An experimental evaluation of the slotted-tension shear test for composite materials

The slotted-tension shear test provides an accurate method of measuring the inplane shear response of fiber-reinforced composite materials. Data from the slotted-tension test is compared with rail, ±45-deg tension, modified lap-shear and off-axis shear tests. It is shown that reinforced materials of any combination of fibers and fiber orientation can be tested using the new shear-testing technique.     

Development of a portable shear test fixture for low modulus porous (foam) materials

The shear properties of brittle and highly porous carbon (graphitic) foam cannot be measured reliably with most standard test methods, such as single rail, double rail, Iosipescu shear, etc. A new testing device has been developed to accurately measure the shear stiffness and strength of carbon foam or other porous materials. Specimens of cylindrical cross section are used to reduce the high stress concentration that normally occurs in the vicinity of the grip section. Since strain gages could not be installed on the specimen surface (due to porosity), the shear strain is determined from the specimen end rotation. A high resolution in the rotational measurement is achieved by using a stepper motor with multiple gear reduction. In view of testing low modulus material, the load cell of the fixture was mounted onto an axial roller to relieve the axial constraint while twisting the specimens. The accuracy of the measurement and calibration of the test fixture has been demonstrated by measuring the shear modulus of two plastic (polyvinyl chloride (PVC) and urethane).     

Experimental investigation of dynamic punch tests on isotropic and composite materials

An experimental investigation is conducted on the two-dimensional punch problem for isotropic materials and unidirectional fiber-reinforced composite materials under quasi-static and impact loading. Singular stresses are generated in the specimen near the punch corners, and the stress intensity factorK _Iis introduced to describe the singular stress field. Laser interferometry is used to measure in-plane stresses (transmission mode) and out-of-plane displacements (reflection mode) and then estimate the stress intensity factor. In the dynamic case, a high-speed photography technique was employed to capture the transient response of the specimen and measureK(t) just after the impact. In all the cases, a good agreement between the measurements ofK and theoretical predictions was found.     

Experimental strain analysis of the losipescu shear test specimen

An experimental strain analysis of the losipescu shear test specimen was performed, utilizing a 20-ply AS4/3501-6 carbon/epoxy unidirectional composite. Using three-element strain-gage rosettes, it was shown that the presence of loading-point-induced transverse normal strains in the gage section do not affect the measured shear strain. Thus, the shear modulus determined using the standard notch specimen is not affected. Likewise, modulus determination is not influenced by cracking at the notch tips, since this occurs at strains beyond the range over which modulus is determined. To further evaluate the effect of notch-tip cracking, material was removed adjacent to the standard V-notches where these cracks initiate. The measured shear strength was unaffected by removing this material, although the shear modulus was reduced slightly (by as much as eight percent for the more grossly exaggerated geometries). E.Q. Lewis, former graduate student, is now Engineer, Lockheed Corporation.     

Measurement of energy release rates for delaminations in composite materials

Conventional measurements of energy release rates,G _I andG _II, for delaminations in composite materials, generally utilize loads, crack lengths and simple standard specimen geometries. In this work, a more widely applicable measurement method, using phase shifting moiré and the J integral, is presented. The experimental technique described requires only fringe-pattern information and the elastic constants for the measurements—thus it can be used when the standard methods are inapplicable. Using conventional double-cantilever beam and end-notched flexure specimens, the energy release rate has been measured simultaneously by the moiré method and the standard methods, with good agreement found between the two. This development will for the first time permit the experimental validation of new finite-element routines as they are developed.Paper was presented at the 1993 SEM Spring Conference on Experimental Mechanics held in Dearborn, MI on June 7–9.     

Experimental evidence of parasitic effects in the shear test on sandwich beams

The present work is an experimental investigation of the standard shear test ASTM C273 carried out on sandwich structures. The goal is to highlight and to quantify some parasitic effects that occur during this test. A suitable optical method providing whole-field measurements has been used to capture the displacement and strain fields during the test. Some parasitic effects have been detected: the steel plates bend during the test, the shear strain reaches zero near the free edges and compressive/tensile strains occur in this zone.     

Asymptotic determination of effective elastic properties of composite materials with fibrous square-shaped inclusions

We propose an asymptotic approach for evaluating effective elastic properties of two-components periodic composite materials with fibrous inclusions. We start with a nontrivial expansion of the input elastic boundary value problem by ratios of elastic constants. This allows to simplify the governing equations to forms analogous to the transport problem. Then we apply an asymptotic homogenization method, coming from the original problem on a multi-connected domain to a so called cell problem, defined on a characterizing unit cell of the composite. If the inclusions' volume fraction tends to zero, the cell problem is solved by means of a boundary perturbation approach. When on the contrary the inclusions tend to touch each other we use an asymptotic expansion by non-dimensional distance between two neighbouring inclusions. Finally, the obtained “limiting” solutions are matched via two-point Padé approximants. As the results, we derive uniform analytical representations for effective elastic properties. Also local distributions of physical fields may be calculated. In some partial cases the proposed approach gives a possibility to establish a direct analogy between evaluations of effective elastic moduli and transport coefficients. As illustrative examples we consider transversally-orthotropic composite materials with fibres of square cross section and with square checkerboard structure. The obtained results are in good agreement with data of other authors.     

An evaluation of the arcan specimen for determining the shear moduli of fiber-reinforced composites

Moiré interferometry was used to examine the strain distributions in Arcan-type specimens under shear loading. The compact geometry allowed longitudinal and transverse shear behavior to be considered. The best results for longitudinal moduli were obtained with fibers running from notch to notch. As with the losipescu configuration, strain averaging or correction factors were required for modulus determination in all fiber orientations. None of the bending problems that have been encountered in the losipescu specimen were observed. Some twisting was noticed, but its extent (less than 2 percent) was much less than has been noted in shear testing with losipescu specimens.     

Analysis of shear localization in porous materials

A set of constitutive equations are derived based on the authors' lower bound yield loci for porous materials. By using these equations, the conditions for shear localization in porous materials are then investigated and the results are compared with those of Gurson's equations and the finite element analysis. The advantages of the present constitutive equations are fully illustrated.     

土石混合体直剪离散元数值试验研究

工程中普遍存在的土石混合体以其复杂的工程地质力学性质越来越受研究者的关注。由于"块石"的存在使得土石混合体在细观层次上呈现明显的结构性特征,这种结构性将影响甚至控制着其变形破坏机制及宏观力学特征。本文借助三维颗粒离散元分析软件YADE分别从含石量、试样尺寸、强度特性等角度对土石混合体的力学性质开展了一系列的数值直剪试验研究工作,并取得了一些有意义的研究成果:在含石量及粒度组成相同的情况下土石混合体的宏观抗剪强度及剪胀性随着试样尺寸的增加而呈现降低趋势,而在相同试样尺寸下将随着含石量的增加而增加;内部块石的存在影响着其细观应力状态,从而影响其宏观力学特性。     

Explicit cross-property correlations for anisotropic two-phase composite materials

Explicit correlations between two groups of anisotropic effective properties—conductivity and elasticity—are established for two-phase composite materials with anisotropic microstructures (non-randomly oriented inclusions of non-spherical shapes). The correlations are derived in the framework of the non-interaction approximation. The elasticity tensor is expressed in terms of the conductivity tensor in closed form. Applications to realistic microstructures, containing mixtures of diverse inclusion shapes are given. Compliance/stiffness contribution tensors of an inclusion, that characterize the inclusion's contribution to the overall elastic response, are derived in the course of analysis; these results are of interest on their own.     

A method for fatigue analysis of metallic and composite materials under asymmetric high-cycle loading

A new method of plotting limit stress diagrams is set forth. The method is based on the hypothesis of unified limit diagram invariant to the number of cycles to failure. The unified diagram is given by a transcendental power function whose exponent is considered an additional material constant characterizing the sensitivity of the material to cycle asymmetry (stress ratio). The equations derived on the basis of this function encompass all forms of limit stress diagrams, including convex, nearly rectilinear, and concave ones. The method is tested for a wide range of metallic and composite materials subjected to asymmetric tension-compression, bending, and torsion.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 106–116, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

ANALYSIS OF INTERPHASE MECHANICAL BEHAVIOR WITH INTERFACE ELEMENT IN THE COMPOSITE MATERIALS

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基于剪切变形的矩形梁剪力滞求解方法

Timoshenko梁通过假设截面的剪切刚度和附加平均剪切转角变形的方式来近似修正初等梁中未考虑剪切变形能的问题,这与梁剪应力沿梁高变化的实际不符。本文基于材料力学剪应力计算式和相应的剪切变形理论,从剪切变形与梁的位移关系入手,导出矩形梁考虑剪切变形时的纵向位移沿梁高方向的函数关系式,证明该位移可分解为纯弯曲引起的位移和剪力引起的剪力滞翘曲位移之和。应用剪力滞广义坐标与广义力的概念,基于能量变分原理得到等截面梁剪力滞控制微分方程组及其通解形式。对均布荷载作用下矩形简支梁的算例分析表明,本文算法与弹性力学精确解对比,两者的应力和挠度剪力滞系数求解结果非常接近,本文算法有足够的精度,且比弹性力学简单。     

Constitutive modeling and the trousers test for fracture of rubber-like materials

The classical constitutive modeling of incompressible hyperelastic materials such as vulcanized rubber involves strain-energy densities that depend on the first two invariants of the strain tensor. The most well-known of these is the Mooney-Rivlin model and its specialization to the neo-Hookean form. While each of these models accurately predicts the mechanical behavior of rubber at moderate stretches, they fail to reflect the severe strain-stiffening and effects of limiting chain extensibility observed in experiments at large stretch. In recent years, several constitutive models that capture the effects of limiting chain extensibility have been proposed. Here we confine attention to two such phenomenological models. The first, proposed by Gent in 1996, depends only on the first invariant and involves just two material parameters. Its mathematical simplicity has facilitated the analytic solution of a wide variety of basic boundary-value problems. A modification of this model that reflects dependence on the second invariant has been proposed recently by Horgan and Saccomandi. Here we discuss the stress response of the Gent and HS models for some homogeneous deformations and apply the results to the fracture of rubber-like materials. Attention is focused on a particular fracture test, namely the trousers test where two legs of a cut specimen are pulled horizontally apart. It is shown that the cut position plays a key role in the fracture analysis, and that the effect of the cut position depends crucially on the constitutive model employed. For stiff rubber-like or biological materials, it is shown that the influence of the cut position is diminished. In fact, for linearly elastic materials, the critical driving force for fracture is independent of the cut position. It is also shown that the limiting chain extensibility models predict finite fracture toughness as the cut position approaches the edge of the specimen whereas classical hyperelastic models predict unbounded toughness in this limit. The results are relevant to the structural integrity of rubber components such as vibration isolators, vehicle tires, earthquake bearings, seals and flexible joints.     

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.The project supported by the National Natural Science Foundation of China (10172023)     

Composite specimen bearing failure reduction in iosipescu shear tests

ASTM losipescu sheart test fixtures often crush the loaded edges of high shear strength specimens before shear failure occurs between the notches. To alleviate this problem, two new shear test fixtures were designed and built. The first uses a pivoting load surface to track the specimen shape as it changes under load. The second uses a rounded load surface optimized to produce a uniform bearing pressure along the loaded edge of a quasi-isotropic sheet-molding compound (SMC) specimen at shear failure. Finite element analyses and strain gage data are presented that describe the behavior of the baseline ASTM, pivoting load surface and rounded load surface fixtures. A substantial reduction in bearing stress and edge crushing was obtained with the rounded load surface fixture. Additionally, the modified surface optimized to test SMC specimens showed no tendency to change the shear strength measured in other composite specimens.     

非均匀脆性材料EOI试验模拟中的动接触法

基于动接触力二步法和有限元原理,从数值模拟角度揭示了碰撞接触-分离过程。本文首先通过建立两杆撞击模型,与ANSYS_LSDYNA结果对比分析,验证了该方法的可靠性;然后进一步基于细观线性行为可以反映宏观非线性行为的原理,根据材料内部应力状态进行损伤判断,成功模拟了EOI（Edge-On Impact test侧向撞击试验）的裂缝扩展过程。通过与前人的研究成果进行对比验证,肯定了该方法对于研究碰撞问题有较高的效率和可靠度,对于研究碰撞问题有较高的参考价值。     

单向纤维复合材料粘弹性性能预测

建立了基于均匀化理论的单向纤维复合材料粘弹性性能预测方法。对单向纤维增强复合材料粘弹性问题的控制方程进行Laplace变换,在像空间中利用均匀化理论建立宏观松弛模量的Laplace变换与微结构描述参数以及变换参数间的关系。用Prony级数模拟松弛模量随变换参数的变化形式,并根据像空间中一系列变换参数对应的松弛模量的数值,采用函数拟合技术确定Prony级数的形式,从而确定用显示形式表示的松弛模量的Laplace变换随变换参数的变化规律。对显式表达式的逆变换获得时间域内的松弛模量。该方法利用拟合函数的逆变换避开了复杂的数值Laplace逆变换,使单向纤维增强复合材料的粘弹性性能的确定变得容易。文中给出了单向纤维复合材料松弛模量的数值预测结果并同有限元法模拟试验的结果对比,验证了预测结果的准确性以及本文方法的有效性。