General size effect on strength of bimaterial quasibrittle structures

This paper presents a general size effect equation for the strength of hybrid structures, which are made of two dissimilar quasibrittle materials with a thin and weak bimaterial interface. Depending on the material mismatch and structure geometry, a singular stress field could occur at the bimaterial corner. For structures with strong stress singularities, an energetic size effect is derived based on the equivalent linear elastic fracture mechanics and asymptotic matching. For structures without stress singularities, a finite weakest link model is adopted to derive the size effect. A general scaling equation that bridges the limits of strong and zero stress singularities is formulated by combining the energetic scaling of fracture of the bimaterial corner and the finite weakest link model.     

The mechanics of self-similar and self-affine fractal cracks

In this paper we study the mechanical attributes of the fractal nature of fracture surfaces. The structure of stress and strain singularity at the tip of a fractal crack, which can be self-similar or self-affine, is studied. The three classical modes of fracture and the fourth mode of fracture are discussed for fractal cracks in two-dimensional and three- dimensional solid bodies. It is discovered that there are six modes of fracture in fractal fracture mechanics. The J-integral is shown to be path-dependent. It is explained that the proposed modified J-integrals in the literature that are argued to be path-independent are only locally path-independent and have no physical meaning. It is conjectured that a fractal J-integral should be the rate of potential energy release per unit of a fractal measure of crack growth. The powers of stress and strain singularities at the tip of a fractal crack in a strain-hardening material are calculated. It is shown that stresses and strains have weaker singularities at the tip of a fractal crack than they do at the tip of a smooth crack.     

铆接界面端三维奇异性应力场的研究

针对铆接结构的特点,应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式,并根据铆钉/被铆接件接触界面端的位移和应力边界条件,建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比,验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题,考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。     

The fourth mode of fracture in fractal fracture mechanics

This paper offers a systematic approach for obtaining the order of stress singularity for different self-similar and self-affine fractal cracks. Mode II and Mode III fractal cracks are studied and are shown to introduce the same order of stress singularity as Mode I fractal cracks do. In addition to these three classical modes, a Mode IV is discovered, which is a consequence of the fractal fracture. It is shown that, for this mode, stress has a weaker singularity than it does in the classical modes of fracture when self-affine fractal cracks are considered, and stress has the same order of singularity when self-similar cracks are considered. Considering this new mode of fracture, some single-mode problems of classical fracture mechanics could be mixed-mode problems in fractal fracture mechanics. By imposing a continuous transition from fractal to classical stress and displacement fields, the complete forms of the stress and displacement fields around the tip of a fractal crack are found. Then a universal relationship between fractal and classical stress intensity factors is derived. It is demonstrated that for a Mode IV fractal crack, only one of the stress components is singular; the other stress components are identically zero. Finally, stress singularity for three-dimensional bodies with self-affine fractal cracks is studied. As in the two-dimensional case, the fourth mode of fracture introduces a weaker stress singularity for self-affine fractal cracks than classical modes of fracture do.     

A study on an effect of geometric singularities on ductile fracture

This paper describes the appearance of fractures in the vicinity of geometric singularities in cold upsetting of three series of slightly different samples between flat and spherical dies. The main goal of the research is to understand an effect of geometric singularities on ductile fracture. To this end, the series of tests are designed such that the site of fracture initiation moves to the geometric singularity, as compared to conventional tests, independently of its effect on the ductile fracture process. The paper concerns with a qualitative effect of geometric singularities on ductile fracture initiation rather than with quantitative values of parameters controlling the ductile fracture process.     

Fracture Resistance of a Cracked Concrete Beam Post-strengthened with FRP Sheets

Fibre-reinforced plastic (FRP) composites have been increasingly used in rehabilitation and strengthening of concrete structures. Significant increases in stiffness and strength have been achieved by applying this technique. However, there is concern about the ductility or toughness performance of FRP/concrete hybrid structures, which is critical in the application of this technology. This paper presents a new theoretical method to predict the fracture resistance behaviour of FRP post-strengthened concrete flexural beams. No slip between the FRP and plain concrete matrix is assumed and Mode I fracture propagation is considered. The model is valid for a wide range of span-to-depth ratios and any crack length. The influence of the bridging stresses provided by the fracture process zone (FPZ) at the tip of a fictitious fracture is examined. The effect of various material and geometric parameters on the resistance curve and toughness of the hybrid structure is discussed, based on the numerical results from the developed theoretical formulae. The results provide a useful insight into the strengthening/toughening and the design of FRP sheet/concrete beam structures.     

A Criterion of Local Strength

We propose a local criterion of brittle strength for structurally inhomogeneous materials based on the size effect of mechanical properties of materials under the conditions of stress concentration. It is assumed that the function of local strength of the material depends on the scaling factor equal to the ratio of the size of the zone of stress concentration to the characteristic structural size of the material. We study the problem of strength of a solid body containing a stress concentrator of any size and shape in tension, including the limiting case of degeneration of a smooth concentrator into a rectilinear (or circular) crack. The requirements to the behavior of the critical stress and critical size of the defect are formulated and the form of the function of local strength is specified. For the fracture stress, we deduce interpolation-type expressions and compare the obtained numerical results with the available experimental data.     

基于材料选型优化的金属-复合材料组合结构-声辐射优化

基于金属铺层假设,以结构材料属性和材料铺层数量为设计变量,建立了基于金属-复合材料的材料选型结构-声辐射优化设计模型。以钢-纤维增强复合材料组合结构为例,开展了多设计变量、多约束条件的结构-声辐射优化研究。最后,采用遗传算法进行求解,实现了结构材料的转换。数值算例表明,通过金属-复合材料组合结构的材料选型优化,可以有效降低钢-纤维增强复合材料结构的振动和声辐射。文中的研究方法为结构材料的分布优化提供了一种可行有效的思路。     

Cohesive zone modeling of interface fracture in elastic bi-materials

Some basic issues regarding the cohesive zone modeling of interface fracture between two dissimilar elastic materials are studied. The dependence of the cohesive energy density on the phase angle is first discussed under small scale cohesive zone conditions. It is then shown that in general the stress singularities in tension and shear cannot be simultaneously removed at the cohesive zone tip if a single cohesive zone length is adopted for both tensile and shear fracture modes. Finally, the energy dissipation at the tip of a prescribed cohesive zone is examined using a bilinear cohesive zone model under the uncoupled tension/shear conditions.     

Correlation between fracture and damage for quasi-brittle bi-material interface cracks

Fracture at a bi-material interface is essentially mixed-mode, even when the geometry is symmetric with respect to the crack and loading is of pure Mode I, due to the differences in the elastic properties across an interface which disrupts the symmetry. The linear elastic solutions of the crack tip stress and displacement fields show an oscillatory type of singularity. This poses numerical difficulties while modeling discrete interface cracks. Alternatively, the discrete cracks may be modeled using a distributed band of micro-cracks or damage such that energy equivalence is maintained between the two systems. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in quasi-brittle bi-material interface beams. The study is aimed at large size structures made of quasi-brittle materials failing at concrete-concrete interfaces. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. It is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

Application of fracture mechanics for weld integrity assessment

The structural integrity assessment of a weld joint by conventional techniques is inadequate, because of unavoidable defects in the weld composite. The stress situation in a component having a defect is quite different from that of a homogeneous material. The significance of fracture mechanics to deal with such integrity assessments is brought out. A brief review on the basic formulations in the application of fracture mechanics is followed by established guidelines for evaluating the integrity of engineering components containing crack-like defects.     

Lattice modelling of size effect in concrete strength

This paper uses a recently improved lattice network model to study the size effect in the strength of plain concrete structures. The several improvements made to the lattice network model are: (i) tension softening of the matrix phase is included in the material modelling; (ii) the structural response is modelled by incrementing the deformation rather than the load. This eliminates the need for introducing arbitrary scaling parameters in the beam element failure criteria and; (iii) a square rather than a triangular lattice beam network is found to be adequate for modelling concrete, thus greatly reducing the computational time.The improved square lattice network has been used to simulate the complete load-deformation response of notched three-point bend beams of different sizes with a view to checking the validity of several size effect models available in the literature. Lattice simulation was found to identify microcracking, crack branching, crack tortuosity and bridging, thus allowing the fracture process to be followed until complete failure. The improved lattice model predicted smooth structural response curves in excellent agreement with test results.The simulated nominal strengths also correlated very well with the test results, apart from that for the smallest beams (depth 38.1 mm). However, even in the relatively broad range of sizes (1:8) of the test beams, there was no clear evidence that one size effect model is superior to the other. In fact, rather surprisingly the test data would appear to be equally well described by all the available size effect models. The lattice simulations however indicated a trend which is better predicted by the multifractal scaling model.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

基于SINTAP-FAD方法的含裂纹缺陷钢结构构件安全性评定研究

在施工和运营过程中,钢结构构件上出现的裂纹缺陷可能会扩展而导致其发生断裂破坏,因此对含裂纹缺陷钢结构构件的安全性进行评估具有重要意义。首先,引入断裂力学K_IC断裂判据和失效评定图（FAD）概念,并介绍了结构整体性评估程序（SINTAP）的原理;给出了裂纹缺陷评定所需材料参数的确定方法,以及含裂纹缺陷构件的断裂力学参数和塑性屈服荷载的计算方法;然后,提出了基于SINTAP-FAD的含裂纹缺陷钢结构构件的安全性评估流程。最后,以华南和华东两个电厂锅炉钢结构大板梁的焊接缺陷为例,进行了基于K_IC断裂判据和SINTAP-FAD的裂纹缺陷安全性评定研究。结果表明,基于SINTAP-FAD的方法为含裂纹缺陷工作的钢结构构件的安全性评估提供了一种行之有效的方法,考虑多裂纹耦合作用的安全性评定方法有待进一步研究。     

Singularity of collapsed Q-8 finite element

The ability of the collapsed Q-8 finite element to model strain singularities is studied in this paper. It is shown that its ability to model an r^?1 singularity in strains depends strongly on the element size and number of Gauss points used for sampling stresses inside an element.     

基于Beach Marking方法的钢结构疲劳裂纹检测研究

研究裂纹的形成和扩展规律是钢结构疲劳断裂的一个重要课题。该文讨论了一种十分经济有效的检测钢结构疲劳裂纹萌生与扩展的方法,即Beach Marking方法。首先简要总结了该方法的发展历史和研究现状,并系统归纳了其基本原理和关键问题。同时,通过焊接H型钢梁的试验案例,探索该方法应用在大尺寸构件上的实际效果,并具体展示该方法的设计步骤和应用过程。试验表明,Beach Marking方法简单实用,关键在于设计合理的疲劳荷载序列;通过分析疲劳断口上留下的疲劳弧线,并结合断裂力学理论,可以获得疲劳裂纹的扩展规律和参数,为钢结构疲劳寿命数值分析提供科学依据。     

On stress singularities in linear elasticity

The stress field in many exact solutions of problems in linear elasticity is found to have singularities which occur at corners and or at points where the boundary conditions change in type. The dependence of the singularities on the local geometry and on the types of boundary conditions is investigated in this paper. It is found that the type of boundary conditions determines the type of singularity but that the geometry largely influences the magnitude of the singularity.     

A calculation-experimental study of crack-tip opening displacement and residual stresses upon warm prestressing

For a reactor pressure vessel steel 15Kh2MFA(III) experiments and calculations have been carried out to study the factors that have an influence on the increase of the lower-shelf fracture toughness in the temperature dependence diagrams upon warm prestressing. Stereoscopic fractography and numerical investigation have demonstrated that after the warm prestressing the crack tip remains blunt. This reduces the stress singularity during subsequent loading and raises the material fracture toughness. The paper gives the calculated data on residual stresses and crack-tip opening displacement during warm prestressing and upon relief. The calculated results are shown to agree well with the known analytical relations and experimental data.