A thermodynamic approach with internal variables using Lagrange formalism. Part II. Continuous symmetries in the case of the time–temperature equivalence

In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium.     

A theoretical model for electroelastic analysis in piezoelectric fibre push-out test

A theoretical model is presented to study the elastic deformation process and frictional sliding behavior in single piezoelectric fibre push-out tests. Based on the theoretical model and some necessary simplifications, stress and electric fields are obtained for push-out tests of a circular piezoelectric fibre embedded in an elastic matrix. Numerical results of a piezoelectric fibre/expoxy matrix system are presented to verify the proposed formulation. The study shows that there is a significant effect of the piezoelectric parameter and embedded fibre length on stress transfer, electric field distribution and load-displacement curve of the frictional sliding process. This study also indicates that the piezoelectric effect has a distinct influence on the mechanical behavior and properties of the interface in a fibre/matrix system.     

应力波传播规律研究中的一种快速分析方法

本文提出了一种能快速、简便、直观地分析了应力波传播状况的方法。该方法利用可视化计算并绘制流前图，而后将其与动光弹条纹图相比较，进而利用所推导的应力波迭加分析式判断出物体边界或其内部的应力波迭加效果。文中对圆盘中的几个典型区域进行了实例分析。     

Stress singularities near the apex of a cylindrically polarized piezoelectric wedge

Summary In this paper, the stress singularities for a cylindrically polarized piezoelectric wedge are investigated. The characteristic equations are derived analytically by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is polarized in the radial, circular or axial direction, respectively. Similar to the rectilinearly polarized piezoelectric problem, the inplane and antiplane stress fields are uncoupled. The results show the variations of the singularity orders with the changes of the wedge angle, material constants, polarized direction, and the boundary conditions.     

The interaction of doubly periodic cracks

In this paper, an extremely accurate and efficient method for computing the interaction of a set of or multiple sets of general doubly periodic cracks has been presented on the basis of superposition principle, pseudo-traction method, and isolating analysis technique. A great number of typical examples are given in this paper. The stress intensity factors (SIF), the minimum strain energy density factors (SED) of crack tip and the critical stress (CRS) of crack growth are calculated with the accuracy of six significant digits for the rectangularly distributed periodic cracks and five significant digits for the general doubly periodic cracks. The relation of the interaction effect of the double periodic cracks with the periods and the ratio of crack length to crack spacing is analyzed. Also in this paper, the key technique problems for this method are discussed.     

反倾层状边坡弯曲折断的应力及挠度判据

以地质分析为基础 ,将反倾层状边坡的任意岩层概化为受复合作用力的板梁模型 ,通过简单的力学解析 ,开展了反倾层状岩石边坡弯曲折断判据的研究。依据岩层折断时和相临岩层的瞬时关系 ,将岩层下部视为瞬时临空状态 ,考虑岩层自重荷载和上部岩层附加荷载 (上部岩层重力荷载、层间摩擦力 )的共同作用 ,基于最大拉应力准则 ,提出了岩层弯曲折断的应力判据 ;依据应力判据 ,得到了岩层弯曲折断的挠度判据 ;利用应力判据及挠度判据 ,可实现反倾层状边坡弯曲折断的现场判定及其控制设计     

Determination of in situ parameters of sandy soils for off-road vehicle mobility

This study focuses on the development of a methodology for the determination of some in situ parameters for off-road vehicle mobility on sandy soils. The stress field in the vicinity of and at the interface between a wedge and soil was determined by solving the stress equations using the method of characteristics. The governing equations were solved numerically by using backward finite difference method. The proposed method allows the prediction of any two of the in situ soil parameters δ, φ, and γ (respectively, the interfacial friction angle between the material of a wedge penetrometer and the soil, the internal friction angle, and the unit weight of the soil), given the value of any one of them and the results of penetration tests of two different apex angle wedges. The predictions and the measured values are in agreement.     

Effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates

A modified shear-lag analysis, taking into account the concept of stress perturbation function, is developed and applied to evaluate the effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates. Effects of number of 90° layers and number of θ° layers in the outer angle-ply laminates on the reduction of the effective axial coefficient of thermal expansion have also been studied. The results of this paper represent well the dependence of the reduction of the effective axial coefficient of thermal expansion on the hygrothermal conditions, the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of un-cracked outer θ° layers in laminate.     

Fatigue crack growth behavior of Al7050-T7451 attachment lugs under flight spectrum variation

This paper discusses an analytical and experimental investigations of the fatigue crack growth behavior in attachment lugs subjected to a randomized flight-by-flight spectrum. In the analysis, the stress intensity factors for through-the-thickness cracks initiating from lug holes were compared by weight function method, boundary element method (BEM), the interpolation of Brussat’s solution. The stress intensity factors of a corner crack at a transition region were obtained using two parameter weight function method and correction factors. Fatigue life under a load spectrum was predicted using stress intensity factors and Willenborg retardation model considering the effects of a tensile overload. Experiments were performed under a load spectrum and compared with the fatigue life prediction using the stress intensity factors by different methods. Changes of fatigue life and aspect ratio according to the clipping level of the spectrum were discussed through experiment and prediction. Effect of the spectrum clipping level on the fatigue life was experimentally evaluated by using beach marks of fractured surface.     

Mixed-mode I/II fields around a crack with a cohesive zone ahead of the crack tip

Considering a cohesive zone ahead of the crack tip, the linear elastic crack problem under Mode I, Mode II or mixed-mode conditions is formulated in an elliptic coordinate system, so that the cohesive surfaces are conveniently represented by straight line segments. It is shown that the displacement and stress fields around the crack tip and the cohesive zone, expressed in terms of elliptic coordinates, have a simple mathematical form, which does not contain a stress singularity at the crack tip due to the existence of the cohesive zone.