Measurement of mode I stress-intensity factors by scattered-light photoelasticity

The feasibility of using the scattered-light technique to determine Mode I stress-intensity factors is demonstrated for the case of an edge-cracked beam subjected to pure bending. Photoelastic-fringe data were utilized to obtain an expression for the fringe gradient in the singular region surrounding the crack tip. Mode I stress-intensity factors were then determined by relating the fringe gradient to the local stresses in the singular region and extrapolating these results to the crack tip. Experimental and analytical results showed good agreement and the technique is suggested for application to three-dimensional fracture-mechanics problems.     

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.     

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.     

Mixed-mode crack-tip deformations studied using a modified flexural specimen and coherent gradient sensing

An optical mapping of deformation fields and evaluation of fracture parameters near mixed-mode cracks in homogeneous specimens under elastostatic conditions is undertaken. A modified edge notched flexural geometry is used in the study and its ability in providing a relatively wide range of mode mixities is demonstrated. A full-field, optical shearing interferometry called ‘coherent gradient sensing’ (CGS) is used in the study. Crack-tip parameters such as stress-intensity factors, mode mixity and energy-release rate are measured from the interference patterns. The patterns are analyzed using Williams' mixed-mode, asymptotic expansion field. An expression for energy-release rate for the specimen is also derived using beam theory. The theoretical stress-intensity factors are then obtained using a mode-partitioning method based on moment decomposition. Experimental measurements and theoretical predictions are found to be in good agreement. Limitations of the mode-partitioning method used in the investigation are also pointed out.     

Photoelastic studies of the two-dimensional dynamic stress-optic law

Studies of the two-dimensional dynamic stress-optic law were made using Castolite circular disks under diametral impact load. The dynamic stress-fringe relationship of Castolite was found to be approximately linear. The dynamic fringe values were slightly lower than the static values. In four of the five specimens used the maximum difference was 8.2 percent. Previous work on the dynamic stress-optic calibration was limited to cases of one-dimensional stress.A new dual-beam cathode ray oscilloscope and two dualtrace plug-in preamplifiers were adapted for this work. Taking advantage of symmetry, three strain components at an arbitrary point in the disk and the birefringence at the symmetrical point were recorded in one photograph during a single impact.was formerly associated with International Business Machines Corp., Endicott, N. Y.Paper was presented at 1962 SESA Annual Meeting held in Milwaukee, Wis., on October 24–26.     

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。     

云纹干涉法研究复合材料构件的应力强度因子

本文采用贴片云纹干涉法，测试并研究了正交异性板纯弯试件及拉伸试件的应力强度因子。文中给出了复合材料纤维加强方向不同时位移与应力强度因子的关系式，通过测试得出受力模型的全场位移，给出云纹图，进而由裂纹尖端位移场推算出应力强度因子Ｋ１及Ｋ值。试验结果与有限元计算结果吻合良好。     

Photovisco-elasto-plastic analysis tested on polyester by the scattered-light method

A three-dimensional photovisco-elasto-plastic model considering the strain rate effect was investigated by the scattered-light method using polyester as a model material. To examine the mechanical and optical properties of the material, tension and torsion tests were carried out on cylindrical specimens under various strain rates at 30°C. The effects of strain rate on the stress-strain relation and scattered-light fringe appearance were evaluated. The equivalent shearing stress-strain relation can be approximated by the Ramberg-Osgood equation with rate-dependent modulus and yield stress. The fringe gradient, when normalized by a rate-dependent yield gradient, can be related to an equivalent strain in the same form regardless of the strain rate. The strain rate can be evaluated from the measurement of the rate of increase of the fringe gradient. Hence, the relation between the fringe gradient and its rate of increase was derived as a function of strain rate. Finally, a method is proposed for the estimation of the visco-elasto-plastic stress and strain in a three-dimensional specimen from the measurement of only the fringe gradient and its rate of increase. The method was successfully applied not only to uniaxial tension but also to pure torsion.     

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.     

An experimental weight function for stress-intensity-factor calibrations

This paper describes a set of experiments conducted to demonstrate application of weight-function methods to experimental stress-intensity-factor calibrations. The weight-function method allows stress-intensity-factor and crack-surface-displacement information obtained for one loading to be generalized in a form which allows direct computation of stress-intensity factors for other load configurations applied to the crack geometry under consideration. The specific results described here demonstrate that experiments with edgecracked strips loaded in four-point bending also provide stress-intensity factors for remote lension and three-point bend-load applications.     

Compressional waves in fluid-saturated porous solid containing a penny-shaped crack

Diffraction of normal compression waves by a penny-shaped crack in a fluid-saturated porous medium is investigated. Two wave types are considered, namely, compressional wave of the first kind, and the second kind. The former, also known as fast wave, propagates primarily through the solid, whereas the latter or slow wave, propagates mainly in the fluid. Each wave propagates in the medium along with induced wave of the same type in the companion constituent of the material. Application of Biot’s theory in conjunction with integral transform technique reduces the problem to a mixed boundary-value problem whose solution is in turn governed by a Fredholm integral equation of the second kind. Near-field and far-field solutions are obtained in terms of the dynamic stress-intensity factor and the scattering cross section, respectively. They are of particular importance to the linear elastic fracture mechanics (LEFM) and in the scattering theory of elastic waves. The mode I stress-intensity factors are computed numerically for a set of selected material property values, and shown graphically for various mass density and viscosity-to-permeability ratios. The obtained results reveal significant impact of the presence of pore fluid upon the stress-intensity factors, both magnitudes and frequencies at their peak values. The influence of the fluid is also observed from the calculated scattering cross sections of the scattered far-field. Accuracy of the present solution procedure is verified by comparing the numerical results with existing results in the limiting case of dry elastic materials.     

Experimentally determined stress-intensity factors for single-edge-crack round bars loaded in bending

Dimensionless stress-intensity factors were determined for single-edge-crack solid and hollow round bars loaded in bending. These factors were calculated from experimental compliance (inverse slope of load-displacement curve) measurements made on round bars loaded in three-point bending. The compliance specimens had span to diameter ratios of 6.67 and 3.33, and measurements were made over a range of dimensionless crack lengths from 0.002 to 0.70. The tests were made using 3-in. (76-mm) and 6-in. (152-mm) solid and hollow round bars notched on one side; the hollow bars had an inner to outer diameter ratio of 0.33. A comparison was made with data in the literature for rectangular bars; for ana/D of 0.0001, the dimensionless stress-intensity factor for a solid round bar is 1.3 vs. 2.0 for a rectangular bar.     

Stress-optic law in a single crystal and its application to photo-anisotropic elasticity

A general stress-optic law in a plate made of a single crystal with birefringence is developed, the plate has an arbitrary crystallographic direction. From the general stressoptic law, a condition for obtaining stress distributions in the plate under a plane stress state is derived. Some optical and mechanical properties when the plate is used as a photoanisotropic model are also explained. Experiments on silicon beams in pure bending are performed by using an infrared photoelastic method. Experimental results show that the stress-optic law is valid. The optical and mechanical properties of silicon beams are shown in tables.     

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.     

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.     

功能梯度矩形板的三维弹性分析

将功能梯度三维矩形板的位移变量按双三角级数展开，以弹性力学的平衡方程为基础．导出位移形式的平衡方程。引入状态空间方法，以三个位移分量及位移分量的一阶导数为状态变量，建立状态方程。考虑四边简支的边界条件，由状态方程得到了功能梯度三维矩形板的静力弯曲问题和自由振动问题的精确解。由给出的均匀矩形板自由振动问题的计算结果表明．与已有的理论解以及有限元方法的计算结果相吻合。假设功能梯度三维矩形板的材料常数沿板的厚度方向按照指数函数的规律变化．进一步给出了功能梯度三维矩形板的自由振动问题和静力弯曲问题的算例分析，并讨论了材料性质的梯度变化对板的动力响应和静力响应的影响。     

Scattered-light flow-optic relations adaptable to three-dimensional flow birefringence

The scattered-light method has been studied with the aim of developing a flow-optic relation which can be used for the analysis of three-dimensional flow problems of Newtonian fluids utilizing flow birefringence. A set of flow-optic relations which potentially can be adapted to three-dimensional scattered-light birefringent analysis has been developed on a phenomenological basis for the aqueous suspensions of Milling Yellow. Good agreement with theoretical solutions was obtained when these relations were applied to flows through channels of three different geometries.     

Diagrams of critical equilibrium for brittle bodies with sharp flaws

Certain forms of the stress-intensity factors close to the tips of sharp flaws (plane problem) are used as the basis of a method for plotting critical equilibrium diagrams for brittle bodies with flaws in the form of pointed cavity-cracks [5]. Concrete examples are discussed, mainly in the context of such diagrams, for a brittle body weakened by a circular cavity flaw with a crack leaving the edge of the flaw. Determination of the stress-intensity factors for this problem is based on approximate solution of an integral equation by the method of collocations. Plots of some familiar diagrams are also analyzed.Translated from Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 98–104, May–June, 1970.     

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.     

Photo-orthotropic-elasticity

A method of producing transparent model materials for photo-orthotropic-elastic studies is presented. This material fabricated from glass fibers and a modified polyester matrix exhibits continuous relatively smooth fringe patterns which are linearly related to the state of stress. As such, the heterogenous material can be treated as a homogenous medium with orthotropic properties. Three photoelastic constantsf _L ,f _T andf _LT are necessary to describe the photoelastic response of the orthotropic materials to a general state of stress. Methods are established for predicting these photoelastic constants from the properties of the constituents. These methods are based on stress proportioning between the fibers and the matrix and upon the linear summation of the retardation from each constituent. The relations derived forf _L ,f _T andf _LT were verified experimentally and found to be in close agreement with measured values. A stress-optic law is derived on the basis of stress partitioning between the two constituents in a unidirectionally fiber-reinforced laminate. The adequacy of this stress-optic relation is confirmed by experimental verification. Comparison of this stress-optic relation with the expression advanced by Pih and Knight shows the validity of their initial concepts but the inadequacy of their partitioning functions. Detailed comparison of the stress-optic law with the analog relation proposed by Sampson shows excellent agreement. Indeed, the use of Sampson's stress-optic law is recommended and the law based on stress partitioning is to be considered as a fundamental theoretical proof of the Sampson relation. Finally, the applicability of Sampson's stress-optic law to bidirectionally reinforced materials was confirmed with a thorough experimental verification.