Mixed mode ductile fracture in metal materials for offshore applications

MIXED-MODE DUCTILE FRACTURE IN METAL MATERIALS FOR OFFSHORE APPLICATIONS YANG WUCHAO NATIONAL UNIVERSITY OF SINGAPORE 2012 MIXED-MODE DUCTILE FRACTURE IN METAL MATERIALS FOR OFFSHORE APPLICATIONS YANG WUCHAO (B. ENG., HUST, M. ENG., HUST) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Yang Wuchao Acknowledgement ACKNOWLEDGEMENT The research work reported in this thesis has been conducted at the Department of Civil and Environmental Engineering, National University of Singapore. Special appreciation is given to the Research Scholarship provided by the National University of Singapore. I wish to express my deepest gratitude to my supervisor Assistant Professor Dr. Qian Xudong for his invaluable and consistent guidance, support and encouragement through my four years research work. My sincere appreciation is also given to the technical staff Mr. Lim Huay Bak, Mr. Ang Beng Oon, Mr. Ow Weng Moon, Mr. Wong Kah Wai, and Mr. Kamsan Bin Rasman from the Structural Engineering Laboratory for their help in doing experiment. Finally and most importantly, I wish to appreciate sincerely the persistent support provided by my lovely wife Mrs. Yu Jing on my research work. -i- Table of contents TABLE OF CONTENTS ACKNOWLEDGEMENT . i TABLE OF CONTENTS ii NOMENCLATURE . vii LIST OF FIGURES xii LIST OF TABLES . xix SUMMARY . xxi 1. INTRODUCTION 1.1 Background . 1.2 Objectives and scopes . 1.3 Content of current thesis . 2. LITERATURE REVIEW 2.1 Introduction . 2.2 Ductile fracture mechanism 2.2.1 Void nucleation 2.2.2 Void growth and coalescence 2.3 Mode I ductile fracture 2.3.1 Theoretical development 2.3.2 Experimental fracture mechanics . 14 2.3.3 Numerical simulation of Mode I ductile fracture . 17 2.4 Mixed-mode I and II ductile fracture 18 2.4.1 Analytical and numerical study on mixed-mode ductile fracture 19 2.4.2 Experimental investigation on mixed-mode I and II ductile fracture 22 2.5 Summary . 25 - ii - Table of contents 3. NUMERICAL MODELLING OF MODE I DUCTILE FRACTURE GROWTH 3.1 Introduction . 26 3.2 Computational cell method for ductile fracture resistance 27 3.2.1 Ductile crack growth using the computational cell method . 27 3.2.2 G-T constitutive model 28 3.2.3 Cell extinction technique . 30 3.2.4 Solution procedures 31 3.3 Calibration of the computational cell method . 32 3.3.1 Finite element models 33 3.3.2 Effect of the computational controlling parameters . 35 3.3.3 Calibration of f0 36 3.3.4 Validation of f0 . 37 3.4 Extension of external circumferential cracks in pipes 38 3.4.1 3D cracks . 38 3.4.2 2D simplified model . 40 3.5 Summary . 43 4. EXPERIMENTAL PROCEDURES FOR MIXED-MODE I AND II SPECIMENS 4.1 Introduction . 44 4.2 Coupon test . 46 4.2.1 Test setup . 46 4.2.2 Test results . 47 4.3 Mode I SE(B) test . 49 4.3.1 Test scope and setup 49 4.3.2 Fatigue pre-crack 52 4.3.3 J-R curve test procedures . 53 - iii - Table of contents 4.3.4 Evaluation of J-R curve 53 4.3.5 Post-test examination . 55 4.4 The mixed-mode crack initiation determined by strain detection method 57 4.4.1 Test scope and setup 57 4.4.2 Mode-mixity 61 4.4.3 The strain measurement . 63 4.4.4 Calculation of J-value for mixed-mode specimen . 64 4.4.5 Elimination of indentation at supports . 67 4.4.6 Verification of the strain detection method 69 4.5 Mixed-mode I/II fracture resistance curve test . 73 4.5.1 Determination of crack extension for Mode I dominant specimens 73 4.5.2 Determination of crack extension for Mode II dominant specimens . 76 4.6 Summary . 78 5. MIXED-MODE I/II TEST RESULTS AND DISCUSSIONS 5.1 Introduction . 80 5.2 Mode I SE(B) specimens 80 5.2.1 Fracture initiation . 80 5.2.2 Crack extension 81 5.3 Mixed-mode I/II specimens 88 5.3.1 Strain responses . 88 5.3.2 Crack initiation . 89 5.3.3 Crack extension angles . 97 5.3.4 Fracture surfaces 99 5.3.5 Stress fields for mixed-mode specimens 100 5.3.5.1 At zero crack extension . 101 - iv - Table of contents 5.3.5.2 At final crack length 104 5.3.6 Fracture resistance curves 112 5.4 Summary . 113 6. DETERMINATION OF THE FRACTURE RESISTANCE BY A HYBRID APPROACH 6.1 Introduction . 116 6.2 A hybrid numerical and experimental method 117 6.2.1 Conventional multiple-specimen approach 117 6.2.2 The hybrid approach 119 6.3 Validation of the hybrid approach 123 6.3.1 Mode I SE(B) specimens . 124 6.3.1.1 HY80 steel 124 6.3.1.2 Al-alloy 5083 H-112 . 129 6.3.2 Mixed-mode I/II specimens . 135 6.3.2.1 Al-alloy 6061-T651 . 135 6.3.2.2 Al-alloy 5083 H-112 . 143 6.4 Summary . 147 7. CONCLUSIONS AND FUTURE WORK 7.1 Introduction . 149 7.2 Main conclusions 149 7.2.1 Numerical study on Mode I ductile fracture growth 149 7.2.2 Crack initiation under mixed-mode I and II loadings 150 7.2.3 Fracture resistance over complete mixed-mode I and II loadings . 151 7.2.4 Crack extension directions under mixed-mode I and II loadings . 153 7.2.5 A hybrid approach to determine fracture resistance 153 7.3 Future work . 154 -v- Table of contents 7.3.1 Experimental study on the mixed-mode ductile fracture . 154 7.3.2 Mixed-mode fracture under low temperature for arctic application 154 7.3.3 Mixed-mode crack extension in large-scale structures 154 REFERENCES . 156 LIST OF PUBLICATIONS 168 - vi - Nomenclature NOMENCLATURE a Crack size n 1, n ACMOD pl Incremental area under the load versus the plastic crack mouth opening displacement curve a0 Initial crack size af Final crack size anotch The machined crack length  Dimensionless constant in HRR solution c Maximum limit of porosity incremental ratio per load step B Thickness of specimen c Length of the circumferential crack b Remaining ligament in the fracture specimen BN Net-thickness of specimen after side-grooving  eq Mode-mixity angle CMODi Crack mouth opening displacement at the crack initiation Ci CMOD-P compliance values from i  Test and i  FE (Finite element) CTOD Crack tip opening displacement dn Dimensionless constant that depends on strain hardening  Load-line displacement (LLD) crack  no M Displacement resulting from the deformation of the beam without the crack  crack M Displacement resulting from the deformation of the beam with crack  eF Elastic displacement component due to shear force  Fp Plastic displacement component due to shear force aFatigue Crack growth due to fatigue loading a Crack extension aL Crack extension measured on the sharpened side aR Crack extension measured on the blunted side f max Maximum void volume fraction increment - vii - Conclusions and future work 7.2.4 Crack extension directions under mixed-mode I and II loadings The direction of crack extension after the initiation of the cracks shows two interesting trends. For Mode I dominant specimens, the cracks extend to the sharpened side near the specimen surface but towards the stretched side near the mid-thickness, caused by the significant variation in the opening stress and the stress triaxiality across the thickness. Near the surface of the specimen, the shear stress is significantly larger than the opening stress, and thus a shear-type fracture is developed. The opening-type fracture happens near the mid-thickness mainly due to the strong triaxiality level and large opening stress, which facilitate the initiation and growth of the voids. However, the Mode II dominant specimens demonstrate a consistent direction of crack extension, nearly aligned with the crack plane over the entire thickness, driven by the uniform shear stress across the thickness. These observations imply the necessity to consider the effect of thickness on the ductile crack extension under mixed-mode loadings. 7.2.5 A hybrid approach to determine fracture resistance In view of the absence of the convenient, easy and accurate method to determine the fracture resistance for the mixed-mode I and II test, this study has proposed and verified a hybrid method, which provides a convenient and reliable approach in deriving the fracture resistance measured from fracture specimens based on both the experimental load-deformation curves ( P-LLD curve and the P-CMOD curve for the Mode I specimens, and M - and FV -V for the mixed-mode I and II specimens). The J - R curves calculated from the hybrid approach follow closely the experimental measurement for the pure Mode I SE(B) specimens made of two different materials, the HY80 steel and the Al-alloy 5083 H-112. In addition, the hybrid method also presents an accurate estimation of the fracture resistance for fracture specimens under mixed-mode I and II loading, as demonstrated by the verification on both Mode I and Mode II dominant specimens made of two different Al-alloy materials, 6061 T651 and 5083 H-112. Therefore, the proposed hybrid approach provides a convenient and reliable means to determine the fracture resistance for specimens under mixed-mode I and II loading conditions. - 153 - Conclusions and future work 7.3 Future work 7.3.1 Experimental study on the mixed-mode ductile fracture Although this research has yielded fruitful conclusions on the mixed-mode I and II ductile fracture, there are still many gaps deserving further research in this field. Firstly, current research focus mainly on the mixed-mode I and II ductile fracture behaviours for the deep cracked specimens with crack depth ratio of a0 / W  0.5 , further research on the effect of crack tip constraint is recommended to be carried out through testing on specimens with varied a0 / W ratios. Secondly, only the combination of Mode I and Mode II fracture is considered in this study, therefore, further work can extend to investigate the ductile fracture behaviours under the complete mixed-mode I, II and III loadings. Thirdly, the effect of thickness on the critical fracture toughness under various mixed-mode I and II loadings should be explored further based on the proposed stain reduction approach. Finally, the striations left on the fracture surfaces of the Mode II dominant Al-alloy specimens deserve further investigations on the mechanism of such phenomenon and the applicability of the striation approach on other types of materials. 7.3.2 Mixed-mode fracture under low temperature for arctic application There is an increasing exploration of oil and gas in the arctic region, where the temperature is below zero degree Celsius. The fracture toughness of the metal materials used for the pipelines, vessels and platforms is sensitive to the temperature. Normally, a lower temperature will result in small fracture toughness. Also, the fracture failure mode may change from the ductile type to the brittle type with the decreasing temperature. Therefore, further investigations on the mixed-mode fracture behaviours for the metal materials under low temperature are recommended in the future. 7.3.3 Mixed-mode crack extension in large-scale structures Both crack front constraint and mode-mixity exert significant effects on the fracture behaviours for a growing crack. The small-scale laboratory specimens can hardly represent both the real level of constraint - 154 - Conclusions and future work and the magnitude of mode-mixity for a real crack in the large-scale structures. Therefore, future research should relate quantitatively the mixed-mode ductile fracture resistance determined from small-scale specimens to that of the large-scale structures. - 155 - References REFERENCES Ahmad, J., Papaspyropoulos, V., Brust, F. W. and Wilkowski, G. M. (1989). A predictive J-estimation method for circumferentially surface-cracked pipes of power-law hardening materials in pure bending. 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Bending modified J-Q theory and crack-tip constraint quantification. International Journal of Fracture, 141(1-2): 115-134. Zhu, X. K., Leis, B. N. and Joyce, A. (2008). Experimental estimation of J-R curves from load-CMOD record for SE(B) specimens. Journal of ASTM International, 5(5): 66-86. - 167 - List of publications LIST OF PUBLICATIONS [1] Qian X, Yang W. (2012) Initiation of Ductile Fracture in Mixed-mode I and II Aluminum Alloy Specimens. Engineering Fracture Mechanics, 93: 189-203. [2] Yang W, Qian X. (2012) Fracture Resistance Curve over The Complete Mixed-mode I and II Range for 5083 Aluminum Alloy. Engineering Fracture Mechanics, 96: 209-225. [3] Qian X, Yang W. (2011) A Hybrid Approach To Determine Ductile Fracture Resistance. 11th International Conference on the Mechanical Behavior of Materials (ICM11), 10: 319-324. [4] Wuchao Yang, Xudong Qian. (2011) Ductile Extension of 3D External Circumferential Cracks in Pipe Structures. Frontiers of Architecture and Civil Engineering in China, 5(3): 294-303. [5] X. Qian, W. Yang. (2010) A Hybrid Approach to Determine Fracture Resistance for Mode I and Mixed-mode I and II Fracture Specimens. Fatigue & Fracture of Engineering Materials & Structures, 34(5): 305-320. - 168 - [...]... therefore, is to investigate the effect of mixed- mode I and II loadings on the ductile fracture behaviors for two metal materials, which are commonly utilized in offshore applications, the aluminium alloy 5083 H-112 and the American Petroleum Institute (API) X65 pipeline steel This study has proposed and verified a strain detection method to indicate the physical moment of crack initiation for mixed- mode. .. shearing takes place when a couple force tears the crack in a direction parallel to the crack front One of the three modes or any combination of the three modes can represent any realistic crack opening Mode II shear or sliding Mode I opening Mode III tearing Figure 1.2: Three modes of fracture (Anderson, 2005) Offshore structures are often designed against Mode I ductile fracture failure by assuming... Simulation of Mode I ductile fracture Investigation on mixed- mode I and II ductile fracture Test methods verification Test results and interpretation Fracture toughness at crack initiation ●Detecting the crack initiation Fracture resistance curves ●Measuring the crack extension ●Crack extension angles Fracture surfaces Proposal of a new hybrid method to determine the fracture toughness for mixed- mode I... the pure Mode I fracture toughness is smaller than that of mixed- mode I and II fracture for the two materials studied Also, the Mode I fracture resistance curve forms the lower bound of the J -R curves for the entire mixed- mode I and II loading range These observations mean that the current design against Mode I ductile fracture is - xxi - Summary conservative and safe In addition, both the fracture. .. experimental investigations The last section summarizes the research gaps for the study on the mixed- mode I and II ductile fracture 2.2 Ductile fracture mechanism From a microscopic view, ductile fracture is a mode of material failure in which voids, either already existing within the material or nucleated during formation, grow until they link together, or coalesce, to form a continuous fracture path... critical fracture toughness for different mixedmode I and II loadings are determined by using the strain detection approach In addition, this study also proposes and verifies a striation marking method, which facilitates the determination of the fracture resistance ( J -R ) curves for the Mode II dominant specimens Furthermore, the fracture surfaces with different dominant failure modes have been investigated... loading -1- Introduction In general, there are three possible crack opening modes for a cracked body (Anderson 2005), as shown in Fig 1.2 Firstly, the Mode I or the opening mode, which occurs when the force is pulling the cracked body perpendicular to the crack plane Secondly, the Mode II or the in- plane shearing initiates as a coupled force tries to slide the crack along the crack plane Thirdly, the Mode. .. crack tip for: (a) Mode I dominant Al-alloy specimens; (b) Mode II dominant Al-alloy specimens; (c) Mode I dominant X65 specimens; and (d) Mode II dominant X65 specimens 90 Figure 5.9: Test results for Al-alloy mixed- mode specimens: (a) The M-θ curves and (b) FV-δV curves, for deep-crack mixed- mode specimens; and (c) M-θ curves and (d) FV-δV curves, for shallow-crack mixedmode specimens... 2001; Pirondi and Dalle Donne 2001), which means that the mixed- mode I and II loading are more crucial than the Mode I loading for ductile materials which contain cracks The second conclusion contradicts with the first one that the Mode I fracture toughness at the crack initiation and the ductile tearing resistance remain smaller comparing with mixed- mode I and II cases (Maccagno and Knott 1992; Bhattacharjee... utilized in the subsea oil and gas piping because of its high strength and high fracture toughness The objectives of the research work are: (1) To investigate the fracture toughness at crack initiation under various mixed- mode I and II loadings by using the strain detection method (2) To study the trend of ductile fracture resistance under variety of mixed- mode I and II loadings based on the strain marking . MIXED- MODE DUCTILE FRACTURE IN METAL MATERIALS FOR OFFSHORE APPLICATIONS YANG WUCHAO NATIONAL UNIVERSITY OF SINGAPORE 2012 MIXED- MODE DUCTILE FRACTURE. - 3. NUMERICAL MODELLING OF MODE I DUCTILE FRACTURE GROWTH 3.1 Introduction 26 3.2 Computational cell method for ductile fracture resistance 27 3.2.1 Ductile crack growth using the computational. Experimental study on the mixed- mode ductile fracture 154 7.3.2 Mixed- mode fracture under low temperature for arctic application 154 7.3.3 Mixed- mode crack extension in large-scale structures