FRACTURE MECHANICS OF PHYSICALLY SHORT CRACKS

Mechanical Engineering Research Institute, Academy of Sciences of the U.S.S.R., Griboedova Str., 4 Moscow Centre, Moscow 101830, U.S.S.R.     

LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS IN RESPECT OF SMALL FATIGUE CRACKS AND MICROSTRUCTURE

The growth characteristics of small fatigue cracks were investigated under rotary bending in a low alloy steel prepared with two prior austenite grain sizes of 15 μm (fine grain) and 91 μm (coarse grain). The influence of grain boundaries on crack growth rate and the crack aspect ratio was examined, and the critical crack length above which linear elastic fracture mechanics (LEFM) is applicable was evaluated for a growing small crack. When the surface crack length is shorter than three grain diameters (3d), crack growth rates decrease near the grain boundaries. Aspect ratios are also affected by the microstructure and thus vary widely. Cracks longer than 3d are not influenced by the microstructure, but they grow faster than would be expected based on LEFM until their lengths reach 3d+ 150 μm. This behaviour may be attributed to the difference in crack closure between small cracks and large cracks. If the contribution of crack closure to the growth of small cracks can be established experimentally or analytically, the critical crack length above which LEFM is applicable would be 3d. However, because it is difficult to evaluate crack closure, 3d+ 150 μm is considered to be the critical crack length for engineering applications.     

非均匀复合材料中反平面裂纹的动态断裂力学研究

对于非均匀复合材料中多个裂纹的动态断裂力学问题, 提出了一种分析方法, 假设复合材料为正交各向异性并含有多个垂直于厚度方向的裂纹, 材料参数沿厚度方向为变化的, 沿该方向将复合材料划分为许多单层, 假设单层材料参数为常数, 应用柔度矩阵/刚度矩阵方法及Fourier变换法, 在L aplace 域内推导出了控制问题的奇异积分方程组, 并用虚位移原理求解, 给出了应力强度因子及能量释放率的表达式, 然后利用Laplace 数值反演, 得出了裂纹尖端的动态应力强度因子和能量释放率。作为算例, 研究了带有两个裂纹的功能梯度结构, 分析了材料参数的优化对降低应力强度因子的意义。      

ELASTIC-PLASTIC FRACTURE MECHANICS FOR INITIATION AND PROPAGATION OF NOTCH FATIGUE CRACKS

Abstract Initiation and propagation are considered to be controlled by the extent of total plastic shear deformation φ. Crack initiation and crack propagation occur when φ, exceeds a critical threshold value which can be equated to threshold conditions determined from linear elastic fracture mechanics analyses. When a crack is in a plastically deformed zone φ_t=φ _p +φ _e . where φ _p is the component of φ _t due to notch bulk plasticity and φ _e , is the component of φ _t due to a linear elastic fracture mechanics (LEFM) analysis of the crack tip plasticity field.
When cracks initiate at notch roots φ _t > φ_th. As the crack propagates in the notch plastic zone the rate of decrease of v _p will be different from the rate of increase of φ _e and it is possible for φ _t to decrease to a level below φ_th thereby creating a non-propagating crack.     

基于概率断裂力学的老龄钢桥使用安全评估

我国交通线上存在大量老龄钢桥,这些老龄钢桥承受着日益繁重的交通荷载,其疲劳剩余寿命已受到桥梁管理部门的高度重视.为确保老龄钢桥的使用安全,避免不必要的维护与更换,建立老龄钢桥疲劳剩余寿命与使用安全评估方法十分必要.建立了反映老龄铆接钢桥疲劳破坏机理的脆断和韧断概率失效模型,给出了用于疲劳可靠性分析的极限状态方程,合理确定了随机变量的参数取值.建立了铆接钢桥构件单角钢概率疲劳破坏模型,基于Monte Carlo算法实现了铆接钢桥构件单角钢疲劳断裂失效概率的计算,编制了相应的概率断裂分析程序SAPFF.进而将铆接构件概率断裂模型应用于上海市浙江路桥的时变疲劳可靠度分析,并给出了浙江路桥概率疲劳剩余寿命评估结果与维护对策.     

AN IMPROVED NUMERICAL TECHNIQUE FOR SIMULATING THE GROWTH OF PLANAR FATIGUE CRACKS

Abstract— This paper describes a versatile technique for simulating the fatigue growth of a wide range of planar cracks of practical significance. Crack growth is predicted on a step-by-step basis from the Paris law using stress intensity factors calculated by the finite element method. The crack front is defined by a cubic spline curve from a set of nodes. Both the 1/4-node crack opening displacement and the three-dimensional J -integral (energy release rate) methods are used to calculate the stress intensity factors. Automatic remeshing of the finite element model to a new position which defines the new crack front enables the crack propagation to be followed. The accuracy and capability of this finite element simulation technique are demonstrated in this paper by the investigation of various problems of both theoretical and practical interest. These include the shape growth trend of an embedded initially penny-shaped defect and an embedded initially elliptical defect in an infinite body, the growth of a semi-elliptical surface crack in a finite thickness plate under tension and bending, the propagation of an internal crack in a round bar and the shape change of an external surface crack in a pressure vessel.     

AN ASSESSMENT OF CRACK CLOSURE IN FATIGUE USING THE WESTERGAARD STRESS FUNCTION

Abstract— The residual stress fields at the tip of a fatigue crack have been evaluated using the Westergaard stress function. Using these values the loads at which the crack tip begins to open have been calculated to give U, Elber's effective stress range factor, as a function of stress ratio R, the ratio of applied stress range to yield stress, Δσ/σ_y, and the cyclic strain hardening exponent n. The computed values of U are shown to be in good agreement with measured values, and the predicted effect of prior high load cycles on the crack propagation rate at a lower cyclic load, on taking crack closure effects into account, is in excellent agreement with experimental results.     

AN ENGINEERING ASSESSMENT OF FATIGUE CRACK GROWTH OF IRREGULARLY ORIENTED MULTIPLE CRACKS

Abstract— Knowledge of the behaviour of interacting and irregularly oriented multiple cracks is very limited. The recharacterisation rules for such cracks are usually empirical. In order to provide more reasonable rules for an engineering assessment of fatigue growth of irregularly oriented multiple cracks, this paper first studies the mechanics of fatigue growth of two-dimensional non-coplanar cracks. Uniaxial and biaxial fatigue testing on specimens with various multiple cracks are then carried out. Possible errors in the assessment of the cracks using the current rules are discussed. An improved procedure for the fatigue life assessment is developed.     

SAFETY ASSESSMENT OF A CAST STEEL VALVE CASING USING NDE AND FRACTURE MECHANICS

Abstract— The possibilities and limitations of failure predictions, based on the determination of defect size and shape by NDE, on material characterization using standard testing methods and on calculations using a failure assessment program for personal computers have been investigated for a control valve casing by comparing analytical calculations with component tests.     

复合材料层合板三维分层问题的断裂力学分析

对复合材料层板中椭圆分层的断裂力学问题进行了研究。根据层板平面剪切型分层和反平面剪切型分层尖端附近位移场、应力场与应力强度因子的关系,利用法向切片法,得到椭圆分层前缘应力强度因子与能量释放率的关系。结合由附加位移所确定的总位能,确定了能量释放率和应力强度因子沿分层前缘分布的表达形式。数值计算给出了二者随分层区形状、载荷以及各层厚度比等参数变化的分布情况。     

ELLIPTICAL SUBSURFACE CRACKS UNDER A NORMAL STRESS AND A RESIDUAL STRESS FIELD

Abstract The distribution of residual stresses due to surface treatments, such as nitriding, induction hardening or shot-peening, is explained in the introduction. The stress intensity factor distribution along an elliptical plane crack near the surface in such a residual field is presented. Existing methods including the weight function method do not allow one to find this distribution directly. Therefore, a finite element study was undertaken showing the complex character of the stress intensity factor distribution. Additionally, the calculation of the stress intensity factor distribution around the crack front for an external tension or bending load stress is explained. In these cases some simplified semi-analytical expressions can be found.     

THE GROWTH OF SMALL FATIGUE CRACKS IN A LOW CARBON STEEL; THE EFFECT OF MICROSTRUCTURE AND LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS

The growth characteristics of small fatigue cracks were studied under rotary bending in a low carbon steel prepared with two ferrite grain sizes of 24 and 84 μm, and were compared with the growth characteristics of large through cracks in fracture mechanics type specimens. The effect of microstructure on crack growth rates and the interaction in growth behaviour between two neighboring small cracks were examined experimentally, and also the critical crack lengths above which linear elastic fracture mechanics (LEFM) is applicable were evaluated for small crack growth and for fatigue crack thresholds. It is found that small cracks grow much faster than large ones and also show growth rate perturbations due to grain boundaries. It is indicated that the critical crack lengths for fatigue crack thresholds are significantly shorter than those for small crack growth.     

我国混凝土断裂力学研究的部分新进展

混凝土、钢筋混凝土及钢纤维混凝土是非均匀的多相复合材料,其断裂性能十分复杂。本文论述了近年来我国在这方面的部分进展情况,内容包括:一、简述了发展历史;二、素混凝土断裂问题的研究;三、钢筋混凝土断裂问题的研究;四、钢纤维混凝土断裂问题的研究;五、指出了值得进一步探讨的问题。     

方块脉冲函数在材料力学中的应用

本文应用方块脉冲函数方法直接求解直梁弯曲的能量泛函极值,给出了计算挠度和转角函数的一种新的计算机方法。     

无限大平面中斜裂纹的压剪断裂分析

根据Muskhelishvili的复势理论,结合裂面边界条件和位移单值条件,将无限大平面受压应力作用的裂纹问题转化为对应的Hilbert问题,并运用复变函数法分别给出了在伪集中力作用下,不同裂面形态的基本解。对不同裂面形态的摩擦力大小和分布进行了详细分析,建立了新的摩擦力计算模型。采用“伪力法”和叠加原理,结合所求的基本解,给出了含中心斜裂纹的岩石类材料在压缩荷载作用下的应力强度因子(SIF)的解法。研究表明:裂面状态对KⅠ的大小没有影响,而对KⅡ的影响却很大,相同应力条件下,裂面状态会影响裂纹的开裂角和开裂方式。     

幂硬化材料解理断裂应力σf的测定

提出了在测定幂硬化材料解理断裂应力σ１的方法，并且测定了１６ＭｎＲ母材及焊缝金属低温下的σｆ。     

AN EVALUATION OF FATIGUE AND FRACTURE MECHANICS PROPERTIES OF ULTRA-HIGH STRENGTH 7XXX SERIES Al-ALLOYS

Abstract— The fatigue and fracture mechanics properties of rapidly solidified ultra-high strength 7XXX series Al-alloys have been studied. With respect to conventional high-strength Al-alloys, these materials exhibited a better fatigue-endurance on both plain and notched specimens at low stress amplitude in constant amplitude fatigue tests, whereas the opposite occurred at high stress amplitudes. Fatigue crack growth tests indicated lower crack growth rates at low Δ K -levels, but at intermediate and high Δ K -values these materials were particularly prone to additional components of "static" crack propagation, which led to steeply inclined d a/ d N vs Δ K curves. Moreover, the increase in tensile strength was linked with some loss of ductility and fracture toughness. Overload regions were characterized by a large amount of intergranular decohesion, possibly facilitated by the presence of incoherent particles at grain boundary regions and by the large strength differential between the matrix and precipitate free zone. The best results in terms of elongation to rupture and toughness were obtained by reducing the amount of Cr/Mn incoherent dispersoid-forming elements, in order to lessen the tendency towards matrix-dispersoid interface decohesion at grain boundaries.     

压力容器接管角裂纹弹塑性断裂的工程分析方法研究

文中系统地研究了接管角裂纹二维平板模型的Ｊ积分全塑性解，新建立了以应力强度因子形状系数β为主导的全塑性解表达式；通过对式中塑性因子ω的特性分析，结合接管角二维模型与准三维模型的数学相似性对比，获得了依赖于二维模型解的准三维模型全塑性解。评定结果表明：使用准三维模型全塑性解可提高容器承压能力１０％～２０％，从而克服了二维平板模型解预测的保守性。     

WEIGHTED AVERAGED STRESS INTENSITY FACTORS OF CIRCULAR-FRONTED CRACKS IN CYLINDRICAL BARS

Stress intensity factors are calculated in weighted average at the surface and the deepest point of a circular-fronted surface crack in a cylindrical bar by use of the weight function method. A wide range of various crack shapes are studied, from a nearly straight-fronted edge crack to a semi-circular crack front. Use of the weight function method requires that the crack opening displacement field of a reference load has to be known. It was obtained by 3-D finite element analysis. Results are presented for the cracked cylinder subjected to a constant stress (tension) and a linear stress distribution acting perpendicular to the crack faces and they are compared with values found by other investigators.     

EXPERIMENTAL DETERMINATION OF STRESS INTENSITY FACTORS FOR CRACKS IN TURBINE DISCS

Stage-II fatigue crack growth paths in firtree fixtures have been predicted using a photoelastic technique. Initiation was assumed to occur at the edge of contact on the load-bearing flanks and, subsequently, the cracks were extended in the direction of the maximum circumferential stress. After a short initial length, in which propagation was perpendicular to the contact surface, the direction of crack growth was, in a broad sense, equivalent to the hoop direction in the disc. Stress intensity factors were found for the majority of the crack path using data taken from the isochromatic fringe patterns. It was concluded that the most catastrophic failure was likely to occur from the innermost land of the firtree and that the width of the firtree had little influence on the stress intensity factors.