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Highlights • The effect of load ratio and temperature on FCG rates for base metal and weldment are investigated. • The FCG rate of base metal is quicker than that of weldment, which is mainly due to microstructure. • The monotone plastic zone is larger than that of cyclic plastic zone. Abstract In this paper, the effects of load ratio and temperature on fatigue crack growth (FCG) rates for commercial titanium alloy (CP-Ti) base metal and its weldment are investigated by experiments. Results show that the fatigue crack growth (FCG) rate of weldment is slower than that of base metal, which is mainly due to the difference of the microstructures between them. The microstructures at the weld are coarse grains and acicular martensite, which can reduce the FCG rate of weldment. The effect of load ratio on FCG rate will gradually weaken or even disappear with the increase of temperature. Also, the effect of temperature on FCG rate will gradually weaken or disappear with the increase of secondary cracks on the fracture surface. The results of finite element simulation show the FCG rate will be increased with the increase of plastic zone size and plastic strain, the increase of load ratio and temperature will reduce the FCG rate difference between weldment and base metal. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • More plastic strain energy will be consumed in the high load amplitude. • Δ J ac and Δ J ′ are suitable to describe phenomena in the fracture surface. • The crack growth resistance is higher under high load ratio. • The fracture morphologies are all dimples at the late stage of crack growth. • The data obey the Paris' law mode in the rapid growth stage using Δ J ′. Abstract In this work, fatigue crack growth behavior of commercial pure titanium (CP-Ti) under different load levels is carried out considering the degree of plastic deformation of crack tip. Results show that there are great differences in the stage of crack stable growth in different loading conditions. In the same crack growth rate, strain energy and plastic zone in high load ratio are much higher than those in low load ratio, when crack growth rate is low. However, when crack growth rate is high, the differences of strain energy and plastic zone between these two loading conditions are much smaller. More plastic strain energy will be consumed and a wider range of plastic deformation in crack tip will be required in the high load amplitude. It seems that Δ K and Δ J cannot describe these phenomena, while Δ J ac and Δ J ac ′ proposed in this paper may be more suitable to describe these phenomena in the fracture surface. In different loading conditions, at the late stage of crack growth, the fracture morphologies are all dimples. The data in all the conditions obey the Paris' law mode, with the same coefficient and index in the rapid growth stage using the parameter Δ J ac ′. [ABSTRACT FROM AUTHOR]

Highlights • A process of inhibiting and promoting crack growth is performed. • The dimples and striations cover up the facet creep fracture characteristic. • The fatigue-creep interaction diagram based on the analyses is depicted. Abstract In this paper, the effect of the cold creep on fatigue crack growth rate are investigated by experiment considering wide ranges of load amplitudes and load ratios with or without certain degrees of dwell time. To further illustrate the cold creep influence, a series of finite element results are carried out. Finally fracture morphology analyses are also made to explain related crack growth behavior. Results show that fatigue crack growth rate either increases or decreases with certain degrees of hold load and dwell time imposed, depending on the values of the load amplitude and load ratio. This finding is the same as that in the fatigue life. Discussion shows that the effect of creep on fatigue crack growth can be attributed to the competition of the creep stress relaxation and creep strain. A process of inhibiting and promoting crack growth is performed. The fatigue-creep interaction diagram based on the analyses is depicted, by which the interaction between cold creep and fatigue can be well understood. Finally further studies and discussion are carried out by fracture morphology analyses from the dislocation pile-ups, which is in accordance with the finite element results from local creep behavior. This research will provide support to the clear understanding of the cold creep effects on the fatigue crack growth behavior. [ABSTRACT FROM AUTHOR]

Multiple cracks have been widely observed in pressure vessels and structure components. When multiple cracks approach each other, the interaction between them could affect the stress field around the cracks. So multiple cracks should be taken into account simultaneously because the interaction could change the stress intensity factor (SIF) of the cracks. In ASME Boiler and Pressure Vessel Code Section XI, a flaw combination criterion is provided for interacting parallel surface cracks. However, the criterion for the offset distance does not consider the influence of crack size on the magnitude of the interaction and is only given by an absolute value. In present paper, firstly, SIF for parallel surface cracks is evaluated as a function of the crack front position, relative position, aspect ratio and relative size by numerical analysis based on M -integral. And the influence of the interaction on SIF is quantified. It is shown that the crack front position, relative position between two cracks, aspect ratio and relative size are important parameters to determine the interaction between parallel surface cracks. Secondly, the new combination criteria for the offset distance are proposed for the fracture evaluation based on analysis results. [ABSTRACT FROM AUTHOR]

Both experimental and numerical investigations are performed to study the fracture behaviors of I-II mixed mode crack for commercially pure Titanium (CP-Ti). Three different types of specimens are considered in this paper, including Compact tension shear specimen (CTS specimen), Four point bending specimen (FPB specimen) and Cracked central plate (CCP). Results show that there exist two fracture modes of these specimens, including tensile-type fracture mode and shear-type fracture mode. For single edge notched specimen, the failure mode is determined by plastic mixity parameter M p , and the critical values of M p distinguishing the fracture modes are dependent on the specimen geometry (CTS or FPB specimen). For central cracked plate, specimens are all in a tensile-type fracture mode. Furthermore, specimen in a shear-type fracture mode has a higher loading capability than that in a tensile-type fracture mode. And the loading capability of specimen in tensile-type fracture decreases almost linearly with M p . Finally, constraints of these specimens are analyzed. Discrepancies of constraint between specimens increase with the component of mode I increasing. And the difference of constraint resulted from specimen type is much greater than that from crack length. [ABSTRACT FROM AUTHOR]

Due to the non-negligible role of T -stress on fracture parameter, T -stresses of three typical specimens, including central cracked plate (CCP), compact tension specimen (CTS) and four point bending specimen (FPB), are calculated using 3D finite element method. From the results, the tensile dominant specimen like CCP is in a lower-constraint state when the component of mode I is significant, and in a higher-constraint state when the component of mode II is significant, compared with bending dominant specimen like CTS and FPB specimens. Further, the crack initiation angles and plastic zones are assessed for the three specimens based on modified maximum tangential stress (MMTS) and modified R-criterion (MR). From the comparison, the effect of T -stresses or constraints induced by specimen geometries and loading modes play a significant role on crack initiation angle and plastic zone around the crack tip, which in turn can affect the fracture of specimen. [ABSTRACT FROM AUTHOR]

• Mechanism of overload effect of mixed mode I-II crack growth at negative load ratio is revealed. • Effect of loading angle and loading ratio on crack growth with overload loading is discussed. • Stress–strain field and plastic deformation at crack tip are revealed by finite element method. Fatigue crack growth (FCG) behavior under mixed mode loading has been received extensive attention, including overload condition. The mixed mode I-II fatigue crack growth behavior of commercial pure titanium (CP-Ti) with tensile overload at negative load ratios was investigated by experiment and finite element method (FEM). The effects of loading angle, load ratio and overload on mixed mode I-II fatigue crack growth were discussed with a modified compact-tensile-shear (CTS) specimen. The mechanism of mixed mode crack growth with overload was revealed. Fatigue crack growth path and fatigue crack growth rate (FCGR) with/without overload were compared experimentally, and overload retardation effect was investigated. The variation of plastic zone and the distribution of stress and strain were simulated through finite element method. The mechanism of overload retardation effect of mixed mode I-II crack growth under compressive load was illustrated by microscopic perspective, crack closure and residual compressive stress at crack tip, and the weakening effect of mode II shear component and compressive load effect on overload retardation effect was demonstrated. [ABSTRACT FROM AUTHOR]

• The proportion of mode II loading component increases with λ under biaxial compression. • There are crucial differences in variation range and tendency of T z subjected to biaxial tensile and compressive loading. • Stress triaxiality factor h is sensitive to a / W , t / W , β and λ under biaxial compression. • h can be adopted as a unified constraint parameter for long crack under biaxial compressive loading. Crack sizes, geometrical configurations of specimens and structures, as well as loading conditions have significant effect on in-plane and out-of-plane constraint effects. Safety assessment with constraint effects can effectively improve the accuracy. There are prominent discrepancies between compressive fracture and tensile fracture. Most of engineering structures are usually under biaxial loading conditions, so that the influence of biaxial compressive loading on fracture analysis with constraint effects is worth paying attention. The size effect factor (relative crack length a / W , thickness to width ratio t / W and crack inclination angle β) and load factor (lateral pressure coefficient λ) of central cracked plate (CCP) specimens with I-II mixed mode crack on constraint effects under biaxial compressive loading have been investigated through theoretical analysis and finite element analysis. In-plane non-singular T -stress (T 11) and its components (T x , T y , and T xy), out-of-plane non-singular T -stress (T 33), out-of-plane constraint parameter T z and stress triaxiality factor h have been adopted to quantify constraint effects. It demonstrates that λ has remarkable influence on SIF, T 11 and T 33 under biaxial compressive loading. The effect of higher a / W (long cracks) on B 11 is more noticeable when I-II mixed mode crack is closer to pure mode II crack or pure mode I crack. The proportion of shear fracture increases under biaxial compression with λ. With the increase of β , B 33 decreases sharply and then increases rapidly with higher λ. T z can directly reflect stress states and adequately describe the loss of out-of-plane constraint. The stress state of crack tip is more likely to asymptotic plane-strain condition ahead of crack tip under compression. There are crucial differences in variation range and tendency of T z subjected to biaxial tensile and biaxial compressive loading. Moreover, T z is insensitive to λ. Stress triaxiality factor h can illustrate in-plane and out-of-plane constraint effects including size effect and load factor (sensitive to a / W , t / W , β and λ), especially can be adopted as a unified constraint parameter for long cracks under biaxial compressive loading. The in-plane T -stress components can be directly calculated by T 11 under biaxial compression. The empirical equations of K II and T 11 containing size effect and load factor simultaneously are effective and convenient for applications. [ABSTRACT FROM AUTHOR]

• SIF and constraint parameters at the crack tip of CCP specimen under uniaxial compression are illustrated quantitatively. • There is a loss of out-of-plane constraint under compression when t/W ≤ 0.9. • The loss of out-of-plane constraint can be directly and evidently investigated through the analysis of T z than T 33. • The empirical equations for K II , T 11 and T z have been obtained are convenient and effective for application. The crack tip constraint effect should be considered in the fracture assessment of structures with cracks, and the in-plane constraint and out-of-plane constraint should be illustrated simultaneously for the three-dimensional cracks in practical engineering structures. The constraint effect of central cracked plate (CCP) specimens with I-II mixed mode crack under uniaxial compression has been investigated quantitatively in present work. The relationship between T -stress components (T x , T y , T xy) and in-plane constraint parameter T 11 has been established. The effects of a wide range of in-plane and out-of-plane geometrical configurations (including relative crack length a / W and thickness to width ratio t / W), material parameters (including elastic modulus E and Poisson's ratio ν), crack inclination angle β and friction coefficient μ corresponding to stress intensity factors (K), in-plane constraint parameter T 11 and out-of-plane constraint parameters T 33 and T z at the crack tip have been calculated and discussed theoretically and numerically. It demonstrates that the constraint parameters can effectively express the stress-strain field at the crack tip. The relative crack length a / W has an influence on the in-plane and out-of-plane constraint parameters, and the thickness to width ratio t / W mainly affects the out-of-plane constraint parameters T 33 and T z. The out-of-plane constraint parameters should be considered for long cracks. There is a loss of out-of-plane constraint under compression when t / W less than or equal to 0.9, which can be much more directly and evidently investigated through the analysis of T z than T 33. The empirical equations for K II , T 11 and T z have been obtained according to theoretical analysis and simulation results, which are convenient and effective for application. [ABSTRACT FROM AUTHOR]

• Anisotropic crack tip behavior in hcp titanium is studied by 2D and 3D atomistic simulations. • The stress triaxiality around the crack tip is lower in 3D simulations. • The activation of the oblique slip mode improves crack tip plasticity in 3D simulations. • The critical stress intensity factor for dislocation emission is lower in free 3D simulations. As three-dimensional (3D) atomistic simulations require much higher computational costs, two-dimensional (2D) atomistic simulations under plane strain condition are widely used to study dislocation emission from the crack tip. In order to study the difference of crack tip behavior in 2D and 3D simulations, both 2D and 3D atomistic simulations of the anisotropic crack tip response in hcp titanium were performed, as well as the comparison of simulation results with linear elastic fracture mechanics (LEFM) predictions. The comparing results find significant discrepancies of the near tip stress fields, incipient crack tip deformation and critical stress intensity factor in 2D and 3D simulations. In consistent with the theoretical predictions, crack tip plasticity is solely contributed by the inclined slip mode with a lower critical stress intensity factor than that for cleavage, otherwise an artificial cleavage behavior may be observed in 2D simulations. In contrast to this, the lower stress triaxiality near the free surface leads to an easier dislocation nucleation in free 3D simulations. Besides, the participation of the oblique slip mode improves crack tip plasticity and facilitates the activation of the inclined slip mode that cannot be activated in 2D simulations. In general, the incipient crack tip behavior observed in 3D simulations shows more consistency with experimental results. [ABSTRACT FROM AUTHOR]

• Plastic deformation and stress-strain response of crack tip under mode I and mixed-mode I-II loading are discussed. • Variation of stress-strain field and monotonic plastic zone at crack tip are revealed. • Effects of evolution of strain energy on fatigue crack growth behavior are analyzed. The mechanical behavior of crack tip under mode I and mixed-mode I-II fatigue loading for commercial pure titanium at negative load ratios are carried out by finite element method in this paper. The effects of maximum fatigue load, load ratio, loading angle and normalized crack length on the mechanical behavior of crack tip are discussed. The change of mechanical behavior of crack tip is analyzed through the evolution of strain energy. The results show that the increase of maximum fatigue load and crack length increase the plastic strain accumulation at crack tip in mode I fatigue crack growth (FCG), which causes the crack tip release more fracture energy to drive crack growth and affect the distribution of stress-strain field. The decrease of load ratio also increases the plastic strain accumulation and the plastic energy dissipation at crack tip. In mixed-mode I-II FCG, the larger loading angle increase the resistance of crack deflection and cause more plastic strain accumulation at crack tip. After the crack deflects, the crack growth increases the crack tip plastic zone and the morphology of plastic zone changes continuously, which cause the crack growth path move away from the mode I crack growth direction. Different loading angles produce different crack growth paths, which deviates from mode I crack growth direction with the increase of loading angle. [ABSTRACT FROM AUTHOR]

• New driving force parameter and crack closure models are proposed respectively. • Proposed crack closure model can reflect the variation of crack closure level. • The merits and demerits of models are analyzed by the dispersion of each model. The fatigue crack growth rate (FCGR) is strongly dependent on the load ratio R and most FCGR models are established on the basis of R. At present, there are more FCGR models with positive load ratio. In this paper, fatigue crack growth (FCG) behavior of commercial pure titanium at negative load ratios is studied. The FCGRs at various load ratios are fitted by driving force parameter model and crack closure model. The advantages and disadvantages of different models are analyzed by calculating the dispersion of FCGR curves which are condensed by each model. Improved two-parameter driving force model and proposed crack closure model are proposed by two FCGR modeling methods, respectively. One is to modify the FCGR by improving the stress intensity factor (SIF) K with the two-parameter driving force method. Another is established by correlating the crack closure ratio U and load ratio R , positive SIF range Δ K +, maximum SIF K max based on the variation of crack closure level in stable crack growth stage. It is found that proposed crack closure model is superior to the former in both the condensation effect and the physical significance. Under different loading conditions, proposed crack closure model can reliably and accurately condense the FCGR curves and reflect the variation of crack closure level in the whole stable crack growth stage. The integrity and validity of proposed crack closure model is also further verified by FCGR data of other researchers. [ABSTRACT FROM AUTHOR]