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.     

Photoelastic analysis of a thick plate with an elliptical hole subjected to simple out-of-plane bending

A three-dimensional photoelastic analysis using the stress freezing and slicing techniques was employed to study the stress distribution and the stress-concentration factors around an elliptical hole in a plate of finite thickness. The plate was subjected to simple out-of-plane bending. A special bending device was designed to produce uniform bending moment at the two opposite free edges of the plate. Six plates with various elliptical holes were studied. The stress variation across the plate thickness at the periphery of the elliptical hole was also investigated. The experimental results were correlated with the existing theoretical solutions.     

Determination of stress-intensity factors for cracks in tubes under torsion

An experimental investigation by two-dimensional photoelastic technique is carried out to study the stress distribution and to determine the stress-intensity factors for arbitrarily oriented cracks in thin cylindrical shells subjected to torsion. A new method is employed to evaluate the pure and mixed-mode SIF's.     

Experimental determination of stress-intensity factors using caustics and photoelasticity

The optical method of caustics has been used with considerable success in recent years for determining stress-intensity factors in both static and dynamic problems. However the midplane analysis explaining the formation of transmission caustics has certain approximations that need to be examined. In this paper it is demonstrated that the midplane analysis is in good agreement with the numerical solution of the exact geometrical optical equations for mapping the light-ray path in a cracked plate. Since both these analyses are obtained by imposing a two-dimensional crack-tip stress field the sensitivity of the method to the deviations from the imposed stress field is examined next. The implications of this examination on the photoelastic technique are then discussed.     

Stress-intensity distributions for corner cracks emanating from open holes in plates of finite width

A series of frozen stress photoelastic tests is carried out in the present investigation. Linear Elastic Fracture Mechanics is used to analyze the problem of a part-through corner crack at an open hole in a plate of finite width loaded in tension. The photoelastic modeling capability of three-dimensional subcritical crack growth problems is assessed. This is achieved by comparing monotonically grown flaw shapes in epoxy models with crack profiles relative to fatigue crack propagation tests in a different material. Photoelastic stress-intensity factor distributions are checked against numerical results obtained for quarter elliptical geometries. The dependence of stress intensity factors on flaw shape is also discussed.     

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.     

Stress-intensity factors in plates with a partially patched central crack

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of patches is related to the reduction they cause in the stress-intensity factor of the crack. Hence, an accurate evaluation of SIF in terms of various parameters is required for reliable patch design.In this paper, the influence of patch parameters on the opening-mode stress-intensity factor for a plate with a central crack is studied by employing transmission photoelasticity. Cracked plates made of photoelastic material are patched on one side as well as both sides by epoxy, phenolic and E glass-epoxy composite materials. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of 50 magnification, converted into a polariscope. Irwin's method with extrapolation is employed to compute the stress-intensity factor from photoelastic data. The reduction in the stress-intensity factor is presented in graphic form as a function of pathch parameters, namely stiffness, width and length.     

Photoelastic determination of stress-intensity factors

The increasing number of analytical and numerical solutions for the crack-tip stress-intensity factor has greatly widened the scope of application of linear elastic fracture-mechanics technology. Experimental verification of a particular solution by elastic stress analysis is often a necessary supplement to provide the criteria for proper application to actual design problems. In this paper, it is shown that the photoelastic technique can be used to obtain rather good estimates of the stress-intensity factor for various specimen geometries and loading conditions. Treated are the following cases: wedge-opening load specimen, several notched rotating-disk configurations, and a notched pressure vessel. A sharp crack is simulated by a relatively narrow notch terminating in a root radius of 0.010 in or less. Stress distributions along the section of symmetry ahead of the notch tip are obtained using three-dimensional frozen-stress photoelasticity. The results are used to determine the stress-intensity factor, cK _I , by three methods. Two of these are based on Irwin's expressions for the elastic stress field at the tip cf a crack, and the other is a result of Neuber's hyperbolic-notch analysis. Agreement, with available analytical solutions is good.     

Single-strand strainwire technique: Comparison with existing methods and a proposed photostrain technique

This paper is the third of three papers evaluating a refined internal strainwire technique. This final paper evaluates the technique by comparing it with two elastic solutions, with a photoelastic solution, and with a new proposed photostrain technique. The problem chosen as the basis of comparison was a plane-stress problem of a plate with a circular hole under uniform tension. The proposed technique is experimental in nature and combines parts of the results of a photoelastic solution with those yielded by a three-wire internal strain-gage-rosette analysis to completely fix the state of stress in the model. The scientific techniques used to compare the three-wire strain technique and photostrain technique are as follows: two elastic solutions, one evaluated at a point and one arrived at by integrating the stress functions over a finite length; a finite-element solution; a photoelastic analysis using the shear-difference technique to separate the principal stresses; and a three-wire-rosette analysis. A comparison is made of the values of principal stresses yielded by these methods.     

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。     

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.     

Experimental analysis of an arbitrarily inclined semiinfinite crack terminated at the bimaterial interface

In this paper, the digital photoelastic technique was employed to investigate the effect of different material combinations and different crack inclination angles on the stress-intensity factors (SIFs). To produce a true bimaterial plate, the two component materials were naturally adhered together by a special casting procedure. The experimental results show that dimensionless combined SIF increases with increasingG ₁/G ₂ (or crack inclination angles) for different crack inclination angles (orG ₁/G ₂'s).     

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved. The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poisson's ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions. The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.     

刚性夹杂角点处奇异场的数值分析及双夹杂间的相互影响

本文采用编制的有限元程序求解了无限大板中含有单个具有角点的刚性夹杂在无限远处均布外载作用下夹杂角点附近的位移场，并结合Ｉｎｓｈｉｋａｗａ的工作，求得了相应的应力强度因子。在此基础上，着重分析了两个刚性夹杂间的相互作用，得到了双夹杂左右角点附近的ＫⅠ，Ⅱ值随夹寻间距离改变而变化的规律。     

Stress distribution in the vicinity of slender notches having arbitrary shapes

It was observed, by a photoelastic investigation of the stress distribution around slender notches having arbitrary configurations, that the symmetricantisymmetric and asymmetric nature of the configuration rather than the overall geometry controls the stress distribution around the notch tip. Since the peak stresses are found to be on the conservative side for symmetric configurations, it is suggested that the available theoretical expressions for the stress-intensity factor of an equivalent circular-arc crack be utilized for further work on crack-propagation studies.     

An edge-cracked Mode II fracture specimen

A proposed edge-cracked Mode II fracture specimen is analyzed using an extended photoelastic-numerical procedure. It is shown that the Mode II stress-intensity factor is significantly higher for the longest edge-crack considered and the Mode I deformation is negligible, demonstrating the merits of this specimen for Mode II fracture-toughness testing.     

Dynamic photoelastic studies of fracture

Dynamic characterization of brittle fracture is possible by relating the instantaneous stress-intensity factorK(t) to the velocity of propagation of the crack. High-speed photographic systems are employed with photoelastic methods to obtain a sequence of isochromatic-fringe patterns representing the state of stress associated with the propagating crack. Methods for determiningK(t) from these isochromatic patterns are reviewed.     

Stress intensity factors of an oblique edge crack subjected to normal and shear tractions

Stress intensity factors (SIFs) were obtained for an oblique crack under normal and shear traction and remote extension loads. The oblique crack was modeled as the pseudodislocation. The stress field due to tractions was solved by the Flamant solution. The SIR of Mode I and Mode II (K_Iand K_II) were then obtained. Finite element analysis was performed with ABAQUS and compared with the analytical solutions. The analytical solutions were in good agreement with the results of FEM. From investigating SIFs and their ranges, the following results were obtained. The growth rate of an oblique edge crack decreased due to the reduction in the SIF ranges. The crack driving force depended on the obliquity, the normal traction and the ratio of crack to traction length. The peak value of shear traction was found as a key parameter to accelerate the crack growth.     

Stress-concentration factors for fatigue configurations

Stress concentrations in thin-plate configurations commonly used in fatigue bending tests were determined by photoelastic means. The test configurations were rectangular and tapered plates with a centrally located hole. These configurations were machined from plates constructed by cementing together two sheets of similar photoelastic material. A reflective-type cement was used. In this manner, photoelastic measurements for the bending case were indicative of the average between maximum fiber stress and the stress at the reflective surface. The maximum fiber stress was then computed assuming that plane sections remain plane. Although bending was of primary concern, tension tests were also performed. The measured stress concentrations are compared with available analytical solutions. In the case of bending, the results are compared with infinite-plate solutions since the perforated finite-width plate bending problem has not been solved.     

A critical review of methods for determining stress-intensity factors from isochromatic fringes

Two-parameter methods of fracture analysis for determining the stress-intensity factor from photoelastic isochromatic-fringe data were critically reviewed. The methods of Irwin, Bradley and Kobayashi, and Smith were developed in detail and differences in the three approaches were noted. Theoretical fringe loops were generated for a crack of length 2a in a semi-infinite plate with biaxial loading. These fringe loops were used to compare the three analysis methods and to determine the accuracy of each method. All three methods give a close estimate of the stress-intensity factor, with the Bradley-Kobayashi differencing procedure providing the most precise estimate ofK. However, if measurement errors become excessive (larger than 2 percent) the differencing procedure magnifies these errors and the original method proposed by Irwin is the recommended approach. The two-parameter methods can be employed to determineK to within ±5 percent, provided the angle of tilt of the isochromatic-fringe loop is 73 ≤θ _m < 139 deg. Ifθ _m is outside this range, the two-parameter methods should not be employed.