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In this paper, the effects of temperature and dwell time on the Fatigue Crack Growth (FCG) behavior of commercial pure titanium were studied under high and low load ratios. Besides, combined with the fracture surface morphology, the specific characteristics of FCG were analyzed under pure fatigue and dwell fatigue conditions. The experiment results show that the FCG rate of commercial pure titanium (CP-Ti) increases with the temperature under low load ratio, and the dwell time increases the FCG rate. Also, the enhancement of the dwell time increases as the temperature rises. The dwell effect tends to be saturated when the temperature rises to 200 °C. Under high load ratio, the FCG rate of CP-Ti also exhibits a temperature-sensitive enhancement. The enhancement effect of the dwell time on the FCG rate under high load ratio is more significant. However, the effect of the hold time on the FCG rate does not increase at 300 °C. The da/dN–ΔK/E FCG curves for CP-Ti have a tendency to approach each other under different load ratios, which indicates that the E-modulus is an important factor for the difference. The effect of dwell time on the FCG behavior of CP-Ti is dominated by the creep deformation mechanism under different load ratios from room temperature to 300 °C. At the same time, the oxidation effect gradually becomes significant as the load ratio increases to 300 °C. The fracture surface morphology shows that the secondary cracks and the roughness increase with temperature or dwell time under low load ratio condition, while, under high load ratio, the effect of creep deformation on the FCG behavior is more obviously enhanced, and plastic deformation is gradually significant with increase of the dimples. [ABSTRACT FROM AUTHOR]

• Effects of load ratio and overload ratio on mechanical behavior of crack tip are discussed by finite element method. • Mechanism of overload effect is explained by residual stress and variation of plastic zone. • Effect of compressive load on overload retardation are revealed. In present study, the fatigue crack growth (FCG) behavior of commercial pure titanium (CP-Ti) at negative load ratio with a single tensile overload was investigated through the combination of experiment and finite element method (FEM). The influence of load ratio and overload ratio was considered to investigate the overload retardation effect of FCG with compact-tensile-shear (CTS) specimens. Changes of the fatigue crack growth rate (FCGR) and crack opening force before and after overload were obtained experimentally under different loading conditions. The mechanical behaviors of stress–strain distribution and evolution of plastic zone size ahead of crack tip were explored by FEM for revealing the mechanism of overload at negative load ratios. The results demonstrate that retardation effect of FCG increases with overload ratio, and decreases with load ratio. The retardation effect of overload occurs after a transient acceleration of FCGR. The excessive residual compressive stress induced within the unloading stage of overload cycle ahead of crack tip, causes a shielding effect, which is one of the main factors of overload retardation effect. The difference of plastic strain at crack tip before and after overload makes the monotonic plastic zone (MPZ) and reverse plastic zone (RPZ) compete with each other, resulting in an increase of residual plastic strain, which hinders the crack propagation. At negative load ratios, the overload retardation effect will be weakened by the compressive load because of the decreasing residual plastic strain. [ABSTRACT FROM AUTHOR]

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]

• 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]

• Changes of fracture criterion and mechanism of I-II mixed mode FCG are revealed. • Competition of crack closure mechanisms of I-II mixed mode FCG is explained. • A new FCGR model is proposed by considering crack closure and fracture criterion. With the increase of design and application parameters for pressurized structures, the mixed mode fatigue crack growth (FCG) behavior has become a concerned problem in the field of structural integrity. In order to understand FCG behavior of I-II mixed mode crack growth at negative load ratios, an improved compact tensile shear (CTS) specimen of commercial pure titanium is taken to study the effects of load ratio and loading angle on I-II mixed mode FCG behavior through experiments and finite element method (FEM), which mechanism is discussed in depth as well. The contribution of mode I and mode II crack growth driving forces to I-II mixed mode FCG is analyzed. The changes of crack fracture criterion and the mechanism of crack growth in I-II mixed mode FCG process are revealed, and the competition relationship between two crack closure mechanisms of I-II mixed mode crack at negative load ratios is explained. An improved fatigue crack growth rate (FCGR) model that can make I-II mixed mode FCGR normalized is proposed by considering both the crack closure and the crack fracture criterion eventually. [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]

• FCG behavior is explained by compressive load effect and crack closure. • Variation of crack closure level at negative load ratio is obtained by experiment. • Influence of crack closure effect is described to explain anomaly in pre-stage. In this paper, the effect of compressive load and crack closure on mode-I fatigue crack growth (FCG) behavior at negative load ratios is studied with compact-tensile-shear (CTS) specimens made from commercial pure titanium (CP-Ti). The FCG behavior at negative load ratios under constant maximum load controlled has been explained by the interaction of compressive load effect and crack closure. The variation of crack closure level at negative load ratios within stable crack growth stage is obtained by the experiment. The crack closure level keeps constant which makes the crack closure effect dominate the FCG behavior in pre-stage. While in post-stage, the crack closure level drops gradually. The crack closure effect can be neglected currently and the compressive load effect plays a dominate role in post-stage. Meanwhile, the influence of crack closure effect on mechanical behavior at crack tip is described by finite element method (FEM) to explain the anomaly in pre-stage. It is confirmed that there exists a maximum reversed plastic zone induced by the crack closure effect during unloading process in pre-stage at negative load ratios. [ABSTRACT FROM AUTHOR]