Stress analysis of thick orthotropic cantilever tubes under transverse loading

In this work, a new high-order displacement-based method is proposed to investigate stresses and strains in thick arbitrary laminated orthotropic cantilever straight tubes under transverse loading. The most general displacement field of elasticity for an arbitrary thick laminated orthotropic straight tube is developed. A layer-wise method is employed to analytically determine the local displacement functions and stresses under transverse loading. The accuracy of the proposed method is subsequently verified by comparing the theoretical results with experimental data, finite-element method (FEM), and Lekhnitskii solution. The results show good agreement. In addition, high efficiency in terms of computational time is shown when the proposed method is used as compared with FEM. Finally, several numerical examples for stress and strain distributions in various thick cantilever composite straight tubes subjected to transverse loading are discussed.     

一种新的铝合金应变疲劳计算方法

提出了一种在铝合金构件应变疲劳分析中,计算局部应力和应变变程的新方法。这种方法称作应力功恒等法。采用这种新方法,计算了2024-T42铝合金试件在恒幅循环载荷作用下的疲劳寿命,并将疲劳寿命计算结果与试验结果进行了对比分析。对比分析结果表明,采用这种新方法计算构件应力集中处的局部应力和应变变程,具有较高的计算精度。     

On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems

The accurate calculation of the opening and closing stresses is an important issue in fatigue crack closure problems, since the effective driving force for crack growth is dependent on accurate calculation of the opening stresses. Often numerical methods such as finite element analysis are used to model plasticity-induced fatigue crack closure problems. There are many difficulties associated with this modelling work, since the results may depend on a wide range of parameters such as mesh refinement, node release scheme and modelling of the contact between the crack faces etc. Even after a great deal of modelling work some arbitrariness is evident in the technique used for assessing the opening and closing stresses. A number of techniques have been proposed in the literature and the current work will assess and compare these approaches. The node displacement method, the change in stresses at the crack tip, and the weight function technique will each be applied to a finite element model of a plane stress crack for a range of stress levels. In addition, an analytical model for plasticity-induced crack closure under plane stress conditions will be used to discuss the accuracy of these techniques. The investigation shows that all these techniques are equivalent provided that the displacement and stress at the crack tip are assessed accurately. However, it will be shown that use of the tensile tip stress method, proposed by some authors for assessing the closing stress, is erroneous.     

大型弯头液压成形的理论分析与实验研究

针对现有弯头制造中存在的问题 ,提出了用环壳液压胀形工艺制造弯头的方法 ,分析了环壳的应力特点 ,并给出了其最后的成形压力 .通过实验研究了环壳胀形过程中位移、应变的变化规律及成形后壳体的几何尺寸 ,并对其成形过程中的起皱进行了分析 .研究表明用液压液压胀形工艺制作弯头是可行的 .     

简支C型檩条在风吸力作用下精确应力计算模型

稳定问题是C型檩条在风吸力作用下的主要控制因素,该文基于薄壁杆件结构力学以及经典梁理论,提出了可以精确计算简支C型檩条在风吸力作用下的应力计算方法,该方法可以同时考虑压型钢板对檩条上翼缘侧向及扭转约束支撑的影响。依据相关试验资料以及数值计算结果,验证了该方法的精度。然后,基于该文所提出的方法,针对檩条横截面应力分布、侧向位移等力学性能,以及有无拉条等构造措施对其极限状态的影响进行了参数分析。研究表明,压型钢板对檩条上翼缘的侧移及扭转约束及拉条措施会改变檩条横截面应力分布及侧向位移,对其稳定极限状态产生显著影响。     

沥青砂粘弹塑蠕变损伤本构模型实验研究

针对沥青砂的非线性材料特性,结合连续损伤力学理论,对传统Burgers模型进行改造,提出了粘弹塑蠕变损伤本构模型,通过对不同实验条件下沥青砂单轴蠕变试验结果的非线性拟合,获得模型参数,然后利用模型进行预测分析,得到了不同应力水平与环境温度下的蠕变曲线和损伤演化曲线,通过比较发现该文模型能够更合理地反映沥青砂加速蠕变的非线性特征,而且蠕变过程中损伤演化的速度受蠕变时间、应力水平与环境温度的影响很大。     

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.     

Design-oriented analysis of imperfect truss structures—part I—accurate analysis

An accurate nonlinear analysis procedure for calculating the displacement stresses and system buckling loads of geometrically imperfect truss structures is developed. The investigation considers both local and system imperfections. This nonlinear analysis takes first-order geometrically nonlinear effects into account. The accuracy of the analysis procedure is confirmed by comparison with analytical and experimental results for truss structures drawn from the literature. The results show that local and system imperfections can have strong influence on the behaviour of truss structures and therefore should be taken into account. It is shown that nonlinear effects play a major role in the phenomena and therefore simplified analyses that neglect nonlinear effects are inadequate.     

Combining X-FEM and a multilevel mesh superposition method for the analysis of thick composite structures

The use of simultaneous multiple plate models offers an attractive and alternative solution to full scale three-dimensional finite element method for the global–local analysis of laminated composite structures. In this paper, an approach is proposed where the less accurate plate model, used to carry out the analysis at the global level, is enhanced by more accurate and complex plate models in each laminate subregion where more accurate transverse stress or strain estimation is required (the local level).The total displacement is represented as the superposition of the displacements of a number of plate models. By appropriately defining boundaries to the enhancing model/region, it is demonstrated that the superposition of displacements can be used to locally enrich the solution where accurate through-the-thickness stresses are required. In this manner, a computationally efficient global model can be used to determine gross displacements, and potentially the enriched models can be used to determine stresses at lamina interfaces for the accurate prediction of localized phenomena such as damage initiation and growth. The model is implemented combining an extended FEM (X-FEM) and multilevel mesh superposition approach (MMSA). Extra degrees-of-freedom are added to the model to represent the additional displacement fields, and the meshing process remains independent for each field.The displacements and stresses computed by this approach are compared to literature data and analytical solutions for various plate geometries and loads showing an excellent correlation. Morevoer, the results showed, as expected, that the accuracy of the approximation is improved by the proposed approach compared to using the global plate model alone.     

Interaction of two nearby CNTs/nanovoids embedded in a metal matrix using modified nonlocal elasticity

Interaction of Carbon Nanotubes (CNTs) and nanovoids embedded in a metal matrix is studied comparatively. For this purpose, two nearby CNTs/nanovoids are modeled as two similar cylindrical inclusions/holes in an infinite matrix. The nonlocal stresses around the CNTs/nanovoids are obtained by applying the integral constitutive equation of the nonlocal elasticity to the stresses from the complex stress potential method. Also, in order to bring different nonlocality effects of dissimilar media into account, the influence function of the nonlocal elasticity is modified. Effects of the CNTs/nanovoids size and distance as well as far-field loading ratio on the stress state in the matrix are investigated. The CNTs strengthening effect on the matrix is shown through lower stresses at the CNTs and matrix interface in comparison to the applied stress. Furthermore, it is indicated that the modified nonlocal analysis brings out the interaction of CNTs/nanovoids at smaller distances in comparison with those the classical analysis used to predict. In other words, higher volume fraction of the CNTs/nanovoids can be incorporated in the metal matrices without devastating effects of their interactions.     

Beitrag zur numerischen Ermittlung elastoplastischer Verzerrungen mittels Finiter Elemente

A Note On the Numerical Calculation of Elastoplastic Strains By The Method of Finite Elements The state of stress and strain of a plate with a circular hole (elastoplastic region) is calculated by the aid of two plane triangular elements (linear and quadratic displacement function) and the Prandtl-Reuss- and Hencky-equations. The procedure of initial strain is used, to approximate the plane stress state to the stress-strain curve of the material. The results agree well with experimental values from the literature. In general stresses and strains, calculated on the base of elements with quadratic displacement function, lie nearer to the measured values. In addition to that a different and exacter course of spreading of elastoplastic regions of material is found. Stresses and strains in regions of high gradients can be calculated more precisely with these elements. A comparison between stresses and strains, calculated by the Prandtl-Reuss- and Hencky-equations, showed very less differences.     

Interaction of two nearby CNTs/nanovoids embedded in a metal matrix using modified nonlocal elasticity

Interaction of Carbon Nanotubes (CNTs) and nanovoids embedded in a metal matrix is studied comparatively. For this purpose, two nearby CNTs/nanovoids are modeled as two similar cylindrical inclusions/holes in an infinite matrix. The nonlocal stresses around the CNTs/nanovoids are obtained by applying the integral constitutive equation of the nonlocal elasticity to the stresses from the complex stress potential method. Also, in order to bring different nonlocality effects of dissimilar media into account, the influence function of the nonlocal elasticity is modified. Effects of the CNTs/nanovoids size and distance as well as far-field loading ratio on the stress state in the matrix are investigated. The CNTs strengthening effect on the matrix is shown through lower stresses at the CNTs and matrix interface in comparison to the applied stress. Furthermore, it is indicated that the modified nonlocal analysis brings out the interaction of CNTs/nanovoids at smaller distances in comparison with those the classical analysis used to predict. In other words, higher volume fraction of the CNTs/nanovoids can be incorporated in the metal matrices without devastating effects of their interactions.     

Strain localization in circular honeycombs under in-plane biaxial quasi-static and low-velocity impact loading

Strain localization in a finite block of circular honeycomb is studied using a phenomenological approach based on the structural response of the honeycombs. The deformation modes characteristic for a circular honeycomb material under in-plane biaxial compression are identified from the experiments and described analytically for compression strains up to about 15%. It is concluded that the particular deformation modes depend on the local strain field, and modes with different dominant strains can co-exist inside a finite block subjected to equi-biaxial remote strains. The relationships between the local strain components for the development of these modes are determined. Using the proposed approach to the strain localization, it is shown that for equal remote strains applied to a finite block of honeycombs, larger remote stresses would occur when assuming homogeneous deformation inside the block in comparison to the calculated stress when the strain inhomogeneity takes place. A comparison between the theoretical and experimental results is made for a finite honeycomb block under quasi-static equi-biaxial compression.     

Interaction diagrams for carbon nanotubes under combined shortening-twisting

A theoretical investigation on the strength and stiffness of carbon nanotubes (CNTs) under combined shortening and twisting strains is presented. CNTs with similar length-to-diameter aspect ratios, L/D, but different atomic structures (zig-zag, armchair and chiral) have been selected. Molecular dynamics (MD) simulations have been performed to study the critical buckling behaviour and the pre-critical and post-critical stiffness of CNTs under combined shortening-twisting conditions. The main results are presented in the form of interaction diagrams between the critical strain and the critical angle of twist per unit of length. An interaction equation is proposed and validated by comparison with the MD results. If shortening is more dominant than twisting, the strain energy at the onset of buckling drops considerably with the increase of the twisting-shortening rate. If twisting is more influential than shortening, the energy at the onset of buckling decreases very slowly with the twisting-shortening rate. We also found an interaction factor of 1.5 for CNTs under combined shortening-twisting, which is much lower than the value 2.0 commonly adopted for circular tubes at macro-scale. We conclude that CNTs are much more sensitive to buckling under shortening-twisting interaction than macro-scale tubes.     

Dynamic and static fracture analyses of graphene sheets and carbon nanotubes

Dynamic and static fracture properties of Graphene Sheets (GSs) and Carbon nanotubes (CNTs) with different sizes are investigated based on an empirical inter-atomic potential function that can simulate nonlinear large deflections of nanostructures. Dynamic fracture of GSs and CNTs are studied based on wave propagation analysis in these nanostructures in a wide range of strain-rates. It is shown that wave propagation velocity is independent from strain-rate while dependent on the nanostructure size and approaches to 2.2 × 10⁴ m/s for long GSs. Also, fracture strain shows extensive changes versus strain-rate, which has not been reported before. Fracture stress is determined as 115 GPa for GSs and 122 GPa for CNTs which are independent from the strain-rate; in contrast to the fracture strain. Moreover, fracture strain drops at extremely high strain-rates for GSs and CNTs. These features are considered as capability of carbon nanostructures for reinforcing nanocomposites especially under impact loadings up to high strain-rates.     

Linear and non-linear 3-D analysis of hybrid composite laminates

In this paper, linear and non-linear 3-D solutions are presented for hybrid composite laminates subjected to uniform transverse loadings. The perturbation method and a variational principle are used to obtain solutions which satisfy the linear and non-linear 3-D differential equations of equilibrium, the strain/displacement relations, the stress/strain relations, the boundary conditions and the continuity conditions at layer interfaces. The distributions of displacements and stresses in the plates are shown. The effect of different non-linearities on laminated plates is considered, and the importance of transverse shear stresses and transverse normal stress is analysed.     

Energy method of longevity calculation under an irregular loading. Report 2. Longevity under programmed block loading

A method of calculating longevity to macrocrack development under a programmed loading in the form of a block repeated many times to failure is proposed. Relationships are derived for calculation of longevity under blocks with stepwise variation in stress amplitude, and also blocks assigned by the probability-distribution density of the stress amplitudes and tables of the differential frequency of repetition of peak and average stresses. Consideration of variation in the material's endurance limit under an irregular cyclic loading is demonstrated. It is shown that a specific type of relationships can be derived for the material under investigation with allowance for its kinetic cyclic-strain diagrams. An example of the longevity calculation, which is compared with experimental data for the block loading of steel 40Kh specimens, is cited.Translated from Problemy Prochnosti, No. 8, pp. 3–11, August, 1995.     

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.     

Superposition method for calculating singular stress fields at kinks, branches and tips in multiple crack arrays

A method is developed for calculating stresses and displacements around arrays of kinked and branched cracks having straight segments in a linearly elastic solid loaded in plane stress or plain strain. The key idea is to decompose the cracks into straight material cuts we call `cracklets', and to model the overall opening displacements of the cracks using a weighted superposition of special basis functions, describing cracklet opening displacement profiles. These basis functions are specifically tailored to induce the proper singular stresses and local deformation in wedges at crack kinks and branches, an aspect that has been neglected in the literature. The basis functions are expressed in terms of dislocation density distributions that are treatable analytically in the Cauchy singular integrals, yielding classical functions for their induced stress fields; that is, no numerical integration is involved. After superposition, nonphysical singularities cancel out leaving net tractions along the crack faces that are very smooth, yet retaining the appropriate singular stresses in the material at crack tips, kinks and branches. The weighting coefficients are calculated from a least squares fit of the net tractions to those prescribed from the applied loading, allowing accuracy assessment in terms of the root-mean-square error. Convergence is very rapid in the number of basis terms used. The method yields the full stress and displacement fields expressed as weighted sums of the basis fields. Stress intensity factors for the crack tips and generalized stress intensity factors for the wedges at kinks and branches are easily retrieved from the weighting coefficients. As examples we treat cracks with one and two kinks and a star-shaped crack with equal arms. The method can be extended to problems of finite domain such as polygon-shaped plates with prescribed tractions around the boundary.     

A comparative study of the heterogeneous local mechanical response of two types of asphalt mixes

Two asphalt specimens featuring very different gradations, types of aggregates and binders are investigated in this study. A full-field measurement technique is used for this purpose: the grid method. Displacement and strain fields are captured during compression tests carried out on these specimens. The displacement and strain fields are analyzed and compared in light of the main characteristics of these materials. It is shown that a close relationship exists between gradation and ratio between local and global strain components. The strain recovery that follows the loading phase of the specimens is also analyzed and the difference between their mechanical response at the local level is also highlighted.