Analysis of surface cracks by holography

Presented here is a combination of holographic interferometry with a smoothing numerical method taking into consideration the balance of momentum. The method permits the experimental determination of strains, stresses as well as related quantities in fracture mechanics. An edge cracked beam subjected to three-point bending and a double torsion specimen have been selected as the specimens for illustrating the hybrid method.     

Shell of arbitrary curvature with cracks of different type and geometry

The interaction of through, surface, and internal cracks in shells of arbitrary curvature is examined. Crack of the same and different types with various geometry are considered. The curvature of the shell, the length and depth of the cracks, their arrangement and distance between them have a strong effect on the stress intensity factors for part-through cracks and on the force and moment intensity factors for through cracks     

A new method of analyzing surface cracks

The authors have developed a new line-spring boundary element method in thepresent paper,which combines the advantage of the line-spring model with that of theboundary element method.This method reduces the three-dimension problem of thesurface cracks into a quasi-one-dimension problem and can be used to analyze thesurface cracked plate under various loading conditions.In this paper theoreticalanalyses and numerical verifications are carried out.The calculated results arereported,which indicate that the present method is efficient and can be used to analyzethe surface crack problem on a personal computer.     

Edge cracks in plastically deforming surface grains

A selection of surface crack problems is presented to provide insights into Stage I and early Stage II fatigue crack growth. Edge cracks at 45^o and 90^o to the surface are considered for cracks growing in single crystals. Both single crystal slip and conventional plasticity are employed as constitutive models. Edge cracks at 45^o to the surface are considered that either (i) kink in the direction perpendicular to the surface, or (ii) approach a grain boundary across which only elastic deformations occur.     

Elastic-plastic models of surface cracks in tensile panels

The surface crack is a common flaw in structures and vessels, and its elastic characterization has been studied extensively as reviewed in Ref. 1 and its references. Elastic-plastic fracture-mechanics (EPFM) technology can be used to characterize surface cracks in tough materials. Two EPFM aprameters are commonly used: the crack-tip-opening displacement (CTOD) and the three-dimensionalJ integral. This paper draws on a series of studies^2–11 at the National Bureau of Standards related to the development and verification of analyticalmodels for the calculation of EPFM parameters in surface-cracked tensile panels. The models previously verified for pipeline steel plates^4–7 are used to calculate the crack-mouth-opening displacement (CMOD) andJ for surface cracks in welded-steel specimens.     

Environmentally assisted initiation and growth of multiple surface cracks

The initial stages of stress corrosion on an amorphous polymer is investigated. This is done by exposing stressed specimens of polycarbonate to an acetone and water solution. The surface develops two distinct features of degradation that appear on different length scales when subjected to tensile stress. Small pits form on the surface and make it rough. These pits are in the order of micrometers, and are found to be randomly distributed. They occur even without load and seem to slightly increase in number with increasing stress. In the millimeter domain, visible to the bare eye, surface cracks are formed transverse to the direction of loading. The occurrence of cracks is seen to have a positive stress threshold value, exceeding which, a linear increase of number of cracks with stress is found. The manners in which the cracks grow and coalesce on the surface are examined. It is seen that they do not meet crack tip to crack tip. Instead, they avoid each other initially and coalesce crack tip to crack side. The results are discussed in the light of mechanical considerations. A stress analysis for a few configurations of meeting cracks supports the experimental observations. With assumptions of stress corrosion crack growth and coalescence, a simulation of cracks growing from randomly distributed initiation sites is performed. Similar crack patterns as obtained in the experiments are found.     

Wave dynamics of cracks and multiple contact surface interaction

This work considers the numerical simulation of crack behavior involving contact surfaces. A surface-slipping algorithm is developed to obtain the deformation of solids containing one or several cracks under dynamic loading. A shear-loading-induced crack is also considered.     

非共面双裂纹扩展相互作用的试验及模拟

对非共面双裂纹进行了疲劳试验,分析认为其裂纹扩展属于三型复合型裂纹;建立了双裂纹结构有限元模型,通过计算裂纹前端应力强度因子并结合复合型裂纹的扩展特性及断裂准则,对裂纹相对尺寸、相对位置对其扩展的影响以进行了研究。结果表明:当偏移距离与较长裂纹尺寸的比值大于较短裂纹尺寸与较长裂纹尺寸的比值时,裂纹间相互作用较小,对疲劳寿命几乎没有影响;反之裂纹间相互作用较大,将会减少疲劳寿命。     

A simple method for measuring surface strains around cracks

A simple system has been developed to measure surface strains that occur during in situ deformation of mechanical test specimens. The system uses photolithographically deposited displacement markers and computer image recognition routines to determine in-plane displacements and strains from digital images. The strain calculating routines are integrated into a simple mouse-driven software package that facilitates the transformation from digital images to useful strain field information. Additional routines have been developed to determine crack tip stress fields and J integrals. Crack tip stress intensities have been calculated from strain maps obtained for traction-free cracks in stainless steel. The J integrals were found to be independent of contour and consistent with applied stress intensities. Crack tip stress intensities were calculated for bridged cracks in lamellar TiAl. The toughening effect of the bridging zones was determined by including the bridged region in the contours. Resistance curves generated from strain maps were consistent with those measured during mechanical testing.     

Collinear periodical cracks with surface separation and frictional sliding

Using the method of Muskhelishvili, an exact solution is obtained for the problem of collinear, periodical cracks whose surface undergo separation and frictional sliding.     

Fatigue crack growth of surface cracks in the rail web

The analytical prediction of surface cracks in the rail web is investigated by two different approaches. The first approach uses engineering fracture mechanics principles with elementary beam theory (i.e., one dimensional) stress analysis. The second approach applies the strain energy density criterion to a three dimensional finite element stress analysis of the rail web. Results are presented in terms of crack size as a function of accumulated tonnage for variations in loading (tangent or curved track), support conditions (foundation modulus), and assumed levels of residual stress. The results of both models are consistent in that the predicted growth rates are fairly slow when compared to other types of rail defects (for example, the detail fracture in the rail head).     

Emergence paths of cracks on a free surface during wedging

Mining Institute, Siberian Division, Russian Academy of Sciences, 630091 Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 6, pp. 142–152, November–December, 1995.     

表面裂纹疲劳扩展形状演化预测

应用新的应力强度因子经验公式预测了拉伸和纯弯曲载荷下疲劳扩展过程中表面裂纹形状的演化,并与Newman和Raju的经验公式以及实验结果进行了比较。结果表明:虽然对应力强度因子估算有一定差别,但两者对裂纹形状演化的预测有很好的一致性,预测结果与实验结果也比较吻合,从而表明所提出的经验公式能够用于预测疲劳扩展过程中表面裂纹形状演化。     

The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation

Numerical simulation of Poiseuille flow of liquid Argon in a rough nano-channel using the non-equilibrium molecular dynamics simulation is performed. Density and velocity profiles across the channel are investigated in which roughness is implemented only on the lower wall. The Lennard–Jones potential is used to model the interactions between all particles. The effects of surface roughness geometry, gap between roughness elements (or roughness periodicity), surface roughness height and surface attraction energy on the behavior of the flow undergoing Poiseuille flow are presented. Results show that surface shape and roughness height have a decisive role on the flow behaviors. In fact, by increasing the roughness ratio (height to base ratio), the slip velocity and the maximum velocity in the channel cross section are reduced, and the density fluctuations near the wall increases. Results also show that the maximum density near the wall for a rough surface is less than a smooth wall. Moreover, the simulation results show that the effect of triangle roughness surface on the flow behavior is more than the cylindrical ones.     

Propagation of surface breathing cracks in shafts under quasi-static rotary bending

Nonlinear Dynamics -     

Variation in stress-intensity factor and back-surface displacement for surface cracks

Knowledge of the magnitude and variation in the stress-intensity factor (SIF) around the perimeter of a surface crack is essential for an accurate analysis of a flawed component. SIFs for surface flaws of various semi-elliptical geometries were analytically determined. Three-dimensional linear-elastic finite-element analysis was performed to determine the maximum SIF for bending and tension for each of 12 crack geometries which represent deep surface flaws in finite-thickness plates. Experimental verification of one of the crack geometries was performed. Interferometry techniques were used to determine the actual variation in SIF along the curve crack front due to bending. In addition to the SIF calculations, physical characteristics are noted as observed in the analytical and experimental evaluations.     

Limit equilibrium of a transversely isotropic spherical shell with two surface cracks

An analog of the δ _c -model is used to reduce the limit-equilibrium problem for a transversely isotropic spherical shell with surface cracks to a system of integral equations. An algorithm for numerical solution of this system is proposed     

Local weight functions for semi-elliptical surface cracks in finite thickness plates

Weight functions for any local point, 0 < Φ < π/2 along a semi-elliptical surface crack in finite thickness plates were derived from an assumed approximate general weight function and two reference stress intensity factors. The resulting weight functions were verified using available finite element results for two nonlinear stress fields and good agreement was achieved. When used together with weight functions for Φ = 0 and Φ = π/2 the weight functions are suitable for the calculation of stress intensity factors anywhere along the crack front for semi-elliptical surface cracks in complex stress fields with aspect ratios in the range 0 ≤ a/c ≤ 1 and relative depths 0 ≤ a/t ≤ 0.8.     

The influence of the curvature dependence of the surface tension on the geometry of electrically charged menisci

We evaluate how the curvature dependence of surface tension affects the shape of electrically charged interfaces between a perfectly conducting fluid and its vapour. We consider two cases: i) spherical droplets in equilibrium with their vapour; ii) menisci pending in a capillary tube in presence of a conducting plate at given electric potential drop. Tolman-like dependence of surface tension on curvature becomes important when the “nucleation radius” is comparable with the interface curvature radius. In case i) we prove existence of the equilibrium minimal radius and estimate its dependence on the electric fields and Tolman-like curvature effects. In case ii) the menisci are subject to the gravitational force, surface tension and electrostatic fields. We determine the unknown surface of the menisci to which the potential is assigned using an iterative numerical method and show that Tolman-like corrections imply: 1) a variation of the height (up to 10% in some cases) of the tip of the menisci; 2) a decrease of the maximum electrical potential applicable to the menisci before their break-down amounting to 40V over 800V in the considered cases. We conjecture that these effects could be used in new experiments based on electric measurements to determine the dependence of the equilibrium surface tension on curvature. Received January 19, 1998