有限宽板偏心裂纹在裂纹面受两对点力时的弹塑性分析

有裂纹的有限宽板的弹塑性解是弹塑性裂断力学最困难的问题之一，本文采用线场分析方法对理想弹塑性有材料有限宽板偏心裂纹在裂纹面上受两对反平面集中力的情形进行弹塑性分析，本文的分析不受小范围屈服条件的限制，求得了裂纹线附近的弹塑性解析解，裂纹线上的塑性区长度随外荷载的变化规律及有限宽板具有偏心裂纹的承载力，其结果在裂纹线附近足够精确。     

裂纹面受两对集中剪力作用下的弹塑性分析

利用裂纹线场方法对理想弹塑性材料无限大板受两对集中剪力问题进行了弹塑性分析,并且获得了理论解。这个解包括:裂纹线附近弹塑性边界上的单位法向矢量、裂纹线附近的弹塑性解析解、裂纹线上的塑性区长度随荷载的变化规律及其承载力。分析不受小范围屈服假设的限制,并且不附加假使条件。结果在裂纹线附近足够精确。     

有限宽偏心裂纹板在裂纹面受两对集中拉力作用时裂纹线的弹塑性解析解

在实际中偏心裂纹板的受力问题比中心裂纹板受力问题更为普遍。利用裂纹线场分析法简化了弹塑性断裂力学问题的复杂性和数学上的困难,求得了偏心裂纹板在裂纹面上受两对集中拉力作用时裂纹线附近弹塑性边界上的单位法向量、裂纹线附近的弹塑性应力场以及裂纹线上的塑性区长度随荷载的变化规律。在理想弹塑性情况下,该文中的理论解在裂纹线场附近是足够精确的。     

含尖角裂纹的有限宽板在弯矩作用下裂纹周围应力场研究

对于含裂纹的板,有时裂纹尺寸与板的宽度相比并不很小,必须按有限宽板来计算。针对含尖角裂纹的有限宽板,建立基于弹性断裂理论的计算模型。通过所求得的复变应力函数,给出裂纹周围应力场的解析计算公式。根据保角变换原理,得到不同裂纹形状所对应的映射函数。对两端受弯矩作用含尖角裂纹的有限宽板,在具有不同的裂纹张开角情况下,对裂纹周围应力分布进行较为详细的仿真分析。另外,对不同的板宽对裂纹周围应力场的影响进行分析,并对不同裂纹张开角的情况进行了计算、比较。     

含裂纹损伤有限加筋板弹塑性承载力分析

基于含直裂纹问题的复应力函数解法,提出了用Dugdale模型分析和求解弹塑性条件下含中心裂纹的有限加筋板承载力问题的方法。通过将加筋板离散为筋、板的结构,将含裂纹有限加筋板的问题转化为边界受切向力作用的含裂纹有限板的问题进行求解。计算了筋、板相对刚度不同的情况下,含中心裂纹有限加筋板裂纹尖端开口位移CTOD(Crack Tip Opening Displacement)值随裂纹长度及承载力情况变化的系列值。     

混凝土构件内Ⅰ型裂纹的一种断裂分析方法

本文在文^[1]的基础上采用裂纹线方法,从平衡方程和混凝土材料的破坏准则出发,对有限宽混凝土构件内受单向拉伸的1型微裂纹进行弹脆性断裂分析,分析过程中认为已扩展的脆断区应变能完全释放,得出了单向位应力的大小与微裂纹脆断区长度之间的关系。     

多裂纹弹塑性干涉效应及其工程解

本文针对Ｒａｍｂｅｒｇ－Ｏｓｇｏｏｄ关系材料进行弹塑性有限元计算，研究分析了平面应力问题下的近似无限宽板中双共线裂纹弹塑性干涉效应的变化规律，利用双裂纹裂纹Ｊ积分值和等载荷比下单裂纹尖Ｊ积分值之比来确定双裂纹间的弹塑性干涉效应，研究发现，弹塑性干涉效应不同于线弹性干步效应。除了与裂纹几何尺寸有关外，且是载荷比和材料性能的函数，由此证明线弹性分析作为裂纹问题处理的依据有可能出现危险的结果，在此基础上     

有限宽混凝土构件内Ⅰ型微裂纹的弹脆性断裂分析

混凝土构件内微裂纹的受荷扩展破坏是土木工程界十分关心的问题。本文采用裂纹线附近分析方法,从平衡方程和混凝土材料的破坏准则出发,对有限宽混凝土构件内受单向拉伸的Ⅰ型微型纹进行弹脆性断裂分析,得出了单向拉伸应力大小与微裂纹脆断长度之间的关系。     

有中间贯穿裂纹无限大板的解析解

在虚裂纹模型基础上，裂缝尖端的有限应力集中和裂缝开口位移可通过加权积分法得到。本文运用复变函数和加权积分法，推导出裂纹面上有均布荷载作用时的中间贯穿裂纹无限大板平面问题的解析解。     

材料和几何线性的有限条分析

本文建立了大挠度弹塑性有限条法,用以计算初曲板在面内荷载作用下的极限荷载。分析中采用了伴随修正的Ilyushin屈服准则或修正的Ivanov屈服准则和Prandtl—Reuss塑性流动法则的面积法。通过与前人对板屈曲后弹塑性分析算例的比较,证明该方法对于板的大挠度弹塑性分析具有相当高的精度。     

Precise elastic-plastic analysis of crack line field for mode II plane strain crack

The near crack line analysis method has been used to investigate the exact elastic-plastic solutions of a mode II crack under plane strain condition in an elastic-perfectly plastic solid. The significance of this paper is that the assumptions of the conventional small scale yielding theory have been completely abandoned. The inappropriateness of matching conditions formerly taken at the elastic-plastic boundary ths been corrected as well. By eatching the general solution of the plastic stress (but not the special solution that was adopted) with the exact elastic stresses (but not the crack tip K-dominant field) at the elastic-plastic boundary near the crack line, the plastic stresses, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary, which are sufficiently precise near the crack line region, have been given. The solutions are suitable not only under the condition that the plastic region is sufficiently small but also under the condition that the plastic region is large.     

A Dugdale–Barenblatt Model for a Plane Stress Semi-Infinite Crack under Mixed Mode Concentrated Forces

In this paper, a mixed mode Dugdale–Barenblatt model has been established for a semi-infinite crack in an ideally elastic-plastic thin plate loaded by a pair of self-equilibrating concentrated forces at the crack lips. Cohesive forces are introduced into a plastic strip in the elastic body. By superposing the two linear elastic fields, one evaluated with the external loads and the other with the cohesive forces, the problem is treated in Dugdale–Barenblatt's manner. The physical domain is mapped with a complementary domain of the unit circle by using the Schwartz–Cristoffel transformation. The Muskhelishvili complex potentials are used to find out the stress-intensity factors due to the two separated fields. The analytical approach leads to establish a few transcendence equations from which the quantities of interest, such as the direction and the length of the plastic strip, the crack opening distance etc., can easily be deduced by standard numerical methods. This revised version was published online in August 2006 with corrections to the Cover Date.     

Application of the distributed dislocation technique for calculating cyclic crack tip plasticity effects

This paper describes a method for modelling cyclic crack tip plasticity effects based on the distributed dislocation technique (DDT). A strip‐yield model is utilised to allow for the determination of the crack opening displacement, size of the plastic zones and in the case of a fatigue crack, the wake of plasticity. The DDT can be easily implemented for a wide range of cracked geometries with reliable control over the accuracy and convergence. Thickness effects can also be incorporated through a recently obtained solution for an edge dislocation in an infinite plate of finite thickness. Results for finite length cracks that have had limited growth, such that there is no plastic wake, are presented for a range of applied loads and R‐ratios. Further results are provided for a steady‐state fatigue crack in a plate of finite thickness. The present results are compared with analytical solutions and they show an excellent agreement.     

金属裂纹板复合材料胶接修补强度的弹塑性有限元预测

金属裂纹板经复合材料补片胶接修补后,其结构强度明显提高,但裂纹板中的裂纹会导致严重的应力集中现象,并易产生塑性变形,呈现强烈的材料物理非线性特性,需要采用弹塑性力学原理,进行复合材料胶接修复结构的静强度预测。为此,考虑金属板材料的非线性特性,建立了金属裂纹板复合材料胶接修补结构的弹塑性有限元模型,并通过试验验证了模型的有效性。在此基础上,提出了基于裂纹尖端的张开位移(COD)判据的拉伸强度预测方法,分析了修复结构的塑性应变、COD以及静拉伸强度。结果表明:相对于应力强度因子K判据, COD判据能更有效地预测修复试件的静拉伸强度。      

Effect of Plate Thickness on Crack-Tip Plasticity

This paper presents an analytical method for determining the three-dimensional stress fields in plates with a through-the-thickness crack, especially under elastic-plastic conditions. Using the generalised plane strain theory in conjunction with the deformation theories of plasticity, exact solutions are obtained for the effects of plate thickness on the crack-tip plastic zone size and a plastic constraint factor, which is shown to correlate well with published finite element solutions.     

The wave propagation and vibrational energy flow characteristics of a plate with a part-through surface crack

In the view of structure-borne sound, vibrational wave and energy flow characteristics of infinite thin plate of finite width with a part-through surface crack are investigated. The case of an all-over part-through crack parallel to the finite side of the plate is considered. The crack is modeled as a line spring and the flexibility of the spring is deduced from the relationship between the strain energy and stress intensity factor in fracture mechanics. The responses of both intact plate and cracked plate under the excitation of harmonic force are reduced with wave propagation approach, then the input energy flow and transmitted energy flow of intact and cracked plates are calculated. The results show that the vibrational energy flow of cracked plate is highly related to the depth and location of the part-through crack. The location and the depth of the crack can be identified by the contour lines of normalized input energy flow with different driving frequencies. The research provides theoretical basis for the crack detection by measuring the vibrational energy flow in cracked plate structures.     

Crack curving under mode-I loading

The whole history of failure of a rectangular panel with two symmetrical notches and a central crack subjected to a progressively increasing tension load normal to the crack plane is studied. The material of the panel exhibits substantial plastic deformation prior to fracture. An elastic-plastic analysis of the plate is first performed based on finite elements. The results of stress analysis are coupled with the strain energy density theory to determine the critical load for crack initiation and the history of stable crack growth up to the point of instability. At instability the crack runs fast through the elastic material bypassing the plastic zone near the plate boundary. The crack deviates from its initial direction and is curved even though the plate is subjected to opening-mode loading. Results for crack trajectories are given for various initial crack lengths and notch radii of the plate.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.