THE FULLY PLASTIC J-INTEGRAL OF CORNER CRACKS AT A HOLE IN A PLATE

The line-spring model of surface cracks is applied to the fully plastic analysis of cornercracks at a hole in a plate.The generalized fully plastic constitutive relations and the fully plastic J-in-tegral,as well as its coefficients in polynomial expressions are given.The model obtained is incorpo-rated into a finite element program.The corner cracks at a hole in a plate subjected pure tensions arecalculated by the present model.The fully plastic J-integral is then estimated.The results obtainedshow that the line-spring model is effective for the analysis of corner cracks.The influence of thecrack depth and the hardening exponent on the fully plastic J-integral is also discussed.     

The scattering of harmonic elastic anti-plane shear waves by two collinear cracks in the piezoelectric plate by using the non-local theory

In this paper, the dynamic interaction between two collinear cracks in a piezoelectric material plate under anti-plane shear waves is investigated by using the non-local theory for impermeable crack surface conditions. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. These equations are solved using the Schmidt method. This method is more reasonable and more appropriate. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The project supported by the Natural Science Foundation of Heilongjiang Province and the National Natural Science Foundation of China(10172030, 50232030)     

Elastoplastic cracks moving in orthotropic crystals

The stress field, crack-tip plastic zones and total plastic displacement created around an infinite row of collinear elastoplastic constant width Griffith-type strip cracks moving within an orthotropic crystal are considered using the powerful method of dislocation layers. The method is applied with the BCS modelled elastoplastic cracks moving under mode III loading at constant crack-tip velocity, according to the Yoffe model. Simultaneously the analysis provides solutions for a corresponding single crack moving similarly within a finite orthotropic plate and a finite plate containing a surface crack. Analogous results for the corresponding mode I, mode II and purely elastic cracks can be deduced.     

A novel method for residual strength prediction for sheets with multiple site damage: Methodology and experimental validation

A unified method for solving the strip yield model for collinear cracks in finite and infinite sheet is proposed. The method is based on the weight function of a single crack. Two collinear cracks in finite and infinite sheets are used to apply and verify this method. The plastic zone size, crack opening displacement and stress distribution along the ligament between cracks obtained by using the present method are extensively compared with existing available results and finite element solutions, and very good agreements are observed. Combined with the Crack Tip Opening Angle (CTOA) criterion, the unified method is used to predict the crack growth behavior and residual strength for 2024-T3 aluminum alloy sheet with Multiple Site Damage (MSD). Thirty-two sheets with four types of MSD are designed and tested to verify this method. It is shown that the present method is able to predict various crack growth behaviors observed in experiment. The predicted residual strengths are within 9% of the corresponding test results. Compared to the elastic–plastic finite element method, the present method is much more efficient.     

Closed form solution for two unequal collinear semi-permeable straight cracks in a piezoelectric media

The problem of two unequal collinear straight cracks weakening a poled transversely isotropic piezoelectric ceramic is addressed under semi-permeable electric boundary conditions on the crack faces. The plate has been subjected to combined in-plane normal(to the faces of the cracks) mechanical and electric loads. Problem is formulated employing Stroh formalism and solved using complex variable technique. The elastic field, electric field and energy release rate are obtained in closed analytic form. A case study is presented for poled PZT-5H cracked plate to study the effect of prescribed mechanical load, electric load, inter-crack distance and crack lengths on crack arrest parameters stress intensity factor (SIF), electric displacement intensity factor (EDIF) and mechanical and total energy release rates (ERR). Moreover a comparative study is done of impermeable and semi-permeable crack face boundary conditions on SIF, EDIF and ERR, and results obtained is presented graphically. It is observed that the effect of dielectric medium in the crack gap cannot be ignored.     

Crack bifurcation predicted for dynamic anti-plane collinear cracks in piezoelectric materials using a non-local theory

A non-local theory of elasticity is applied to obtain the dynamic interaction between two collinear cracks in the piezoelectric materials plane under anti-plane shear waves for the permeable crack surface boundary conditions. Unlike the classical elasticity solution, a lattice parameter enters into the problem that make the stresses and the electric displacements finite at the crack tip. A one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and electric displacement near the crack tips. By means of the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations in which the unknown variable is the jump of the displacement across the crack surface. The solutions are obtained by means of the Schmidt method. Crack bifurcation is predicted using the strain energy density criterion. Minimum values of the strain energy density functions are assumed to coincide with the possible locations of fracture initiation. Bifurcation angles of ±5° and ±175° are found. The result of possible crack bifurcation was not expected before hand.     

连铸板坯热轧中角部裂纹变化的研究

采用有限元方法对轧件角部横向和纵向裂纹在多道次立-平轧制过程中变形行为进行了模拟,分析了裂纹的闭合与扩展行为．结果表明:采用平立辊,裂纹很好闭合,但变形程度大,可能延伸和往轧件顶面移动,对角部横向裂纹,裂纹尖端节点往外扩散,对三角形横向和纵向裂纹,裂纹可能发生折叠;采用孔型立辊,立轧后,轧件裂纹很好地闭合,平轧后,横向和侧面纵向裂纹可能被拉开,顶面纵向裂纹闭合较好,只有三角形横向裂纹可能发生折叠．     

Interaction of microcracks with a macrocrack yielded in a narrow strip

Plastic zone growth of collinear cracks has had a longstanding interest in ductile fracture. This work further considers yield zone growth in an isotropic, homogeneous elastic–perfectly plastic infinite plate containing a macrocrack with several neighboring microcracks. Normal loading is considered at distances far away from the cracks. The strip yield is adopted where the plastic zone is assumed to be confined to two narrow strips extending from the ends of a finite length crack while the microcracks are assumed to be elastic. The plastic zone length and crack opening displacement are found from asymptotic solution and compared with finite element solution.     

Numerical simulation of loading edge cracks by edge impact using the extended finite element method

The extended finite element method is used to analyze a plate with two parallel edge cracks impacted by a cylindrical projectile. The influence of the impact speed, crack length,plate thickness and notch tip radius on the crack initiation and propagation is studied. Dynamics equations are solved by an implicit time integration scheme which is unconditionally stable. Very good agreement is achieved between numerical predictions and experimental results. The critical velocity of the crack initiation under different conditions is examined. The influence of the crack length is greater than that of the impact speed, plate thickness and notch tip radius.     

INVESTIGATION OF ANTI-PLANE SHEAR BEHAVIOR OF TWO COLLINEAR CRACKS IN PIEZOELECTRIC MATERIALS BY A NEW METHOD

In this paper, the interaction between two collinear cracks in piezoelectric materials under anti-plane shear loading was investigated for the impermeable crack face conditions. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using Schmidt's method. This process is quite different from that adopted previously. This study makes it possible to understand the two collinear cracks interaction in piezoelectric materials. The authors are grateful for financial support from the Post-Doctoral Science Foundation and the Natural Science Foundation of Heilongjiang Province.     

Non-singular terms for multiple cracks in anisotropic elastic solids

The non-singular and bounded terms for the stresses near the crack tip are investigated. This paper deals with the multiple crack problem for an infinite plate. The original problem is decomposed into three elementary subproblems: (1) the problem for remote uniform stress filed without cracks; (2) the single crack problem with traction applied along the crack face and (3) the problem for the influence of the other cracks. Several examples for collinear and non-collinear cracks are discussed and the results are shown.     

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采用有限元方法对表面含有两个不同大小半椭圆裂纹的有限厚矩形板在拉伸载荷作用下 进行参数化求解，得到两裂纹取不同尺寸和位置坐标时附属裂纹(尺寸较小裂纹)对主 导裂纹(尺寸较大裂纹)前沿参考点($\theta= 0, \pi/2, \pi $)处的应力强 度因子的影响系数$\beta$, 然后结合神经网络技术建立了相邻裂纹尺寸和位置参 数到主导裂纹前沿点处$\beta$的多变量非线性映射关系.     

DYNAMIC BEHAVIOR OF TWO COLLINEAR PERMEABLE CRACKS IN A PIEZOELECTRIC LAYER BONDED TO TWO HALF SPACES

IntroductionIn the fracture mechanics studies for piezoelectric materials,differently electricboundary conditions at the crack surfaces have been proposed by many researchers.Forexample,for the sake of analytical simplification,the assumption that the cra…     

Electrothermal stress in conductive body with collinear cracks

The temperature and stress field in a thin plate with collinear cracks interrupting an electric current field are determined. This is accomplished by using a complex function method that allows a direct means of finding the distribution of the electric current, the temperature and stress field. Temperature dependency for the heat-transfer coefficient, coefficient of linear expansion and the elastic modulus are considered. As an example, temperature distribution is calculated for an alloy (No. GH2132) plate with two collinear cracks under high temperature. Relationships between the stress, temperature, electric density and crack length are obtained. Crack trajectories emanating from existing crack are predicted by application of the strain energy density criterion which can also be used for finding the load carrying capacity of the cracked plate.     

Nonlocal theory solution of two collinear cracks in the functionally graded materials

In this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials.     

Investigation of the dynamic behavior of two parallel symmetric cracks in piezoelectric materials use of non-local theory

In this paper, the dynamic behavior of two parallel symmetric cracks in piezoelectric materials under harmonic anti-plane shear waves is investigated by use of the non-local theory for permeable crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the problem to obtain the stress occurs near the crack tips. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations that the unknown variables are the jumps of the displacement along the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the frequency of the incident wave, the distance between two cracks and the lattice parameter of the materials, respectively. Contrary to the impermeable crack surface condition solution, it is found that the dynamic electric displacement for the permeable crack surface conditions is much smaller than the results for the impermeable crack surface conditions. The results show that the dynamic field will impede or enhance crack propagation in the piezoelectric materials at different stages of the dynamic load.     

Analysis of two-dimensional finite solids withmicrocracks

A general method is presented for solving the plane elasticity problem of finite plateswith multiple microcracks. The method directly accounts for the interactions between differentmicrocracks and the effect of outer boundary of a finite plate. Analysis is based on a superpositionscheme and series expansions of the complex potentials. By using the traction-free conditions oneach crack surface and resultant forces relations along outer boundary, a set of governingequations is formulated. The governing equations are solved numerically on the basis of aboundary collocation procedure. The effective Youngs moduli for randomly oriented cracks andparallel cracks are evaluated for rectangular plates with microcracks. The numerical results arecompared with those from various micromechanics models and experimental data. These resultsshow that the present method provides a direct and efficient approach to deal with finite solidscontaining multiple microcracks.     

矩形夹层板稳定性分析

本文在Reissner理论基础上,应用功的互等定理推导了夹层矩形板稳定问题的基本解,在已推导出的夹层板基本解的基础上,利用功的互等法求解了两对边固定一边简支一边自由、两邻边简支另两邻边自由且角点支承、两邻边简支另两邻边自由且角点悬空三种不同边界条件下夹层板的稳定问题,给出了挠曲面方程及其对应的执行方程;进行了数值计算,并与有限元结果进行对照分析.结果表明:本文方法求解过程更简单,提供了一种求解夹层板稳定问题的新方法,计算结果对解决工程实际问题具有一定的参考价值.     

层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质,引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式,给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性,同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子,发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．     

Initiation and growth characterization of corner cracks near circular hole

The finite element analysis of crack problems often incorporates the asymptotic character of the local solution into the formulation. Embedment of stress or strain singularities can impose serious restrictions on the outcome and inconsistencies in predicting crack and/or growth. These restrictions are discussed in connection with the problem of two diametrically opposite corner cracks near a circular hole subjected to remote uniform tension. Enforced in the numerical treatment is the 1/r character of the strain energy density function local to the corner crack border where r is the radial distance measured from the crack front. The tendency for the corner crack to become a through crack is predicted by assuming that each point of the crack border extends by an amount proportional to the strain energy density factor. The path would correspond to the loci of minimum strain energy density function. Numerical results are displayed graphically and discussed in connection with crack initiation and non-self-similar crack growth.