PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING STP 536 AMERICAN SOCIETY FOR TESTING AND MATERIALS PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING Proceedings of the 1972 National Symposium on Fracture Mechanics A symposium presented by Committee E-24 on Fracture Testing of Metals, AMERICAN SOCIETY FOR TESTING AND MATERIALS Philadelphia, Pa., 28-30 Aug 1972 ASTM SPECIAL TECHNICAL PUBLICATION 536 J G Kaufman, symposium chairman List price $33.25 04-536000-30 AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa 19103 © by American Society for Testing and Materials 1973 Library of Congress Catalog Card Number: 73-76198 NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication Printed in Baltimore, Md July 1973 Foreword The Symposium on Progress in Flaw Growth and Fracture Toughness Testing was presented 28-30 August 1972, in Philadelphia, Pa and was sponsored by Committee E-24 on Fracture Testing of Metals of the American Society for Testing and Materials J G Kaufman, Aluminum Company of America, presided as the symposium chairman, and the six sessions were presided over by J L Swedlow, H T Corten, J E Srawley, R H Heyer, E T Wessel, and G R Irwin Related ASTM Publications Fracture Toughness Testing at Cryogenic Temperatures, STP 496 (1971), $5.00, 04-496000-30 Probabilistic Aspects of Fatigue, STP 511 (1972), $19.75, 04-511000-30 Fracture Toughness, STP 514 (1972), $18.75, 04-514000-30 Contents Introduction Theory and Stress Analysis Application of Strip Model to Crack Tip Resistance and Crack Closure Phenomena-C L Ho, O Buck, and H L Marcus Crack Tip Resistance and Closure Experimental Procedure Experimental Results and Conclusions 11 13 Some Observations on Fracture Under Combined Loading—G H Lindsey Correlation of Fracture Criteria Example Plexiglass Summary 22 23 26 31 Interaction of Cracks with Rigid Inclusions in Longitudinal Shear Deformation II Further Results—G P Sendeckyj Crack Between Two Rigid Inclusions Pull-Out of Partially Bonded Fiber Debonding of a Rigid Fiber Discussion 32 33 39 40 42 Local Stresses Near Deep Surface Flaws Under Cylindrical Bending Fields— M A Schroedl and C W Smith Analytical Considerations The Experiments Results and Discussion Summary and Conclusions 45 46 51 53 60 Prior to Failure Extension of Flaws in a Rate Sensitive Tresca Solid— M P Wnuk Quasi-Static Extension of the Crack Subcritical Growth 64 65 68 Subcritical Crack Growth Threshold for Fatigue Crack Propagation and the Effects of Load Ratio and Frequency-/? A Schmidt and P C Paris Results on Frequency Effects 79 80 vi CONTENTS The Effect of Load Ratio Load Ratio and Crack Closure A Crack Closure Explanation of Data Trends for Load Ratio Effects Direct Experimental Determination of Kcg Conclusions Overload Effects on Subcritical Crack Growth in Austenitic Manganese Steel-/? C Rice and R I Stephens Nomenclature Material and Test Procedures Test Results Discussion and Results Conclusions Discussion 80 81 83 86 90 95 95 97 101 108 111 113 Effect of Multiple Overloads on Fatigue Crack Propagation in 2024-T3 Aluminum Alloy— V W Trebules, Jr., R Roberts, and R W.Hertzberg Nomenclature Experimental Procedures Testing Procedure Test Results Summary and Interpretation of the Multiple Overload Curve Using Closure Concepts 139 Fatigue-Crack Growth Under Variable-Amplitude Loading in ASTM A514-B Steel-/ M Barsom Material and Experimental Work Results and Discussion General Discussion Summary 147 149 155 161 162 115 115 118 119 120 Temperature and Environment Effect of a Loading Sequence on Threshold Stress Intensity Determination-W C Harrigan, Jr., D L Dull, and L Raymond Experimental Procedure Results Discussion Conclusions 171 172 174 178 180 CONTENTS vii Fatigue and Corrosion-Fatigue Crack Growth of 4340 Steel at Various Yield Strengths-^1 / Itnhof and J M Barsom Materials and Experimental Work Results and Discussion Summary 182 183 192 204 Fatigue Crack Propagation and Fracture Toughness of 5Ni and 9Ni Steels at Cryogenic Temperatures—/? / Bucci, B N Greene and P C Paris Materials Specimens Test Apparatus and Experimental Procedures Experimental Results and Discussion Summary 206 208 211 212 216 226 Methods Some Further Results on J-Integral Analysis and Estimates—/ R Rice, P C Paris, andJ G Merkle The Double Edge Notched Plate in Tension The Internally Notched Plate in Tension The Notched Round Bar in Tension The Remaining Uncracked Ligament Subject to Bending Charpy and "Equivalent Energy" Toughness Measures Estimates of/ From Single Points on Load Displacement Records Summary A Comparison of the J-Integral Fracture Criterion with the Equivalent Energy Concept—/ A Begley and J D Landes J-Integral The Equivalent Energy Concept /Ic and the Equivalent Energy Procedure in the Linear Elastic Range The Lower Bond Equivalent Energy Procedure and Approximate J-Solutions /Ic and Equivalent Energy for a General Load Versus Load Point Displacement Curve Examination of the Condition for Agreement of/jc and the Equivalent Energy Procedure A Graphical Interpretation of the Constant J/A Condition Summary and Conclusions 231 233 234 235 235 237 238 244 246 247 248 250 251 253 255 258 259 viii CONTENTS Analytical Applications of the J-Integral—/ G Merkle Nomenclature Current Approaches to the Development of Elastic-Plastic Fracture Analysis Discussion and Conclusions 264 264 267 279 Experimental Verification of Lower Bond K\c Values Utilizing the Equivalent Energy Concept-C Buchalet and T R Mager Equivalent Energy Method Materials, Specimens, and Test Procedure Method of Analyzing the Test Data Experimental Results Discussion 281 282 285 285 286 291 A Method for Measuring Kic at Very High Strain Rates—D A Shockey and D R Curran A Method for Achieving Very High Crack-Tip Loading Rates Experimental Procedure Results Discussion Summary 297 298 300 303 306 309 Influence of Stress Intensity Level During Fatigue Precracking on Results of Plane-Strain Fracture Toughness Tests—/ G Kaufman and P E Schilling Material Test Procedure Results and Discussion Conclusions 312 313 314 315 319 Materials Influence of Sheet Thickness upon the Fracture Resistance of Structural Aluminum Alloys-A M Sullivan, J Stoop, and C N Freed Experimental Parameters Geometrical Dependencies of Kc Applicability of a Model for the Sheet Thickness Dependency of Kc Thickness Reduction and Crack-Tip Opening Critical Crack Length at Various Levels of Operating Stress Summary 323 324 326 329 330 331 332 CONTENTS ix Plane-Stress Fracture Toughness and Fatigue-Crack Propagation of Aluminum Alloy Wide Panels-Z) Y Wang Test Program Discussion Conclusions 334 336 340 349 Fracture Toughness of Plain and Welded 3-In.-Thick Aluminum Alloy Plate-F G Nelson andJ G Kaufman Material Procedure Discussion of Results Summary and Conclusions 350 351 353 357 374 Dynamic Tear Tests in 3-In.-Thick Aluminum Alloys—R W Judy, Jr., and R J Goode Materials and Procedures Discussion of Results Conclusions 377 378 380 389 Structure of Polymers and Fatigue Crack Propagation-/? W Hertzberg, J A Manson, and W C Wu Experimental Procedure Experimental Results and Discussion Conclusions 391 393 394 401 Effects of Strain Gradients on the Gross Strain Crack Tolerance of A533-B Steel-P N Randall and J G Merkle Procedure Experimental Results Discussion Conclusion 404 405 411 415 419 Applications Applications of the Compliance Concept in Fracture Mechanics— H Okamura, K Watanabe, and T Takano Deformation of a Cracked Member Analysis of Statically Indeterminate Structure Containing a Cracked Member Extension to the Multiple Loads 423 424 427 430 KIEFNER ETAL ON FAILURE STRESS LEVELS OF FLAWS 479 predicted value of Mpap/a value corresponding to the parameter, 12cv —— En 8ceqG2 The propensity for a surface flaw to produce a leak or a rupture in a toughness-dependent situation is still determined by whether or not the resulting through-wall flaw is critical Predicted values of failure stress (pp2) computed for 35 experimental results on the basis of Eq from tensile and impact properties are presented in Table Charpy data for 12 of the 48 experiments were unavailable; hence, no computations were made for these experiments Experiment 48 was deleted from the reliability analysis which follows even though its Charpy shelf energy was known and ap2 was calculable This is because it contained a blunt U-shaped surface flaw rather than a V-shaped flaw as did the other experiments The effect of the U-shaped flaw is illustrated by comparing Experiments 47 and 48 The two experiments are identical except that Experiment 47 contains a standard sharp V-shaped surface flaw The actual failure stress level (ap) for Experiment 47 was 28.2 ksi, whereas for Experiment 48 it was 51.7 ksi The failure stress level predicted for both experiments on the basis of the model (which ignores notch accuity) was 24.7 ksi Hence, the predictive capability of Eq is valid for sharp notches only Blunt flaws such as the U-shaped flaw of Experiment 48 are much more likely to fail on a flow-stress-dependent basis even in ordinarily toughness-dependent situations Reliability of the Equation for Surface Flaws—The degree of reliability of predicting the failure stress levels of surface flaws on the basis of tensile and impact properties using Eq is illustrated in Fig (a probability plot) The ratios of actual failure stress to predicted failure stress ap/ap2 ranged from 0.95 to 1.67 for the 35 experiments considered Disregarding the upward trending higher values of ap/ap2 as in the case of through-wall flaws, one finds that the average of op/ap2 is 109.5 percent with a standard deviation of percent Because the values of observed failure stress which are not closely represented by the suggested probability line of Fig are on the conservative side, the ability of the surface flaw model to predict lower bound values of failure stress is correctly stated by the suggested line and standard deviation As one can verify by inspecting Table the extreme underestimated values of failure stress for surface flaws are associated primarily with either very shallow or very deep flaws (that is, d/t < 0.3 or d/t > 0.7) This is believed to be the result of the inherent stratification of properties in most pipe materials The greatest number of nonmetallic inclusions (which are detrimental to toughness) are located near 480 PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING 99 98 95 90 80 70 60 50 40 30 —T— - — —- "T~ Avero ge 10 >.5 p< Standarc Devia ion _ - rcer t >pe cei t ^ < —— - ;. — —- ^ ^ : _ i • : • ;- — —i 120 —!— K) i ! 140 20 - - ^x i • : — 100 \~~ 2S tone ard De 'iati >ns80 10 20 ! i i 30 40 50 60 70 80 " 90 95 98 99 Percent of Sample FIG ^-Frequency distribution of oplop2- mid-wall thickness Hence, the shallow and deep flaws which are located in tougher zones performed between than one would expect on the basis of small scale tests such as Charpy specimens are significantly affected by the midthickness properties The surface flaw data are plotted on Fig along with the through-wall data on the basis of actual failure stress and the tensile and impact properties of the material Summary In review, it is seen that equations representing the behavior of through-wall and surface flaws in pressurized pipe materials have been developed which are quite satisfactory The equation for through-wall flaws when compared with actual experimental results was found to give predicted failure stress levels just slightly higher than the actual values The ratio of actual failure stress to predicted failure stress was 0.985 with a standard deviation of percent Similarly, the ratio for surface flaws was 1.095 with a standard deviation of percent It is particularly significant that for surface flaws, the most realistic simulator of pipe defects, the model can be expected to predict lower bound values for failure stress over 83 percent of the time Furthermore, it can be KIEFNER ETAL ON FAILURE STRESS LEVELS OF FLAWS 481 expected to predict the failure stress level within 10 percent on the low side of the actual value 98 percent of the time These findings suggest that currently available equations are giving a relatively good mathematical analog to the behavior of defects in pipe materials References [1 ] Kiefner, J F in Fourth Symposium on Line Pipe Research, American Gas Association, Catalog No L30075, Nov 1969 [2] Duffy, A R., McClure, G M., Maxey, W A., and Atterbury, T J., "Study of the Feasibility of Basing Natural Gas Pipeline Operating Pressure on Hydrostatic-Test Pressure," American Gas Association, Catalog No L30050, New York, Feb 1968 [3] Folias, E S., "The Stresses in a Cylindrical Shell Containing an Axial Crack," ARL 64-174, Aerospace Research Laboratories, Oct 1964 [4] Hahn, G T., Sarrate, M., and Rosenfield, A R., International Journal of Fracture Mechanics, Vol 5,1969, pp 187-210 [5] Maxey, W A., Kiefner, J F., Eiber, R J., and Duffy, A R in 77je Fifth National Symposium on Fracture Mechanics, University of Illinois, 1971 [6] Kiefner, J F., Maxey, W A., Eiber, R J., and Duffy, A R., "Recent Research on Flaw Behavior During Hydrostaic Testing," American Gas Association Operating Section Transmission Conference, 1971 STP536-EB/Jul 1973 R.W.Derby1 Experimentally Determined Shape Factors for Deep Part-Through Cracks in a Thick-Walled Pressure Vessel REFERENCE: Derby, R W., "Experimentally Determined Shape Factors for Deep Part-Through Cracks in a Thick-Walled Pressure Vessel," Progress in Flaw Growth and Fracture Toughness Testing, ASTM STP 536, American Society for Testing and Materials, 1973, pp 482491 ABSTRACT: Fracture mechanics shape factors for deep, part-through cracks in thick-walled epoxy pressure vessel were determined experimentally and compared with three theoretical estimates The agreement was especially good for cracks of depth approximately equal to half the wall thickness The fracture toughness, K\c, of the epoxy was measured with Vi-in square beams loaded in four-point bending and was found to be 929 psi \/in7 KEY WORDS: fracture properties, pressure vessels, cracks, mechanical properties Approximately 20 thick-walled, epoxy cylinders were cast as control specimens for a previous investigation [1,2]} At the conclusion of this investigation, eleven of these specimens were used to determine the shape factors for deep, part-through cracks The shape factor, Q is defined by the equation " *- 0) where Ky is the stress intensity, an is the nominal stress, and a is the crack depth For the thick-walled vessels a„ is taken to be the average stress across the section Assistant section chief, Experimental Mechanics Section, Reactor Division, Oak Ridge National Laboratory, Oak Ridge, Tenn 37830 The italic numbers in brackets refer to the list of references appended to this paper 482 Copyright © 1973 by ASTM International www.astm.org DERBY ON EXPERIMENTALLY DETERMINED SHAPE FACTORS 483 There were two reasons for this study The first was to find out if experimentally determined shape factors agree with theoretical predictions If it turned out that no such agreement existed then the use of the same experimental procedures in regions where current theory is inapplicable is not justified The second reason was simply to get experimental data on the influence of a stress-free back surface near the tip of a crack Information of this kind is quite scarce Procedure Pressure vessels were fabricated from the cylindrical bodies by gluing on hemispherical end caps These caps were cast from the same epoxy, Araldite 506, as the cylinders Young's modulus for this epoxy used with Lancast A hardener is 350 000 psi; the tensile strength is 7200 psi The important dimensions of the vessel were as follows: Inside radius Outside radius Wall thickness Length cylindrical section = = = = 2.69 in 3.23 in 0.59 in in Following gluing, the vessels were stress relieved for 24 h by rapidly heating to 150°F and then slowly lowering the temperature to room conditions The part was then inspected with a glassblower's polariscope for residual stresses Next, a slot was machined in the outside wall with a cutting wheel which was 5/8 in wide and 0.010 in thick Two sizes of slots were used For vessels destined for deep cracks the slots were approximately 1.1 in long and 0.2 in deep For vessels destined for shallower cracks the slots were approximately 0.7 in long and 0.1 in deep After the slots had been completed the vessels were pressurized approximately three times per minute It was found that because of self-heating, higher cycling rates would result in very low crack growth rates Extreme care was required to select the correct cyclic pressure If too high, the vessels would burst prematurely; if too low, no crack would grow Another difficulty related to the self-heating was "start-up" brittleness When cyclic pressure was applied to the vessel after a shutdown of more than an hour, overnight for example, the pressure needed to cause failure might be considerably less than what the vessel would tolerate after, say, 30 of operation Hence, the vessels were cycled at reduced pressure whenever the equipment was started up after an extended shutdown Because of the transparency of the epoxy, the approximate size and shape of the growing fatigue cracks could be estimated When the cracks had finally reached a suitable size, the vessel was allowed to stand at room temperature, untouched for many hours, usually overnight Note that this interval put the 484 PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING vessel in a state of start-up brittleness The final step was a burst test in the start-up condition with pressure measured to the nearest psi Following the burst test the remains were cut up into small beams approximately lA in square and in long (The exact number of beams depended on the shape of the fragments, but usually seven or eight were made.) These beams were then slotted and a fatigue crack was grown from the slot The same cyclic rate of loading, cpm, was used as with the vessels The start-up problem for the beams was never completely solved The best solution was, as implied, to keep the machine going continuously The beams required much closer attention than the vessels, because a crack would often grow from an unacceptably small size through to failure in about 20 Once a crack had reached the desired depth, about 40 percent of beam depth, the specimen was removed and, like a pressure vessel, was allowed to remain undisturbed for many hours Finally, the beams were loaded in four-point bending to failure Given the load at failure, the crack depth, and the geometry of the beam, the fracture toughness, A^c, was calculated using a widely accepted procedure[3] Returning to the pressure vessels, it was then possible to solve Eq for C, the shape factor The nominal stress term was taken asPr/T, where P is pressure, r is the inside radius, and T is wall thickness The crack depth, a, was measured with a steel rule or a comparator to one hundredth of an inch Since Ki = Kic at failure, the value of K\c determined in the beam tests was substituted into Eq forifi Results The raw data for the vessel burst tests are presented in Table The actual shape of the cracks can be seen in Figs and The specimen shown in these pictures were cut from the remains of each vessel after the burst test The starter notches are on the outside surfaces and can be identified because they are darker than the actual fatigue cracks The distance shown as surface length in Table is the actual length of the starter notch along the outside surface of the vessel This distance was used later as the major axis of a semiellipse Note that for the shallow notches the fatigue crack does not grow out of the complete length of the starter notch In both figures a small, white paper wedge was placed on each specimen to show the exact point at which failure occurred The experimental data presented in Table were used with the procedure described in the previous section to calculate a shape factor for each crack The results are shown in the Experiment column in Table Paris and Sih[4] have suggested that the stress intensity for deep cracks can be determined from DERBY ON EXPERIMENTALLY DETERMINED SHAPE FACTORS TABLE 1-Rawdata Vessel Number Failure Pressure, psi Crack Depth,0 in Surface Length,6 in 104 103 102 105 108 99 106 110 109 112 114 158 175 180 180 180 184 194 275 285 300 320 0.52 0.48 0.44 0.43 0.41 0.45 0.42 0.24 0.27 0.29 0.21 1.15 1.12 1.14 1.14 1.25 1.13 1.14 0.75 0.65 0.65 0.67 a in Eq ' 2b, major axis of ellipse (Eq 2) FIG -First series of part-thro ugh cracks in a pressure vessel wall 485 486 PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING FIG 2-Second series of part-through cracks in a pressure vessel wall Note that the cracks in this series are considerably deeper than those in the first series TABLE 2- Comparison between experiment and theory Vessel Number a/T a/b 104 103 102 105 108 99 106 110 109 112 114 0.88 0.81 0.75 0.73 0.69 0.76 0.71 0.41 0.46 0.49 0.36 0.90 0.86 0.77 0.75 0.66 0.80 0.74 0.72 0.83 0.89 0.63 C Paris-Sih[i] Equation 1.32 1.12 1.05 1.03 1.05 1.06 1.02 0.821 0.781 0.765 0.853 C Experiment C Irwin[4] Equation C Kobayashi Moss[5] 0.999 0.939 0.954 0.965 0.988 0.922 0.906 0.845 0.769 0.705 0.776 0.735 0.753 0.787 0.794 0.836 0.777 0.801 0.810 0.763 0.739 0.849 0.772 0.765 0.794 0.765 0.837 0.780 0.801 0.777 0.722 0.699 0.819 DERBY ON EXPERIMENTALLY DETERMINED SHAPE FACTORS 487 where 0 is the elliptic integral: By grouping the appropriate terms it can be seen that the shape factor as previously defined is c -['* »('-f)][f •"#]/•* (4 > The fourth column in Table is simply a tabulation of the values obtained by substituting the appropriate values into Eq The fifth column in Table is a tabulation of the values of shape factor as determined from the Irwin[5] equation l.lff„v^ f) Thus C, according to Eq 5, is C = l.l/*0 (6) (The value of C in Eq as in Eq is strictly speaking only applicable at the very deepest part of the crack.) Kobayashi and Moss [6] have presented a series of curves for an elastic magnification factor, Me, as a function of crack depth divided by thickness According to the notation of these authors Ki - -^r~ (7) where Me is the product of the front and back surface magnification factors Using the notation of this paper C = Mel0 (8) The last column in Table shows the values of C calculated according to Eq The predicted shape factors tabulated in Table are shown in Fig Inspection of the figure suggests that for very deep cracks, such as those shown in Fig 2, the Paris-Sih equation results in shape factors slightly too high and the Irwin equation in values a little too low The Paris-Sih values, however, are 488 PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING 1.4 1 1 ORNL-DWG 71-14089 1 EXPERIMENT = PREDICTIOh 1.2 - u 1.0 < H UJ or tu Q X ° s 0.8 / Sao - 5° m - 0.6 - - - o PREDICT ON BY PARIS-SIH EQ._ o PREDICT ON BY IRWIN EQ 0.4 0.2 -/ 1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 C, PREDICTED FIG 3-Comparisons between experimentally determined shape factors and the predictions of two theories somewhat closer to the experimentally determined values Furthermore, the Paris-Sih values are generally within the 10 percent limits suggested by these authors The values of C based on Ref and Eq represent little or no improvement over Eq For smaller cracks, such as those shown in Fig 1, both theories give an excellent prediction The result was particularly gratifying in view of the difficulties involved in controlling scatter Discussion The reliability of the experimental method of determining shape factors described in this paper depends on controlling the scatter in the K\c determinations To control scatter the specimens must be precisely machined and symetrically loaded without friction Furthermore, the environment must be carefully controlled In our first determinations of K\c, which were made for another investigation, 49 specimens from 19 vessels were tested The cracks were grown under mineral oil The average Kic for these specimens was 922 psi\/irL with a standard deviation of 95 and a range from 760 to 1195 (A histogram of these results appears in Ref 2.) For nine specimens from four vessels which were cycled in air and then tested, the average was 929 psi VhT with a standard DERBY ON EXPERIMENTALLY DETERMINED SHAPE FACTORS 489 deviation of 89 and a range from 806 to 1061 It should be added that the original intention was to test at least several dozen specimens with air-grown cracks Unfortunately, nine specimens failed prematurely at one time in the fatigue machine during start-up A similar number had to be rejected because of eccentric crack growth Hence, the value of 929 psi yj\n as determined from the nine good specimens was used to calculate the experimental shape factors One other point about the interpretation of the results should be mentioned; the cracks are not true ellipses Note especially the regions in Fig where the cracks have not grown out of the complete notch It is, however, unlikely that the idealization of the cracks has a significant effect on the usefulness of the results The reader should look again at the white paper wedges in the photographs It is noteworthy that no crack failed at the exact middle This is particularly surprising in view of the fact that the cracks are projecting into a region of increasing stress A detailed study of this observation was beyond the scope of the project as were several other interesting phenomena Every time the pressure cycling device was turned off after some hours of operation a distinct mark was left on the fatigue crack surface These marks are not always visible with the naked eye, but are always found easily with an optical microscope under low magnification With good lighting the lines can be photographed with a studio camera as in Fig Equally interesting is the fracture surface In the 60 or so vessels tested to failure the pattern was always the same HG -Enlarged view of a fatigue crack and fracture surface Note the beach markings on the fatigue crack See text for discussion of fracture surface 490 PROGRESS IN FLAW GROWTH AND FRACTURE TOUGHNESS TESTING In the region of initiation the surface is very shiny Under the microscope, tiny lines can be found pointing to the exact point of failure As the distance from this point increases, the lines become more and more coarse until they can be seen by the naked eye (see Fig 4, particularly just to the right of the crack and also above the label) Just beyond the region of radiating lines the fracture surface becomes very coarse or knurled This region is clearly seen on the far right of Figs and It is usually only about Yi in long Beyond the knurled area the fracture surface becomes very smooth and shiny This last region is not shown in any of the figures Summary and Conclusions Eleven, notched, epoxy pressure vessels were fatigued to produce deep, part-through cracks The vessels were then burst From the burst pressure, material properties, and the geometry of the vessel a fracture-mechanics shape factor was inferred for each crack The results were compared with three theoretical estimates For cracks approximately half as deep as the vessel wall, the relatively simple relationship due to Irwin [5] and shown in Eq was found to be satisfactory For deeper cracks, say about three quarters as deep as the wall, the shape factor implied by Paris and Sih[4] and shown in Eq was found to be higher than those found by experiment; whereas, those calculated by the Irwin equation were low Thus, for practical calculations, the Irwin equation should be used for shallow cracks because of its convenience, and the Paris-Sih equation should be used for the deep cracks because of its conservatism Finally, the shape factors implied by Eq should probably not be used since they are neither convenient nor conservative The interpolation required between the curves presented in Ref makes the use of Eq quite inconvenient Finally, the shape factors implied by Eq represent little improvement over those of Eq and thus appear to be nonconservative for the range of deep cracks covered in this study Acknowledgments The author thanks H T Corten and J G Merkle for their advise and encouragement The photographs of cracks are the work of Ward Bandy The careful laboratory work of T A King is gratefully acknowledged Research was sponsored by the U S Atomic Energy Commission under contract with the Union Carbide Corporation References [1] Abbatiello, A A., Derby, R W., and King, T A., "Producing Epoxy-Model Pressure Vessels for Fracture Tests," Experimental Mechanics, Vol 11, No 1, 1971 [2] Derby, R W., "Shape Factors for Nozzle Corner Cracks," Experimental Mechanics, Vol 12, No 12,1972 [3] Brown, W F., Jr and Srawley, J E in Plane Strain Fracture Toughness Testing of High DERBY ON EXPERIMENTALLY DETERMINED SHAPE FACTORS 491 Strength Materials, ASTM STP 410, American Society for Testing and Materials, Philadelphia, Pa., 1967 [4] Paris, P C and Sih, G C in Stress Analysis of Cracks, ASTM STP 381, American Society for Testing and Materials, Philadelphia, Pa., 1965, pp 51-52 [5] Irwin, G R., Journal of Applied Mechanics, American Society of Mechanical Engineers, Dec 1962, pp 651-654 [6] Kobayashi, A S and Moss, W L., "Stress Intensity Magnification Factors for Surface-Flawed Tension Plate and Notched Round Tension Bar," Proceedings, 2nd International Conference on Fracture, Brighton, England, 1969