Buckling behavior of a central cracked thin plate under tension

The buckling characteristics of cracked plates subject to uniaxial tensile loads are analysed by the aid of the finite element method. Owing to the fact that crack buckling behavior is affected by the in-plane stress distribution around a crack, to get more accurate results, pre-buckling in-plane stress fields are analysed by the finite element method. For the critical loads calculation, the finite element approach adopted is based on Von Karman's linearize theory for buckling of plates subjected to pre-buckling state of plane stress. Several singular elements based on the Willian series are used in this plate bending approach. In this study, the effect of crack length, the effect of boundary condition, the effect of Poison's ratio and the effect of biaxial force on critical loads are analysed and discussed. Furthermore, the effect of initial imperfection is also discussed. There is a good agreement between other researcher's work and present results.     

含孔CFRP正交层合板的双轴拉伸力学行为

采用加载臂开槽的中心开孔等厚度十字形试样,实验研究了正交对称铺层碳纤维增强聚合物基复合材料（CFRP）层合板在双轴拉伸载荷作用下的力学行为,分析了3种双轴加载比对其拉伸强度和破坏行为的影响。研究表明:纤维被切断的铺层部分在拉伸作用下容易与其相邻铺层脱粘,导致层合板承载力下降;等双轴加载时,在孔边的被切断纤维与连续纤维间基体在横向拉伸和纵向剪切组合作用下首先开裂;非等双轴加载时,在垂直于快速拉伸方向的铺层中沿孔边应力集中处先出现基体裂纹;随着加载比的增大,快速拉伸方向的细观结构损伤随载荷的增大发展更快,刚度下降更快,破坏时主裂纹的扩展方向更趋于垂直于快速拉伸方向;强度包络线的分析表明快速拉伸方向的拉伸强度随加载比的增大呈缓慢增大的趋势。      

Analysis of the stress-strain state of a rectangular orthotropic plate under the action of biaxial tension and shear

We propose a method for the analysis of the stress-strain state of rectangular orthotropic plates under the conditions of biaxial tension and shear. According to this method, we specify a field of displacements in the plate in the form of the product of a matrix of differential operators by an unknown vector function or a column of three scalar functions, each of which admits a representation in the form of the sum of the products of an unknown function of one variable by a trigonometric function of the other variable. The number of independent coefficients of each function is determined from the boundary conditions by the method of Fourier series. We also performed calculations of the stressed state in the plate depending on the ratio of its sides and the type of loading. ^aKarpenko Physicomechanical Institute, National Academy of Sciences of Ukraine, Lviv.^bInstitute for Applied Problems in Mathematics and Mechanics, National Academy of Sciences of Ukraine, Lviv.^cLutsk Industrial Institute, Lutsk, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 47 – 55, January – February, 1998.     

Circular inclusion in a viscoelastic plate subjected to uniaxial tension

The effects of a circular inclusion in an infinite viscoelastic plate subjected to monotonically increasing uniaxial tension are investigated, in particular the stress distributions around the inclusion. An elastic inclusion is considered and both rough and smooth contact treated. The solution is limited to complete contact around the inclusion circumference. The results hinge on two lemmas concerning the monotonicity and sign of reciprocal and combined viscoelastic response functions.     

Closed-form solution for a coated circular inclusion under uniaxial tension

A coated circular inclusion embedded in an infinite matrix is analyzed in the framework of two-dimensional isotropic linear elasticity. A closed-form solution is obtained for the case of far-field uniaxial tension using Muskelishvilis complex potential method. The solutions for the stress and strain distributions for all three regions, that is, matrix, coating, and inclusion, were obtained for various coating-to-matrix shear modulus ratios, while keeping the fiber and matrix shear moduli the same. Test cases for an inclusion without the coating and hollow inclusion were also studied. The energy release rate was evaluated using the path-independent M-integral, which is used to calculate the energy release rate for the self-similar expansion of defects surrounded by the closed contour of the integral. The results for the stress and strain concentrations along with the energy release rate due to this material inhomogeneity were analyzed to yield a better understanding of the mechanics of materials with circular inclusions. This can be helpful in designing intelligent composite structures with embedded optical fiber sensors.     

An estimation of plastic zones in a plate with a central hole

A method is described for estimating the size of the plastic zone developing around a central hole in a finite width plate subjected to a monotonically increasing tensile load from a knowledge of the elastic stress field only. The plate is assumed to be subjected to plane stress conditions and to be made from an elastic, linearly strain-hardening material. Yielding is considered to occur when the Mises criterion is satisfied. Stresses within the plastically deformed area of the plate are evaluated by means of the Prandtl-Reuss incremental flow rule together with strains increments calculated from the elastic stress distributions. The predicted plastic zone sizes correlate well with those determined experimentally by other workers.     

Finite strip with a central crack under tension

In this study, a symmetrical finite strip with a length of 2L and a width of 2h, containing a transverse symmetrical crack of width 2a at the midplane is considered. Two rigid plates are bonded to the ends of the strip through which uniformly distributed axial tensile load of magnitude 2hp₀ is applied. The material of the strip is assumed to be linearly elastic and isotropic. Both edges of the strip are free of stresses. Solution for this finite strip problem is obtained by means of an infinite strip of width 2h which contains a crack of width 2a at y = 0 and two rigid inclusions of width 2c at y = ±L and which is subjected to uniformly distributed axial tensile load of magnitude 2hp₀ at y = ±∞. When the width of the rigid inclusions approach the width of the strip, i.e., when c → h, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. Fourier transform technique is used to solve the governing equations which are reduced to a system of three singular integral equations. By using the Gauss–Jacobi and the Gauss–Lobatto integration formulas, these integral equations are converted to a system of linear algebraic equations which is solved numerically. Normal and shearing stress distributions and the stress intensity factors at the edges of the crack and at the corners of the finite strip are calculated. Results are presented in graphical and tabular forms.     

Effects of strain-gradient on the stress-concentration at a cylindrical hole in a field of uniaxial tension

Summary The solution of the plane-strain problem of a circular cylindrical hole in a field of uniaxial tension is obtained in the linear theory of elasticity in which the potential energy function depends on both the strain and the gradient of the strain. The stress-concentration factor at the surface of the cylindrical hole and the stress-concentration away from the hole are found and they are compared with the analogous results obtained in couple-stress theory and in classical elasticity.As of Oct. 1970, The Negev University, Beer-Sheva, Israel.     

Cracks emanating from a square hole in rectangular plate in tension

A numerical analysis of cracks emanating from a square hole in a rectangular plate in tension is performed using a hybrid displacement discontinuity method (a boundary element method). Detailed solutions of the stress intensity factors (SIFs) of the plane elastic crack problem are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. By comparing the calculated SIFs of the plane elastic crack problem with those of the centre crack in a rectangular plate in tension, in addition, an amplifying effect of the square hole on the SIFs is found. The numerical results reported here also prove that the boundary element method is simple, yet accurate, for calculating the SIFs of complex crack problems in finite plate.     

Deformation micromechanisms of collagen fibrils under uniaxial tension

Collagen, an essential building block of connective tissues, possesses useful mechanical properties due to its hierarchical structure. However, little is known about the mechanical properties of collagen fibril, an intermediate structure between the collagen molecule and connective tissue. Here, we report the results of systematic molecular dynamics simulations to probe the mechanical response of initially unflawed finite size collagen fibrils subjected to uniaxial tension. The observed deformation mechanisms, associated with rupture and sliding of tropocollagen molecules, are strongly influenced by fibril length, width and cross-linking density. Fibrils containing more than approximately 10 molecules along their length and across their width behave as representative volume elements and exhibit brittle fracture. Shorter fibrils experience a more graceful ductile-like failure. An analytical model is constructed and the results of the molecular modelling are used to find curve-fitted expressions for yield stress, yield strain and fracture strain as functions of fibril structural parameters. Our results for the first time elucidate the size dependence of mechanical failure properties of collagen fibrils. The associated molecular deformation mechanisms allow the full power of traditional material and structural engineering theory to be applied to our understanding of the normal and pathological mechanical behaviours of collagenous tissues under load.     

Limiting state of two-phase composites under uniaxial tension

We propose a model based on the statistical analysis of fracture processes and a concept of effective medium when a system of structural elements of different kinds is regarded as a quasihomogeneous medium with certain effective properties. This approach enables one to compute parameters of the stable stage of fracture of composite materials. The suggested model is used for the prediction of critical values of the parameters corresponding to the transition to unstable fracture under uniaxial tension. We also compare two-phase composites with brittle and plastic phases with strong and weak interfaces between the structural elements, respectively.Frantsevich Institute for Problems in Materials Science, Ukrainian Academy of Sciences, Kiev. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 6, pp. 51–58, November–December, 1995.     

Fatigue behavior of laminated composites with a circular hole under in-plane uniaxial random loading

A modified fiber failure fatigue model is presented to evaluate the behavior of laminated composites with a central circular hole under in-plane uniaxial random/block loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane uniaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Degradation of material strength as a function of applied number of cycles is considered in the model presented. Random loading case is analyzed based on rainflow counting technique. Analytical predictions are compared with the experimental results for uniaxial block loading.     

Stresses in a thick plate with a circular hole under axisymmetric loading

An exact theoretical solution is given for the stresses and displacements in an infinite plate of finite thickness having a circular hole and subjected to axisymmetric normal leading. The solution is given in the form of Fourier-Bessel series and integral. Numerical results are given for stresses in plates having different thickness to hole diameter ratios and loadings. The results are compared with the available approximate theoretical and experimental results.     

The solution of a rectangular orthotropic sheet with a central crack under anti-plane shear

Making use of the basic theorem of the Fourier transform and series, the solution of the stress intensity factor of a rectangular orthotropic plate containing a central crack under anti-plane shear, is obtained in this study. The result to the mixed boundary value problem is expressed in terms of a Fredholm integral equation of the second kind. It is easily proved that the problem of a strip with a central crack of mode III, are the special cases of the solution in this article.     

Peripheral edge crack around a spherical cavity under uniaxial tension field

The singular stress problem of a peripheral edge crack around a spherical cavity under a uniaxial tension field is investigated. The problem is analyzed by means of integral transforms and reduced to that of solving a singular integral equation of the first kind. The stress-intensity factors and crack opening displacements are obtained by means of the numerical technique due to Erdogan, Gupta and Cook [6].     

Experimental characterization of orthotropic technical textiles under uniaxial and biaxial loading

The paper deals with the development of an experimental protocol for the mechanical characterization of plain weave technical textiles. The textiles are modelled as orthotropic materials with known directions of material symmetry, and a “linear-by-step” approximation is introduced to account for the nonlinearity exhibited by the stress–strain behaviour. Material coefficients are determined by fitting uniaxial stress–strain curves along the warp, weft and 45° directions. The full-field evaluation of the strain distribution on the specimen surface, carried out by an optical approach, allows to assess the absence of edge effects and to quantify the shear strains introduced by off-axis loading.The protocol is applied to the characterization of a monofilament polyester textile and the model identified upon uniaxial data is validated by comparing analytical simulations with experimental data obtained under biaxial stress conditions. Finally the reliability of failure criteria based upon both uniaxial and biaxial data is investigated.     

Effect of loading rate on the strength of concrete subjected to uniaxial tension

In the context of an international co-operation project between the University of Delft (The Netherlands) and the LCPC, an experimental study was made of rate effects in the behaviour of concrete under tensile stress. Very high speed tests ( between 1 and 80 GPa s⁻¹) were carried out in Delft on a Hopkinson bar, and quasi-static tests ( between 5×10⁻⁵ and 5×10⁻³ GPa s⁻¹) were carried out by the LCPC on a hydraulic press. This investigation had two objectives. 1. To verify on a mini-concrete (diameter of the largest particles 10 mm) a result obtained with a micro-concrete (diameter of the largest particles 2 mm) in the course of a previous study. Rate effects are produced by the presence of pore water in the material. 2. To investigate the influence of the water/cement ratio (i.e., the compressive strength of the concrete) on these rate effects. The three main conclusions that can be drawn from this study are (i) it is indeed the presence of pore water in the concrete which is at the origin of rate effects where this materials is concerned, (ii) the effect of speed on the tensile strengthf ₁ increases with the water/cement ratio, and (iii) in absolute value, the increase in strength (f _tdyn-f _tstat ) seems to be independent of the water/cement ratio.

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Resume Dans le cadre d'une coopération internationale entre l'Université de Delft (Pays-Bas), et le Laboratoire Central des Ponts et Chaussées (LCPC), une étude expérimentale a été menée sur les effects de vitesses dans le comportement en traction du béton. Les essais très rapides ( compris entre 1 et 80 GPa s⁻¹) ont été réalisés à Delft sur une barre d'Hopkinson, les essais quasi-statiques ( compris entre 5×10⁻³ et 5×10⁻⁵ GPa s⁻¹) étant réalisés au LCPC sur une presse hydraulique. Deux objectifs sont visés dans cette étude: (i) vérifier sur un mini-béton (diamètre du plus gros grain égal à 10 mm) un résultant obtenu sur micro-béton (plus gros grain égal à 2 mm) lors d'une étude précédente: c'est la présence d'eau libre au sein du matériau qui induit les effects de vitesse; et (ii) étudier l'influence du rapport eau/ciment (c'est-à-dire de la résistance en compression du béton) sur ces effets de vitesse. Les conclusions principales que l'on peut tirer de cette étude sont les trois suivantes: c'est bien la présence d'eau libre dans les bétons qui est l'origine des effects de vitesse relatifs à ce matériau; l'effet de vitesse sur la résistance en traction f₁ augmente avec le rapport eau/ciment; et en valeur absolue, l'augmentation de la résistance (f _tdyn-f _tstat ) semble indépendante de ce rapport eau/ciment.