Analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam specimen using higher order beam theories

Mathematical models, for the stress analysis of unidirectional (0°) fiber-reinforced laminated composite double cantilever beam (DCB) specimen using classical beam theory, first and higher order shear deformation beam theories, have been developed to determine the mode I strain energy release rate (SERR) for unidirectional composites. In the present study, appropriate matching conditions at the crack tip of the DCB specimen have been derived by using variational principles. SERR has been calculated using compliance method. In general, the performance of shear deformation beam models of DCB specimen with variationally derived matching conditions at the crack tip is good in determining the SERR for medium to long crack lengths. Performance of higher order shear deformation beam model (having quadratically varying transverse displacement over the thickness) of DCB specimen, with non-variationally derived matching conditions at the crack tip, is good in determining the SERR for all the crack lengths in comparison with the available theoretical and finite element solutions in the literature. Higher order shear deformation beam theories having varying transverse displacement over the thickness are more appropriate to analyze DCB specimen as they predict the appropriate nature of the interlaminar normal stress at the crack tip and its distribution ahead of the crack tip.     

Transverse shear and pressurization effects in the bending of plates with reinforced cracks

The authors develop an eigth-order model for bending of transversally isotropic plates and use integral transforms and a collocation method to form a line-spring model for a cracked plate. The eigth-order model allows satisfaction of the three standard plate bending boundary conditions; the normal moment, twisting moment, and transverse shear force, and an additional shear stress resultant that allows analysis of transverse normal stresses near the crack tip. The line-spring model is used to develop geometry correction factors for bending of finite-thickness plates, accounting for transverse shear deformation and pressurization of the plate near the crack tip. The line-spring model is then applied to the problem of a plate with a reinforced crack, and the results are used to validate an interpolation solution based on an energy method. While not explicitly analysed, the models are applicable to many problems, including bending of bonded repairs, fracture and fatigue of composite and layered materials, surface cracks, crack tip plasticity and crack closure or crack face interaction.     

Fracture surface evolution and apparent delamination toughness in split composite beam specimens subjected to mixed mode I–III loading

The influence of specimen twisting during global anti-plane shear loading in composite split beam specimens is studied. Tests were conducted on specimens with different thicknesses and delamination lengths to produce different amounts of specimen twisting prior to fracture. It is shown that specimen twisting causes mode I stresses to develop, thereby producing mixed mode I–III conditions along the delamination front. This causes near-tip transverse cracks to initiate, prior to delamination advance, at an orientation related to the mode mix. Unlike in homogeneous materials, transverse crack extension is accompanied by planar delamination advance, and transverse crack rotation during extension is restricted by the laminate’s fibers. The overall fracture surface evolution is therefore strongly controlled by specimen geometry. The influence of these findings on the apparent delamination toughness as obtained from composite split beam and other types of mode III tests is discussed.     

Dynamic behavior of thin and thick cracked nanobeams incorporating surface effects

Free transverse vibration of cracked nanobeams is investigated in the presence of the surface effects. Two nanobeam types, thin and thick, are studied using two beam theories, Euler–Bernoulli and Timoshenko. The influences of crack severity and position, surface density, rotary inertia and shear deformation, nanobeam dimension, mode number, satisfying balance condition between the surface layers and the bulk, boundary conditions and satisfying compatibility and boundary conditions with appropriate resultant moment and shear force are studied in details. It is found out that satisfying compatibility and boundary conditions with the resultant moment and shear force in presence of the surface effects and considering surface density neglected in previous work have significant effects on the natural frequencies of cracked nanobeams. In addition, rotary inertia and shear deformation cause a reduction in the crack and surface effects on the natural frequencies.     

7055铝合金T型型材的应力腐蚀行为研究

通过拉伸性能测试、C环应力腐蚀试验、金相分析、扫描电镜和透射电镜观察等研究了7055铝合金T型型材的应力腐蚀开裂(SCC)行为.结果表明:7055铝合金T型型材纵向试样的抗拉强度、屈服强度、伸长率及断面收缩率均大于横向试样的;在间浸腐蚀和恒温恒湿环境下,纵向C环试样的开裂时间均长于横向试样的.型材纵向截面晶粒变形特征明...     

A single-lap shear specimen for determining the effect of strain rate on the interlaminar shear strength of carbon fibre-reinforced laminates

A new design of single-lap shear specimen for determining the effect of loading rate on the interlaminar shear strength of laminated composites is described. Finite element analyses are used to optimize the specimen geometry and minimize the variation in the shear stress and the magnitude of the normal stress along the interlaminar failure plane. Experimental results are obtained at a quasi-static and an impact rate of loading for the interlaminar shear strength parallel to the fibres in both unidirectional carbon/epoxy and unidirectional carbon/polyetheretherketone (peek) laminates and at interfaces across which the fibre orientation is 0°/90° and ±45°. Results for carbon/epoxy laminates are compared with those from an earlier investigation using a double-lap specimen geometry and show a similar small dependence on loading rate. No significant effect of loading rate was observed for the carbon/peek laminates.     

Characterization of interlaminar shear failures of graphite/epoxy composite materials

Research undertaken to develop a more fundamental understanding of interlaminar shear failure in laminated graphite/epoxy composites is described. A test method capable of producing a state of pure interlaminar shear stress within a specified region of a composite test specimen was devised. The test method consisted of the four-point flexural testing of a unique test sample constructed of a coupon of Hercules AS4/3501-6, unidirectional, graphite/epoxy material bonded between two strips of steel using a room-temperature-curing epoxy adhesive. The major advantage of the test method is that the interlaminar shear failure of the composite coupon results from an induced state of pure shear stress, rather than from damage resulting from a complex stress state affecting the region of loading as typically occurs in the case of conventional flexural-type shear tests. The resulting shear failures were characterized with respect to fracture surface appearance, mode of failure, and stress state on the failure plane. A specially designed crack detection device was used to determine the site of fracture initiation and the direction of crack propagation.     

Mode II interlaminar fracture properties of Moso bamboo

Bamboo is a kind of biological composites reinforced by unidirectional long fiber. Once there exists crack, the propagation of delamination is controlled by the interlaminar fracture toughness instead of by strength. In this paper, the end notched flexure (ENF) beam specimen was used to test the Mode II interlaminar fracture toughness G_IIC along grain of Moso bamboo internode and the fracture surface was analyzed. The results were obtained that the Mode II interlaminar fracture toughness G_IIC calculated by the experiment parameter substitution method was more accurate and the value was 1303.18 J/m² (coefficient of variation = 8.96%) which was about three times higher than the value of Mode I interlaminar fracture toughness; the crack propagation of Mode II interlaminar fracture was mainly self-similar cracking, but the fracture surface was rougher. Ground tissue in the zone of Mode II crack propagation was characterized by hackle shearing deformation. The SEM photos showed that ground tissue separated from fiber along middle lamella under shear stress and as the increasing of the dislocation of upper and lower layer, the thin-walled ground tissue would fracture transversely by tension, while to thick-walled fiber cell, only middle lamella and primary wall were torn then debonded, fragments remained.     

Influence of silane coupling agents on interlaminar fracture in glass fibre fabric reinforced unsaturated polyester laminates

The relationship between the adhesive properties of the interphase of glass fibre/resin and the resultant composite Mode I delamination fracture toughness in glass fibre fabric laminate (GFFL) was studied. The Mode I interlaminar fracture toughness of GFFL was obtained by using a double cantilever beam (DCB) specimen. The delamination resistance of GFFLs which have two silane coupling agents and three concentration finishes is discussed on the basis of interlaminar fracture toughness. The crack propagation behaviour of DCB testing was mainly divided into stable and unstable manners. The fracture toughness and the crack propagation behaviour were dependent on the types and concentration of silane coupling agents.     

Modelling of stable and unstable fracture of short beam shear specimens

Finite element analysis of interlaminar shear failure in unidirectional carbon fibre/epoxy is carried out. A short beam shear test with a large loading roller is modelled including the effects of large displacements and varying contact between the rollers and the specimen. The shear stress/deformation characteristics of the interfacial layers between plies are included by means of non-linear spring elements, and shown to determine whether the overall response of the specimen is stable or unstable. The span-to-thickness ratio also affects the stability of the response. The effect of specimen geometry on stability, which has also been observed experimentally, is difficult to explain by conventional analysis approaches. These results suggest that a good representation of the interface between plies is crucial for accurate modelling of overall structural response involving interlaminar shear failure.     

三维编织SiC/SiC复合材料拉伸和弯曲损伤机制

为了研究三维编织SiC/SiC复合材料损伤机制,开展了室温条件下的单调拉伸和三点弯曲试验。实验前,利用CT扫描手段,明确了三维编织SiC/SiC复合材料试样的编织组织形态。对拉伸和三点弯曲试样的微观分析表明:原生孔洞和微裂纹导致了材料在单调拉伸过程中形成局部应力集中,随着拉伸载荷的增大,基体的横向开裂和纤维束间纵向层间裂纹逐渐演化形成纤维内部裂纹,导致材料最终的脆性断裂失效;在三点弯载荷作用下,表现为剪切、拉压共生的多耦合破坏模式,拉应力一侧首先发生失效,随后在中性面处发生剪切破坏,紧接着失效迅速向上下两侧扩展,直至截面在整个厚度方向发生失效;断口与纤维束的走向相关性很大,裂纹基本上沿着纤维束之间的界面进行扩展,导致最终失效未发生在理论失效位置处。      

Multilayered shell finite element with interlaminar continuous shear stresses: a refinement of the Reissner–Mindlin formulation

A finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness is presented. An underlying shell model is a direct extension of the first‐order shear‐deformation theory of Reissner–Mindlin type. A refined theory with seven unknown kinematic fields is developed: (i) by introducing an assumption of a zig‐zag (i.e. layer‐wise linear) variation of displacement field through the thickness, and (ii) by assuming an independent transverse shear stress fields in each layer in the framework of Reissner's mixed variational principle. The introduced transverse shear stress unknowns are eliminated on the cross‐section level. At this process, the interlaminar equilibrium conditions (i.e. the interlaminar shear stress continuity conditions) are imposed. As a result, the weak form of constitutive equations (the so‐called weak form of Hooke's law) is obtained for the transverse strains–transverse stress resultants relation. A finite element approximation is based on the four‐noded isoparametric element. To eliminate the shear locking effect, the assumed strain variational concept is used. Performance of the derived finite element is illustrated with some numerical examples. The results are compared with the exact three‐dimensional solutions, as well as with the analytical and numerical solutions obtained by the classical, the first‐order and some representative refined models. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading

The present paper is concerned with multi-axial ductile fracture experiments on sheet metals. Different stress-states are achieved within a flat specimen by applying different combinations of normal and transverse loads to the specimen boundaries. The specimen geometry is optimized such that fracture initiates remote from the free specimen boundaries. Fracture experiments are carried out on TRIP780 steel for four different loading conditions, varying from pure shear to transverse plane strain tension. Hybrid experimental–numerical analyses are performed to determine the stress and strain fields within the specimen gage section. The results show that strain localization cannot be avoided prior to the onset of fracture. Through-thickness necking prevails under tension-dominated loading while the deformation localizes along a band crossing the entire gage section under shear-dominated loading. Both experimental and simulation results demonstrate that the proposed fracture testing method is very sensitive to imperfections in the specimen machining. The loading paths to fracture are determined in terms of stress triaxiality, Lode angle parameter and equivalent plastic strain. The experimental data indicates that the relationship between the stress triaxiality and the equivalent plastic strain at the onset of ductile fracture is not unique.     

The interlaminar crack-tip response in a fiber-reinforced composite laminate

A solution is presented for the problem of an interlaminar crack in a laminated fiber-reinforced composite material. The theory of anisotropic elasticity under a state of generalized plane deformation is employed as a basic framework of this study. In the analytical model, dissimilar anisotropic half-spaces with different fiber orientations which are bound together by a matrix interlayer are considered. The interlayer approximates the matrix-rich interlaminar region containing the crack. The stiffness matrix approach is utilized and the current crack problem is reduced to solving a system of singular integral equations. The singular response of an interlaminar crack to in-plane normal, in-plane shear, and anti-plane shear loadings is evaluated in terms of mixed-mode stress intensity factors. Under each of the leading conditions, the parametric effects of laminate stacking sequence, relative crack size, crack location, and fiber volume fraction are addressed.     

Bending effect of through-thickness reinforcement rods on mode II delamination toughness of ENF specimen: Elastic and rigid–perfectly plastic analyses

In this paper, a new simple metallic z-rod model is proposed to study the bending effect of the metallic z-rods on mode II delamination toughness of laminated composites. A new transverse shear force–deformation relationship for a metallic z-rod is obtained by using the classical beam theory and modeling its surrounding matrix as linearly elastic, rigid–perfectly plastic or linearly elastic–perfectly plastic springs. The bridging traction provided by a metallic z-rod to the mode II delamination toughness is assumed to be only the shear force carried by a z-rod created by the relative slippage between two substrate beams in an end-notched flexure (ENF) specimen, whereas the longitudinal sliding friction is assumed to make negligible contribution to the bridging traction. Mode II strain energy release rate (SERR) is employed to evaluate the influence of the metallic z-rods on the interlaminar fracture toughness of end-notched flexure (ENF) specimens. A parametric study of ENF specimens reinforced with the z-rods is conducted to demonstrate the effect of the new bridging mechanism by the metallic z-rods on the mode II delamination toughness.     

裂纹板贴补应力分析

本文采用含裂纹无限大板特殊基本解和合力边界条件,用体积力法对含裂纹金属薄板的胶贴补强问题进行应力分析。使用一满足胶贴层位移连续条件的剪切单元,把问题转化为对裂纹板和贴片的分析。由于使用的特殊基本解精确满足裂纹面自由力边界条件,避免了对裂纹尖端附近的奇异场进行离散处理,因而可以比较精确地求出裂纹尖端附近的应力分布,同时由于单位集中力引起的裂纹尖端应力强度因子可以解析得到,因而可以较准确地反映出用应力强度因子的降低来表征的贴补效果。作为贴补计算的例子,文中计算了受拉力和剪力作用时,含中心裂纹的金属裂纹板在贴补前后裂纹尖端应力强度因子的降低,给出了贴片的厚度、弹性模量和尺寸及肢贴层厚度等对贴补效果的影响。     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

Debonding and crack kinking in foam core sandwich beams—I. Analysis of fracture specimens

Sandwich beam specimens, recently developed for the study of facing/core debond fracture, were analyzed using the finite element method. Peel fracture was approached using a modified double cantilever beam (DCB) sandwich specimen with a precrack between the facing and core, while shear fracture employed a modification of the ASTM block shear test to include a facing/core precrack. Complex and conventional stress intensity factors were calculated for bimaterial cracks located between facing and bondlayer and bondlayer and core over a large range of core moduli. Overall, much larger stress intensity factors were observed for an interfacial crack between the facing and bondlayer than for a crack between the bondlayer and core for both types of specimens. Crack kinking analysis of the DCB specimen revealed that the debond tends to remain interfacial for stiff core materials, but may deflect into the core for compliant core materials. In shear loading of a debonded sandwich beam it was demonstrated that crack kinking is possible for any core material.     

Laminated beams subjected to transverse load

A simple elastic solution has been developed for predicting the shear stress distribution in a laminated beam subjected to a variety of transverse loading conditions. Photoelastic tests on composite models involving a single bonding layer have been used to validate the theory, and also to comment upon the significance of these results in interpreting the interlaminar shear strength and bending modulus of the simplest form of laminated strip.