FATIGUE PROPAGATION OF SURFACE FLAWS IN ROUND BARS: A THREE-PARAMETER THEORETICAL MODEL

A three-parameter fracture mechanics model is proposed to theoretically analyse the propagation of an elliptical-arc part-through flaw in a round bar subjected to constant cyclic amplitude axial or bending loads. The edge flaw presents an aspect ratio α=a_el/b_el (a_el, b_el= ellipse semi-axes) and a relative crack depth ζ=a/D, where a and D are the depth of the deepest point on the crack front and the bar diameter, respectively. Additionally a parameter s=a_el/a (ellipse shifting) defines the distance of the ellipse centre from the bar circumference. The surface flaw growth occurs according to preferred patterns which tend to converge to an inclined asymptotic plane in the diagram of α against s and ζ.     

THE COALESCENCE OF VOIDS IN PRESTRAINED NOTCHED ROUND COPPER BARS

Notched round copper bars are prestrained to various extents, recrystallized, and finally strained until fracture. Void nucleation and growth during prestraining cause a decrease in the macroscopic void coalescence strain. Modelling of this experiment requires a proper account of the changes in void sizes and their interdistances during prestraining. Modelling based on the Gurson–Leblond–Perrin model for void growth and the Thomason model for void coalescence is proposed. Comparison with experimental results allows a demonstration of the validity of the Thomason model and the inadequacy of models based on a critical porosity value. Porosity at coalescence is found to depend on the initial void volume fraction, the flow properties and the stress state.     

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.     

FATIGUE GROWTH OF SURFACE CRACKS IN THE ELASTIC-PLASTIC REGION

Surface crack growth has been studied in centre notched and smooth panels of low carbon steel under symmetric axial elastic-plastic cyclic straining. The crack shape, followed by heat tinting, has been found to be approximately semi-circular for crack radii 0.3–5 mm. Both smooth and notched specimens have been fatigued until fracture. The smallest notches of 0.1 mm in radius and depth approximately represent defects of a critical size under present loading conditions. Crack propagation rates have been measured and plotted vs ΔJ. Both present part through-crack data and previous long through-crack data in the elastic and the elastic-plastic regions are compatible. A single dependence of dl/dN vs ΔJ is obtained.     

STRESS INTENSITY FACTORS FOR CIRCUMFERENTIAL SURFACE CRACKS IN PIPES

Abstract Stress intensity factors for circumferential surface cracks in pipes have been derived using the finite element method. Both cracks located at the in- and outside of the pipes have been analysed. The derived solutions cover a wide range of geometry and load configurations and are presented in a tabular form that defines influence functions for the stress intensity factor along the whole crack front. The solutions show good agreements in comparisons to other published solutions.     

CLOSURE BEHAVIOUR OF SURFACE CRACKS

Abstract— The fatigue crack closure response was investigated for a surface crack in BS4360 50B structural steel, subjected to (1) constant amplitude loading and (2) constant amplitude loading interrupted by a single peak overload. A variety of compliance techniques was employed to determine closure behaviour. The crack mouth gauge measured the bulk, plane strain closure load, while the near tip strain gauge indicated the surface, plane stress closure response. For constant amplitude loading it was found that the surface regions of a surface crack are closed for a greater portion of the load cycle than the maximum depth point. A single peak overload caused different closure and growth rate transients at the surface of the thumbnail crack and at the maximum depth point. For growth rates above 10^-6 mm/cycle, such behaviour agrees with the response of a through crack when subjected to constant amplitude loading, and a single peak overload.     

残余应力平板表面裂纹的线弹簧模型

建立了残余应力平板表面裂纹的线弹簧模型,利用边裂纹权函数得到了裂纹表面上沿厚度非线性分布残余应力向线性分布转化的公式;基于Reissner板理论和连续分布位错思想,通过积分变换方法,推导了问题的控制方程和应力强度因子表达式;利用Gauss-Chebyshev方法给出了数值计算结果,并与现有的有限元解进行了比较,结果表明:该模型简单有效,而且精度较高。     

J-ESTIMATION FOR SEMI-ELLIPTICAL SURFACE CRACKS IN WIDE PLATES UNDER DIRECT TENSION

Large marine structures can be subjected to extensive localized damage, with strains reaching 10  times the yield strain. Small defects might propagate, and accurate defect assessment is required for safe operation. To simulate this problem, J -integrals have been computed for semielliptical cracks in wide steel plates under tension. Three-dimensional (3D) elastic–plastic finite element analysis was used to model shallow crack geometries with 0.2 ≤ a / c ≤ 0.57 and 0.05 ≤ a / t ≤ 0.15. The material responses were linear elastic followed either by power hardening, or perfect plasticity and power hardening. It was found that, in contrast to previous studies on single edge notch geometries, the material law does not have a major influence on the J –strain behaviour. Results obtained from the 3D analyses form the basis for the development of a J -based estimation scheme.     

新的估算表面裂纹应力强度因子经验公式

该文给出了新的估算拉伸和纯弯曲载荷下表面裂纹应力强度因子的经验公式。根据疲劳裂纹扩展的数值模拟结果确定强度因子分布函数;利用按已知应力强度因子分布函数求裂纹形状及相应应力强度因子的方法计算给定尺寸的表面裂纹的应力强度因子;通过对数值结果的曲线回归得到估算表面裂纹应力强度因子经验公式。利用该公式对有限厚度和宽度平板内表面裂纹的应力强度因子进行了估算,并与已知的半椭圆形表面裂纹的应力强度因子解进行了比较。该文结果为估算表面裂纹应力强度因子提供了一种新的途径。     

含曲线裂纹柱体扭转问题的新边界元法

研究了带曲线裂纹柱体的扭转断裂问题,推导出了可以直接应用于任意形状截面含有任意形状曲线裂纹的柱体扭转问题的新的边界积分方程,并建立了带裂纹柱体扭转问题的边界元数值计算方法,提出了裂纹尖端的奇异元和线性元插值模型,给出了抗扭刚度和应力强度因子的边界元计算公式。该文对含有圆弧裂纹、曲线裂纹及直线裂纹的不同截面形状柱体的典型问题进行了数值计算,所得结果证明了边界元方法的正确性和有效性。     

GROWTH OF SEMI-ELLIPTICAL SURFACE CRACKS IN FERRITIC STEEL PLATES UNDER CYCLIC THERMAL SHOCK LOADING

Abstract— Investigations of crack growth under thermal fatigue loading are presented. The experiments were performed with a ferritic reactor pressure vessel steel. A plate, containing a semi-elliptical surface crack is heated up to a homogeneous temperature and cyclically cooled down by a jet of cold water. On the basis of linear elastic fracture mechanics, stress-intensity factors are calculated with the weight function method. The prediction of crack growth under thermal fatigue loading using data from standard specimens is compared with the experimental result.     

ELECTRON BACKSCATTERING PATTERN IDENTIFICATION OF SURFACE MORPHOLOGY OF FATIGUE CRACKS IN TA6V

Abstract— Fatigue crack growth in an α+β titanium alloy (TA6V) with three microstructural conditions is studied in high vacuum at 300°C. The faster growth rates are observed in the material with a low content of primary α phase and a fine equiaxed microstructure. Near the threshold regime, a slow crystallographic Stage I-like propagation is observed in the three microstructural types where slip occurs along a single-plane system which develops within the α grains. These crystallographic facets are identified using an electron backscattering pattern (EBSP) technique and were found to lie on basal planes.     

SURFACE CRACKS AND THE FATIGUE LIMIT OF METALS

Abstract— A technique based on indenting a sphere into a material has been developed for measuring the yield strength of metals at various depths from the surface. Proceeding from the experimentally established reduction in the yield strength of the metal surface layer and cyclic crack growth resistance characteristics, the authors suggest a model simulating fatigue fracture based on the continuum mechanics assumptions which allows the fatigue limit to be estimated on the basis of a critical non-propagating fatigue crack size for components of various thickness in tension-compression or in bending; considering stress concentrations under both alternating and oscillating loads in the presence of near-surface stresses. Theoretical predictions using the model for three martensitic stainless steels and a titanium alloy showed a fair agreement with experimental data.     

多条表面裂纹相互作用的应力分析

脆性材料在热冲击载荷作用下,表面上经常会出现一些裂纹.含裂纹的构件可能会突然出现部分的或完全的失效.多条表面裂纹之间的相互作用通常会影响机械构件的寿命.该文采用迭加法研究了在热载荷下有限厚度的无限大板中N条中心对称分布的半圆形表面裂纹的相互作用问题:首先解析地求得板中不含裂纹时的应力分布;然后,根据叠加原理,有限元建模将反向等值载荷加在裂纹面上,从而得到问题的解.该文研究了多种裂纹构型下的应力强度因子,并以图的形式给出.     

THREE-DIMENSIONAL CRACK-SHAPE EFFECTS DURING THE GROWTH OF SMALL SURFACE FATIGUE CRACKS IN A TITANIUM-BASE ALLOY

Abstract— A basic study was performed on the evolution of three-dimensional shapes of small surface fatigue cracks during fatigue, and the effect of this evolution on small-crack growth behavior of a titanium-base alloy. Specifically, the nature and the magnitude of variations in crack aspect ratio, a/c (a is the crack depth and c is the half-surface crack length), during cyclic crack growth and its impact on growth rates have been studied. Experiments were performed on naturally initiated micro-cracks in a microstructure consisting of equiaxed primary-α₂ phase in a Widmanstätten (transformed β) matrix. Several cracks under stress ratio (R) levels of 0.1 and ?1, were studied. A specialized experimental system, consisting of a laser interferometer (to measure precisely the small-crack surface displacements), and a photo microscope (to automatically and continuously photograph the fatigue micro-cracks) was employed in the study. Apparent aspect ratios of surface cracks were calculated from the compliance response and the surface crack length data as a function of fatigue cycles. These data enabled accurate calculations of growth rates at the surface crack tip as well as the tip at depth in the bulk over the entire crack growth period, thus giving an insight into the crack growth process. Measurements of closure levels of small cracks were also performed and were used to partly account for the differences in growth rates. In the comparisons of small-crack growth data with the large-crack data, surface growth rates correlated relatively well with the large-crack data. Growth rates at depth exhibited large variations due to the irregularity of crack fronts at this location, and these rates deviated significantly from the large-crack behavior. Additionally, these growth rates varied between different cracks. An attempt was made to rationalize these observations in terms of the effects of inhomogeneities present in the microstructure.     

FATIGUE ANALYSIS OF SURFACE CRACKS AT FILLET WELDED TOES

This paper reports a study of fatigue crack growth and coalescing behaviour at semi-elliptical cracks in the stress concentration region of steel plates with fillet shoulders or fillet welds. Fatigue tests were carried out on machined plate specimens with a fillet geometry similar to a fillet welded joint. These specimens were notched and precracked to provide single and multiple coplanar semi-elliptical surface cracks at the fillet toe region. Finite element stress analysis results were used to obtain approximate Mk factors (i.e.: stress concentration magnification factors) for the fillet toe geometry with a semi-elliptical surface crack. An analytical model was developed to simulate crack shape development and growth to failure in the case of multiple coplanar semi-elliptical cracks. In this model, a simple crack coalescing procedure is applied to merge coplanar cracks when they meet by recharacterising the coplanar cracks into a single semi-elliptical crack. Alternative crack growth laws were investigated and comparisons made between actual and predicted shape developments and lives.     

双金属带锯条表面裂纹分析

对双金属带锯条表面裂纹的形成原因进行了分析。结果表明,双金属居条基体表面存在着含Ｍｇ,Ｓｉ,Ｃｕ和Ｓ等元素的Ａｌ２Ｏ３和Ｆｅ２Ｏ３复合氧化物夹杂组成的微凹坑,是表面裂纹形成的主要原因。     

STRESS INTENSITY FACTORS AND WEIGHT FUNCTIONS FOR SEMI-ELLIPTICAL SURFACE CRACKS IN FINITE-THICKNESS PLATES UNDER TWO-DIMENSIONAL STRESS DISTRIBUTION

Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤ a/c ≤ 1 and relative depth in the range of 0 ≤ a/t ≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.