corrosive fatigue **crack** **propagation** life decreases obviously. Hydrogen generate at cathode when polarization potential -1200mV、-1100mV and -1050mV, which penetrate into metal easily. So the **crack** tip becomes fragility. Superfluous hydrogen evolution occurred at the **crack** tip and **crack** **propagation** rate N a

In this study, we present a mathematical derivation and numerical implementation that can achieve these goals, solving for conservation of momentum in both the spatial and material domains. The spatial (or physical) domain can be considered as a description of what we physically observe and the material domain is the evolving reference domain due to **crack** evolution. The theory is an interpretation of linear elastic fracture mechanics and consistent with Griffith’s fracture criterion. This paper represents a generalisation of the authors’ previous work on static **crack** **propagation**, Kaczmarczyk et al. (2014). The approach taken is based on the principle of global maximum energy dissipation for elastic solids, with configurational forces determining the direction of **crack** **propagation**. This approach has been successfully adopted by a number of other authors in the context of quasi-static analysis, e.g. Kaczmarczyk et al. (2014) and Gurses and Miehe (2009). At present we restrict ourselves to the consideration of elastic bodies with energy dissipation limited to the creation of new **crack** surfaces.

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In order to simulate fatigue **crack** **propagation** under linear elastic condition, the **crack** path direction must be determined. There are several methods use to predict the direction of **crack** trajectory such as the maximum circumferential stress theory, the maximum energy release rate theory and the minimum strain energy density theory. Bittencourt et al. [12] have shown that, if the **crack** orientation is allowed to change in automatic fracture simulation, the three criteria provide basically the same numerical results, since the maximum circumferential stress criterion is the simplest, presenting a closed form solution, it is briefly described below.

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The CT specimen were subjected to constant amplitude loading with different R-ratios (the minimum load over the maximum load in a loading cycle), R=0, R=0.1, R=0.5. Although there have been several investigations of the effect of the complex load sequences involving overloads and underloads on fatigue **crack** growth rates (retardation and acceleration), the phenomena are still not completely understood. The effects of variable amplitude loading on the fatigue **crack** **propagation** is studied using the Finite Element Method with the overload ratios of 1.8 and 3.

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Abstract. The present paper exposes the development of a specific Digital Image Cor- relation (DIC) method to ensure a fast calculation of fracture parameters such as stress intensity factors and **crack** length. This measurement is used to control a fatigue **crack** **propagation** using the load shedding method in order to ensure a limited plastic damaged **crack**. The experimental procedure has the main advantage to be fully automotive. The parameters’ identification is compared with a more sophisticated identification method and shows a good accuracy.

loading like compression, tension, internal pressure, bending or any combination of these may initiate and propagate a **crack**. This becomes more important if the pipes carry hazardous fluid. To predict fatigue **crack** **propagation** in circumferentially cracked pipe using its three dimensional data becomes cumbersome. In the first part of this project the pipe is converted into a beam using conformal transform. After the pipe was converted to beam it was found that the **crack** in the beam is not through. Hence the fatigue **crack** **propagation** cannot be simulated using FRANC2D as it is finite element based two dimensional **crack** **propagation** simulator software. In the second part of the project, the fatigue **crack** growth tests were carried out on an EN8 steel specimen in Instron 8800 machine. The **crack** **propagation** in EN8 steel beam was also simulated using FRANC 2D. Then the results obtained experimentally and from FRANC 2D were compared.

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The study of the different types of intermetallic compound (IMC) formed in different type of solder joints is important as to investigate the **crack** **propagation** behavior due to the issue on reliability of solder joint interconnection and the performance of electronic appliances. The intermetallic compound is the actual bond formed in soldering from the diffusion of solder alloy and substrate. In addition, consequence from the brittle property of intermetallic compound effected the solder interconnection. This is caused by a strong stress concentration during the thermal cycles. Hence, the cracks were found to initiate and propagate near the intermetallic compound layers. The **crack** **propagation** is analyzed to understanding the role of the different IMC on the morphology of the solder joints after **crack** propagated. Furthermore, this project will provide an understanding of the failure mode mechanism of lead free solder particularly on the IMC layer morphology and the role of the IMC formation and growth rate on the thermal **crack** **propagation** of lead-free solder.

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Abstract. Typical penny-shaped microcracks at their propagating in spallation of Zr-based bulk metallic glass (Zr-BMG) samples were captured by a specially designed plate impact technique. Based on the morphology and stress environment of the microcrack, a damaged zone or **propagation** zone around the **crack** tips, similar to the cohesive zone in classical fracture theories, is applied. Especially the scale of such a damaged zone represents a scale of the **crack** **propagation**. Its fast **propagation** would quickly bring a longer **crack** or cause cracks coalesce to form another longer one. The estimated **propagation** scales of microcracks are reasonable compared with what occurred in the Zr-BMG samples.

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The **crack** initiation from corrosion pits and the characteristic morphology of **crack** **propagation** exhibit a ductile fracture-like appearance at the **crack** tip. The maximum depth of corrosion pits and their size increase with increasing number of cycles. Thus, it can be concluded that the corrosion fatigue process of Ni-16Cr alloy is controlled by initiation and growth of corrosion pits.

Fatigue **crack** growth resistance properties are obtained through fatigue **crack** **propagation** tests. The results, obtained from a log-log plot presents three regions: region I, where the microstructure, mean stress and environment have a high influence. Region II, that presents a linear behavior and region III where the material reaches the fracture toughness and results in an instable fracture. In this work it is studied the behavior of corrosion resistant USI SAC 50 steel welded joints, using compact tension specimens with notch localized on the base metal, heat affected zone and melted zone. It is obtained stable **crack** **propagation** equations type Paris equation for the region II, with 95% confidence limit. It is observed that the heat- affected zone presents a major scatter.

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Different methods are used for modeling **crack** **propagation** by numerical techniques. Using the finite element method, one can find the stress intensity factors (SIF) at the **crack** tips. The precision of the SIF values depends to established finite element mesh. A fundamental difficulty in the computational simulation of discrete **crack** **propagation** is, the requirement that the spatial discretisation accommodates the changing topology of the domain. Different methods are now being actively used to render accurate and reliable, simulations of **crack** advance in arbitrary domains. Among these are adaptive finite element mesh refinement, various mesh overlay procedures, mesh less methods, XFEM methods and boundary elements methods .

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The existence and **propagation** of a **crack** on an engine’s nonlinear rotor can easily cause a serious accident, so it is quite essential to detect a **crack** in the rotor system through analysis of the rotor’s vibration signals and to delay the **crack** **propagation**. The vibration signals of the cracked rotor show the non-periodic and the nonlinearity within a transient response. The fault characteristics of the **crack** can be easily hidden in other vibrational components and are difficult to extract from transient signals. In the paper, the Hilbert-Huang marginal spectrum (HHMS) method is proposed to realize the extraction of crack’s fault characteristics in a nonlinear rotor system. In addition, the crack’s opening and closing degrees at any rotating position are also put forward representing the **crack** **propagation**, and some tactics of the delaying **crack** **propagation** are proposed based on the effect on the crack’s opening and closing degree caused by the change of different rotor parameters. The simulation results show that the HHMS method can detect a **crack** early at about five per cent of the depth of the rotor’s diameter, and the methods of delaying **crack** **propagation** can effectively delay **propagation**. Experimental results verify the effectiveness of the proposed HHMS method.

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Pop-in cracking exists in ductile materials in a particular condition which is aﬀected by the size and shape as well as the microstructure of the specimen. Using the temperature changes due to the thermo-mechanical eﬀects, the **crack** **propagation** can be easily identiﬁed in three stages: (1) thermo-elastic stage where the temperature will initially drop until yielding occurs; the temperature drop is related to the reduction of the kinetic energy and the probability of collision of the atoms in the considered system volume; (2) stable **crack** extension stage where the macro-fractography shows the typical pop-in features and the increasing temper- ature curve presents a step-like feature; it was concluded that the step-like feature is due to the complex eﬀects of dislocation interactive with the precipitation particles in a constrained size and shape (the thickness is 1/4 inch); (3) unstable **crack** extension stage where the temperature has a higher rate of increase and a higher temperature ﬂuctuation, compared to the SCE stage; the change in the temperature trend correlates to the change of the slip mode of the dislocation. In this ﬁnal stage, most dislocations perhaps cannot slip on their original slip system because the dislocation is kinked. They need more energy to overcome the kinking, and develop another slip system to adapt to the instantaneous stress state.

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Fracture mechanics involves correlating analytical predictions of **crack** **propagation** and failure with experimental results. The analytical predictions are made by calculating fracture parameters such as stress intensity factors in the **crack** region, which you can use to estimate **crack** growth rate. Typically, the **crack** length increases with each application of some cyclic load, such as cabin pressurization-depressurization in an

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without any external changes in the system, i.e., the **crack** propagates without additional load. The distinction between stages is important for avalanche hazard evaluation because initiation may only result in a local failure, e.g., cracking at the trigger, while **propagation** can result in the failure of a slope, i.e., an avalanche. **Crack** **propagation** is an open area of avalanche research, with a debate on whether cracks propagate in shear (McClung, 1979) or in mixed-mode col- lapse/shear (anticrack; Heierli et al., 2008) waves. Recently, two tests were developed to examine **crack** **propagation**: The ECT (Simenhois and Birkeland, 2006, 2009) and the PST (Sigrist and Schweizer, 2007; Gauthier and Jamieson, 2008). Stability tests will always suffer from edge effects because they use isolated beams that are orders of magnitude smaller than avalanche slabs. For instance, the longest **crack** propaga- tion length recorded in previously published studies has been about 3 m (van Herwijnen and Jamieson, 2005; Gauthier and Jamieson, 2008; van Herwijnen et al., 2010; van Herwijnen and Birkeland, 2014). Also, cracks likely propagate radially from a trigger in an avalanche, while in PSTs and ECTs, cracks are forced to travel in a straight path. Attempts have been made to reduce edge effects by, for example, not cut- ting the far end of the beam in PSTs (McClung, 2009). An “uncut” back end showed significantly shorter **crack** prop- agation lengths (Ross and Jamieson, 2012), suggesting that beam isolation aids **propagation**. In contrast, the critical cut length r c , the cut length needed to initiate self-**propagation**,

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Different procedures have recently been proposed to overcome, or at least mitigate, the above-mentioned drawbacks. Nevertheless, in spite of the technological developments, nearly all procedures present limitations in what concerns monitoring **crack** **propagation** within a time interval. Typically, the **crack** pattern is depicted for each time instant independently from any previous history and is not possible to accurately identify changes occurring within a given time interval. Most existing techniques can only be applied in very simple tests, under strictly controlled conditions regarding surface and lighting conditions, mainly to avoid false detections.

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This procedure is validated on three tests which can be found in the literature. The first one is the study of concrete **crack** **propagation** for a bracket specimen, described in [13]. Results obtained are in good agreement with the experimental ones, in terms of trajectory and load-displacement curve. It could still be improved using an exponential law for the cohesive zone rather than a linear or bilinear one. The second validation is performed with respect to a three point bending test of a Plexiglas specimen with a pre-**crack** at an angle with respect to the load direction [14,15]. In this case, only the **crack** trajectories are compared between the numerical simulations and the experiment, which show a good agreement. The last example focuses on the torsion of a parallelepiped concrete specimen pre-cracked at 45 degrees (see figure 8) [16]. The **crack** trajectory is complex, presented in figure 9, with an S shaped form. Once more the agreement between simulations and experiment in figure 10 is rather good from the point of view of trajectories and load-displacement curves, with a similar remark on the type of law used for the cohesive model.

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To determine the **crack** growth speed and fracture toughness of materials, usually using the rectangular double cantilever beam specimens. Malluck JF, King WW [3] et.al, used the kanninen’s model for simulation of fast fracture in the DCB specimen. Kanninen MF [4] et.al, the DCB (double cantilever beam) test specimen is used for dynamic analysis of unstable **crack** **propagation** and arrest. Simple beam or shear beam theories related theoretical analysis of the RDCB specimens. The applications of beam theory to the dynamic **crack** **propagation** are particularly attractive because it is one dimensional analysis. The **crack** tip stress or strains were cannot predicted by the beam theory and it does provide an accurate account of energy quantities which form the basis of the fracture criterion. Nishioka and Atluri [5] et.al, introduced a moving singular element procedure for dynamic **crack** **propagation** analysis. In their method, a special singular element that follows the moving **crack** tip is used, a special singular element that follows the moving **crack** tip is used, and during the simulation of **crack** **propagation** only the conventional elements immediately surrounding the singular element are distorted. Nishioke and Atluri [6] et.al,carried out the dynamic fracture analysis of RDCB specimen using the moving finite element method. In this paper, a finite element simulation is based on the remeshing technique compatible with the actual dynamic fracture process. Under the fixed displacement loading condition the analysis is done on the RDCB specimen. The analysis results show good agreement with those obtained via the experimental procedures and other numerical techniques.

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