Discrete Dislocation Dynamics Approach to Dynamic Fracture Toughness under Short Pulse Loading January, 2009 Doctor of Engineering Tran Huu Nhan Toyohashi University of Technology Contents 1 Introduction 1 1.1 Loading rate effect on dynamic fracture .5 Discrete dislocation dynamics .6 Objectives of the research. 9 2 Experiment of Dynamic Fracture Toughness 12 2.1 Material and specimens .3 Measurement method of dynamic stress intensity .4 Stretched zone size .2 Cleavage fracture mechanism .3 Dimple fracture mechanism. 35 i 3 Basic Concept of Discrete Dislocation Dynamics 37 3.1 Discrete dislocation dynamics .5 Dislocation bundling technique. 47 4 Models of Microscopic Fracture Mechanisms Based on Dis- crete Dislocation Dynamics 49 4.2 Dislocation emission and movement .3 Cleavage fracture model .1 DDD approach to dimple fracture .2 GTN modeling approach.
67 5 Numerical Calculation Results 68 5.1 Dislocation density distribution .2 Resolved shear stress on the slip line .3 Average velocity of leading dislocation .4 Plastic zone size .5 Crack tip opening displacement .1 Local tensile stress .3 Dislocation density distribution .4 Crack tip opening displacement .1 Local tensile stress contributed by macro crack .2 Stress component vs time .3 Stress component along the inner ligament .4 Stress component rate .5 Void volume fraction along the inner ligament .6 Evolution of void volume fraction .7 Dynamic fracture toughness .8 Crack tip opening displacement. 85 6 Conclusions 87 iii List of Figures 1.1 Effect of time on the fracture behaviors and mechanisms .1 Specimen configuration .3 Schematic illustration of the three regions and definition of coordinate systems Oxy and Px’y’ .4 Strain gage position .5 Profile of broken specimen near pre-crack tip .6 Output of strain gage near crack tip (L = 180 mm) .7 Output of strain gage near crack tip (L = 100 mm) .8 Output of strain gage near crack tip (L = 50 mm) .9 The time history of dynamic stress intensity for three specimen geometries .10 The observed stretched zone for 180 mm length .11 The observed stretched zone for 100 mm length .12 The observed stretched zone 50 mm length .13 The CTOD as a function of the applied stress intensity factor for three pulse durations - the logarithm scale .14 Time history of dynamic stress intensity for three specimen geometries .15 Dynamic stress intensity as a function of stress pulse duration 29 2.16 The observed stretched zone for the largest specimen .17 The observed stretched zone for the medium specimen .18 The observed stretched zone for the smallest specimen .19 The observed crack tip opening displacement .20 Microscopic fractograph indicating cleavage fracture for the largest specimen .21 Microscopic fractograph indicating cleavage fracture for the medium specimen .22 Microscopic fractograph indicating cleavage fracture for the smallest specimen .23 Cleavage origin distance for three stress pulse durations .1 Schematic illustration of the dislocation model .2 Relation between shear stress and stress components .3 Schematic illustration of the simulation process .4 Schematic illustration of bundle process .1 Schematic illustration of the dimple fracture mechanism model 51 4.2 Schematic illustration of the dislocation model .3 Local tensile stress illustrated schematically .4 Schematic illustration of the dislocation model .1 Dislocation density distribution along the slip plane for three pulse durations .2 The resolved shear stress along the slip plane at the terminal time for three pulse durations .3 Average velocity of leading dislocation for three pulse durations 71 5.4 Plastic zone size as a function of time for three pulse durations 72 5.5 Crack tip opening displacement as a function of time for three pulse durations .6 Crack tip opening displacement as a function of applied load- ing rates .7 Local tensile stress as a function of time .9 Dislocation density distribution along the slip line for three pulse durations .10 Crack tip opening displacement .11 Local tensile stress raised by macro crack as a function of time 78 5.12 Stress component as a function of time .13 Stress component in x-direction along the inner ligament .14 Stress component in y-direction along the inner ligament .15 Macroscopic stress component rate .16 Void volume fraction along the inner ligament .17 Evolution of void volume fraction at position of xL = 50 µm .18 Dynamic fracture toughness .19 Crack tip opening displacement. 83 vi List of Tables 2.1 Chemical compositions of SM490A steel .2 Mechanical properties of SM490A steel at room temperature .3 Chemical compositions of Al 7075-T651 alloy .4 Mechanical properties of Al 7075-T651 alloy at room temper- ature. 14 vii Acknowledgements The author is very much appreciated and greatful to the Japanese Govern- ment for giving me an opportunity to study in Japan at Toyohashi University of Technology under Mobukagakakusho Scholarship and also thankful to Ho Chi Minh City University of Technology for granting study leaves.
I would like very much to express my appreciation to Prof. Hiroomi Homma for his guidance and support for the last three and half years. He has exposed to me many new aspects of the fracture mechanics field and provided a great working environment. I have been benefited greatly from deep knowledge and the enthusiasm of Prof.
Thanks to Dr. Gunawan not only for his valuable suggestions but also for continuous encouragement which contribute to progress of this work. Many thanks to all colleagues at Toyohashi University of Technology for helping to create a pleasant and inspiring working atmosphere. In particular I would to thank Mr.
Inoue for their working together during experiments and technical support. My greatest thanks to Ho, my wife, best friend and the love of my life. She has helped me at all times and with all things. She is always there to provide moral support, strength, and affection.
And I also would like to thank my family members for their endless pa- tience during my research involvement which took so much time away from them. viii Abstract The effect of loading rate on both cleavage and dimple fracture mecha- nisms had been experimentally investigated by the previous researchers. The crack initiation of both cleavage and dimple fracture was sensitive with the short life of impulsive loading. The dynamic fracture toughness was measured for several materials and it was shown that the dynamic fracture toughness was remarkably increased when the duration of impulsive stress intensity is shorter than 20 µs.
Experimental results of the cleavage fracture from a crack tip in welding structure steel SM490A indicated that the remarkable increase in dynamic fracture toughness was obtained under the short pulse loading or high loading rate, for instance, the duration of less than 25 µs. It is obviously contrary to the usual understanding that the higher the yield strength is, the lower the fracture toughness is. The same trend of the fracture toughness was also obtained by the ex- periment of aluminum alloy 7075-T651, in which dimple fracture was domi- nant. This material is insensitive against loading rate.
The dimple fracture mechanism model indicates that a dominant void plays an important role on the dimple fracture initiation. The crack initiation is a result of coales- cence between a dominant void and a crack tip. The coalescence is caused by nucleation of many fine voids in the inner ligament and their subsequent linkage. This work is carried out to explain and obtain the physical meaning of the remarkable increase in both the cleavage and the dimple fracture toughness under short pulse loading as mentioned above.
Discrete dislocation dynamics (DDD) method is utilized to construct models of the cleavage and dimple fracture initiation. Since, in both of the cleavage and the dimple fracture mechanism, mobility of dislocations plays an important role on initiation of a crack. In addition, especially under dynamic loading, dynamic crack behavior can be simply treated by the DDD method. The dynamic plasticity ahead of the crack tip in mode I condition is experimentally measured for the low alloy carbon steel JIS SM490A by us- ing the one-point bend test at room temperature.
Three different lengths of specimens are used to generate 25, 50 and 100 µs pulse durations of dy- namic stress intensity. The experimental results of the stretched zone width are used to calculate the crack tip opening displacement (CTOD) and it is indicated that the CTOD decreases with the pulse duration for the same am- plitude of dynamic stress intensity pulse. CTOD is proportional to square of applied stress intensity as seen in linear elastic fracture mechanics. The numerical analysis is carried out by a DDD model.
The obtained dislocation array parameters such as the number of dislocations, dislocation distribution density, crack tip opening displacement and plastic zone size increase with the magnitude of stress intensity factor, KI and pulse duration. The validity of the DDD model is proven by the good agreement between the numerical results and the experimental ones. Following the investigation on crack tip plasticity, the specimens of the same material are chilled at low temperature of −80◦ C to examine the cleav- age fracture. The remarkable increase in the dynamic fracture toughness value, KId is obtained under high loading rate or short pulse duration.
The value of CTOD is also closely correlated with KId. The distance from the crack tip to the cleavage origin is almost independent of the pulse duration and equal to around 100 µm. The numerical simulation to the experiment is carried out by the discrete dislocation dynamics model of cleavage fracture considering the pile-up of dislocations. The time effect on dynamic yield strength can be estimated by the previous experimental results of dynamic plasticity.
The numerical results are compared with the experimental ones in reasonable agreement. Dimple fracture of aluminum alloy 7075-T651 subjected to various stress intensity pulses with durations of 20, 40 and 80 µs is investigated by combina- ii tion of discrete dislocation dynamics and the Gurson-Tvergaard-Needleman constitutive model (GTN-model). A dominant void ahead of a macro crack tip is modeled by a micro crack. The time evolution of principal stress com- ponents along the inner ligament is computed by the sum of the crack tip stress field and the interaction stress field of dislocations emitted from both the micro crack and the macro crack.
The yielding flow of GTN-model is used to estimate void volume fraction, which is used for a fracture initiation criterion. The numerical results of the dimple fracture are obtained in a reasonable agreement with the experimental ones. On the basis of the microscopic observations of both the cleavage and the dimple fracture mechanisms, the appropriate microscopic DDD models have been proposed. The validity of the numerical analysis model is verified by the good agreement between the numerical results and the experimental ones.
The physical sense of the time effect on the fracture parameters, which causes the remarkable increase in dynamic fracture toughness and crack tip opening displacement for both the cleavage and the dimple fracture of a crack subjected to very short pulse loading, has been explained well by the movement of dislocations ahead of crack tip. iii Chapter 1 Introduction 1.1 Loading rate effect on dynamic fracture To ensure structural safety and develop new advanced materials, fracture mechanics provides an effective concept to ensure operational safety and structural integrity adequately. In general, at a quasi-static loading rate, the crack begins to propagate in an unstable manner when the stress intensity equals or exceeds the fracture toughness. Toward the fracture prediction it is very important to determine one of the most important mechanical properties, fracture toughness of materials.
Quite difference from static fracture mechanics is that dynamic fracture mechanics contains three complicating features, which are not present in the static one, inertia forces, rate-dependent material behavior and reflected stress waves. The local crack tip stress and strain fields are affected by the inertia forces and arrival of reflected stress waves. The linear elastic approach, is still applicable when the plastic zone is restricted to a small region near the crack tip in the dynamic problem[1]. Recently, dynamic fracture analysis has been extended to include nonlinear and time-dependent material behavior.