Comparison of the Optical Techniques of Caustic and Photoelasticity as Applied to Fracture

Photoelastic and caustic experiments are conducted to obtain stress intensity factor, K, for both stationary and moving cracks. For the stationary crack the values of K are compared with the available theoretical and numerical solutions. Results show that the accuracy varies with the location of the crack tip for both the methods. Six parameter analysis of the photoelastic data gives better values as compared to the caustic results which in turn are better than the values obtained by three parameter photoelastic analysis. Dynamic photoelastic experiments are conducted with SEN, DCB and DCB/SEN specimens. The data obtained from these experiments namely the stress intensity factor and crack velocity, is compared with existing results and also with the values obtained from dynamic caustic experiment with SEN specimen. significantly lower. of crack velocity Values from caustic analysis are Stress intensity factor as a function is plotted and the results show a dependence on specimen geometry for cracks moving at high velocities.

Stress intensity factor is one of the most important parameters that describes the stress field around a crack tip [3]. It is of both theoretical and practical interest.
Practical because most of the fracture criteria are based on it. Even the fatigue failure depends on the instantaneous values of K [4]. Theoretical interest arises from the fact that dynamic fracture characterization may be possible in terms of the stress intensity factor and crack velocity for a given material [5,6].
The value of K is currently obtained by investigators using two different optical techniques, the method of caustics [1] and the method of photoelasticity [2].
Till now photoelasticity has been the most widely used experimental technique for fracture related studies. In recent years the technique of caustics has been used by some investigators but the stress intensity factor-crack velocity data obtained through it is not seen to tally with the existing photoelastic data [6]. Kalthoff [6], who has used the method of caustics, and Kobayashi,et al. [7],who have used photoelasticity, have measured such data and conclude that the K-v-curves are not unique but depend on specimen geometry. Dally et al. [8] also performed such experiments and argue that the K-v -curves are unique for a material and the variation in the data is due to the variation in experimental conditions and analysis procedure. The controversies yet remain unresolved. The scatter in the data obtained from these is large. It is partially because of the nature of the problem and partially because of the techniques being used. So there is a need to establish a confidence in experimental methods employed for such studies.
This study critically evaluates the optical techniques of caustic [1] and photoelasticity [2] as applied to fracture. Post [10] and Wells and Post [11] in the early 50's were the first investigators to show the application of photoelasticity to fracture mechanics. Irwin [12], in a discussion to reference [11], showed that the stress Rosakis with Freund [34] also studied the effect of the crack tip plasticity on the determination of dynamic stress intensity factors and found that the error introduced through the neglect of plasticity effects in the analysis of data will be small as long as the distance from the crack tip to the initial curve ahead of the tip is more than about twice the plastic zone size. They also found that the error introduced through the neglect of inertial effects will be small as long as the crack speed is less than about 20 percent of the longitudinal wave speed.
Effect of higher order stress terms on mode-I caustics in birefringent materials has been recently studied by Phillips and Sanford [35].  [36].
In this project the two techniques have been studied and the results compared. The dynamic experiment data generated has been used to verify the K-v relationship described above.  figure 2 and figure 3.
For photoelastic experiments two circular polarizers are kept on either side of the specimen. As an example, light from the spark SG1 passes through a field lens, the first polarizer, the specimen, the second polarizer and the second field lens onto the camera lens L1.  Like wise, all twenty gaps fire. The light from the spark gap is let out of the camera by fiber optics.

Control Circuit
The control circuit is used to initiate the firing sequence at a required delay after the dynamic event has started. A schematic of the circuit is shown in figure   6 [44]. When the conductive paint on the specimen is broken by the moving crack, a 20volt pulse is emitted which  8 where N is the total number of the data points considered.
The above equation can be put in the form where Gi.
( Gt ) : The correction factors are given by The iterative procedure is employed till the series constants are determined to obtain a close fit of the function G to the N data points.  · 11) d GtK ::: .L (lli d\.llt. In six parameter model the stresses are represented as the sum of two series with three terms each. The coefficients of the six terms are the six parameters to be evaluated. These coefficients happen to include KI and ~ox which are of primary interest. A short description of the model is given here. Irwin [19] has shown, that for a crack tip stress pattern translating in the positive x-direction at a fixed speed, stresses at a point (x,y) can be expressed as 23 V: 11 :r i [('-t1s;-s~) ReZ, _QReZt1 t.n -(, ... !i:n + ) ( $,t -S11) .1 S.i.. Now from equations(4.24) and (4.25) we get The first three terms in each of the series Z and Y are included in the analysis. So Z1 and Z2 can be expressed as follows: A .,..Jr.z.
where Ao..f27r = KI, the stress intensity factor and remote stress ~ox = 2Bo. Due to a tensile load, its initial thickness h and its refractive index n are reduced to h-Ah and n-An, respectively. Then for normally incident light, As is given as ('4. 16) The correlation between the change An of the refractive index and the principal stresses ~1,a-2 and ~3 in the plate 28 is described by Maxwell-Neumann's law: For plane stress conditions ~3=0 and due to Hooke's Where V is Poisson's ratio and E is Young's modulus. Then, where As 1 and .C.S2 are the path length changes for light polarized parallel to the principal srtesses '1"1 and ~2, respectively. It can be written in a convenient form as where the positive (negative) sign of ~ relates to As1 (~s2), and c.: For a crack under mode I loading conditions in linear elastic materials the stress distribution in the vicinity of the crack tip is given by Sneddon and Williams [45]: Where m is a scale factor. In present work parallel incident light is used, therefore m=1. Using equations The principal stresses ~1,~2 can be determined from the equations(4.45) using the relations For a crack propagating with a crack velocity v, the near field stress distribution is given in (46] as 1. (4·s-4c) x,y now represents a moving co-ordinate system with its origin in the crack tip. The co-ordinates r1,e1 and r2,e2 are connected with this system by the relations ;'= h11SiYIO-hch~1' 1 F G 1 (5,,8) ,,m,.
where the abbreviations used are: with where C1 and C2 are functions of s1 and e, and influence the shape of the caustic. In analogy to equation ( These experiments are discussed below in the above order. Again as for the case of static isochromatic data various least square fits are provided and KI is plotted against l/w in figure 44. The values are listed in table 6.

Dynamic Isochromatic Experiments
Experiments with three specimen geometries were performed in an attempt to obtain a wide range of crack velocities and stress intensity factors ranging from the crack arrest value to crack branching value. Analysis was done with both three and six parameter models. Loading was such that mode II conditions did not exist and three parameter analysis was effectively two parameter analysis.

Dynamic Caustic Experiment
The specimen geometry, material and the loading were the same as for the case of SEN dynamic isochromatic experiment.The purpose was to compare the results with the ones obtained using photoelasticity, so the conditions were kept identical. The crack was again initiated at a load of 4.8kN.
The experimental setup is shown in figure 3. In caustic experiment the camera is not focused on the specimen but on a reference plane away from it. For this reason the crack tip is not visible but has to be calculated by measuring the · distance to the end of shadow pattern and subtracting the value k*D from it as described in [1]. D is the caustic diameter and k is a constant given in table 11.
The crack length vs time plot is shown in figure 61.   fig.1 and in fig.66. A plot of K vs v for the values KI3 and KI6 given in fig.67 and fig.68 shows that at Homalite-100 [48]. From the split in the plateau region it can be concluded that K does depend upon the specimen geometry at higher velocities while the stem is independent.
But the split observed by Kalthoff [6] is not seen.                          s...