Investigation of Dynamic Fracture Using Strain Gages and Photoelastic Coatings

This study is divided into two parts namely, the use of strain gages and photoelastic coatings to investigate dynamic fracture. In the first part use of electrical resistance strain gages to determine instantaneous stress intensity factors for running cracK is presented. Dynamic strain field equations are developed using the Westergaard's stress function approach. These equations are then analyzed to study the effect of various parameters li-Ke cracK velocity, distance from the cracK tip, etc. on the dynamic strain profile. Finally, a series of experiments was conducted with two different geometries on brittle birefringent polyester, Homalite 100 to determine dynamic stress intensity factors with strain gages. The K-values thus determined were compared with similar results obtained from the method of photoelasticity in transmission mode. In the second part of this thesis, mirror 1 iKe reflective photoelastic coatings were used to study dynamic fracture in brittle structural metals. Dynamic fracture experiments are conducted on heat-treated 4340 Steel and 7075-T6 Aluminum with face grooved SEN specimen geometry. The mirror liKe reflective coating used in conjunction with


approach.
These equations are then analyzed to study the effect of various parameters li-Ke cracK velocity, distance from the cracK tip, etc. on the dynamic strain profile.                 Isochromatic fringe loops obtained with photoelastic coatings on 7075-T6 aluminum specimen.
cracK length, a/W, as a function of time, t, for 4340 steel specimen. stress intensity factor Kid as a function of crack length to width ratio, a/W and time , t for 4340 steel specimen. cracK length, a/W, as a function of time, t , for 7075-T6 aluminum specimen.
Stress intensity factor Krd as a function of crack length to width ratio, a/W and time, t for 7075-T6 aluminum specimen.
Strain Gages on SEN 4340 steel specimen.

LIST OF TABLES
Orientation, a, as a function of Poisson's ratio, v.
Where u and v are the displacements in the x and y directions and c the crack velocity.

· AVERAGING EFFECTS DUE TO FINITE SIZE OF THE STRAIN GAGE 18
Since the strain gage has a £inite size i t averages the strain over its grid size area. This average strain is not equal to the strain at the grid geometric center. The error due to this averaging effect is calculated by considering a strain gage with grid size (lXb) positioned at height, H, above the crack propagation path and oriented at an angle a = 120. 6 deg. Now the peak strain at the geometric center of the gage, (eGC)P, is calculated using To evaluate the average strain the strain gage grid is divided into a matrix of 100x100 points and strain at each point is evaluated using equation (3.6) .
From this the average peak strain (eGAV)P is computed. This strain is infact the peak strain recorded by the strain gage in an experiment . Since (eGAV)P, instead of (eGC)P is used for the evaluation of K-value, the error in peak strain is ((eGC)P-(eGAV)P)/(eaC)P. The results are presented in Fig. 8 which shows the percentage error due to averaging effect as a function of gage grid length for the gage grid aspect ratio, The fracture specimen geometries used in this study are shown in Fig . 10 and 11. These model geometries were selected so as to collect data over a wide range of crack representing the stress 'field which is related to the stress intensity 'factor. The great advantage of the method over other experimental techniques is that it provides a direct measure of the crack tip field and the corresponding crack speed without concern of the geometry of the specimen, the boundry conditions, or the complex stress wave pattern in the bulk of the specimen.

REVIEW OF RELATED RESEARCH ON PHOTOELASTIC COATINGS
The concept of birefringent coatings was first introduced by Mesnager (25) was examined by Oppel (26] in  where Gm is the far field stress a is the crack length W is the specimen width f(a/W) is the back surface correction factor (38) F is the correction factor for the groove To account for the face grooves Kid-value is multiplied by the factor Fas given in eq. (11) The dimensions of the specimen used for steel and aluminum are shown in Fig. 20 and Fig.21 respectively. Steel specimens were machined out of 1/4" thick hot-rolled 4340steel. They were given the following heat-treatment: 20 min. at 1550·F, oil quenched to 150·F, air cooled to room tempered at 650·F for 1% hr followed by temperature, and straightening on a screw press and sand blasting. The hardness thus achieved was close to Rc49. The initial crack was a vertical mill cut sharpened by a broaching tool, with cracK length to width ratio of 0.25. Aluminum specimens were cut out from 1/4" thick 7075-T6 aluminum sheet. The In the fringe patterns obtained from aluminum models, the effect of the approachin~ front bound.ry can be clearly seen.
The crack length to width ratio, a/W, as a function of time is plotted in Fig. 24  Since the polycarbonate coating (PS-1) has a strain limit of 10 percent, wh1ch is higher than the strain limit of the steel as well as the aluminum, a rough estimate of the plastic zone width in fractured steel and aluminum Instantaneous stress intensity factor were calculated from the Peak strain using eq. (3. 8). The results obtained are shown in Fig. 27  a-K curve can be obtained for different materials using photoelastic coatings and the method of strain gages .
It must be pointed out that the method of strain gages will need many strain gages on the model for accurate crack velocity measurements.
4 . coefficient of higher order terms in the series representation of strain can be evaluated using the method of strain gages by mounting more than one strain gage . At least one strain gage should be at an angle alpha for which the contribution OY the second term goes to zero. This gage will identify the crack tip position. A set of simultaneous equations will be obtained to be solved for the evaluation of the coefficients in the series.  Instrum. , Tokyo, Vo 1. 52, pp. 17-40, 1958 . Kawata , K., Takeda,N., andHashimoto,S., "Photoelasticcoating Analysis of Dynamic Stress Concentration in Composite Strips," Expt. Mech., vol. 24, No. 4, Dec . 1984, pp. 316-327         ...  .....