表面裂纹疲劳扩展的数值模拟(Ⅱ)

根据Paris疲劳裂纹扩展规律,对拉伸和纯弯曲疲劳载荷下表面裂纹扩展进行了数值模拟。数值模型中,用三次样条函数曲线拟合裂纹尖端,在裂纹扩展增量计算中考虑了裂纹闭合影响。裂纹形状演化的模拟结果与Newman和Raju经验公式预测结果进行了比较,表明了所采用的数值模拟方法的实用性。研究发现,裂纹闭合对疲劳裂纹扩展过程中的裂纹形状演化以及裂纹尖端的应力强度因子(SIF)分布都有明显影响。同裂纹形状演化一样,疲劳裂纹扩展过程中裂纹尖端的SIF分布表现出明显的特征。最后,建议了一个简单函数来统一描述表面裂纹尖端的SIF分布。     

Cracks’ closure in 3-D fracture dynamics: the effect of relative location of two coplanar cracks

In this paper, the problem of two equal coplanar cracks with allowance for the crack faces contact interaction was investigated. The problem of the cracks located in homogeneous, isotropic, and linearly elastic solid subjected to normally incident tension–compression wave is solved by the boundary integral equations method. The influence of the distance between two cracks on the stress intensity factors (opening mode and transverse shear mode) is studied for a range of wave numbers. The results are compared with those obtained neglecting cracks’ closure.     

Effects of the curvature radius of a cylindrical shell on the stress intensity factors of surface cracks

The effects of the curvature radius of a cylindrical shell on stress intensity factors are investigated in circumferential (inner and outer) semielliptical surface cracks in a cylindrical shell. What is new in this paper is to have given: (1) The stress intensity factors for surface cracks in a cylindircal shell are determined by photoelastic technique. (2) By a special method photoelastic slices are handled for obtaining a clear caustic curve, and the stress intensity factors for surface cracks in a cylindrical shell are determined by the caustic method. (3) An approximate equation of curvature correction factor F_c is proposed. (4) Effects of the curvature radius R of a cylindrical shell on the stress intensity factors of surface cracks are obtained. The results of this paper are in fair agreement with already existing analytical results. The approximate equation of curvature correction factor F_c can be widely used for engineering purposes.     

任意多孔多裂纹板的裂纹闭合接触分析

基于摩擦接触问题的数学规划解法，采用各向异性体平面弹性理论中的复势方法，建立了含多椭圆孔及裂纹群有限大各向异性板，在任意载荷作用下裂纹闭合或局部闭合问题的有效分析方法。通过在可能闭合的裂纹边界引入互补变量函数并将其展成Fourier级数形式，以Faber级数为工具，应用保角映射技术和最小二乘边界配点法，导出无卸载情况下裂纹面摩擦接触的线性互补模型，并通过算例验证了方法的有效性。数值结果表明，由于采用级数解描述板应力场和位移场，该方法具有较高的计算精度和效率，便于研究裂纹闭合对应力强度因子等断裂参数的影响。     

Modeling of partial closure of cracks in a perforated isotropic medium reinforced by a regular system of stringers

A mathematical model of partial closure of a crack in a perforated isotropic medium with a system of rectilinear foreign inclusions is constructed. Such a medium can be interpreted as an unbounded plate reinforced by a regular system of ribs whose cross sections are shaped as narrow rectangles. The medium is assumed to be attenuated by a periodic system of circular holes and straight-line cracks. Determination of unknown contact stresses and contact zone sizes is reduced to solving a singular integral equation, which is transformed by an algebraization procedure to a system of nonlinear algebraic equations solved by the method of consecutive approximations.     

A Linearly Elastic Shell over an Obstacle: The Flexural Case

We study the equilibrium of a three-dimensional solid having a uniform thickness \(2 \varepsilon \) along a middle surface which satisfies the usual assumptions of shell theory. The solid is linearly elastic at small strains and is submitted to unilateral contact conditions with an obstacle on a part of its boundary. When \(\varepsilon \) tends to zero, the three-dimensional domain tends to a two-dimensional one, so that the contact conditions pass from a part of the boundary to the interior of the domain. We restrict our attention to the so-called bending case, that is when the shell undergoes only inextensional deformations. As a major difference with the case of a shallow shell, we get in general a coupling between the three components of the displacement in the contact conditions. The work is closed by explicit examples showing the corresponding variation of the non-penetrability condition along the surface of the shell and by comments about the model and the remaining difficulties.     

Approximate solution to the problem of the interaction of a soft shell with a viscous incompressible fluid

The method of finite differences on a nonuniform mesh is used to study the nonstationary flow of a viscous incompressible fluid generated by traveling axisyiametric elastic waves along the surface of a soft cylindrical shell. Expressions are found for the fields of the velocities, vorticities, flow functions, and hydrodynamic forces acting on the body, and also the displacements and velocities of the points of the shell under the influence of the internal driving load and the external hydrodynamic pressure. The boundary conditions of contact between the fluid and the shell are satisfied on the deformed and nondeformed surfaces of the shell.Translated from Izvestiya Akadeinii Nauk SSSR, Mekhanika Zhidkostl i Gaza, No. 3, pp. 132–137, May–June, 1980.     

Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads

Partial separation of variables and reexpansion of cylindrical and plane waves are used to find the solution describing the uniform motion of a load along a thin circular cylindrical shell in an elastic half-space with the free surface parallel to the axis of the shell. This is a model problem for studying the dynamics of tunnels and shallow-buried pipelines under transport loads. Dispersion curves for the cases of sliding and tight contact between the shell and the half-space are plotted and analyzed. The effect of the shell parameters on the stress–strain state of the half-space is examined     

Fracture initiation in the contact region under shear

In the contact region between sliding elastic bodies, there are subregions where the interacting shores are bonded and subregions where they can slide along each other. It is convenient to interpret the latter as transverse shear cracks with slip resistance forces acting on their closed shores. In the end regions of such a crack, stress concentration may lead to fracture initiation in the contacting bodies. Experimental results and an analytic model of the phenomenon are given for a situation where the fracture intersects the contact plane tilted with respect to the direction of the loads.     

Effects of partial crack–face contact for the bending of thin shell structures

The physical occurrence that crack surfaces are in contact at the compressive edges when a flat or a shell is subjected to a bending load has been recognized. This article presents a theoretical analysis of crack–face contact effect on the stress intensity factor of various shell structures such as spherical shell, cylindrical shell containing an axial crack, cylindrical shell containing a circumferential crack and shell with two non-zero curvatures, under a bending load. The formulation of the problem is based on the shear deformation theory, incorporating crack–face contact by introducing distributed force at the compressive edge. Material orthotropy is concerned in this analysis. Three-dimensional finite element analysis (FEA) is conduced to compare with the theoretical solution. It is found that due to curvature effect crack–face contact behavior in shells differs from that in flat plates, in that partial contact of crack surfaces may occur in shells, depending on the shell curvature and the nature of the bending load. Crack–face contact has significant influence on the stress intensity factor and it increases the membrane component but decreases the bending component.     

Stresses in shallow axisymmetric shells using a casting procedure

Normal and radial displacements of a shallow thin sheil of revolution are related by theoretical considerations. Radial displacements are calculated from slope measurements on the generatrices of the initial shell surface (before loading) and of the final shell surface (after loading). Membrane and bending stresses over the entire shell surface are then computed from the measured slope values and the calculated radial displacements. A measuring technique is developed which is especially suitable for shallow shells enclosed in small spaces. It consists mainly of making a cast of the initial and final shell surface using an epoxy platic. The disklike cast is cut along its diameter. The slope values are measured optically along the line which is formed by the intersection of the cutting plane with the deflection surface. The method is applied to a shallow thin shell of revolution in contact with a concentric piston and to a clamped circular plate, both experiencing large axisymmetric deflection.     

STUDY ON THE SURFACE CRACK GROWTH BEHAVIOR IN 14MnNbq BRIDGE STEEL

Three-dimensional crack closure correction methods are investigated in this paper.The fatigue crack growth tests of surface cracks in 14MnNbq steel for bridge plate subjected to tensile and bending loadings are systematically conducted.The experimentally measured fatigue crack growth rates of surface cracks are compared with those of through-thickness cracks in detail.It is found that the crack growth rates of surface cracks are lower than those of through-thickness cracks.In order to correct their differences in fatigue crack growth rates, a dimensionless crack closure correction model is proposed.Although this correction model is determined only by the experimental data of surface cracks under tensile loading with a constant ratio R=0.05, it can correlate the surface crack growth rates with reasonable accuracy under tensile and bending loadings with various stress ratios ranging from 0 to 0.5.Furthermore, predictions of fatigue life and crack aspect ratio for surface cracks are discussed, and the predicted results are also compared with those obtained from other prediction approaches.Comparison results show that the proposed crack closure correction model gives better prediction of fatigue life than other models.     

Shell of arbitrary curvature with cracks of different type and geometry

The interaction of through, surface, and internal cracks in shells of arbitrary curvature is examined. Crack of the same and different types with various geometry are considered. The curvature of the shell, the length and depth of the cracks, their arrangement and distance between them have a strong effect on the stress intensity factors for part-through cracks and on the force and moment intensity factors for through cracks     

45钢柱壳爆炸膨胀断裂的SPH模拟分析

金属柱壳爆炸膨胀断裂存在拉伸、剪切及拉剪混合等多种断裂模式,目前其物理机制及影响因素还不清晰。本文中采用光滑粒子流体动力学方法（smoothed particle hydrodynamics, SPH）对45钢柱壳在JOB-9003及RHT-901不同装药条件下的外爆实验进行了数值模拟,探讨柱壳在不同装药条件下发生的剪切断裂、拉剪混合断裂模式及其演化过程,模拟结果与实验结果一致。SPH数值模拟结果表明:在爆炸加载阶段,随着冲击波在柱壳内、外壁间来回反射形成二次塑性区,沿柱壳壁厚等效塑性应变演化呈凸形分布,壁厚中部区域等效塑性应变较内、外壁大;在较高爆炸压力（JOB-9003）作用下,柱壳断裂发生在爆轰波加载阶段,损伤裂纹从塑性应变积累较大的壁厚中部开始沿剪切方向向内、外壁扩展,形成剪切型断裂模式;而在RHT-901空心炸药加载下,虽然裂纹仍从壁厚中部开始沿剪切方向扩展,但随后柱壳进入自由膨胀阶段,未断区域处于拉伸应力状态,柱壳局部发生结构失稳,形成类似“颈缩”现象,裂纹从剪切方向转向沿颈缩区向外扩展,呈现拉剪混合断裂模式。拉伸裂纹占截面的比例与柱壳结构失稳时刻相关。可见,柱壳断裂演化是一个爆炸冲击波与柱壳结构相互作用的过程,不能简单将其作为一系列膨胀拉伸环处理。     

Thin-walled conical shell drawing from a plane blank

We present a model of the nonstationary process of drawing a thin-walled conical shell from a plane blank, which is based on the membrane theory of plastic form change of a rigidplastic body with the contact friction, the thickness variation in the sense of von Mises, the material strengthening, and the die and the matrix radii of rounding taken into account. The computational model determines the thickness and strengthening distributions along the shell generator, the graph of technological force, and the process critical parameters at which the blank fracture may occur.     

Study on failure process of delaminated stiffened composite plates under compression

Failure behavior of the delaminated stiffened composite plates under compression is studied by the finite element method, based on a Global-Local variational model. A virtual crack closure technique and a self-adaptive grid moving scheme are proposed to predict the delamination growth process. The contact effect along the delamination front is considered. The numerical results show that the influences of the distribution and location of the stiffeners, the configuration and size of the delamination, the boundary condition and the contact upon the failure behavior of the plates are significant. The project supported by the National Natural Science Foundation of China (59975014)     

Refined Mixed-Finite-Element Solution of the Problem on the Stress State of Laminated Spherical Shells

The functional of total potential energy is corrected for the perfect contact between the thin layers of a spherical shell by the method of Lagrange multipliers. A mixed finite element scheme in displacements and contact stresses is constructed with the use of the {m, n}-approximation. The bending of a shell with a square planform under external pressure is studied for various support conditions on the sides and at the corner points. The distributions of the contact stresses are found for two- and three-layer structures     

Cracks with interfacial bonds in the hub of a friction pair

The contact deformation of the hub of a plunger pair is considered. It is assumed that, during the repeated reciprocating motion of the plunger, fracture of the materials of the elements of the contact pair occurs. The friction surface of the bushing contains rectilinear cracks with the end zones characterized by the presence of interaction between the cracks faces. The boundary-value problem of equilibrium of the hub of a friction pair with a crack reduced to solving system of nonlinear singular integro-differential equations with a Cauchy type kernel.     

厚壁胞体多孔结构接触强度研究

选用H59黄铜为材料,制备了含圆形单孔、双孔、三孔以及四孔的圆柱体试样,采用型号为YE-600的液压式压力试验机对试样进行压缩试验,探讨了布孔方式对厚壁胞体多孔结构接触强度的影响;并用有限元法探讨了多孔结构的破坏机理.结果表明:双孔材料水平布孔方式优于垂直布孔方式;三孔材料斜正三角形布孔方式优于正三角形布孔方式;四孔材料正方形布孔方式优于菱形布孔方式;微孔分布半径的增大和微孔个数的增加均有助于提高厚壁胞体多孔结构的接触强度;裂纹萌生于微孔边缘且离初始接触点最近的地方,它由最大拉伸主应力引起并沿着微孔拉应力集中区进行扩展.