstrate that the acid treatment and the proper addition of VGCF can effectively improve the critical load and mode II fracture toughness of GFRP/Al laminates. The specimens with acid treatment and 10 g m⁻² VGCF addition possess the highest mode II fracture toughness, i.e., 269% and 385% increases in the 0° and 90° specimens, respectively compared to those corresponding pristine ones. Due to the induced anisotropy by the rolling stripes on the aluminum plate, the 90° specimens possess 15.3%–73.6% higher mode II fracture toughness compared to the 0° specimens. The improvement mechanisms were explored by the observation of crack propagation path and fracture surface with optical, laser scanning and scanning electron microscopies. Moreover, finite element analyses were carried out based on the cohesive zone model to verify the experimental fracture toughness and to predict the interface shear strength between the aluminum plates and GFRP laminates.     

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.     

Crushing response of composite corrugated tubes to quasi-static axial loading

This paper is devoted to examine the crushing behaviour of axially crushed composite corrugated tubes. Two types of composites were tested, namely, carbon fibre/epoxy in a filament form and glass fibre/epoxy in woven roving form. A series of experiments was conducted for tubes with corrugation angle (β) ranging from 10° to 40°. Typical failure histories of their failure mechanisms are presented and discussed. The results showed that the crushing behaviour of composite corrugated tube is found to be sensitive to the change in corrugation angle and fibre type. Carbon/epoxy tubes with corrugation angle of 40° displayed the highest specific energy absorption capability. It is also found that introducing of corrugation could significantly enhance the energy absorption capability of composite tubes in a uniform manner.     

Continuous cooling transformation behavior of Alloy 718

The transformation behavior of Alloy 718 is affected significantly by the cooling rate. The γ″-phase appears at cooling rates less than 20 °C/min and δ-phase appears at grain boundaries as well as the MC type carbides at cooling rates below 5 °C/min. The δ-phase nucleates and grows preferentially at grain boundaries, and less preferentially at the MC carbides. The size of the γ″ and δ-precipitates increases consistently with decreasing cooling rate for the given conditions. The hardness varies with the transformation behavior. A hardness peak was noticed for a cooling rate of 5 °C/min. The hardness peak corresponded to the maximum volume fraction of γ″ which in turn was strongly affected by the presence of the δ-phase.     

Numerical investigations of free edge effects in integrally stiffened layered composite panels

A linear finite element analysis is conducted to examine the free edge stresses and the displacement behavior of an integrally stiffened layered composite panel loaded under uniform inplane tension. Symmetric (+Φ, −Φ, 0, −Φ, +Φ) graphite-epoxy laminates with various fiber orientations in the off-axis plies are considered. The quadratic stress criterion, the Tsai-Wu criterion and the Mises equivalent stresses are used to determine a risk parameter for onset of delamination, first ply failure and matrix cracking in the neat resin. The results of the analysis show that the interlaminar stresses at the +Φ/−Φ and −Φ/0 interfaces increase rapidly in the skin-stringer transition. This behavior is observed at the free edge as well as at some distance from it. The magnitude of the interlaminar stresses in the skin-stringer transition is strongly influenced by the fiber orientations of the off-axis plies. In addition, the overall displacements depend on the magnitude of the off-axis ply angle. It is found that for Φ < 30° the deformations of the stiffener section are dominated by bending, whereas for 45° < Φ < 75° the deformations are dominated by torsion. The failure analysis shows that ply and matrix failure tend to occur prior to delamination for the considered configurations.     

Structure, texture and mechanical properties of AlZnMgCuZr alloy rolled after heat treatments

The aluminium alloy containing 6.7 wt.% Zn, 2.6 wt.% Mg, 1.6 wt.% Cu and 0.1 wt.% Zr was continuously cast and either quenched from 465°C, or furnace cooled down to 100°C to find the best ductility for further cold plastic deformation. The alloys were then cold rolled down to the highest possible degree of deformation. The initial texture in both alloys can be described by (211)[111], (321)[346] and (110)[112] ideal orientations. With increasing deformation other orientations like {110}001 and cubic {100}001 appear after both types of treatments. TEM studies revealed increase of subgrain misorientation up to approx. 9° after 75% of deformation by rolling. On ageing at 120°C for 24 h the maximum hardness of 210 HV was reached. The alloys deformed prior to ageing at 120°C attained 230 HV. Very small GP zones, up to a few nanometers in size, grow after several days of ageing giving diffused diffraction effects. After ageing for 1 day at 120°C, precipitates grow and were identified as η′.     

Compression of a 0°-ply/acrylic sandwich

The compressive behaviour of a 0°-ply (AS4/PPS) inserted between two acrylic layers is studied experimentally, and results are compared with existing theoretical predictions. A transparent acrylic is chosen so that kink formation in the 0°-ply may be directly observed. Experiments show that failure occurs by catastrophic formation of an in-plane kink band with a kink band angle of 20° to the horizontal axis. Then, as the compression strain is further increased, several additional kink bands appear. The load corresponding to the formation of the first kink is in agreement with theoretical predictions. These experiments confirm that failure initiates by in-plane kinking, and shed light upon the behaviour of an internal 0°-ply inside a multidirectional laminate, especially the propensity for in-plane kinking versus out-of-plane kinking.     

Low-temperature, direct synthesis of β-SiC by metal vapor vacuum arc ion source implantation

Crystalline β-SiC surface layers with strong (111) preferred orientation were synthesized by direct ion implantation into Si(111) substrates at a low temperature of 400°C using a metal vapor vacuum arc ion source. Both X-ray diffraction and Fourier transform infrared spectroscopy reveal an augment in the amount of β-SiC with increasing implantation doses at 400°C. Scanning electron microscopy shows the formation of an almost continuous SiC surface layer after implantation at 400°C with a dose of 7×10¹⁷/cm². The full width at half maximum of the X-ray rocking curve of β-SiC(111) was measured to be 1.4° for the sample implanted at a dose of 2×10¹⁷/cm² at 700°C, revealing a good alignment of β-SiC with the Si matrix.