New Concepts on Caustics and Applications

Experimental Mechanics, 1995

This contribution focuses on the theoretical development of the method of caustics and its applicability to anisotropic materials. The method displays its full power when employed in conjunction with interactive numerical data reduction and evaluation procedures. For the analysis the selection of data points along the experimentally recorded caustic curve is done automatically, the selected points are marked on the screen and if necessary interactive correction of the positions is possible. Final proof of the correctness of the result of the automatic data point selection is achieved by comparing for acceptable coincidence the numerically generated caustic determined on the basis of the results of the data-reduction technique with the experimentally recorded caustic.

Procedia Materials Science, 2014

Glassy polycarbonate (PC) is a widely used engineering material in industries, since it has high strength and toughness as well as good transparency. However, these advantages of PC can be suppressed by physical aging, especially its dynamic fracture toughness. In addition, the material properties of PC can be changed dramatically after large plastic compressive deformation, and it can show obvious orthotropic behavior. Here, the combined effect of aging and plastic compressive deformation on dynamic facture of PC was investigated by the optical method of caustics. The dynamic reflective method of caustics for orthotropic materials was developed here to study the dynamic fracture property of PC with plastic deformation. The samples were prepared with different extents of plastic compressive strain up to approximately 50% engineering strain, followed by aging with various aging times up to 300 hours. The shadow spot patterns during the fracture processes were recorded by a high speed camera. Results show that the PC with plastic compressive deformation has different fracture toughness even quite different fracture modes on its different orientations. Aging affects the fracture property of PC with or without plastic flow in similar trend. Under large plastic compressive strain, PC has more strong anisotropy and dynamic fracture tolerance, which has great potential for optimal material design.

Engineering Fracture Mechanics, 1991

Abstrac-A least-squares approach for evaluating stress intensity factors from mixed-mode caustics is presented. The motivation for this work is first explained by illwtrating the limitations of the commonly used method of principal diameters. It is then shown that the least-squares approach can be used successfully for different test cases including numerically and experimentally generated caustics.

Strain, 2010

Some critical points related to the applicability of the optical method of reflected caustics in the case of a plate with a central hole are explored in the present paper. The study is carried out in a combined experimental and numerical procedure: poly-methyl-meth-acrylate plates with a central hole are subjected to uniaxial tension and the diameter of the caustics developed is measured for various load steps from a series of successive photographs with the aid of suitable software. The remote stress is then calculated according to the method of caustics and the results are compared with those of the load cell. In addition, the finite element method is employed for the determination of the stress field and the shape and magnitude of the plastic zones around the hole. Conclusions are drawn concerning the range of the external load for which the results of the method of caustics are valid as a function of the relative dimension of the width of the plate versus the diameter of the hole. In addition, the factors influencing the results of the method are considered and the sensitivity of the results to the even the slightest misalignments of the experimental setup , to the kind of the optical setup preferred and to the slightest deviation from flatness of the lateral faces of the plate is pointed out. This sensitivity of the method was proved to be responsible for discrepancies between theory and experiment, which sometimes exceed 100%.

1995

The Open University's repository of research publications and other research outputs Crack Closure Measurement by the Optical Method of Caustics Thesis How to cite: Wallhead, Ian (1995). Crack Closure Measurement by the Optical Method of Caustics. PhD thesis The Open University. For guidance on citations see FAQs.

In this paper a comprehensive approach to the problem of determining the stress intensity factors in various gear tooth geometries as a function of the crack length using numerical and experimental techniques is presented. The stress field in both uncracked and cracked loaded teeth is calculated using FEA. The crack path (fracture path) is obtained through a series of static experiments and the stress field developed inside uncracked and precracked tooth models is measured with photoelasticity. Finally the stress concentration hence the stress intensity factors are calculated using the stress optical method of caustics.

ABSTRACT Comparative study of stress intensity factor (SIF) for modes I, II and III were investigated for some engineering materials. The materials are alumina, iron, mild steel, low carbon steel, stainless steel, concrete, silica glass and PVC. Special crack-tip element method was implemented to evaluate the stress intensity factor (SIF) for centre, single-edge and doubleedge crack for various values of shear modulus and symmetric crack-tip element size. Different SIF for various modes were compared for these materials and the results from the plots show that low carbon steel for mode III and alumina for mode II have high resistance to crack-growth at 12.43 m MPa and 12.2 m MPa SIF, respectively between the bounds of shear modulus 1.39 and 2.23. Also alumina for mode I exhibited crack growth at 1.42 m MPa SIF and 1.15 bounds of shear modulus. Mode I for mild steel, iron and stainless steel exhibited crack-growth at 0.691 m MPa SIF and 1.08 bounds of shear modulus. Mode I is anomalo...

Engineering Fracture Mechanics, 1982

In the present technical report, an application of the optical method of caustics (Theocaris and Gdoutos [13], Papadopoulos [14]) on spur gear root cracks is presented. The method is used for the experimental determination of the Stress Intensity Factors (SIFs) for different gear tooth geometries (standard involute 20 o spur gears with z=15, 18, 28, 50 teeth and module m=20mm) and varying crack depth. This report begins with an introduction to the method of caustics and with a presentation of the experimental set-up. Several gear tooth test specimens were cut, and in order to determine the crack initiation and propagation, each test specimen was loaded normal to the highest point of its working tooth profile until fracture occurred. In order to verify the repeatability of the above method, several tests were performed. Numerical and experimental methods (photoelasticity) were applied to define the distribution of the maximum shear stress in the interior of the tooth. Cracks of specific depth were manufactured on each specimen and the corresponding stress intensity factors were measured using the method of caustics. The analysis demonstrates that both Mode I (Tensile) and Mode II (Inplane shear) SIFs exist in all crack tips. Inplane shear SIF is about 10% of the Tensile and reaches its maximum value midway to the tooth axis. Considering gear tooth bending as three-point-bending, K I was calculated also using empirical equations (Ewalds and Wauhill [15]), which yield results close to the experimental findings at small crack depths but exhibit considerable difference at medium to large depths. In addition, FEA was used to determine the stress distribution in cracked gear tooth. Experimental stress distribution of cracked tooth was obtained by photoelasticity indicated good agreement with the numerical analysis results.

Journal of the Mechanical Behavior of Biomedical Materials, 2008

Lithium disilicate, leucite and apatite glass-ceramics have become state-of-the-art framework materials in the fabrication of all-ceramic dental restorative materials. The goal of this study was to examine the crack propagation behaviour of these three known glass-ceramic materials after they have been subjected to Vickers indentation and to characterize their crack opening profiles (δ meas vs. (a − r)). For this purpose, various methods of optical examination were employed. Optical microscopy investigations were performed to examine the crack phenomena at a macroscopic level, while high-resolution techniques, such as scanning electron microscopy (SEM) and atomic force microscopy (AFM), were employed to investigate the crack phenomena at a microscopic level. The crack patterns of the three glass-ceramics vary from fairly straightforward to more complex, depending on the amount of residual glass matrix present in the material. The high-strength lithium disilicate crystals feature a high degree of crosslinking, thereby preventing crack propagation. In this material, the crack propagates only through the residual glass phase, which constitutes 30%-40% by volume. Having a high glass content of more than 65% by volume, the leucite and apatite glass-ceramics show far more complex crack patterns. Cracks in the leucite glass-ceramic propagate through both the glass and crystal phase. The apatite glass-ceramic shows a similar crack behaviour as an inorganic-organic composite material containing nanoscale fillers, which are pulled out in the surroundings of the crack tip. The observed crack behaviour and the calculated K tip values of the three types of glassceramics were compared to the K IC values determined according to the SEVNB method.

Corrosion Science, 2007

A fracture mechanics-based novel approach, i.e. circumferential notch tensile (CNT) testing has been employed for determination of threshold stress intensity factor for susceptibility of engineering materials to stress corrosion cracking (K ISCC ) using small specimens. Using CNT technique, K ISCC of a carbon steel at an open circuit potential (E corr ) in 500 g L À1 NaOH at 100 °C was determined to be 42.9 MPa m 1/2 . In order to establish the application of the CNT technique in understanding the mechanistic aspects of caustic cracking as well as for developing guidelines for mitigation, tests have also been performed under the imposed electrochemical potentials. An imposed potential in the active-passive potential regime (E a-p ) caused an extremely rapid failure (than observed at E corr ) whereas, at an imposed potential in the passive region (E p ), the specimen did not fail even after relatively very long exposure time. The fractography of the CNT specimens tested at E corr and E a-p presented evidence of SCC. The study has established the use of experimental CNT testing as a simple, relatively fast and cost-advantageous approach for generating the K ISCC data, which are also consistent with the electrochemical mechanism for caustic cracking.

EPJ Web of Conferences, 2010

Supervising and health monitoring of structures can assess the actual state of existing structures after initial loading or in the state of operation. Structural life management requires the integration of design and analysis, materials behavior and structural testing, as given for several examples. Procedure of survey of structural elements and criteria for their selection must be strongly defined as it is for the offshore gas platforms. Numerical analysis of dynamic loading is shown for the Aeolian vibrations of overhead transmission line conductors. Since the damper's efficiency strongly depends on its position, the procedure of determining the optimum position of the damper is described. The optical method of caustics is established in isotropic materials for determination of the stress intensity factors (SIFs) of the cracks in deformed structures and is advantageously improved for the application to fiberreinforced composites. A procedure for simulation of crack propagation for multiple cracks was introduced and SIFs have been calculated by using finite element method. Crack growth of a single crack or a periodical array of cracks initiated at the stiffeners in a stiffened panel has been investigated.

Experimental Mechanics, 1986

The coherent-light-shadow field formed by crack-tip deformation under Mode I loading is studied theoretically and experimentally. First-order approximation of geometrical optics and higher order expansions are examined in the theoretical development. The wave-optical analysis shows that the interference fringe spacing around the caustic is approximately proportional to K -2/~~ for the ~lear-tip singular field, and, that the peak amplitude of the light-intensity distribution around the caustic is proportional to K 4/'~. The effects of diffraction on the measurement of the caustic diameter are examined in detail. The analysis and accompanying experiments show that the diffraction effect a~one could lead to K estimation errors of +_ 20 percent or more, if the edge of the shadow spot or if the peak-intensity point is used to determine the caustic diameter. An alternate measure of caustic diameter is therefore suggested for practical use. EIfects of the size of the nominal initial curve and crack-tip bluntness on K measurements are included. Finally, possible applications of the coherent-light-shadow spot in fracture mechanics are outlined.

EPJ Web of Conferences, 2010

Regions with high stress gradients represent critical zones of engineering structures such as crack tip or vicinity of the contact zone. The optical method of caustics is one of the few experimental methods which provide applicable results in these locations. This method was originally developed for crack-tip measurements of stress intensity factors and J-integral for isotropic and then for anisotropic materials. Subsequently, it was extended to contact problems where the size and shape of caustics on the screen are related to the amount and the inclination of loading force. Here, the method of caustics is extended to the analysis of contact problems for mechanically anisotropic materials. This makes the caustics method widely applicable to the analysis of any high stress gradient locations in a structure.

Nuclear Engineering and Design, 1993

In this paper, the digital caustic technique was used to determine the transient thermal stress intensity factors (SIFs) of edge-cracked semi-infinite plates subjected to a sudden temperature change on the plate edge. Effects of different crack lengths and orientations on SIFs were studied. By using the self-developed image processing software on a locally supported digital caustic system, caustic patterns were analyzed and SIFs were then obtained. The correlation expressions between the variations of transient thermal SIFs with the time, temperature difference and geometrical parameters of the cracks were obtained by a regression procedure.