THE STRESS INTENSITY FACTOR OF SMALL CRACKS AT NOTCHES

Abstract— It was found in a previous publication that stress fields around notches are quantitatively very similar, if the peak stress at the notch root (σ_peak) and the notch root radius ( ρ ) are the same. As a consequence, small cracks (length l ) should have the same stress intensity factor, if σ_peak and ρ are similar. This implies that the geometry factor C in
should primarily depend on l/ρ only, and not on other dimensions. Available data on calculated K values was analysed, which confirmed the similarity concept. An equation for C as a function of l/ρ was obtained. It was shown that K -values calculated with this equation are an accurate approximation for the stress intensity factor of small cracks at notches.     

ESTIMATIONS OF STRESS INTENSITY FACTORS FOR SMALL CRACKS AT NOTCHES

This paper presents a simple method for determining the stress intensity factors for small notch-emanating cracks. The proposed method is based on similarities between elastic notch-tip stress fields described by two parameters; the stress concentration factor K₁, and the notch-tip radius ρ. The method developed here is rather general, and can be used for a variety of central and edge notches with through-thickness of semi-elliptical cracks. The predicted values are in good agreement with the available numerical data.     

STRESS DISTRIBUTIONS FOR V-SHAPED NOTCHES UNDER TENSILE AND BENDING LOADS

Abstract— An analytical solution has been proposed recently by the authors to describe, with a unified approach, the stress fields in the neighbourhood of sharp cracks, V-shaped notches and re-entrant corners in plates subjected to remote tensile loading. In the present paper, the above solution is revised and extended, by also determining the relevant displacement fields and the degree of accuracy of the solution for both the longitudinal and transverse stress fields. Afterwards, since the stress field depends on the type of loading, the circumferential principal stress component is modified to account for bending in fatigue life predictions, while the radial principal stress is almost negligible in this case. The analytical results are compared with finite element values obtained for different geometries loaded under tensile or bending conditions, as well as with other closed-form solutions. The new expressions seem to give better stress estimates than the currently available approximate solutions, whether analytical or numerical, when the opening angle of the re-entrant corner is equal to or greater than π/2. Hence they should represent a good starting point to describe stress distributions induced by stress raisers with large and well defined opening angles such as shafts with shoulder fillets, gears and weldments.     

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch-crack problem is treated in two different ways: if the non-dimensional crack length l /ρ ( l = crack length; ρ= notch root radius) is smaller than the transition crack length l _T/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ ρ is larger than l _T/ρ, the notch-crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, l _T, and for the geometric factor F = K _I/(1.1215K_tσ√π l ) are developed for various notch problems for the crack length range l ≦ l _T. It is found that the stress (σ_yy) normalized by the peak stress (σ_peak), σ_yy/σ_peak, for the pre-cracked component is very similar to the geometric factor for short cracks.     

STRESS INTENSITY FACTORS FOR CORNER CRACKS AT A SEMI-CIRCULAR NOTCH UNDER STRESS GRADIENTS

Abstract— A weight function method, recently developed by the authors, is applied to calculate stress intensity factors for corner cracks emanating from a semi-circular notch under crack face polynomial pressure loading. A wide range of configuration parameters are considered. These results, combined with superposition principle, allow determination of stress intensity factors under general loading conditions. The approach is demonstrated by obtaining stress intensity factors for the load cases of remote tension and shot-peening residual stresses at the notch.     

半圆孔板承受拉伸和弯曲时的三维应力集中

根据Hellinger-Reissner原理建立了具有一个无外力圆柱表面三维8节点杂交应力元,元内假定应力场满足以柱坐标表示的三维平衡方程及无外力圆柱面上的外力边界条件,当元退化为二维时也满足协调方程。单元位移场选取与相邻元协调。用这种特殊杂交应力元,在相当粗的网格下即能准确地分析具有半圆孔厚(薄)板的三维(二维)应力集中。     

基于单元应力级数展开的下限原理有限元法

基于Taylor级数,将三角形单元内的应力场在三角形单元中心点处展开,从而可以借助于中心点应力及应力场梯度来表达整个单元应力场,再利用平衡方程中应力场梯度之间的线性关系,使单元中未知量的个数从9个减少到7个。由于已经满足了平衡方程,因此得到下限问题的数学规划模型不仅减少了变量的个数,而且也减少了等式约束的个数,从而降低了模型的规模。该方法丰富了下限原理有限元法的理论,为进一步提高求解效率打下了基础。计算结果表明与经典Sloan方法得到的结果完全一致。     

A LOCAL GRID REFINEMENT METHOD FOR DETERMINING STRESS INTENSITY FACTORS FOR CRACKS AT NOTCHES

Abstract— Stress intensity calibrations have been determined for cracks at the root of a semi-circular edge notch loaded in tension using a localised grid refinement technique for finite element analysis. The technique is of particular value in situations where a fully connected mesh model is difficult to achieve or where enhanced accuracy is needed in a small sub-region of a model. Solutions were as accurate as those from a conventional refined mesh but with an approximately two fold reduction in run time. The resulting stress intensity factors are in good agreement with those estimated using a notch correction function and the equivalent un-notched crack solution.     

不同热处理的铝合金在应力梯度影响下表面裂纹扩展特性的评价

本文在弹塑性范围中以循环轴向拉压和旋转弯曲负载条件和两种不同热处理的铝合金材料为研究对象,对１型微小裂纹扩展速率统一评价方法进行了研究,虽然在不同材料,不同负载条件下都可以用名义应力　和裂纹长度　评价Ｉ型裂纹扩展特性（　）但其表达式中的系数Ｃ、ｎ随这些试验条件变化而变化。因此,利用材料的循环应力－应变关系（　）,可以用塑性应交代替名义应力统一地评价Ｉ型裂纹扩展特性（　）,而不受负载条件的影响。     

STRESS DISTRIBUTION AROUND HOLES AT THE ENDS OF A CRACK

Stresses around holes of equal size drilled at the ends of a crack are determined for uniaxial tension normal to the crack by a combined photoelastic and brittle lacquer technique avoiding difficulties of exactly locating isoclinics. The stress concentration factor decreases continuously with increasing hole size until the crack is displaced by a single hole.     

单层带孔玻璃板孔边破坏应力的力学分析

因为轴对称性,圆盘模型可以减少玻璃材料离散性的影响,所以比较适合进行测量孔边破坏应力的试验.通过对带孔圆盘模型的力学分析和理论推导得到了板内最大主应力分布的表达式,并用该表达式分别拟合有限元计算结果和试验结果,通过比较分析,最终提出了点式玻璃板孔边破坏应力建议限值,为进一步完善幕墙结构的设计提供依据.     

有限大层板承载孔的孔边应力分析

含圆孔的复合材料层合板, 在孔内轴销加载下的孔边应力分析, 是一个比较复杂的弹性接触问题, 板与轴销均处于十分复杂的受力状态。在文献中, 作者曾提出一个计及轴销变形与接触区摩擦效应的弹性轴销模型。本文在上述工作的基础上, 采用解析-有限元混合解法, 研究了有限大层合板承载销孔的孔边应力。分析表明, 讨算结果与实验相符。      

NON-DAMAGING NOTCHES IN FATIGUE*

The fact that very small notches (cavities, holes, scratches, etc.) have no effect on the fatigue limit of metallic materials is well known. This paper presents both a qualitative explanation for the existence of non-damaging notches and a quantitative derivation of their critical sizes. The condition for a notch (characterized by the stress concentration factor K_t and the notch root radius ρ) to be non-damaging in a metallic material (characterized by a critical crack size l₀) is (K²_t? 1)ρ≤ 4.5 l₀. The critical crack size can be expressed with good approximation in terms of the threshold stress intensity for fatigue crack growth and the plain fatigue limit. Therefore the above relation can be applied for an engineering evaluation of non-damaging notches. Test results obtained for copper and a pressure vessel steel demonstrate the applicability of the proposed method.     

层内混杂复合材料断裂纤维附近的应力重分布

研究了层内混杂复合材料的高模量纤维断裂引起的邻近各层应力重分布问题。通过建立适当的计算模型,利用二维弹性力学精确解和付氏变换法,建立问题的奇异积分方程组,通过求解方程组,计算高、低模量层和基体层的应力集中因子,计算结果对"混杂效应"作出了理论解释,并与一般采用的Shear-Lag理论计算结果作了比较,本文结果更精确、合理,可应用于层内混杂复合材料的设计。     

各向异性地层中井孔周围应力场的研究

由于问题的复杂性,在以往研究井壁稳定性的文献中,大多将地层介质简化为各向同性的。该文基于各向异性弹性理论,利用复变函数方法,建立了各向异性地层中倾斜井孔周围应力场的计算模型,得到了能够反映地层各向异性性质、地层倾向和走向、井斜角和方位角、井孔液柱压力、原始地应力方位和原始地应力比等多种因素影响的井孔周围应力场的解析表达...     

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。     

粘弹性土体中深埋圆形隧道的应力和位移分析

基于Biot固结理论,采用渗流-力学耦合模型,研究分析了粘弹性饱和土体中因开挖深埋圆形隧道而引起的周围土体的应力和位移场。假设衬砌和土体均为多孔介质,隧道处于半封闭状态,边界半透水。在拉普拉斯变换域中得到的应力、位移场和孔隙水压力解答,运用拉普拉斯数值逆变换得到数值计算结果,分析了隧道周围土体中应力、位移场及孔隙水压力的消散规律,讨论了隧道边界的渗透特性和土体的流变性质对应力、位移场以及孔隙水压力消散的影响。     

压气机叶轮孔边动应力集中现象的研究

本文对某压气机叶轮内均压孔的孔边动应力分布进行了试验研究。试验分别采用正弦激励模态共振法和锤击激励传递函数测量法。两种试验方法得出的应力集中系数基本一致．所得数据对压气机叶轮裂纹故障的诊断及对策有重要价值，试验方法和数据对一般结构的应力集中问题有通用的参考意义。     

无限板内椭圆孔周的应力分析

应用复变函数的方法，对于含有椭圆孔的各向异性板或各向同性板，导出了当椭圆孔周作用任意集中力或分布力时孔周周向应力的解析表达式；其特例与前人结果一致．     

裂纹深度及尖端曲率对尖角裂纹周围应力场的影响

对于尖角裂纹,裂纹深度和裂纹尖端曲率对于裂纹附近应力场的影响有可能要大于裂纹张开角度的影响。根据弹性断裂理论和复变函数理论建立了一个计算模型,利用保角映射方法解决了尖角裂纹的边界条件问题,得到了具有不同深度和尖端曲率的裂纹周围应力分布,并对此应力分布规律进行了分析。