Determination of mixed-mode stress-intensity factors K I and K II for a subsurface crack near a concentrated force

Two-dimensional photoelastic experiments were conducted to obtain isochromatic fringe fields in the region between a crack tip and a concentrated load on the boundary of a half plane. An analysis method is developed to determine the mixed-mode stress-intensity factors due to two interacting stress singularities. The results obtained showed the dominance of the opening mode in extending a delamination crack by sliding surface loads. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

Determination of fracture toughness by photoelastic coating

The photoelastic-coating method was applied to the determination of fracture toughness in aluminum plates. The specimens were plates with a central transverse crack. Determinations were made first by the compliance method. The specimens were loaded statically to failure. The opening displacement across the crack was measured with a clip gage. In using this photoelastic-coating method, the stress-intensity factor was obtained in terms of the radius and fringe order of various isochromatic fringe loops using an extrapolation law. An apparent stress-intensity factor was obtained from several isochromatic fringe patterns away from the crack tip and then extrapolated to the crack tip to determine the true value. Results obtained by the photoelastic-coating method are higher than those obtained by the compliance method for all loads, due to the bluntness of the crack tip in the first set of specimens. Theoretical predictions fall between the compliance method and photoelastic-coating results. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Stress intensity factors for curved and kinked cracks in plane extension

A singular integral equation containing the crack opening displacement (COD) is developed for solving plane elasticity problems. The crack may contain any number of kinks at different intervals and orientations, such as a saw-tooth shape. Cracks in the form of a sine wave can also be treated. The crack tip stress intensity factors are evaluated for a variety of crack shapes and the results are displayed graphically. The distance between the crack tips is found to be a dominant factor on the crack tip stress intensity while the angle between the tangent to the crack tip and load direction determines the proportion of Mode I and II stress intensity factors.     

An analytical and experimental stress analysis of a practical mode II fracture test specimen

A boundary-collocation method has been employed to determine the Mode II stress-intensity factors for a pair of through-the-thickness edge cracks in a finite isotropic plate. An elastostatic analysis has been carried out in terms of the complete Williams stress function employing both even and old components. The results of the numerical analysis were verified by a two-step procedure whereby the symmetric (Mode I) and antisymmetric (Mode II) portions of the solution were independently compared with existing solutions. Since no previous analytical solutions existed for the asymmetric loading of an edge-cracked plate, the complete solution was verified by comparison with a photoelastic analysis. A compact shear (CS) specimen of Hysol epoxy resin was loaded in a photoelastic experiment designed to study the isochromatic-fringe patterns resulting from the Mode II crack-tip stress distribution. The experiment verified that a pure mode II stress distribution existed in the neighborhood of the crack tips, and confirmed the accuracy of the boundary-collocation solution for the Mode II stress-intensity factors. Specimen center-line stress-distribution data were obtained photoelastically and employed to refine the boundary-collocation analysis. Agreement between the analytically and experimentally determined Mode II stress-intensity factors was excellent.     

相干梯度敏感(CGS)干涉测量技术及其应用研究

首先介绍了相干梯度敏感(CGS:Coherent Gradient Sensing)光学干涉测量技术的最新研究进展;其次,详细介绍了透射CGS方法和反射CGS方法的基本原理及实验技术;最后给出了CGS技术在各种断裂力学研究中的应用,不仅给出了各向同性均匀聚合物材料I型、混合型、V型裂纹及梯度材料I型裂纹尖端奇异场的控制方程,而且给出了对应各自情况下的CGS光学条纹模拟与实验图像。研究结果将为实验断裂力学研究提供基础性理论和实验应力分析手段。     

Three-dimensional speckle interferometric investigation of the stress-intensity factor along a crack front

The variation in Mode I stress-intensity factor throughout the thickness of an ASTM standard compact tension specimen was determined using scattered-light speckle interferometry. Two very thin sheets of coincident coherent light traveling in opposite directions were passed through a Plexiglas specimen normal to the crack faces. A double-exposed photograph of the scattered-light speckle pattern was taken while the specimen was subjected to a small load increment. From this double-exposed photograph, the change in the crack-opening displacement could be determined. From the information about the crack-opening displacement in the region of the crack tip, the stress-intensity factor was calculated for various interior planes and on the surface of the specimen. For the compact tension specimen tested, the stress-intensity factor did not vary throughout the specimen's thickness. The method of scattered-light speckle interferometry proved to be very powerful in solving this complex three-dimensional problem.     

Photoelastic determination of dynamic crack-tip stresses in an anisotropic plate

The paper outlines a technique of determining the dynamic stress-intensity factors (SIFs) in structurally anisotropic composites from photoelastic measurement data. A composite is considered a linear elastic, homogeneous, orthotropic body. An equation is derived that relates the fringe order with the SIFs and the far-field stresses at the tip of a crack, which is parallel to the orthotropy axis __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 95–103, May 2006.     

The determination of mode I stress-intensity factors by holographic interferometry

The use of linear elastic fracture mechanics generally depends upon the availability of suitable analytical or numerical solutions for the relevant crack-tip stress-intensity factor,K. Convenient experimental verification of such solutions is a valuable aid to their correct application and can provide a practical substitute in real design situations of great complexity. A convenient, new experimental technique for estimating the Mode I stress-intensity factor using holographic interferometry and test pieces cut from thin sheets of commercially available polymethylmethacrylate is described and demonstrated. The test pieces can readily be prepared to model any desired Mode I geometry and boundary conditions. In addition, a prior self-calibration procedure can be employed to enhance both convenience and accuracy. Real-time interference-fringe data from the crack-tip region are easily reduced and plotted to yield a straight line whose slope provides a one-parameter evaluation of the effect of geometry on the stress-intensity factor. This information, together with the crack length and applied stress, completely definesK.     

Numerical evaluation of generalized stress-intensity factors in multi-layered composites

The problem of the evaluation of the generalized stress-intensity factors for re-entrant corners in multi-layered structural components is addressed. An approximate analytical model based on the theory of multi-layered beams is presented. This approach provides a simple closed-form solution for the direct computation of the Mode I stress-intensity factor for the general problem of a re-entrant corner symmetrically meeting a bi-material interface. For the self-consistency of the theory, re-entrant corners in homogeneous materials and cracks perpendicular to bi-material interfaces can also be gained as limit cases of this formulation. According to this approach, the effects of the elastic mismatch parameters, the value of the notch angle and the thicknesses of the layers on the stress-intensity factor are carefully quantified and the results are compared with FE solutions. FE results are obtained by applying a combination of analytical and numerical techniques based on the knowledge a priori of the asymptotic stress field for re-entrant corners perpendicular to a bi-material interface and on the use of generalized isoparametric singular finite elements at the notch tip. A good agreement between approximate and analytical/numerical predictions is achieved, showing the effectiveness of this approach.     

Logarithm strain singularity at tip of mode I growing crack in elasticand perfectly-plastic material

Reanalyzed in detail is the stress and strain distribution near the tip of a Mode I steadily growing crack in an elastic and perfectly-plastic material. The crack tip region is divided into five angular sectors, one of which is singular in character and represents a rapid transition zone that becomes a line of strain discontinuity in the limit as crack tip is approached. It is shown for an incompressible material (ν=0.5) under plane strain that the local strain in all the angular sectors possesses the same logarithm singularity, i.e., In r where r is the radial distance measured from the crack tip. This result also prevails for the compressible material ( v < 0.5) and resolves a long standing controversy concerning the strain singularity in the sector just ahead of the crack tip.     

Thermoelastic stress intensity factors for a cracked layer between two different anisotropic solids

Steady-state anisotropic thermoelasticity equations are used to obtain the stress intensity factors for a cracked layer sandwiched between two different anisotropic elastic solids. The anisotropy is assumed to arise from discrete fibers whose orientation could alter with reference to the crack edges. A generalized plane deformation prevails in the dissimilar media domain with a line of discontinuity disturbing a uniform heat flow. The flexibility/stiffness matrix approach is used such that the crack problem reduces to solving two sets of singular integral equations. Numerical values of the crack tip stress-intensity factors are obtained for various crack size, crack location, crack surface insulation, fiber volume fraction and orientation angles. The results are displayed graphically.     

Application of the least-squares method to photoelastic analysis

In this paper, the linear and nonlinear leastsquares methods are developed in matrix notation as solution schemes to determine key parameters from whole-field fringe patterns. Examples of the proposed methods to the determination of the photoelastic-fringe constant from a disk in diametral compression and the opening-mode geometric stress-intensity factor from the photoelastic-fringe loops in the neighborhood of a crack tip are presented. In the latter example, the location of the crack tip is treated as an unknown to be determined from the analysis.     

Scattered-light determination of mode I stress-intensity factors by a fringe gradient independent technique

Integration of the scattered-light stress-optic law and established bending and singular crack-tip relationships yielded new experimental equations for calibration and for the determination of mode I stress-intensity factors which are independent of a stress-fringe gradient. Scattered-light stressoptic coefficients determined from four-point bending tests and an integrated scattered-light bending equation show good agreement with values based on stress-fringe gradients computed with polynomials. Excellent agreement was also shown between mode I stress-intensity factors predicted by the integrated stress-optic equation and analytical solutions available in the literature. Favorable comparisons were also made with predictions based on a polynomial-finite-difference method of determining a stress-fringe gradient. Analyses were limited to flaw geometries and locations where there was minimal rotation of the refraction tensor.     

A numerical approach for a crack problem by Gauss–Chebyshev quadrature

In this paper, a problem of a crack in an orthotropic strip is studied under plane strain conditions. It is assumed that normal displacements and shear stresses do not act on neither of the boundaries of the strip. Cauchy-type singular integral equation for the crack problem is derived by using the theory of plane elasticity and the Fourier transformation technique. A quadrature collocation approach is adopted for the numerical solutions of the singular integral equation. The effect of relative thickness and mechanical properties of strip on Mode I stress intensity factors (SIFs) are examined under different loading conditions. Some sample results are given for SIFs; also, material orthotropy and geometrical effects are discussed in detail.     

Interfacial transient thermal fracture of adhesively bonded dissimilar materials

The effect of a transient thermal load on an interface crack in adhesively bonded dissimilar materials was experimentally studied by using photothermoelasticity. It is determined that the effect of the thermal load is to cause mostly shearing deformations at the crack tip. For two configurations, a horizontal crack (normal to the heat flow direction) and a vertical crack (parallel to the heat flow direction), it is shown that increasing the adhesive thickness results in steady-state and maximum transient strain-energy release rates and stress-intensity factors of smaller magnitudes. It is also found that the ratio of mode I to mode II stressintensity factors for the vertical crack is larger than the one for the horizontal crack.     

Crack growth induced by thermal-mechanical loading

Advanced aerospace structures are often subjected to combined thermal and mechanical loads. The fracture-mechanics behavior of these structures may be altered by the thermal state existing around the crack. Hence, design of critical structural elements requires the knowledge of stress-intensity factors under both thermal and mechanical loads. This paper describes the development of an experimental technique to verity the thermal-stress-intensity factor generated by a temperature gradient around the crack. Thin plate specimens of a model material (AISI-SAE 1095 steel) were used for the heart transfer and thermal-mechanical fracture tests. Rapid thermal loading was achieved using high-intensity focussed infrared spot heaters. These heaters were also used to generate controlled temperature rates for heat-transfer vertification tests. The experimental results indicate that thermal loads can generate stress-intensity factors large enough to induce crack growth. The proposed thermal-stress-intensity factors appear to have the same effect as the conventional mechanical-stress-intensity factors with respect to fracture.     

用光弹性法测定复合应力强度因子

工程结构裂纹尖端应力强度因子(SIF)由于形状、荷载的复杂性及边界条件的不确定性,难以用解析法得到,数值计算也有困难,而光弹性法弥补了上述方法的不足。本文用环氧树脂制作圆轴模型,采用机加工的方法制作圆轴模型裂纹,然后将加载模型进行应力冻结,通过光弹性实验研究分析了圆轴裂纹尖端应力分布。由于带环形裂纹的圆轴在弯扭组合变形时,离中性轴最远的裂纹尖端处于复合裂纹状态,而三维光弹性应力冻结法是测定复杂三维问题复合裂纹的有效方法。本文用双参数法测定I型应力强度因子,用切片逐次削去法测定Ⅲ型应力强度因子,实验误差较小。     

Circular welding problems with a crack

In this paper,the problem of an infinite plane with acircular hole welded by a nearly circular plate with a crackof different material is considered.The problem is tran-sformed into solving a certain boundary value problem ofanalytic functions and then reduced to solving a singularintegral equation along the crack.The formulas and somenumerical results of the factors of stress intensityfor the cases Mode Ⅰ and Mode Ⅱ are obtained at the endof this paper.     

Scattered-light analysis of a surface-flawed plate subjected to cylindrical bending

The scattered-light photoelastic technique was utilized to determine Mode I stress-intensity factors associated with a semi-elliptical surface flaw in a plate subjected to cylindrical bending. Stress-intensity factors were experimentally determined for the point of maximum flaw penetration and the point of intersection of the flaw border with the free surface of the plate. Experimental results compare favorably with those obtained in a three-dimensional finite-element analysis.     

DeterminingK and related stress-field parameters from displacement fields

A general algorithm is presented that computes the stress-field parameters for opening-mode crack problems in a least-squares sense from full-field moiré or speckle-displacement fringe patterns. The algorithm can be used in the presence of rigid-body rotation and does not require absolute fringe numbering. Extensive numerical experiments were conducted with the algorithm to determine the sensitivity of the method to experimental errors. Small random position errors in locating the fringe maxima were found to have a negligible influence on the stress-intensity-factor calculation when the number of data points was about ten times greater than the number of unknown stress-field parameters. It was also found that systematic position errors due to an incorrectly specified crack-tip location could be minimized by assuming various crack-tip locations in the vicinity of the actual crack tip and selecting the best fit results. Bothu andv fields were found to be equally suitable for determination of the stress-intensity factor. Paper was presented at 1983 SESA Spring Meeting held in Cleveland, OH on May 15–19, 1983.