粘弹性材料中裂纹增长的仿真研究

针对含裂纹的粘弹性材料结构,根据粘弹性断裂理论分析裂纹增长的条件.建立基于裂纹周围小范围滑动的计算模型,采用Laplace转换关系,可以将粘弹性边界值问题变为弹性边界值问题处理,在所得到的表达式中并不直接含有弹性常数,因此它能较好地描述粘弹性问题.得到描述含裂纹粘弹性材料在不同的时间裂纹增长情况的裂纹增长速率以及蠕变时间解析解.并按照所建立的计算模型对不同的材料性质、不同的裂纹尖端应力强度因子、不同的外载荷对裂纹增长速率及蠕变时间的影响进行探讨.     

Analysis of a cracked lug loaded by an interference fit pin

In the present study, a lug joint fitted with an interference fit (oversized) pin is considered with radial through cracks situated at diametrically opposite points perpendicular to the loading direction. A finite element contact stress algorithm is developed with linear elastic assumptions to deal with varying partial contact/separation at the pin-plate interface using a marching solution. Stress Intensity Factor (SIF) at the crack tips is evaluated using the Modified Crack Closure Integral (MCCI) method. The effect of change in crack length and edge distance on the load-contact relation, SIFs and stress distributions are studied. A rigorous plane stress elasticity solution of the pin-plate interface at the crack mouth confirmed the existence of the stress concentration leading to a local peak in the radial stress at the crack mouth and provided a method of estimating it quantitatively.     

Stress intensity factors and kink angle of a crack interacting with a circular inclusion under remote mechanical and thermal loadings

A problem of a circular elastic inhomogeneity interacting with a crack under uniform loadings (mechanical tension and heat flux at infinity) is solved. The singular integral equations for edge and temperature dislocation distribution functions are constructed and solved numerically, to obtain the stress intensity factors. The effects of the material property ratio on the stress intensity factor (SIF) are investigated. The computed SIFs are used to predict the kink angle of the crack when the crack grows.     

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

     

TRANSVERSE VIBRATION CHARACTERISTICS OF VISCOELASTIC RECTANGULAR PLATE WITH CRACK

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory, the differential equations of motion of the viscoelastic plate with an all-over part-through crack are established and the expression of additional rotation induced by the crack is derived. The complex eigenvalue equations of the viscoelastic plate with crack are derived by the differential quadrature method, and the 8method is used at the crack continuity conditions. Dimensionless complex frequencies of a crack viscoelastic plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated. The effects of the crack parameter, the aspect ratio and dimensionless delay time of the material on the transverse vibration of the viscoelastic plate are analyzed.     

关于表面裂纹线弹簧模型的改进

对表面裂纹线弹簧模型进行改进,初步解决未改进的线弹簧模型在远离裂纹最深处(即靠近自由表面处)误差较大的问题.着重对线弹簧本构关系(即模型的内部解)作改进.在内埋椭圆裂纹应力强度因子解的基础上,籍助应变能方向导数的关系将它转变为二维穿透裂纹,引入修正系数得到改进的边裂纹板条解,即改进的线弹簧本构关系(改进的内部解).外部解采用Reissner板理论.用改进的模型计算表面裂纹前缘法向应力强度因子,结果与Newman有限元解进行较系统的比较,表明改进的模型能在较大范围内更好地与Newman解相符.     

基于安定理论的微小裂纹疲劳门槛值的分析

通过弹塑性有限元法 ,利用 Melan的安定理论 ,分析了单缺口试件 ,在含有与试件材料晶粒尺寸相当的微小裂纹下的疲劳门槛值。通过对航空齿轮材料试件进行算例分析 ,其结果与相应实验结论比较吻合 ,并且表明 :利用静力安定法所研究微小裂纹疲劳门槛值 ,预测航空齿轮的寿命是较安全的。     

Validation of stresses and stress intensity factor in a notched bilayer system under four point bending, as determined by the solution of the Navier's equation

We use a previously formulated solution of the Navier's equation to calculate stress intensity factor in a notched bar bonded to a substrate. We evolve a procedure for determining the stress distribution. We validate the stress analysis in four-point bending by measuring surface strains for different combination of materials in the bilayer (the Young's modulus ratio of the materials in the bilayer varied from 28 to 86). We also determine the stress intensity factor (SIF) experimentally using a notched photoelastic bar bonded to a substrate and validate our estimation of SIF.     

双排交错铆钉连接对接结构裂纹尖端应力强度因子分析

双排交错铆钉连接对接结构是飞机进行损伤容限设计的重要结构件之一,其应力强度因子分析一直受到工程上的广泛关注。文中采用有限元方法,充分考虑不同开裂模式造成裂纹面上铆钉传力作用不同的特点,建立合理的铆钉传力模型,对双排交错铆钉对接结构进行裂尖应力强度因子分析,给出计算曲线。分析中讨论了裂纹垂直与平行于对接缝两种开裂模式以及单向与双向两种受载模式,并分析了铆钉特定传力作用下的柔度效应。所得计算结果及分析结论对飞机结构损伤容限设计具有直接参考价值。     

Method of caustics for the study of cracked plates made of viscoelastic materials

The optical method of caustics was used for the evaluation of the stress intensity factor at the crack tip in a viscoelastic plate made of polycarbonate of bisphenol A and containing a single external crack under conditions of generalized plane stress. It was assumed that the crack developed in a linear viscoelastic material. The reflected rays from both lateral faces, as well as the transmitted rays of a normally incident light beam were significantly dispersed at the close neighborhood of the crack tip because of the excessive lateral constraint and the strong variation of the refractive index, and concentrated along singular curves (caustics) at some distances from the plate. The reflected caustics formed two branches. While the internal branch, which was formed by reflections from the front face, depended only on the elastic modulus (E) and Poisson's ratio (v) of the material, the external branch, formed by reflections from the rear face, depended on E and v, as well as on the refractive index of the material (n). The transmitted rays formed the same type of caustic as that which was formed by reflections from the rear face, but with a different size.

By studying the relative position and shape of the two reflected branches and their variation with time, information was derived concerning the viscoelastic state of the material at fracture. The transmitted light caustic was used as a check on the results.

A series of viscoelastic tests in pure tension at various stress and strain levels yielded the variation of the mechanical (E, v) and optical (n, c_r, c_f) properties of the material with applied stress and strain. The values of these quantities at each stress level allowed the plotting of the relative positions of the two branches of the reflected caustics. Comparison of the actual position of the caustics at the crack tip with the caustic nomogram yielded the viscoelastic behavior of the material during the progress of loading. It was shown that by increasing the loading mode a strong viscoelastic behaviour was apparent which influenced considerably the fracture mode of the plate.     

Nonlinear viscoelastic analysis of thick-walled cylindrical composite pipes

This paper analyzes the effect of the polymer matrix non-viscoelastic behaviour in the mechanical behaviour of thick multilayered cylinders. The original contribution of this work is to provide novel approximate analytical solutions to compute the time-dependent internal stress state through the pipe thickness within the framework of nonlinear viscoelasticity theory. The structures considered are thick, multilayered anisotropic infinitive long cylinders subjected to axisymmetric mechanical loading. Under such conditions there is an exact elastic solution which naturally satisfies equilibrium, strain-displacement, compatibility and boundary conditions for the stated constitutive equations and loading. Due to the continuous stress variations through the cylinder thickness, the proposed nonlinear viscoelastic solution assumes the averaged stress state to calculate the nonlinear elastic and viscoelastic factors in each layer. Furthermore, the solution is obtained assuming that the creep strains, within each layer, are constant through the thickness. The proposed algorithm converges to the exact solution when the number of layers is artificially increased. For the linear viscoelastic case, the proposed solution proved to match the exact known solution for isotropic viscoelastic materials. Finally several invented cases are run to illustrate the importance of the viscoelasticity phenomenon on the internal stress field in thick-laminated cylinders.     

高频谐振载荷作用下Ⅰ型疲劳裂纹尖端力学参数变化规律

为研究高频谐振式疲劳裂纹扩展试验中带有Ⅰ型预制裂纹的紧凑拉伸(CT)试件裂纹尖端力学参数的变化规律,利用动态有限元方法,采用ANSYS和MATLAB软件编写程序,计算了CT试件在高频恒幅正弦交变载荷作用下,在一个应力循环及裂纹扩展到不同长度时裂纹尖端区域的位移、应变场及裂纹尖端的应力强度因子,并分析了其变化规律。在计算裂纹尖端应力强度因子时,首先采用静态有限元方法和理论公式验证了有限元建模和计算的正确性,然后采用动态有限元方法研究了裂纹扩展过程中裂纹尖端应力强度因子的变化规律。最后进行了高频谐振式疲劳裂纹扩展试验,采用动态高精度应变仪测量了裂纹扩展到不同阶段时裂纹尖端点的应变,并对有限元计算结果进行了验证。研究结果表明：在稳态裂纹扩展阶段,高频谐振载荷作用下Ⅰ型疲劳裂纹尖端位移、应变及应力强度因子均为与载荷同一形式的交变量;随着裂纹的扩展,Ⅰ型疲劳裂纹尖端的位移、应变及应力强度因子幅不断增大;静态应力强度因子有限元计算值和理论值的误差为2.51%,裂纹尖端点应变有限元计算结果和试验结果最大误差为2.93% 。     

一种求解复杂结构三维裂纹应力强度因子的工程方法--推广的片条合成法

以现有的片条合成法为基础,发展了一种可用于计算含复杂边界条件结构的三维裂纹应力强度因子的方法———推广的片条合成法,推导了相应的位移协调公式。应用推广的片条合成法,对一般结构表面裂纹的裂尖应力强度因子进行了验证性的分析和讨论,计算结果与Newman解进行对比,趋势合理、精度完全满足工程要求;同时,计算了具有复杂边界的凸台结构表面裂纹的裂尖应力强度因子,给出可供工程参考的结果和结论。     

Modified boundary layer analysis for a mode III crack problem

A modified boundary layer problem of a semi-infinite crack in an elastic-perfectly plastic material under a Mode III load is analyzed. The analytic solution of elastic fields is derived by using complex function theory. It is found that the size and the shape of the plastic zone near the crack tip depend on the elastic T-stress given on the remote boundary. A method for determining higher order singular solutions of elastic fields is also proposed. In order to determine the higher order singular solutions of the elastic fields, Williams expansion of the solution is used. Higher order terms in the Williams expansion are obtained through simple mathematical manipulation. The coefficients of each term in the Williams expansion are also calculated numerically with the J-based mutual integral     

Hydrodynamic calculation of a thrust plain bearing that operates with viscoelastic lubricant under turbulent friction conditions

An accurate self-similar solution of the problem on hydrodynamic calculation of the thrust plain bearing that operates at viscoelastic lubricant under turbulent friction conditions has been found. Two fluid states are examined separately: 1) the lubricant is fed into the bearing under total relaxation of an elastic component of deformation, and 2) the lubricant should be under an unstressed state outside the bearing and subjected to sudden shear with a certain speed at the moment of its entering into the bearing. Analysis of the obtained analytical expressions for the bearing’s basic operating performances, including bearing capacity and friction force, makes it possible to design thrust plain bearings with turbulent viscoelastic lubricant, which operate with less power loss than similar bearings with laminar viscoelastic lubricant.     

Finite crack propagation in a micropolar elastic solid

The dynamic propagation of a finite crack under mode-1 loading in a micropolar elastic solid is investigated. By using an integral transform method, a pair of two-dimensional singular integral equations governing stress and couple stress is formulated in terms of displacement transverse to the crack, macro and micro rotations, and microinertia. These equations are solved numerically, and solutions for dynamic stress intensity and couple stress intensity factors are obtained by utilizing the values of the strengths of the square root singularities in macrorotation and the gradient of microrotation at the crack tips. The motion of the crack tips and the load on the crack surface are not prescribed in the formulation of the problem. Therefore, the method of solution is applicable to nonuniform rates of propagation of a crack under an arbitrary time-dependent load on the crack surface. As an example, the diffraction of a micropolar dilatational wave by a stationary crack is considered. The behavior of the microrotation field and the dynamic couple stress intensity factor, influenced by microinertia, in addition to the dynamic stress intensity factor, are examined. The classical elasticity solution for the corresponding problem arises as a special case when the micropolar moduli are dropped from the present solution.     

Hydrodynamic Behavior of Viscoelastic Liquids in a Simulated Journal Bearing

The hydrodynamic effect of viscoelasticity in bearing performance was investigated experimentally by measuring the pressure distribution of viscoelastic liquids and Newtonian liquids in a simulated plain journal bearing. The pressure distribution of the viscoelastic liquids was somewhat different from that of the Newtonian liquids, showing a flattening of the pressure profile and a shift of the circumferential position of the peak pressure. Such a difference contributes to a small recovery of the loss of the load-carrying capacity due to the non-Newtonian viscosity for viscoelastic liquids. It may also contribute to a further reduction of friction beyond the effect of shear thinning. The difference of cavitation on the divergent region of the bearing for these two different kinds of liquid was evident. The viscoelastic liquids showed less extent of cavitation. The experimental conditions conform closely to those used in the classical hydrodynamic lubrication theory. The experimental data indicate that the full fluid film occupies half a bearing starting at 0° and ending at 180°, and the subatmospheric pressure in the divergent region is leveled off at a certain negative pressure. Based on this boundary condition, a computer solution in solving the Reynolds equation for a finite bearing gives very good agreement with experiment.     

Crack propagation in non-proportionally scaled elastic structures

Scaling laws for load, stress, displacement and crack velocity are given for crack propagation in non-proportionally scaled elastic structures where the scaling factors for height, width, thickness and crack length can all be different. Problems are addressed where only one or two of the scaling factors are important, in contrast to geometrically similar scaling where all factors are equal. Examples discussed include pipelines and plate-like structures of ships or bridges. The conditions under which strength of materials design criteria, based on yielding, prove inadequate for such large structures are investigated. In addition, the validity of determining “brittle” fracture toughness by “equivalent energy” scaling procedures from small laboratory specimens is discussed.     

一种加筋板多裂纹应力强度因子的试验验证方法

给出一种加筋板多裂纹应力强度因子试验验证方法,是基于等幅载荷下裂纹扩展速率反推得到的.该方法不仅能确定复杂问题的应力强度因子,而且能验证确定加筋板多裂纹应力强度因子的类比法.进行LY12CZ铝合金加筋板多裂纹裂纹扩展试验,给出试验验证反推应力强度因子的方法及过程.并给出用类比法近似计算的结果和试验验证结果及平均值.同时也指出这一方法可解决复杂问题应力强度因子的确定,但裂纹扩展速率存在一定的分散性.得到的结果表明试验验证方法和类比法对于确定加筋板多裂纹应力强度因子是可用的.     

非对称斜耳片钉孔单边穿透裂纹应力强度因子计算研究

运用ANSYS软件建立非对称斜耳片受纵向拉载的平面有限元计算模型,在耳孔面上施加符合真实受载情况的余弦分布载荷;通过分析耳片量纲一裂纹长度a/R1、外内径比R2/R1、耳孔内径R1、裂纹斜切角β1和β2等参数对应力强度因子值的影响规律,拟合得到非对称斜耳片受纵向拉载的耳孔单边穿透裂纹尖端应力强度因子表达式;开展含不同孔边裂纹长度的非对称斜耳片剩余强度试验,将采用此方法计算得到的各试验件断裂时的临界应力强度因子值与试验数据进行对比,结果表明,拟合得到的应力强度因子表达式具有较高的计算精度;此计算方法同样适用于其他形式耳片结构,从而为工程上对飞机典型耳片结构的损伤容限设计与评估工作提供参考。