Optical Method Of Caustics Research Articles

An experimental study of the dynamic features of shadow areas of caustics in response to loading/unloading fracture

Using a plexiglass sample and by means of real-time holographic interferometry and shadow optical method of caustics, the different features of dynamic variation in stress (strain) field, plastic area and nucleation zone (shadow area) when the sample fractures during loading (loading-fracture) and unloading (unloading-fracture) are studied visually. The results show that the strain nuclei (zones with dense fringes) appear first at the tips of prefabricated cracks at low stress, and then the shadow areas of caustics form with the increase of load. These nuclei and shadow areas can become larger, or smaller, when the process of loading, or unloading, goes on. When the stress is kept within a certain range, the shadow areas of caustics can become larger and smaller alternatively with repeated loading and unloading (cyclic loading). However, when loading and unloading at high stress, in particular when the macrofracture is about to appear, the variations of the shadow areas of caustics are irreversible and quite different. The shadow areas of caustics expand rapidly at an increasing speed when loading-fracture appears. In contrast, the shadow areas of caustics expand at a lower speed when unloading-fracture appears; besides, there is a circular shadow in front of the sharp-angle shaped area.

523 熱応力場におけるコースティック特性の基礎的検討 : 軸対称一次元応力場の例

We applied shadow optical method of caustics to measure the thermal stress distribution around a cylindrical heater inserted in a thin disk of acrylic. The caustics pattern has a circular shape centered to the heater. Heating rate range is 0.25,0.5,0.75 and 1℃/sec. Caustics pattern appears at a certain stress value increase in diameter size up to reach the steady state as well increasing in brightness. A strong relation between caustics pattern and radial stress peak had been found. For that, Caustics experimental method could be used to show thermal stress distribution.

A combination optical method of lateral shearing interferometry and caustics

A novel experimental technique is presented that combines the optical method of caustics and the full-field lateral shearing interferometer of coherent gradient sensing (CGS) in one setup. Collimated light transmitted through a deformed specimen is separated into two legs. One is processed by the lateral shearing interferometer and is recombined with the other on a single image plane. By adjusting the optical path length of each leg, a combination lateral shearing interferogram/caustic image is generated. When this technique is applied to a fracture specimen, information about the stress intensity factor can be obtained from the caustic and the CGS interference fringes for exactly the same deformation field. This allows for a direct comparison between the two methods when investigating phenomena such asK-dominance, three-dimensional deformation and so on. In this paper, the technique is presented in detail, and its feasibility is tested by application to mode I and mixed-mode crack tip deformation fields.

A general method for automated analysis of caustics

In most published work on the optical method of caustics, experimental results were obtained by manually measuring some characteristic dimensions of the shadow pattern and, therefore, used only a limited amount of data from the caustic. However, some previous work has been done using digital image processing and light intensity plots combined with least-squares techniques to analyse the shape of a caustic obtained from a particular problem. All of these methods have been developed to solve only one specific problem. This paper highlights the essential guidelines of an automated method, which has the novelty of generalising the whole analysis, such that only the parametric equations of a particular problem are required to solve it. In the proposed method the image is digitised, the central line of the caustic pattern is identified, and the parameters in the mapping equation of the caustic are determined. The method has been validated, and the aim of this paper is to describe the key features of the method, i.e. the optical arrangement, digital image processing, and numerical analysis.

A study of crack closure using the optical method of caustics and consequences for the use of Δ Keff as a fatigue crack driving force

Using the optical method of caustics, measurements of the crack-tip stress field have been used to experimentally determine stress intensity factors in 2024-T3 centre-cracked panel aluminium alloy specimens during fatigue loading. The aim of the work was to directly, remotely and non-destructively measure crack-tip shielding as a result of closure, and so determine Δ K eff, under conditions of both constant and variable amplitude loading. Results show that this novel technique clearly detects crack closure under steady-state constant amplitude loading. However, although transient changes induced by, say, tensile overloads modify the extent of closure and so have a dramatic effect on crack growth rate, they do not change the crack-tip stress field in the K-dominant zone. Consequently, it is concluded that the successful application of Δ K eff as the fatigue crack driving force can only be justified on phenomenological rather than physical grounds.

コースティックス法による直交異方性ＣＦＲＰ積層材の応力拡大係数の測定

The optical method of caustics is a useful technique for determining the stress intensity factor K. The method has been mainly applied to isotropic materials. For anisotropic materials, however, the method has not been much studied. In this paper, the method of caustics is examined for a highly orthotropic unidirectionally reinforced carbonepoxy composite under mode I loading by using a coating technique, and the results are compared with those of finite element analysis. As a result, it was found possible to apply the method of caustics to orthotropic CFRP laminate material.

A practical guide to the measurement of the elastic stress intensity factor in engineering materials by the method of caustics

The optical method of caustics is an experimental technique which, particularly when used in reflection, has recently found increasing applicability to the fracture mechanics of engineering materials. Having been widely applied to stress intensity factor measurement, it has found a niche in areas where an analytical prediction has been impossible or in need of experimental verification, such as in dynamic fracture. This paper provides an accessible introduction to the method, covering its historical background and theoretical basis, together with a comprehensive guide to, and review of, its practical application to materials such as aluminium and steel.

Experimental and modelling studies of the shadow optical method of caustics

Direct measurement of the complex stress conditions at the tip of a crack are difficult if possible to achieve. A useful indirect technique is the shadow optical method of caustics which obtains a measurement of crack tip conditions from the depressions formed on the surface of the material at the free ends of the crack front. This caustics technique has been conveniently simulated by a model that can be hosted on a Personal Computer (PC) of a type frequently used in laboratories to capture and process experimental data. Both caustics experimental results and data from the PC model are compared with theoretical predictions of crack tip stress conditions. This study is pan of an investigation into the possible wider use of the caustics technique to research crack tip conditions in joints and other situations where direct measurements are not feasible.

Theoretical simulations of a propagating crack subjected to in-plane stress wave loading by caustic method

The optical method of caustics for measuring the dynamic stress intensity factor in a transient process is investigated in this study. The transient full-field solutions of a propagating crack contained in an infinite medium subjected to step-stress wave and ramp-stress wave loadings are used to establish the exact equations of the initial and caustic curves. The results of the stress intensity factor obtained from the caustic method are compared with theoretical predictions and some experiments. The results demonstrate that a significant deviation can occur in the determination of the dynamic stress intensity factor from shadow spot measurements. The factors, such as screen distance, magnitude of loading, crack speed and rising time which can influence the accuracy of the experimental measurements are discussed in detail. In addition, the valid region of the dynamic stress singular field for the propagating crack is discussed in detail and it gives a better understanding of the appropriate region of measurements for investigators.

Study of the 3-D region around a crack tip by caustics

The result of the present investigation are of particular significance in the study of problems of stress corrosion crack growth by the optical method of caustics

The method of caustics in conjunction with the method of birefringent coatings for the solution of fracture mechanics problems

Optical methods of stress analysis including photoelasticity, moirr, holographic and moire interferometry and caustics have extensively been used in fracture mechanics problems. Among them, the optical method of caustics is gaining ground in the determination of stress intensity factors in crack problems under static and dynamic loading. In this method [ 1,2], the area in the vicinity of the crack tip is illuminated by a collimated light and the reflected or transmitted rays from an envelope in space. When this envelope is cut by a reference plane, a highly illuminated curve, the caustic, is formed. By measuring a diameter of the caustic the stress intensity factor is determined. The caustic is the image of the circumference of a circle on the specimen centered at the crack tip, which is called the initial curve. In the application of the method care should be taken to ensure that the initial curve lies in the plane-stress region, so that the plane-stress assumption made in developing the evaluation equations of caustic is valid. The implication of this assumption regarding the selection of material, load level, specimen size and optical arrangement has been discussed by Konsta-Gdoutos and Gdoutos [3-5]. In the beginning, the method of caustics was applied to transparent specimens and later on its use was extended to metals by Theorcaris and Gdoutos [6,7]. The optical quality of the specimens used in the method of caustics should meet high standards. Specimens used in transmission arrangements must have constant thickness and density. On the other hand, specimens used in reflection arrangements must have an optically planar surface of high reflectivity at least in the neighborhood of the crack tip where the caustic is generated. In metal specimens mirrored surfaces are prepared by grinding, lapping and polishing their front surface. Preparation of mirror-like surfaces of specimens used in the method of caustics constitutes not only an elaborate task but difficulties arise in a number of cases. A characteristic example is bone, which due to its spongy nature cannot be adequately polished to the point that Snell's reflection law applies. Analogous problems are encountered in fiber or particulate composite materials. Another class of problems in which the method of caustics cannot be

Measurements of Stress Intensity Factors of an Interface Crack Under Mixed Mode Loading

The optical method of caustics has been utilised to measure both the stress intensity factor for a crack lying along the interface of an aluminium/epoxy bimaterial specimen, and the mode mixity arising from the difference in the elastic properties across the interface. Measurements were carried out by using a novel modification to the method whereby caustics are produced and measured from both sides of the specimen, so compensating automatically for the distortion induced in the specimen due to misaligned loading fixtures. A flat reflective surface across the interface was obtained by adhering a reflective coating to the specimen. Verification that this coating does not affect measurement accuracy was obtained by comparing stress intensity factors measured from coated and uncoated monolithic aluminium specimens where good agreement was found to exist between both measurements.

Recent developments of fracture mechanics in Greece

To somewhat broaden the scope covered in companion papers of this special issue, which covers fracture research currently being reported in Greece, the author has briefly reviewed associated developments in the region, although rather than being comprehensive, it reflects mainly his own interests. Topics covered include: new trends in the optical method of caustics, kinking and temperature distribution in dynamic crack problems, fatigue crack growth studies, partially bonded inclusions in elastic media, local and global instability in cracked bodies, fracture behavior of composite materials and transient elastodynamic problems.

The investigation of the interfacial crack by the optical method

The possibility of using the optical method of caustics in analysis of the interfacial crack is investigated in this study. The explicit full field solution for applying arbitrary point loadings on interfacial crack faces is used in analyzing this problem. The size of the yielding zone and the pattern of the caustics in the oscillatory and singular regions are studied by numerical simulation. The oscillatory region is found to be extremely small for most material combinations. The size of the yielding zone predicted by the Von Mises criteria is significantly larger than that of the oscillatory region. It is also very interesting to find that the patterns of the caustics inside the oscillatory region are similar to that in the singular field.

High accuracy stress intensity factor measurement using the optical method of reflected caustics

A comprehensive guide to the application of the optical method of caustics to opaque engineering materials is provided. Practical recommendations are given which facilitate the measurement of stress intensity factors at considerably higher accuracies than is currently achieved and also permit measurements at stress intensities as low as 1 MPaρ/m. Also included is a novel modification to the method whereby simultaneous measurement from both sides of the specimen automatically compensates for specimen aplanarity induced by a marginally misaligned loading fixture which produces errors of which most researchers may not be aware.

A Study of Fatigue Crack Propagation in a Glassy Polymer by the Optical Method of Caustics

A Study of Fatigue Crack Propagation in a Glassy Polymer by the Optical Method of Caustics

Solution of stress-corrosion crack problems by the method of caustics

Since its appearance more than 20 years ago, the optical method of caustics has been used extensively for the solution of a host of static and dynamic problems in fracture mechanics. In the present work, the applicability of the method of caustics to the solution of stress-corrosion crack problems is briefly reviewed. As was recently pointed out, the changing state of stress in the neighbourhood of the crack tip from plane strain at the tip to plane stress at a critical distance from the tip should seriously be taken into account in the evaluation of the optical patterns. This condition is even more critical in stress-corrosion crack problems, due to the rapidly changing specimen thickness because of the corrosive environment. We provide a thorough discussion of the limits of applicability of the method of caustics in stress-corrosion crack problems.

Study of Fatigue Internal Damage of Aluminum Alloy by Means of Caustics

The influence of the fatigue on the local internal Damage at crack tip area in a cracked plate of Aluminium alloy was studied by using the optical method of caustics. The variation of the modulus of elasticity and the Damage factor at the the crack-tip were estimated.

Optimisation of the optical method of caustics for the determination of stress intensity factors

A detailed guide to the practical application of the optical method of caustics to stress intensity factor measurement is provided which should prove invaluable to the experimenter using this technique. A thorough error analysis is given highlighting a collimated incident beam arrangement as the optimum configuration for generating caustic measurements. Other sources of experimental error which are not immediately apparent, such as the quality of the incident beam, specimen surface preparation and the alignment of the specimen loading fixture are also considered.

Use of the shadow optical method of caustics to predict fatigue crack growth in compression: Leftheris, B. P. and Papazian, J. M. J. Eng. Mater. Technol. (Trans. ASME) (Oct. 1992) 114 (4) 399–405

Cyanovirin-N (CVN) is a novel cyanobacterial protein that selectively binds with nanomolar affinities the mammalian oligosaccharides Man8 and Man9. Consequently, CVN potently blocks HIV entry through highly avid carbohydrate-mediated interactions with the HIV-envelope glycoprotein gp120, and is under preclinical investigation as an anti-HIV microbicide. CVN contains two non-overlapping carbohydrate-binding sites that bind the disaccharide Manα(1-2)Manα (which represents the terminal disaccharide of all three arms of Man9) with low to sub-micromolar affinities. The solution structure of a 1:2 CVN:Manα(1-2)Manα complex revealed that CVN recognizes the stacked conformation of Manα(1-2)Manα through a deep hydrophilic-binding pocket on one side of the protein (site 2) and a semi-circular cleft on the other (site 1). With the prominent exception of the C1 hydroxyl group of the reducing mannopyranose ring, the bound disaccharide is positioned so that each hydroxyl group is involved in a direct or water-mediated hydrogen bond to the polar or charged side-chains comprising the binding pocket. Thus, to determine whether the next-most reducing mannopyranose ring will augment CVN affinity and selectivity, we have characterized by NMR and ITC the binding of CVN to three synthetic trisaccharides representing the full-length D1, D2 and D3 arms of mammalian oligomannosides. Our findings demonstrate that site 1 is able to discriminate between the three related trisaccharides methyl Manα(1-2)Manα(1-2)Man, methyl Manα(1-2)Manα(1-3)Man and methyl Manα(1-2)Manα(1-6)Man with remarkable selectivity, and binds these trisaccharides with KA values ranging from 8.1×103 M−1 to 6.6×106 M−1. Site 2 is less selective in that it binds all three trisaccharides with similar KA values ranging from 1.7 to 3.7(±0.3)×105 M−1, but overall binds these trimannosides with higher affinities than site 1. The diversity of pathogenic organisms that display α(1-2)-linked mannosides on their cell surfaces suggests a broad defensive role for CVN in its cyanobacterial source.