~ fiflwj This is to certify that the thesis entitled CTOD AND GOD MEASUREMENTS ON COMPACT TENSION SPECIMENS OF DIFFERENT THICKNESSES presented by SONNUEK PALEEBUT has been accepted towards fulfillment of the requirements for 7)}, 6 degree inW / 4'71 4 if J Major professor Date ZM7 / 8; 1975 / 0-7639 CTOD AND COD MEASUREMENTS ON COMPACT TENSION SPECIMENS OF DIFFERENT THICKNESSES BY Somnuek Paleebut A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1978 ABSTRACT CTOD AND COD MEASUREMENTS ON COMPACT TENSION SPECIMENS OF DIFFERENT THICKNESSES BY Somnuek Paleebut The occurrence of yielding at the crack tip has suggested that the value of crack opening displacement at a fracture is a measure of toughness analogous to K In C' this report the IDG technique was used to measure crack opening displacement near the tip of a crack. The measure- ment near the crack tip may be a more sensitive measure of ”pap-in” than crack Opening displacement (COD) at the mouth of a notch. A critical value of the crack tip opening displacement, (CTOD), can be used to calculate K The experimental CTOD value can be compared with IC' simple plasticity theory. A method is described for measuring COD at the mouth of the notch and the CTOD at a distance 100 microns from the crack tip on precracked compact tension specimens of aluminum alloy 7075-T651 and 2024-T351. A clip gage was used to measure COD across the notch following the method outlined in ASTM standard E399-74. The IDG Somnuek Paleebut technique was used to measure the crack Opening displace- ment at the crack tip. ‘The experimental CTOD values were in agreement with the CTOD values calculated from the Dugdale model for displacement measured 100 microns behind the crack tip. The relation between CTOD and COD did not depend upon specimen thickness but depended upon material. The IDG technique can identify pop-in as well as clip gage, but it has no advantage. The IDG technique can measure very small crack tip opening displacements (less than 10 microns total). The measured KIC values obtained from critical CTOD are in agreement with those obtained from the ASTM standard E399-74 only for standard compact tension speci- mens 25.4 mm in thickness. ACKNOWLEDGMENTS I would like to give grateful thanks to the Royal Thai Air Force which sponsored my graduate program. I wish to express my sincerest appreciations and gratitude to my thesis advisor, Dr. William N. Sharpe, Jr., for his helpful information and many valuables guidances during the course of this work. Thanks are also due to Dr. G. H. Martin, my academic advisor, for his helpful suggestions in my M.S. program, and to Dr. N. Altiero for his suggestions during the course of this investigation. Finally, I wish to thank my wife for her patience and encouragement. ii LIST OF TABLES. LIST OF FIGURES Chapter 1 1.1. 1.2. 1.3. 1.4. Chapter 2 MN 0 O NH Chapter 3 3.1. 3.2. 3.3. 3.4. TABLE OF CONTENTS INTRODUCTION. . . Purpose and Motivation. KIC Measurement and POp-In CTOD. Organization of Thesis. MATERIAL SPECIFICATION AND PREPARATION . . . Material Specification. Specimen Preparation 2.2.1. 2.2.2. EXPERIMENTAL TECHNIQUE SPECIMEN Fatigue Pre-cracking. Indentation Application. Testing Machine . . Crack Opening Displacement (COD) Measurement and KIC Determination Interferometric Displacement Gage (IDG) 3.3.1. 3.3.2. Crack Tip Opening Displacement (CTOD) Basic of the IDG . The IDG Technique. Measurement . . . 3.4.1. 3.4.2. Measurement of CTOD Using Stripchart Recorder . Measurement of CTOD Using a Minicomputer iii Page vi QUINN l'-' 10 10 13 13 17 20 20 23 26 26 29 30 30 33 Chapter 4 EXPERIMENTAL RESULTS. 4.1. 4.2. Aluminum . 4. 3. Chapter 5 5.1. 5.2. 5.2.1. Chapter 6 CONCLUSIONS- REFERENCES. CRACK TIP OPENING DISPLACEMENT Comparison of CTOD Measurement with Dugdale Model and Dis- cussion. iv Discussion of Results. Crack Tip Plastic Zone The Dugdale Model . The Relationship between CTOD and COD Results and Discussion Effect of Specimen Thickness on Pop-in . Comparison of Crack Tip Displacement for Test Specimen 7075-T651 and 2024-T351 Page 39 52 55 55 59 59 62 65 68 70 78 81 LIST OF TABLES Table Page 4.1. Experimental Data. . . . . . . . . . 53 LIST OF FIGURES Figure Page 1.1. Principal type of load-displacement records. . . . . . . . . . . . . 4 1.2 Typical load-displacement record illus- trating Pop-in behavior . . . . . . . 6 2.1 Stress-strain curve for the test specimen of 7075-T651 aluminum . . . . . . . . 11 2.2 Stress-strain curve for the test specimen Of 2024-T351 aluminllm o o o o O o o o 12 2.3a Dimensions of the compact tension specimen . . . . . . . . . . . . 14 2.3b Envelope for crack starter notches and fatigue crack. . . . . . . . . . . 14 2.4 Fatigue loading schedule . . . . . . . 16 2.5 Two indentations 100 microns apart placed across a fatigue crack. . . . . . . . 19 3.1a Overall view of the experimental setup . . 21 3.1b Specimen setup on the Instron Testing MaChine . . . . . . . . . . . . . 22 3.2 Double-cantilever clip-in displacement gage. . . . z . . . . . .' . . . 24 3.3 Schematic of the Interferometric Displace- ment Gage . . . . . . . . . . . . 27 3.4 Schematic of the IDG and recording teChnique . . . . . . . . . . . . 31 3.5 Typical stripchart recorder of fringe motion . . . . . . . . . . . . . 32 vi Figure 3.6 3.7 3.8 3.9 4.2 4.6 4.9 Typical load versus time from Instron Chart Paper. . . . . . . . . Typical load-displacement curve Stripchart Recorder . . . . from Schematic of one channel of the minicomputer- controlled fringe measuring system . . . . Typical load-displacement curve computer. . . . . . . . Comparison of load-displacement crack tip and mouth of notch of 7075-T651 aluminum SN-3l,32 . Comparison of load-displacement crack tip and mouth of notch of 7075-T651 aluminum SN-27,28 . Comparison of load-displacement crack tip and mouth of notch of 7075-T651 aluminum SN-23,24 . Comparison of load-displacement crack tip and mouth of notch of 7075-T65l aluminum SN-l9,20 . Comparison of loadrdisplacement crack tip and mouth of notch of 2024-T351 aluminum SN-15,16 . Comparison of load-displacement crack tip and mouth of notch of 2024-T351 aluminum SN-ll,12 . Comparison of load-displacement crack tip and mouth of notch of 2024-T351 aluminum SN-7,8 . . Comparison of load-displacement crack tip and mouth of notch of 2024-T351 aluminum SN-3,4 . . from Mini- curves at test specimen curves at test specimen curves at test specimen curves at test specimen curves at test specimen curves at test specimen curves at test specimen curves at test specimen Load-displacement curves at crack tip of test specimen 7075-T651 aluminum SN-27 that were obtained from minicomputer vii Page 34 35 36 38 40 41 42 43 44 45 46 47 48 Figure 4.10 5.5 5.6 5.7 5.8 5.9 Page Load-displacement curve at crack tip of test specimen 7075-T651 aluminum SN-23 that was obtained from minicomputer. . . . . . . 49 Load displacement curves at crack tip of test specimen 7075-T651 aluminum SN-19,20 that were obtained from minicomputer . . . 50 Load displacement curves at crack tip of test specimen 2024-T351 aluminum SN-3,4 that were obtained from minicomputer . . . . . 51 The photograph of test specimen 7075-T651 aluminum when the crack was extended . . . 56 The photograph of test specimen 2024-T351 aluminum when the crack was extended . . . 57 Details of crack border repositioning to account for crack tip plastic zone . . . . 61 Dugdale Strip Yield Model . . . . . . . 63 Comparison of load-displacement curves at crack tip of specimen 7075-T651 aluminum With Dugdale MOdel . . . . . . . O . 66 Comparison of load-displacement curves at crack tip of specimen 2024-T351 aluminum with Dugdale Model . . . . . . . . . 67 Schematic showing calculation of Rotational Constant. . . . . . . . . . . . . 69 The relation between CTOD and COD of test specimen 7075-T651 aluminum . . . . . . 71 The relation between CTOD and COD of test specimen 2024- T351 aluminum . . . . . . 72 Comparision of CTOD versus COD curves of test specimen 7075-T651 and 2024-T351 aluminum. . . . . . . . . . . . . 73 Position of center of rotation versus CTOD of test specimen 7075-T651 aluminum. . . . 74 viii Figure 5.10 5.11 Page Position of center of rotation versus CTOD of test specimen 2024-T351 aluminum. . . . 75 Comparison of Rotational Constant versus CTOD curves of test specimen 7075-T651 and 2024-T351 alminuln o o o o o o o o o 76 ix CHAPTER 1 INTRODUCTION Fracture toughness testing requires that the dimensions of the specimen be large enough to produce plane strain at the point of crack initiation and catas- trophic growth. For ductile materials, this requires excessively large specimens. There are two possible solutions here; either develop a more sensitive technique to measure the "pop-in" associated with unstable crack growth or use another criterion. A displacement measure- ment near the crack tip may be a more sensitive measure of "pop-in." A critical value of the crack tip opening dis- placement (CTOD) has been proposed as a toughness criterion. Both of these require measurement of the displacement very near the tip of a fatigue crack. This thesis describes the results of laser-based displacement measurements near the crack tip and comparison with clip gage displacement measurements at the mouth of a crack (COD) in compact tension specimens. 1.1. Purpose and Motivation The purposes of this research are to a) Determine if a sensitive measurement of CTOD is a better indicator of KIC than the COD procedure given in ASTM E399-74. b) Compare the measured CTOD with those predicted by simple plasticity theories. The key element in this work is the interferometric displacement gage (IDG) which is capable of measuring dis- placements on the order of microns at positions as close as 100 microns to the tip of a crack. 1.2. KIC Measurement and Pop-In The fracture toughness of material has been studied for several years, and ASTM committee E-24 has made several recommendations concerning the types of test that are most reliable for determining the fracture toughness of metal (1,3). These have evolved through several stages: consideration was given first to the center-notch panel and thickness dependent mixed-mode fracture (1), then the single-edge-notched tensile specimen (2,3) and thickness- invariant plane strain fracture and the notched bend specimen. The final result is the standard method for plane-strain fracture toughness testing of metallic materials, ASTM E399-74. The method involves tension or three-point bend testing of notched specimens that have been precracked in fatigue. Load versus displacement across the notch at the specimen edge is recorded auto- graphically. The general requirement can be divided into three main categories: 1) specimen geometric requirements, 2) pre—cracking requirements, 3) testing requirements. For a valid KIC determination all specimens used must meet the following requirements: the plastic zone size must be small with respect to the thickness, as indicated by the limita- tions that the thickness of test specimen must be 32.5 (KIC/oys)2, the fatigue pre—crack must be at least 1.3 mm in length from the tip of the machined notch, the total crack length, a, 32.5 (RIC/oys)2, and the load ratio Pmax/PQ _<_ 1.10. In order to establish that a valid KIC has been determined, it is necessary first to calculate K On the 0' test record as shown in Figure 1.1 draw the secant line OP5 through the origin with a slope 5 percent less than the slope of the tangent 0A to the initial part of the record. P5 is the load at the intersection of the secant with the record. If the load at every point on the record which proceeds P is lower than P5, then P is equal to P 5 Q 5 (Figure 1.1 Type I). If, however, there is a maximum load preceding P which exceeds it, then this max load is P 5 Q (Figure 1.1 Type II and III). The load PQ will be used to calculate the KO. If KQ values meet all requirements of ASTM E399-74, then KQ is valid KIC At this point, it is convenient to discuss the concept of the pop-in method of measuring K , which IC .mpuooou ucmEmomHmmflplpmoa mo max» Hmmwocflum 5.3.1.530 meta Chained-Ema. .H.H magmas a!) gun 0'01 applies to several types of specimens and which makes it possible to use thinner specimens than would be required to obtain an almost entirely square fracture. When the test specimen is loaded the pop-in will occur at the point that the crack starts to propagate under plane strain conditions in the interior. If the loading of the specimen is maintained at a steady rate, the load will drop at pop-in, then may increase again slightly as can be seen in Figure 1.2. Here the load displacement curve was obtained from clip gage measurements of compact tension specimen 7075-T651 aluminum. One can use the load at pop-in to calculate KIC' but pop-in does not always occur for all types of material. Sometimes pop-in does occur, but it is not clear enough to calculate KIC' 1.3. CTOD Under conditions of general yield, plastic flow is no longer contained and the plastic zone spreads through the entire cracked section. Thus plastic deformation at the crack tip can occur freely. The crack must be expected to start prOpagating if the plastic strain at the crack tip exceeds a critical value. Assuming negligible strain hardening, the stress at the crack tip hardly increases after general yield and the fracture condition is reached upon the occurrence of a sufficiently large strain. A measure for the plastic strain at the crack tip is the crack tip opening displacement (CTOD). There are 4.. POP-m \ r 3 r- 2: X I o 2 - it C) J '- .2 .3 .4 .5 .5 COD-mm Figure 1.2. Typical load-displacement record illus- trating Pep-in behavior. difficulties, both theoretical and experimental, with the CTOD characterization of fracture toughness. The critical values of CTOD are generally quite small of the order of 15 microns to 30 microns, so that gross differences in local crack tip stress and strain patterns may be reflected by rather small differences in crack opening displacement. Moreover, precise measurement of CTOD is not always possible. The nature of the relationship between crack tip opening displacement and stress intensity factor is explored using the concept of linear elasticity and model analyses proposed by Dugdale. The Dugdale crack model has been used with varying degrees of success to predict plastic-zone size, crack tip opening displacement, and crack speed in materials. In his original paper, Dugdale (4) reported successful prediction of the size of plastic zone in mild steel. Heald gt 31. (5) calculated the apparent fracture toughness by using the Dugdale model that obtained from a "non-valid" ASTM test, as a function of crack size and found good agreement with experimental results. Liu and Ke (6) studied crack tip deformations, the measure CTOD's were in agreement with the Dugdale model. Baskes (7) used the Dugdale model to calculate KIC of various heat treatments and temperatures for a number of materials representing a wide range of strength, modulus, ductility, work hardening and fracture toughness. The crack tip opening displacement is related to strain distribution at the crack tip and the critical value of CTOD can be used to predict K This area has been IC' investigated by making use of a recently developed tech- nique for measuring CTOD. Well (8) pr0posed CTOD as a ductile-fracture criterion at and beyond general yielding and verified the criterion experimentally with mild steel specimens. He related CTOD to the crack extension force G (G = oy x CTOD). Fearnehough, Watkins and Mills (9) measured CTOD in zirconium alloy tubes at failure with transducers and optical methods. Luxmoore and Wyatt (10) measured CTOD at fracture of slotted zirconium bend speci- mens smaller than 0.025 mm with the Moire' Method, the critical value of CTOD at fracture was obtained by extra- polating the curve to the fracture load. Robinson and Tetleman (11) measured the crack tip opening displacement at midsection of precracked three-point bend specimen by infiltration of silicone rubber. The relationship between CTOD and COD was investi- gated by Robinson and Tetleman (11). They have shown that the CTOD can be calculated from.measurements of COD and specimen geometry only. The ratio of CTOD and COD depend on specimen width, total crack length, the height of the knife edges above the specimen surface, and the rotational constant, where rotational constant is a single valued function of CTOD from three-point bend specimens. In this investigation the IDG technique, which employs laser interferometry, is quite sensitive and pro- vides most acceptable results. It was used to measure the CTOD smaller than 0.01 mm. The Dugdale model was used to calculate CTOD and compared with experimental results. 1.4. Organization of Thesis The description of the material used in this investigation, its properties, and specimen preparation are given in the beginning of Chapter 2. The experimental procedures for fatigue cracking the specimens are also described in Chapter 2. The experimental technique for measuring COD and CTOD and the interferometric displacement gage (IDG) are described in Chapter 3. Chapter 4 describes and discusses the results from the experiments. The results are compared with the theoretical solutions from the Dugdale model and the relation between COD and CTOD are discussed in Chapter 5. The thesis concludes with Chapter 6, which summarizes the findings of this investigation. CHAPTER 2 MATERIAL SPECIFICATION AND SPECIMEN PREPARATION 2.1. Material Specification The material used for this study was aluminum type 7075-T651 and 2024-T351. All compact tension specimens and tensile specimens were designed to use the specimen orien- tation T-L, where T and L are the long transverse and longitudinal directions respectively. The T-L specimen has a fracture plane whose normal is in the width direction of a plate and an expected direction of crack pr0pagation coincident with the rolling direction of the plate. Standard round tensile specimens 12.83 mm in diameter were machined from the same plate as the compact tension specimens. Two foil gages were applied on each specimen to measure the strain. A11 tensile tests were performed in a tensile testing machine in accordance with standard methods of tension testing of metallic materials, ASTM E8-69. The stress-strain curves are shown in Figures 2.1 and 2.2. 10 11 600 V 500 (400“ 300 STRESS-MPO 200) IOO -2 -4 '6 '8 P0 P2 STRAIN-PERCENT Figure 2.1. Stress-strain curve for the test Specimen of 7075-T651 aluminum. 12 ‘O 4001 300 200 STRESS - MPO I00 l l l 1 I l n .2 .4 .6 -B IO (2 I4 STRAIN- PERCENT Figure 2.2. Stress-strain curve for the test specimen of 2024-T351 aluminum. 13 The tensile strengths obtained are: for 7075-T651 Yield strength (0.2% offset) 543 MPa Ultimate strength 620 MPa for 2024-T351 Yield strength (0.2% offset) 360 MPa Ultimate strength 487 MPa 2.2. Specimen Preparation The dimensions of the compact tension specimens are shown in Figure 2.3a. Different thicknesses, 25.40 mm, 12.70 mm, 6.35 mm, and 3.68 mm, were used to determine if KIC could be measured in smaller specimens. All specimen dimensions conformed with the requirements of ASTM E399-74. Knife edges were machined into the specimen itself for clip gage attachment to the crack mouth. The crack starter slot lies within the envelope as shown in Figure 2.3b. 2.2.1. Fatigue Pre-cracking The purpose of the test specimen is to simulate an ideal plane crack with essentially zero root radius to agree with the assumption made in the K analysis. Because I the fatigue crack is considered to be the sharpest crack that can be reproduced in the laboratory, the machine notch is extended by fatigue. The fatigue crack should extend at least 0.05 W ahead of the machine notch to eliminate any effects of the geometry of the machine notch. The fatigue crack must be sufficiently sharp, flat and normal 14 k—w—q T- /— 0 212-7 mm 1 germ-f 27-94 mm 7 l 604Hhun cl: fi -7 mm «d b—so-eo mm —.l 10—43-50”. Figure 2.3a. Dimensions of the compact tension specimen. 1. final“ Envelope < i. . 4 Straight Tuna ----~< Figure 2.3b. Envelope for crack starter notches and fatigue crack. 15 to the specimen edge. To ensure that the plastic-zone size during the final fatigue cycle is less than the plastic- zone size during actual K testing, the last 2.5% of the IC overall length of notch plus fatigue crack is loaded at a maximum stress intensity level during fatigue KF(max) such 1/2 that K x)/E §_0.00032 m . Kf(max)must not exceed 60% F(ma of the KQ value determined from the actual fracture test results. Fatigue cracking was done on a 20 kip electro- hydraulic closed loop test machine (MTS). Two traveling microscopes were used to measure progress of the crack tip on both sides. Tests were run using an inverted haversine function which stopped with the crack in an open position to facilitate observation of the crack tip. All compact tension specimens in this study had fatigue cracks approximately 11.45 mm long grown from machined starter notches. These cracks were grown by cyclic loading at the constant value of AK = Kf(max) Kf(min) f(max) : 0.6K0. Assume KQ = 27 MPa - m for the materials that were used in this investigation, 1/2 with K 1/2 therefore K = 16 MPa - m , and R =' f(max) Kf(min)/ Kf(max) = 0.1. To maintain constant AK ranges and crack growth rates during the test, the minimum and maximum loads had to be reduced (Figure 2.4) in accordance with the crack length. Crack lengths were measured during the fatigue testing with the aid of a small plastic scale taped to the specimen surface parallel to the crack and 16 .maspmsom mcfiomoa oomflumm .v.~ ousmflm 5:. I 1.5.0sz x0<¢0 0.0. 0.0. 0.! ON. 0.0. 0.0 0.0 0* ‘l‘ ‘ d N\-EIDQ: D. I”! N\-El°a: a. I x l _ T if x0<¢0 m30_.__.<.._ |\ All 105.02 mz_:0Jan3m 5263... Al ‘ 520.. r 53.. . Ii P¢(:0¢_¢.—.m 02¢ , ¢u_u_..a$< 32 .cowuoe mmnfluw mo HOOHOOOH phonomwuum HMOflmma m2.» .m.m unease m0<¢P zcuhhIx n .Eoumhm mcwunmmmfi omcwum OOHHOHDGOOIHODSQEOOMGHE on» no Hoccmno moo mo Owumaocom . mun». mgr—2530205.??- 5.24.53.00.38 T _ 5.5.... 4 ’ .m.m magmas zugomam F can} _u mcmgs 37 The load-displacement curves were recorded on an X-Y plotter (Figure 3.9), the displacement scale was calibrated from the voltage per bit Of the D/A and it was computed by the equation number of counts 1 _1____ 8 s1n a0 6d = (3.5) In this investigation the maximum displacement measurement is approximately 100 microns, and the voltage per bit is 5 mV. 38 LOAD- KN A A A A ~ ~0I ~02 ~03 ~04 ~05 CTOD - nun Figure 3.9. Typical load-displacement curve from Minicomputer. '00 CHAPTER 4 EXPERIMENTAL RESULTS In this chapter Figures 4.1-4.8 show the load- displacement curves Obtained from the clip gage at the mouth Of the notch and the load-displacement curves that were Obtained from the IDG technique at 100 microns from the tip Of the crack. The specimen was mounted with a clevis and pin in an Instron testing machine. When the specimen was loaded the crack was Opened. The load versus crack Opening displacement was recorded by x-Y plotter. The lOad-displacement curves at the mouth Of the notch are linear because the material that was used in this research has an elastic behavior. At the same time the set Of indentations at the tip Of the crack was moved, the fringe patterns moved and caused the stripchart recorder to record the fringe number for both upper and lower fringe patterns and the output from the minicomputer was recorded by X-Y plotter as shown in Figures 4.9-4.12. The load-displace- ment at the tip Of the crack is nonlinear. The relation between the crack Opening displacement at the mouth Of the notch and at the tip Of the crack will be described in Chapter 5. 39 40 M: LOAD-KN SPECIMEN THICKNESS Sl‘I-32 25 . 37 mm. CTOD-nun Ah .3 .5 .I .f sf 000-.- b. Figure 4.1. Comparison Of load-displacement curves at crack tip and mouth Of notch Of test specimen 7075-T651 aluminum SN-31,32. I01 LOAD-KN 41 spzcxnzn THICKNESS 3NJ27 13.03 mm. Figure 4.2. I’ V V V V V 1 32 ea .04 on oe - or oe .oe croo-ee I 7 .i .i I .6 000-0. 5. 1 Comparison Of load-displacement curves at crack tip and mouth Of notch Of test specimen 7075-T651 aluminum SN-27,28. 42 0 1 23 24 Q 4 Q 0 k 0 2 x I n C o .1 2 fl SPECIMEN THICKNESS m"23 5099 we SN-24 5.92 m. g 4 0? 0'2 o: 64 60 co or de CTOD-Inn ' i 2 i 3 .6 5 7 COD-nun Figure 4.3. Comparison Of load-displacement curves at crack tip and mouth Of notch Of test specimen 7075-T651 aluminum SN-23,24. 43 .o~.mHszm assassam Hmmaumsos emsnommm one» no £000: 00 canoe one may xomuo um m0>uao unmfioomammflplomoa MO :Omflummeoo ee-aoo e. 9 m. 9. e. ? m. ’e .e-m9& 1&1! .ne sa.~ mquu alasua_nn898 .v.v masons RI-CVO‘I 20] LOAD-KN 44 SFHHMHITHHXNE“! SN-15 25e22 Me oi .03 .03 64 0': 3e - .67 do ' 3e CTOD-nu If -i 1 3 CF 3 .6 7 COD-an Figure 4.5. Comparison Of load-displacement curves at crack tip and mouth Of notch Of test specimen 2024-T351 aluminum SN-15,16. LOAD-KN IO‘I C-I 45 SPECIMEN THIMESS SIC—11 12.95 mm. 314-12 12.98 mm. v V ' Y ‘ U V o: .03 .0: 04 co oe or oe or» 0700 - Inn 4 .e e .7 e -I é .5 . 000 - I. Figure 4.6. Comparison Of loadedisplacement curves at crack tip and mouth Of notch Of test specimen 2024-T351 aluminum SN-ll,12. 46 44 3d LOAD-KN SFHHMHITWHXNEfi SN -7 5.97 mm- mI-8 5.77mm. oi 62 o': o3 do be . .67 6e 69 CTOD-an E .i .E S 3 .3 .3 .i .i COO-nu Figure 4.7. Comparison Of loadrdisplacement curves at crack tip and mouth of notch Of test specimen 2024-T351 aluminum SN-7,8. 47 .¢.muzm assessam Hmmenvwow cmEHommm ummu o souo: mo £9508 can map xomuo um mw>uno ucmfimomammwolnmoa wo Gomanmmswu II loco m up .m.v musmem a. 6+ 2 8 I a 4. '( ‘O .l 2. Figure 4.9. 48 27 SPECIMEN‘THICKNESS SNLZT' 13.03 mm» A 1 A A A '0! -02 ~03 '04 '05 06 CTOD - mm Load-displacement curve at crack tip of test specimen 7075-T651 aluminum SN-27 that was obtained from minicomputer. 3. LOAD-KN 9 Figure 4.10. 49 SPECIMEN THICKNESS “.23 5099 m. l J A A -Ol .02 .03 .04 .05 CTOD-mm Load-displacement curve at crack tip of test specimen 7075-T651 aluminum SN-23 that was obtained from minicomputer. 50 20 IO 24% 24% LG‘ LOAD-KN lih SPE¢DHEFTHBQUESS O 5 391-139 2.97 mm. SN-ZO 2;95 m. -Ol -02 ~03 -O4~ -05 .06 CTOD-mm ‘ Figure 4.11. Load-displacement curves at crack tip of test specimen 7075-T651 aluminum SN-l9,20 that was obtained from minicomputer. 52 In this experiment the stress-intensity factors were obtained by using the standard test method for plane strain fracture toughness of metallic materials E399-74. The critical crack tip Opening displacement values were obtained from load displacement curves at the point that pop-in does occur. The critical crack tip opening dis- placement was used to calculate stress intensity factor by using an equation that developed from the Dugdale model. 80 Sa noF acrit = _LTTE 1n (sec(20ys) (4.1) where CF is the failure stress. This equation can be reduced to 6 . NB OF =-%% sec.l e ys (4.2) or o /?a < SiitZE> KI = -&90— sec‘1 e Y3 (4.3) where KI is stress intensity factor = oF/na The results are shown in Table 4.1. 4.1. Effect of Specimen Thickness on Pop-in Typical load-displacement records are shown in Figures 4.1-4.4 for a series of tests on 7075-T651 aluminum of various thicknesses and Figures 4.5-4.8 for test specimens 2024-T351 aluminum. For test specimen 707S-T651 that is a brittle material, the load displacement diagram 53 II II II II m.v~ m.v~ h.mH N.VN v.mm m.om mvm mam mm h.e~ mmao. nflvw mmflo. v.c~ c.v~ m.m~ v.v~ m.m~ m.om mom mam an o.o~ mmao. m.m~ memo. oeam>cH a.m~ om.o m.qm o.ma ¢.om mvm . ado mm o.m~ mH~o. o.mm mama. ceao>ca m.m~ mm.m ~.v~ o.ma m.om nvm mac pm m.o~ mmao. o.om ovmo. uflau>cH m.o~. mm.m m.v~ ~m.m m.om mom was cm m.m~ mmao. m.om ammo. owam>cH ~.m~ 5H.v o.¢~ ma.m m.om new mac mm m.>~ omao. ~.Hm ammo. owam>ca «.mm mm.~ m.q~ mm.~ m.om mvm mam om m.m~ mmao. m.Hm owmo. ofiam>cH w.~m ov.~ w.v~ hm.~ m.om mqm mac ma Hmoenmuoe m.Hm ooqo. m.am oovo. m.m~ m.m~ v.mH m.v~ «.mm w.om own new we ~.Hm memo. ~.Hm mmmo. ~.om ~.om n.- n.mm ~.m~ m.om own awe ma nn nu nn nn ofiam>cH «.mm m.o~ o.v~ o.ma m.om com um” NH un nn nu nu nfiam>cH n.am m.oH H.¢~ a.~H m.om com nmv Ha nn un nu nn ceam>cu H.mm mo.v n.v~ nh.m w.om can sue a nu nn un uu owam>cH H.~m ~v.v m.v~ hm.m m.om com awe n nu nu nu nn nflam>cH v.~m n~.~ m.v~ mm.~ m.om own am. e un nn nn nn ofiam>cH o.~m nm.~ m.q~ mm.~ m.om own new n Hmmenvwow «xawmmmz MW ~\H%mmmz WM ~\w%mmmz ~\H%mmmz zx as as ea mm: am: .02 .oQO wauouo: cHudom umuwm u< :Hnaom manna u< vnnmmmm zem< on m m 3 mxo uaso .mumo Hmucwefluomxmuu.a.v manna 54 produced an increment of crack extension at a load close to the maximum, the pop—in occurred as indicated in Figure 4.1. The stress intensity factor was calculated by the load that corresponded with this point. Then reducing the thickness of the test specimen by one-half yields the records shown in Figure 4.2. These records are readily interpretable in that they consist of a well-defined large pop-in and a more distinct pop—in is observed well below the maximum load. If the thickness is reduced by a factor of about four or eight, distinct pop-in indications become more steps and smaller than the thicker specimen, as can be seen in Figures 4.3 and 4.4. Obviously, the significance of these small steps depend on the thickness of the specimen which fracture to produce the indications. For test specimen of 2024-T351 aluminum that is more ductile, the pOp-in occurred with only small steps for standard compact tension specimen (W/B = 2) about 25.4 mm in thickness as can be seen in Figure 4.5. For thinner specimens, pop-in indica- tions become completely indefinite. It is difficult to get large pop-in for ductile materials with a small thickness. The load displacement records that obtained from the IDG technique can identify pop-in at the tip of the crack the same as the load displacement records that obtained from a clip gage at the mouth of the notch as can be seen in Figures 4.1-4.8. The results that obtained from stripchart recorder and minicomputer are the same. 55 4.2. Comparison of Crack Tip Displacement for Test Specimen 7075-T651 and 2024-T351 Aluminum In the case of more brittle materials, a crack will grow gradually under the influence of the environment until the level of K reaches the value of KC, when unstable frac- turing will occur. For the tougher materials, the fracture will not occur until K exceeds the value of KC. In this experiment the crack tip opening displace- ment measurements of 2024-T351 aluminum were more than the crack tip Opening displacement measurements of 7075-T651 for all specimen thicknesses. Photographs of test speci- mens of 707S-T651 and 2024-T351 when the crack was extended are shown in Figures 4.13 and 4.14. 4.3. Discussion of Results The load-displacement curves were lost for some test specimens, because the alignment of specimen was not good enough. When the load was increasing the set of indentation moved out of the laser beam. In this case the area of the laser beam on the specimen surface was not large enough to cover a set of indentation while the crack was extended. A lens was used to magnify the area of the laser beam on the specimen surface. The results were good enough for later tests. In this set of experiments the minicomputer recorded good load-displacement curves for only six test specimens. The results were used to compare with the plots of load versus displacement at the crack tip from 46 44 SPECIMEN THICKNESS m -7 5097 mm. SN -8 5.77 m. on m 0': oi 03 60 ~ .07 on 09 crop-an V T v f V V ' ' v 4 .2 3 4 a .3 .7 .. COO-n- Figure 4.7. Comparison of loadrdisplacement curves at crack tip and mouth of notch of test specimen 2024-T351 aluminum SN-7,8. 47 .4.mnzm escaesam Hmmenqmom cmeflommm ammo mo nouoc no space can map xomuo um mm>uao ucoawomammflclcmoa mo conflummfioo Illooo r» g D h .m.v musmflm a. can a 8 I o 4. “ ‘0 .1 2. Figure 4.9. 48 27 SPECIMEN". THICKNESS “*2? 13003 Me A A A A A O! '02 '03 '04 '05 06 CTOD - mm Load-displacement curve at crack tip of test Specimen 7075-T651 aluminum SN-27 that was obtained from minicomputer. 44 24 LOAD-KN l-u Figure 4.10. -Ol .02 ~03 ~04 -05 49 SPECIMEN THICKNESS “’23 5099 m. A A A CTOD-mm Load-displacement curve at crack tip of test specimen 7075-T651 aluminum SN-23 that was obtained from minicomputer. 50 20 IO 24% 24% LG‘ LOAD-KN l4? snmnnnmumzmnmss 0 5 ail-19 2.97 mm. SN-ZO 2c95 m. ~0l ~02 ~03 ~04~ ~05 ~06 CTOD-mm ‘ Figure 4.11. Load-displacement curves at crack tip of test specimen 7075-T651 aluminum SN-19,20 that was obtained from minicomputer. 51 LOAD-KN A .0: .02 .03 B4 .05 .06 CTOD-mm Figure 4.12. Load-displacement curves at crack tip of test specimen 2024-T351 aluminum SN-3,4 that was obtained from minicomputer. 52 In this experiment the stress-intensity factors were obtained by using the standard test method for plane strain fracture toughness of metallic materials E399-74. The critical crack tip Opening displacement values were obtained from load displacement curves at the point that pop-in does occur. The critical crack tip Opening dis- placement was used tO calculate stress intensity factor by using an equation that developed from the Dugdale model. 80 Sa “OF scrit = —F%—— 1n SGC(§E——) (4.1) ys where CF is the failure stress. This equation can be reduced to 6 . NE ( grit ) o _ o a CF =~§§ sec 1 e ys (4.2) or 6 . NE crit K _ O vaa _l ( Boysa ) I " 90 sec e (4.3) where KI is stress intensity factor = oF/na The results are shown in Table 4.1. 4.1. Effect of Specimen Thickness on Pop-in Typical load-displacement records are shown in Figures 4.1-4.4 for a series of tests on 7075-T651 aluminum of various thicknesses and Figures 4.5-4.8 for test specimens 2024-T351 aluminum. For test specimen 7075-T651 that is a brittle material, the load displacement diagram 53 nn un nn nn m.v~ m.v~ n.ma ~.e~ ¢.m~ m.om new man mm h.v~ mmao. ”New mmao. v.v~ v.v~ m.ma v.v~ m.m~ o.om mom man an m.o~ mmao. m.m~ moNo. Oaam>ca m.m~ om.m m.v~ o.ma m.om mom mam om o.¢~ mama. o.m~ mama. paao>cH m.m~ mm.m m.v~ o.ma m.om mvm mam hN m.m~ mmao. o.om ovmo. Oaam>ca m.o~ mm.m m.v~ ~m.m m.om mom mam v~ m.w~ mmao. m.om mmwo. caam>ca ~.m~ na.v o.q~ mm.m m.om mam mac mm m.nm omao. ~.am ammo. caam>ca m.~m mm.~ w.v~ mm.~ m.om mam mam o~ m.o~ mmao. m.am oomo. Oaam>cH w.~m ov.~ m.v~ hm.~ m.om mvm mam aa amoaumNOF m.am oovo. m.am ooqo. m.m~ m.m~ «.ma m.vm ~.m~ m.om own nmv ma ~.am mmmo. ~.am memo. ~.om ~.om n.5a n.m~ ~.m~ m.om own new ma nu nn nn nn naam>ca «.mm m.oa o.v~ o.ma m.om own awe ~a nn nu nn un caam>ca n.am m.oa a.v~ m.~a m.om com new aa nu un nu nu paaw>ca a.mm mo.v n.v~ nh.m m.om own hmv m nn un nn nu vaam>ca a.~m mv.v m.v~ hm.m m.om com paw a nu nu nu nu Oaam>ca v.am e~.~ m.v~ mm.~ m.om com saw v nu nu nu nn caao>ca o.~m nm.~ o.v~ em.~ m.om can sue m ammenemow .~\a%mmmz WW «\awmmmz w” ~\wwmmmz «\awmmmz zz as as as mm: mm: .02 .OOdm amauwumz cannon umuam u< cannon magma a: «humane 29mg Om m m 3 mac uaso .muwn Hmucmsauwmxmul.u.v wanna 54 produced an increment of crack extension at a load close to the maximum, the pop-in occurred as indicated in Figure 4.1. The stress intensity factor was calculated by the load that corresponded with this point. Then reducing the thickness of the test specimen by one-half yields the records shown in Figure 4.2. These records are readily interpretable in that they consist Of a well-defined large pop-in and a more distinct pop-in is Observed well below the maximum load. If the thickness is reduced by a factor of about four or eight, distinct pop-in indications become more steps and smaller than the thicker specimen, as can be seen in Figures 4.3 and 4.4. Obviously, the significance of these small steps depend on the thickness of the specimen which fracture to produce the indications. For test specimen of 2024-T351 aluminum that is more ductile, the pop-in occurred with only small steps for standard compact tension specimen (W/B = 2) about 25.4 mm in thickness as can be seen in Figure 4.5. For thinner specimens, pOp-in indica- tions become completely indefinite. It is difficult to get large pop-in for ductile materials with a small thickness. The load displacement records that obtained from the IDG technique can identify pop-in at the tip of the crack the same as the load displacement records that Obtained from a clip gage at the mouth of the notch as can be seen in Figures 4.1-4.8. The results that Obtained from stripchart recorder and minicomputer are the same. 55 4.2. Comparison of Crack Tip Displacement for Test Specimen 7075-T651 and 2024-T351 Aluminum In the case of more brittle materials, a crack will grow gradually under the influence of the environment until the level of K reaches the value of KC, when unstable frac- turing will occur. For the tougher materials, the fracture will not occur until K exceeds the value Of KC. In this experiment the crack tip opening displace- ment measurements of 2024-T351 aluminum were more than the crack tip Opening displacement measurements of 7075-T651 for all specimen thicknesses. Photographs of test speci- mens of 7075-T651 and 2024-T351 when the crack was extended are shown in Figures 4.13 and 4.14. 4.3. Discussion of Results The load-displacement curves were lost for some test specimens, because the alignment Of specimen was not good enough. When the load was increasing the set of indentation moved out of the laser beam. In this case the area of the laser beam on the specimen surface was not large enough to cover a set of indentation while the crack was extended. A lens was used to magnify the area Of the laser beam on the specimen surface. The results were good enough for later tests. In this set of experiments the minicomputer recorded good load-displacement curves for only six test specimens. The results were used to compare with the plots of load versus displacement at the crack tip from 56 Figure 4.13. The photograph of test specimen 7075-T651 aluminum when the crack was extended. 57 “n In 'l" '4"; ’ Figure 4.14. The photograph of test specimen 2024-T351 aluminum when the crack was extended.. 58 stripchart recorder. The characteristic curves came out the same as that Obtained from the stripchart recorder. This technique will be very useful to use for measuring small displacement at the tip of the crack for further research. The results from Table 4.1 are shown that 6crit from CTOD measurement are quite in agreement with KIC that was calculated from the standard test method for plane- strain fracture toughness of metallic materials ASTM E399-74 for standard compact tension specimen (W/B # 2) 25.4 mm in thickness for both materials. For thinner specimens the 6 that was obtained at first small crit pop-in and was used to calculate stress intensity factor is in better agreement with K than using 6 at large IC crit pop-in, but it is not clear enough to show that the pop-in really occurred at that point. By using IDG technique the pop-in does not occur for thinner specimens of 2024-T351; they are the same as the results that were Obtained from the clip gage. CHAPTER 5 CRACK TIP OPENING DISPLACEMENT The concept of a critical crack opening displace- ment as a criterion for fracture initiation is claimed to Offer a basis for a general yield fracture mechanics which is fully compatible with linear elastic fracture mechanics in the case of small crack tip plastic yield. When a cracked metallic solid is stressed, plastic deformation takes place first at the crack tip and spreads across the solid as the applied load is increased. 5.1. Crack Tip Plastic Zone Problems of accounting for crack tip plasticity were to some extent overcome by the approximate method of crack border repositioning developed by Irwin (15). Since an increment of crack length may be used to account for the apparent increase in the K value when applicable crack tip plasticity is present, it is possible to develop a relationship between the stress intensity factor, K, and the near tip crack Opening displacement, 6. The plane stress plastic-zone size may be approximately evaluated by the expression 59 60 __;_ K 2 ys where ry is the extent, along the crack plane, of the plastic zone which is assumed to be circular in shape, Oys is the yield property controlling the plastic zone, K is the acting stress intensity factor. The equivalent model due to Irwin is shown in Figure 5.1. This is achieved by proposing a new distribu- tion of stress by translating the original distribution a distance ry parallel to the crack plane. The corrected K value is determined as K = o/fi(a + ry) (5.2) For the equivalent model the y direction, displacement (v) within the crack above the crack tip may be shown to be __2_I_<,/—— v - nE any (5.3) where v is the displacement from the centerline of the slit to the flank of the crack, as shown in Figure 5.1. For the equivalent model, the displacement at the elastic plastic interface corresponds to the displacement at the tip Of the real crack. The near tip crack Opening displacement, therefore, is 61 CT Figure 5.1. Details of crack border repositioning to account for crack tip plastic zone. ' 62 4K 2 5 = 2v = i?//::1 (5.4) This may be reduced to 2 4K "Boys This method of crack border repositioning to take account of the extent of the plastic zone is only appropri- ate for small o/oys, and it has not extended the practical application of the analyses and techniques of linear elastic mechanics to any great extent (16). A further extension of the CTOD concept was pro- vided by the Dugdale model. 5.2. The Dugdale Model Dugdale (4) proposed that the extent of yielding ahead of a slit in tension in mild steel could be deter- mined by considering the yield zone to consist of a region of constant stress acting to prevent the crack opening. The system proposed by Dugdale is shown in Figure 5.2 and consists of a through-thickness crack in a finite plate that is subjected to a tensile stress normal to the plane of the crack. The crack is considered to have a length equal to 2a + 2p. At each end of the crack there is a length p that is subjected to yield-point stresses that tend to close the crack, or in reality, to prevent it from Opening. Thus the length of the real crack would be 2a. 64 Another way of looking at the behavior of this model is to assume that yield zone of length p is spread out from the tip Of the real crack, a, as the loading is increased. Thus the displacement at the original crack tip, 6, which is the CTOD, increases as the real crack length increases or as the applied loading increases. The basic relation- ship develOped by Dugdale is 80 a w o 5 -%§- ln sec (-2- '0‘") (5.6) YS where Oys is the yield strength of the material, MPa, 0 is the nominal stress, MPa, 2a is the real crack length, mm, E is the modulus of elasticity of the material, MPa. The coefficient of the expansion of the ln sec term may be determined using McLaurin's method as follows: 80 a 6 = _Y_S_ (1/2017. _9'__)2 4. 1__(1T. .52..)4 4. NE 2 Cys 12 2 oys 74-54321 3245 +. . .) (5.7) ys For o/oys, very small, a reasonable approximation for 6, using only the first term of this series, is ‘ EU (5.8) 65 5.2.1. Comparison of CTOD Measurement with Dugdale Model and Discussion The plots of load versus crack tip Opening dis- placement for various thicknesses of test specimen 7075-T651 and 2024-T351 aluminum are shown in Figures 5.3 and 5.4. These plots were measured at a distance about 100 microns from the tip of the crack with a distance about 100 microns between indentations across the fatigue crack by using the IDG technique. They were Obtained from the strip chart recorder and using the equation 3.3 to calculate the displacement as can be seen in Figure 3.7. The crack tip displacement has been studied by Liu and Ke (6). They measured the crack opening displacement at the near tip Of the crack of the steel specimen by using the Moire method; the results were compared with the calculated opening displacements using the elastic model and the Dugdale model. The measured values are in better agreement with the Dugdale model especially very near the tip. In this investigation the measurements of crack tip opening displacement using the IDG technique were compared with the Dugdale model. The dark lines in Figures 5.3 and 5.4 were calculated from equation 5.6 developed by Dugdale. The results show that the test specimens of 7075-T651 are in better agreement with the Dugdale model than the test specimens of 2024-T351. However, for all test specimens before the crack was extended, the agreement is good except the test specimen 2024-T351 12.98 mm thick as can be seen M‘ l2 I0 E E n 0 ¢ 0 4 Figure 5.3. 66 Comparison of load-displacement curves at crack tip Of specimen 7075-T651 aluminum with Dugdale Model. , OO CffiiD DUGDALE MODEL 0 SPECIMEN THICKNESS . O 25.32 mm. o A 12.98 mm. V7 13.03 mm. C a 5099 mm- 0 5.92 mm. 0 O 2.95 mm. 0 2.97 mm. 0 A O A V thr ‘7 V O A v A v A v D D O O . '0 00 CO , 0) CD 1') ~0| 402 ~03 ~04~ ~06 CTOD-mm 67 no ~ A MA WVV ‘ V7 IGL " V DUGDALE MODEL A.§7 1. v SPECIMEN THICKNESS 25.16 mm. 25.22 mm. 12.98 mm. 5.77 mm. 2.99 mm. 2.98 mm. M- '2- 00no LOAD-KN ~66 3n Figure 5.4. Comparison of load-displacement curves at crack tip of test specimen 2024-T351 aluminum with Dugdale Model. 68 in Figure 5.4 because the distance from the indentations to the crack tip was larger than the other specimens (it was approximately 190 microns). 5.3. The Relationship between CTOD and COD In order to calculate the opening at the crack tip, CTOD, from the clip gage displacement, COD, it is usually assumed that the crack faces Open using a simple hinge mechanism with a fixed rotation axis at a position defined as the fraction, r, of the remaining ligament width, W—a, i.e., at a position r(W-a) beyond the crack tip as shown in Figure 5.5. Geometrical considerations then indicate that COD = (a+z) + (r(W%a)) CTOD r(Wea) COD = a+z + 1 CTOD r(W-a) CTOD = C0” _ a+z + 1 rZW-a) a+z r cog'a (5.9) 0—-—- - 1) CTOD where W is the specimen width a is the total crack length 2 is the distance between load line and crack mouth r is the rotational constant 69 leHDMENOBfiI FWEKKEIflMfiK |*’ T . —+|.——[unn..]———.| COD croo Io———- q+z ———*H rDfl-o] Figure 5.5. Schematic showing calculation of Rotational Constant. 70 From experimental data the rotational constant, r, increases during loading. 5.4. Results and Discussion The plots of CTOD versus COD and CTOD versus r for test specimen 7075-T651 and 2024-T351 aluminum are shown in Figures 5.6, 5.7, 5.9, and 5.10 where the CTOD and COD were obtained from the IDG technique and clip gage, and r was calculated from equation 5.9. The dark lines in Figures 5.6, 5.7, 5.9, and 5.10 are the average curves Of CTOD versus COD and CTOD versus r, respectively. In Figures 5.7 and 5.10 the plots of CTOD versus COD and CTOD versus r of the test specimen 2024-T351 12.98 mm thick were not on the average curve because the distance from the inden- tations to the crack tip was larger than the other speci- mens (it was approximately 190 microns). .The results show that the relationship between CTOD and COD, and CTOD and r are the same for all specimen thicknesses of the same material. But the comparison of the curves Of CTOD versus COD is given in Figure 5.8 of the test specimen 7075-T651 and 2024-T351 aluminum are not the same. SO it is shown that the ratio of CTOD and con of the same specimen geometry is different for different materials. The curves of r versus CTOD given in Figure 5.11 have shown that the rotational constant, r, is a function of CTOD dependent on material. Robinson and '71 .ascaeuam amoenmaoa :msaommm ummu mo moo can ooeo cmmspmn aoaumamu was .m.m magmam EEIOOO o. t. o. u c. n a. .. q q a a a q ‘ “U. .5... agent! b (a. n 4 ) ‘46“. q .‘Ld. q 1 6| >\. 4 ..‘ ‘ 4 ." 1N0. n o 4 0 . . . w e DEE mmoN 0 Inc. 0 .5 ~me 0 D O .5 mm... 0 .ea mo.ma D .5 3.3 < .co. 0 .EE Nm.mN O mmmZMUHme zmseommm 72 1F- Hmmauvmom cmEHommm ummu no 000 com 0080 cowzuon GOHDMHOH one .EscwEdam .aa mm.m .EE mm.m .EE >>.m .ea mm.ma .EE mw.mm .58 wH.mN n mmmZMoame zmeHommm ‘4 D>() l .9 ¢Q .n.m magmam WW-OOLO 73 .ESGHEUHM Hmmalwmom can Hmmeum505 cofiflommm ummp mo mm>Hdo GOO msmuo> 0090 no cOmemmfioo .m.m muamam ssuooo p. o. o. t. n u. . J .0. .NO. .no. .\. ammenemom ul \.\ amoanmeou in. .6. “ml-00.1.3 74 ~l2 . .uo - b :2" 0.. :5 U) 2 On 3 SPECIMEN THICKNESS ‘21 .os~ O 25.32 mm. 9 A 12.98 m. g... E V 13.03 mm. 2 D 5099 mm. ’04 " 0 5092 mm. 0 2.95 mm. 0 2.97 mm. .02- 0: .02 .03 .03: .05 CTOD- mm Figure 5.9. Position of center of rotation versus CTOD of test specimen 7075-T651 aluminum. 75 44 - ~uzn Jon 3. .5 Z a 0 g .03. SPECIMEN THICKNESS 8 A 25.16 m. z V 25.22 mm. 2 o 12.98 mm. a '06” U 5077 mm. 2 O 2.99 mm. 0 2.98 min. ~04!~ oz- -oln ~03 ~03 ~64 ~05 CTOD-mm Figure 5.10. Position of center of rotation versus CTOD of test specimen 2024-T3Sl aluminum. 76 44F "2 n- ./' .m- b .: 3 p. 0’ g .05. J ‘ z 9. = '06- ; ....... 7075-T651 ‘ __ 20244351 or ~02-lf .on .62 ~63 .03 ~65 CTOD-mm Figure 5.11. Comparison of Rotational Constant versus CTOD curves of test specimen 7075-T651 and 2024-T351 aluminum. 77 Tetleman (11) suggested that r is a single-valued function of CTOD and a least squares fit to the r versus CTOD Curve is 2 3 r = A0 + AlCTOD + AZCTOD + A3CTOD (5.10) where A0, A1, A2 and A3 are constant values. The constant values in equation 5.10 can be solved using equation 5.9, 5.10 and CTOD and COD values from the experiment. In this investigation for 7075-T651 aluminum at CTOD < 0.3 mm r = 0.01563 + 3.10207CTOD - 62.34755CTOD2 + 830.87828CTOD3 (5.11) for 2024-T351 aluminum at CTOD < 0.3 mm. r = 0.01209 + 4.65021CTOD - 129.45333c'r002 + 1916.05429CTOD3 (5.12) The CTOD values can be found directly from.measurements Of on-load clip gage displacement, COD, and specimen geometry by combining equations 5.9 and 5.10. CHAPTER 6 CONCLUSIONS The experimentally measured results in this research are restricted to the particular specimen thick- nesses and materials tested. A set of laser-based Interferometric Displacement Gage measurements were con- ducted in order to study crack tip Opening displacement for compact tension specimens with a crack length 0.45 < a/W < 0.55 and for two types of material 7075-T651 and 2024-T351 aluminum, and in thicknesses 25.4 mm, 12.7 mm, 6.35 mm, and 3.18 mm. The IDG technique was used to measure crack Opening displacement at 100 microns from the crack tip. The crack Opening displacement at the mouth of the notch was measured by a clip gage. The measurements of valid KI value (ASTM E399-74) can be Obtained only from C specimens 25.4 mm in thicknesses for both types of material. The fracture toughness of test specimen 7075-T651 and 1/2 and 30MPa-m1/2, 2024-T351 aluminum are 24MPa-m respectively. In this investigation, the IDG technique was used to identify pop-in for two types of material 7075-T651 and 2024-T351 aluminum and various thicknesses. The results 78 79 have shown that the IDG technique can identify pop-in the same as a clip gage, but it is not better than the clip gage. Therefore the IDG technique has no advantage in identifying pop-in. The critical crack tip Opening displacement, acrit' was obtained from the CTOD value at pop-in of the load displacement curve. The Gcrit can be used to calculate the stress intensity factor. The calculated stress intensity factor values Of specimen thickness, 25.4 mm for both materials are in better agreement with the measurements of stress intensity factor from standard method ASTM E399-74 than thinner specimens. For test specimen 7075-T651 and 2024-T351 aluminum 25.4mm in thickness, the agreement between K measurement from clip gage and 6 IC (1 1.6 percent and i 5 percent, respectively). For thinner crit is good specimens the IDG technique cannot identify pop-in, so that the problem of 6c is how large a pop-in indication rit should be required from plots of load-displacement curve at the crack tip to get 6 In this investigation the crit“ results have shown that 6c can be used to predict K rit IC' and the stress intensity factor values that were calculated from 6c at first pop-in are in better agreement with rit measured K values (ASTM E399-74) than from 6c IC at large rit pop-in. The Dugdale model was used to calculate CTOD for various thicknesses of test specimen 7075-T651 and 2024- !r351 aluminum. The calculated CTOD values were compared 80 with the experimental CTOD values. The agreement between calculated and experimental values of CTOD is good for 100 microns location. The calibration curve relating CTOD to clip gage displacement was derived from measurements on compact tension specimens. This calibration curve can be used to calculate CTOD from clip gage displacement and specimen geometry. The comparison curve in Figure 5.8 has shown that the relation between CTOD and COD does not depend upon specimen thickness, but it depends upon material. In these experiments the IDG technique is not very difficult to use. Preparation of the Specimen surface is straightforward, and the application Of the indentations is easy. In this work the main problem in using the IDG tech- nique is the alignment of the specimen, but it is not difficult to take care of this problem. The CTOD values have been successfully measured by the IDG technique for total displacements less than 10 microns. The IDG tech- nique is quite sensitive for very small displacements. In this investigation the results that were Obtained from minicomputer are more accurate than the reSults that were Obtained from stripchart recorder. The IDG technique with minicomputer can be used with small specimens, and it will be very useful to measure a very small displacement in a small area of test section for further research. REFERENCE S 10. REFERENCES "Fracture Testing of High-Strength Sheet Materials," A report Of a special ASTM committee ASTM No. 243, pp. 29-40 (1960); No. 244, pp. 18-28 (1960). Kaufman, J. G. and Hunsicker, H. Y., "Fracture Toughness Testing at Alcoa Research Laboratories," ASTM Spec. Tech. Publ. NO. 381, pp. 290-309 (1965). 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