Effect of on-axis tensile loading on shear properties of an orthogonal 3D woven SiC/SiC composite

The present study examines in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix composite. A composite beam with rectangular cross-section was subjected to a small torsional moment, and the torsional rigidities were measured using an optical lever. Based on the Lekhnitskii’s equation (Saint–Venant torsion theory) for a orthotropic material, the in-plane and out-of-plane shear moduli were simultaneously calculated. The estimated in-plane shear modulus agreed with the modulus measured from ±45° off-axis tensile testing. The effect of on-axis (0°/90°) tensile stress on the shear stiffness properties was also investigated by the repeated torsional tests after step-wise tensile loading. Both in-plane and out-of-plane shear moduli decreased by about 50% with increasing the on-axis tensile stress, and it is mainly due to the transverse crack propagation in 90° fiber bundles and matrix cracking in 0° fiber bundles. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shear modulus of ceramic matrix composites, because a thick specimen is not required.     

Mechanical characterization of graphite/epoxy nanocomposites by multi-scale analysis

Mechanical properties of nanocomposites consisting of epoxy matrix reinforced with randomly oriented graphite platelets were studied by the Mori–Tanaka approach in conjunction with molecular mechanics. Elastic constants of graphite nanoplatelets, which are the inclusion phase in the micromechanical model, were calculated based on their molecular force field. The calculated elastic constants compared well with both experimental data and other published theoretical predictions. The results of the Mori–Tanaka micromechanical analysis, using the graphite platelet moduli calculated by molecular mechanics, were found to be insensitive to the variation of out-of-plane modulus E₃ and Poisson’s ratio ν₁₃. However, the nanocomposite modulus is sensitive to the in-plane modulus E₁ and out-of-plane shear modulus G₁₃ of the graphite platelets and less sensitive to the in-plane Poisson’s ratio ν₁₂ for its small range of variation under consideration. The calculations confirm that the modulus of the nanocomposites studied here is strongly dependent on the aspect ratio of the reinforcing particles, but not on their size. The predicted moduli compare favorably with experimental results of several nanocomposites with graphite particles of various aspect ratios and sizes.     

自相似多级纳米蜂窝铝结构力学性能的分子动力学模拟

首次采用分子动力学方法预测了自相似多级纳米蜂窝铝面内和面外（轴向）的压缩力学性能（弹性模量和压缩强度）。重点研究了相对密度、层级数和长度比对自相似多级纳米蜂窝铝结构力学性能的影响。在Gibson模型中引入了表面效应因子,结果表明修正的Gibson-Ashby模型与分子动力学计算结果更加吻合。此外,通过比较一级、二级和三级纳米蜂窝铝结构的变形机制发现,二级和三级纳米蜂窝铝结构由于分别在单级蜂窝和二级蜂窝的角点处接入六边形,在压缩过程中,多级纳米蜂窝铝结构激发的位错远高于单级蜂窝铝结构。也就是说,在压缩载荷下,多级蜂窝铝结构可以更好地利用结构的承载能力,吸收更多的能量。但是,自相似纳米蜂窝铝结构的力学性能无法通过增加级数的方法来无限增强,在相对密度和长度比不变的情况下,当纳米蜂窝铝结构的级数达到二级时,其综合力学性能最佳。研究结果还表明,相对密度不变时,二级纳米蜂窝铝结构长度比分别在0.3和0.4附近时,二级蜂窝铝结构具有最佳的面内和面外力学性能。研究成果对自相似多级纳米蜂窝结构的优化设计具有重要的指导作用。      

Some elastic properties of reinforced solids,with special reference to isotropic ones containing spherical inclusions

Based on Mori and Tanaka's concept of “average stress” in the matrix and Eshelby's solutions of an ellipsoidal inclusion, an approximate theory is established to derive the stress and strain state of constituent phases, stress concentrations at the interface, and the elastic energy and overall moduli of the composite. Both “stress-free” strain (polarization strain) and “strain-free” stress (polarization stress) are employed in these derivations under the traction- and displacement-prescribed conditions. The theory was developed first for a general multiphase, anisotropic composite with arbitrarily oriented anisotropic inclusions; explicit results are then given for a suspension of uniformly distributed, multiphase isotropic spheres in an isotropic matrix. Numerical results for stress concentrations in the spherical inclusions and at the interface are given for a 2-phase composite. Further, it is shown that the derived moduli are related to the Hashin-Shtrikman bounds and that, when the shear moduli are equal, the overall bulk modulus of a 2-phase composite reduces to Hill's exact solution. As compared with experimental data, the theory also provides reasonably accurate estimates for the Young's modulus of some 2- and 3-phase composites.     

Micromechanics determination of electroelastic properties of piezoelectric materials containing voids

This paper examines the electroelastic properties of piezoelectric materials that contain voids. A unified micromechanics approach is adopted for determining the properties. Voids are treated as spheroidal inclusions with zero elastic moduli. The surrounding material is assumed to be linearly piezoelastic and transversely isotropic. The electroelastic Eshelby tensors for spheroidal inclusions have been evaluated numerically for different aspect ratios. Utilizing these tensors and applying the Mori–Tanaka mean field theory that accounts for the interaction between inclusions and matrix, the effective electroelastic properties of the materials are obtained. Numerical examples are given based on PZT-5H and BaTiO₃. Influences of the volume fraction and aspect ratio of voids on the material properties have been studied. Emphasis has been placed on the piezoelastic coupling effect of the material. For both materials, the piezoelastic coupling provides a stiffening effect on the materials, and the influence is more pronounced when void volume increases and when the aspect ratio of voids becomes shorter.     

On application of classical Eshelby approach to calculating effective elastic moduli of dispersed composites

The problem of finding effective elastic moduli of media with spheroid inclusions in case of small concentration of these inclusions is addressed. A number of particular solutions, both known and new, were obtained as limit transitions and asymptotical expansion of the general solution, based on Eshelby’s approach. A special attention was paid to determining the ranges of applicability of the obtained asymptotical solutions. It was shown that for spheroid inclusions the areas of applicability of the asymptotic solutions are determined by two parameters: the ratio of elastic moduli of the inclusion and the matrix and aspect ratio of the inclusions.     

Influence of thermal residual stresses on the composite macroscopic behavior

The influence of the thermal residual stress on the deformation behavior of a composite has been analyzed with a new micromechanical method. The method is based on secant moduli approximation and a new homogenized effective stress to characterize the plastic state of the matrix. It is found that the generated thermal residual stresses after cooling and their influence on the subsequent deformation behavior depends significantly on the aspect ratio of the inclusions. With prolate inclusions, the presence of thermal residual stresses generate a higher compressive hardening curves of the composite, but it is reversed with oblate inclusions. For particle reinforced composite, thermal residual stresses induce a tensile hardening curve higher than the compressive one and this is in agreement with experimental observations.     

Overall elastoplastic property for micropolar composites with randomly oriented ellipsoidal inclusions

Overall linear and non-linear properties for micropolar composites containing 3D and in-plane randomly oriented inclusions are examined with an analytical micromechanical method. This method is based on Eshelby solution for a general ellipsoidal inclusion in a micropolar media and secant moduli method. The influence of inclusion’s shape, size and orientation on the classical effective moduli, yielding surface and non-linear stress and strain relation are examined. The results show that the effective moduli and non-linear stress–strain curves are always higher for micropolar composites than the corresponding classical composites. When the inclusion’s size is sufficiently large, the classical results can be recovered.     

High strain rate behavior of 4-step 3D braided composites under compressive failure

The out-of-plane and in-plane compressive failure behavior of 4-step 3D braided composite materials was investigated at quasi-static and high strain rates. The out-of-plane and in-plane direction compressive tests at high strain rates from 800/s to 3,500/s were tested with the split Hopkinson pressure bar (SHPB) technique. The quasi-static compressive tests were conducted on a MTS 810.23 tester and compared with those at high strain rates. The comparisons indicate that the failure stress, failure strain and compressive stiffness both for out-of-plane and in-plane loading directions are rate sensitive. For example, the failure stress, failure strain and stiffness are 55.19 MPa, 6.70% and 1.35 GPa respectively as opposed to 145.00 MPa, 1.21% and 13.50 GPa respectively for strain rate of 2,500 s⁻¹ under in-plane compression. The 3D braided composites have higher values of failure stress and strain for out-of-plane than for in-plane compression at the same strain rate; however, the in-plane compression stiffness is higher than that of out-of-plane compression at high strain rates. The compressive failure mode of 3D braided composites in the out-of-plane direction is mainly shear failure at various strain rates, while for the in-plane direction it is mainly cracking of matrix.     

Electroelastic fields and effective moduli of a medium containing cavities or rigid inclusions of arbitrary shape under anti-plane mechanical and in-plane electric fields

Summary We examine the two-dimensional problem of an infinite piezoelectric medium containing a solitary cavity or rigid inclusion of arbitrary shape, subjected to a coupled anti-plane mechanical and in-plane electric load at the remote boundary of the matrix. Conformal mapping techniques are employed to analyze the boundary value problems. Specific results are given for elliptical, polygonal and star-shape inclusions. Local fields of this type are used to estimate the overall moduli of a medium containing voids or rigid inclusions. This is accomplished with the help of an extension of Eshelby's formula which evaluates the total electric enthalpy by a particular line integral. Explicit estimates of the effective moduli are derived for dilute as well as for moderate area fractions of inclusions. The formulae depend solely on the cross area of the inclusion, area fraction and one particular coefficient of the mapping function. In addition, the stress and electric displacement singularities around the sharp corners of the inclusion are examined. The existence of uniform fields inside the inclusion is also envisaged. The present results, with appropriate modifications, apply equally well to those of thermoelectric and magnetoelectric effects.     

Plane problems of multiple piezoelectric inclusions in a non-piezoelectric matrix

Based on the complex variable method, this paper addresses the plane problems of multiple piezoelectric inclusions in a non-piezoelectric matrix. The inclusions are assumed to be perfectly bounded to the matrix, which is loaded by in-plane mechanical loads while the inclusions are applied by anti-plane electric loads at infinity. The general solutions are first derived for the complex potentials both in the matrix and inside the inclusions, and then numerical results are presented to show the effects of applied electric field, inclusion arrays and material properties on the electroelastic fields around the inclusions. It is shown that the inclusion arrays have a significant influence on the stress distribution at the interface between the matrix and piezoelectric inclusions.     

Influence of the prebuckling stress-field on the critical loads of inhomogeneous composite laminates

The paper studies the uniaxial buckling behavior of composite laminates in which preselected variations of fiber spacing in the constituent laminae are adopted. Such laminates are referred to as inhomogeneous laminates because of the variable elastic stiffness along the coordinate axes. A non-uniform prebuckling stress state observed even under constant uniaxial compression has a pronounced influence on the buckling behaviour of an inhomogeneous laminate. A procedure is summarized for computing the critical load of a laminate using the Ritz method which exploits an analogy between the bending and stretching formulations and utilizes Gram-Schmidt orthogonal polynomials. The paper illustrates that the variation in fiber spacing is an innovative way of increasing the critical load for a prescribed amount of fiber and highlights its remarkable sensitivity to the nature of fiber spacing, in-plane and out-of-plane boundary conditions, fiber type and the aspect ratio of the laminate.     

Interactions between N circular cylindrical inclusions in a piezoelectric matrix

Summary This paper studies the interactions between N randomly-distributed cylindrical inclusions in a piezoelectric matrix. The inclusions are assumed to be perfectly bounded to the matrix, which is subjected to an anti-plane shear stress and an in-plane electric field at infinity. Based on the complex variable method, the complex potentials in the matrix and inside the inclusions are first obtained in form of power series, and then approximate solutions for electroelastic fields are derived. Numerical examples are presented to discuss the influences of the inclusion array, inclusion size and inclusion properties on couple fields in the matrix and inclusions. Solutions for the case of an infinite piezoelectric matrix with N circular holes or an infinite elastic matrix containing N circular piezoelectric fibers can also be obtained as special cases of the present work. It is shown that the electroelastic field distribution in a piezoelectric material with multiple inclusions is significantly different from that in the case of a single inclusion.     

Micromechanics modeling of viscoelastic properties of hybrid composites with shunted and arbitrarily oriented piezoelectric inclusions

A comprehensive micromechanics model is developed to estimate the effective viscoelastic properties of hybrid composites containing polymer matrix, conductive inclusions and shunted piezoelectric inclusions. The model is derived using the viscoelastic correspondence principle in conjunction with the Mori-Tanaka approach and the orientation averaging scheme. Three dimensional complex moduli are explicitly presented for hybrid composites with any orientation distribution. The model is first validated by comparison with available experimental results. Then, the loss factors are examined for hybrid composites with inclusions of various volume fractions and of shapes ranging from thin disks to long fibers. It is seen that hybrid composites with randomly oriented inclusions exhibit shear loss factors which are not possible with monolithic piezoelectric plate. Furthermore, the numerical results indicate that composites with long spheroid inclusions provide the best damping performance. The results recommend that aligned inclusion composites are good for alleviating longitudinal oscillations. If oscillation energy needs to be dissipated in all directions and for all modes, three dimensional random composites should be used. It is also observed that spherical inclusion composites cannot improve shear damping irrespective of the orientation and the volume fraction. In general, to achieve a pronounced damping piezoelectric inclusions that lie in aspect ratio range 0.1?α?2 should be avoided.     

Analytical modeling of effect of interlayer on effective moduli of layered graphene-polymer nanocomposites

Nanocomposites enhanced with two-dimensional, layered graphene fillers are a new class of engineering materials that exhibit superior properties and characteristics to composites with conventional fillers.However, the roles of "interlayers" in layered graphene fillers have yet to be fully explored. This paper examines the effect of interlayers on mechanical properties of layered graphene polymer composites.As an effective filler, the fundamental properties(in-plane Young's modulus E_(L1), out-of-plane Young's modulus E_(L2); shear modulus G_(L12), major Poisson's ratio V_(L12)) of the layered graphene were computed by using the Arridge's lamellar model. The effects of interlayers on effective moduli of layered graphene epoxy composites were examined through the Tandon-Weng model. The properties of the interlayer show noticeable impact on elastic properties of the composites, particular the out-of-plane properties(Young's modulus E_2 and shear modulus G_(12)). The interlayer spacing is seen to have much great influence on properties of the composites. As the interlayer spacing increases from 0.34 nm to 2 nm, all elastic properties of the composites have been greatly decreased.     

面外波纹对复合材料层合板弹性性能的影响

基于经典层合板理论（CLT）,提出一个多参数解析模型,定量研究了面外波纹缺陷对含波纹缺陷的复合材料层合板弹性模量、剪切模量和泊松比等弹性性能的影响。 结果表明:面外波纹对主弹性模量、Z向弹性模量、X - Z平面剪切模量和面内泊松比都产生了显著影响;对于碳纤维/环氧树脂材料体系算例,在特定波纹比和波纹区域范围内,面内泊松比出现了负值。该建模方法为研究波纹缺陷对复合材料层合板弹性性能影响提供了参考。      

Analysis of the single-fiber fragmentation test

An analysis of the single-fiber fragmentation test was investigated.An approximate solution for the stress fields of a fiber embedded in a polymer matrix of different elastic moduli was obtained by the Eshelby method. The fiber was modeled as a prolate spheroid. The axial stress of the fiber increases with increasing aspect ratio and fiber-matrix shear modulus ratio and decreases with increasing matrix and fiber Poisson's ratios. Using this analysis, the fracture stress of a single-fiber fragmentation specimen was derived. The applied stress at fiber fracture decreases monotonically with increasing aspect ratio of the fragmented fiber and increases with increasing fiber and matrix Poisson's ratios. This model is in qualitative agreement with published experimental data.     

Transversely isotropic mechanical properties of PVC foam under cyclic loading

Cyclic material tests were done on Divinycell PVC H100 foam to obtain out-of-plane and in-plane compression and shear material properties after foam yielding. The compression and shear stress–strain behaviors were very similar to each other except that a plateau (flow) stress occurred after yielding in compression, while the foam underwent mild strain hardening after shear yielding. The ratio of out-of-plane to in-plane stiffness and yield strength for the PVC H100 was found to be approximately 3/2 in both the compression and shear modes. After viscoplastic yielding, the foam underwent permanent damage and exhibited hysteresis, mainly in the form of viscoelasticity. Damage that occurred in the foam after it yields followed the pattern of Mullins damage, i.e., the damage was essentially fixed at a given strain amplitude, and more damage occurred with increasing the strain amplitude. Hysteresis was much more pronounced as the damage grew, suggesting that viscoelastic properties of the foam could be changing with the amount of damage.     

圆管拱结构平面外弹塑性二次分岔屈曲性能

该文使用一种新的数值跟踪策略对无平面外支撑和有顶点平面外支撑的弹塑性圆管拱的平面外二次分岔屈曲的荷载-位移曲线的全过程进行跟踪分析,得到了跨中集中荷载和全跨均布荷载作用下,相同截面不同矢跨比的拱的平面外弹塑性二次分岔屈曲荷载,将其与平面内二次分岔屈曲荷载比较。计算结果表明:对于具有相同截面的无平面外支撑弹塑性圆管拱,在跨中集中荷载作用下,平面内二次分岔屈曲荷载小于平面外二次分岔屈曲荷载,平面内二次分岔屈曲会先于平面外屈曲发生,矢跨比0.2 时平面外二次分岔屈曲荷载最大。全跨均布荷载作用下的拱平面外二次分岔屈曲会先于平面内二次分岔屈曲发生;矢跨比0.3 时平面外二次分岔屈曲荷载最大。矢跨比为0.1 时,拱的平面内与平面外屈曲荷载相差最大。对于有顶点平面外支撑拱,在集中荷载作用下,支撑对分岔屈曲荷载作用不明显,只是改变了屈曲形式。全跨均布荷载作用下,支撑可以大幅提高全跨均布荷载作用下拱的平面外屈曲荷载,尤其是对矢跨比小的拱的影响更大一些,平面外二次分岔屈曲会先于平面屈曲发生。     

In-plane and out-of-plane constraint effects on creep crack growth rate in Cr–Mo–V steel for wide range of C*

Abstract

In this work, the stress dependent creep ductility and strain rate model have been implemented in a ductility exhaustion based damage model and the creep crack growth (CCG) rates of a Cr–Mo–V steel in compact tension (C(T)) and middle tension (M(T)) specimens with different thicknesses and crack depths have been simulated over a wide range of C*. The effects of in-plane and out-of-plane constraints on CCG rates are examined. The results show that the in-plane and out-of-plane constraint effects on CCG rate are more pronounced for the high constraint specimen geometry (C(T)), while such effects are less significant for low constraint specimen geometry (M(T)). The constraint effects on CCG rates mainly occur in low and transition C* regions and the CCG rate increases with increasing in-plane and out-of-plane constraints. There exists interaction between in-plane and out-of-plane constraint in terms of their effects on CCG rate. The higher in-plane constraint strengthens the out-of-plane constraint effect on CCG rate and higher out-of-plane constraint also strengthens the in-plane constraint effect on CCG rate. The constraint effects on creep crack growth behaviour for a wide range of C* mainly arise from the interaction of crack-tip stress states and stress dependent creep ductility of the steel in different C* levels.