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By experimental methods, 26 specimens were designed to conduct elastic and elastic–plastic buckling tests on cylindrical shells containing cracks. This study discusses the influence of factors such as the length–diameter ratio, the diameter–thickness ratio, the crack length, the inclination of the crack, etc., on the buckling load. Additionally, finite element models were established to compare with experimental results. For the PMMA cylindrical shell, the results showed that as the length–diameter ratio of the cylindrical shell increased, the buckling load first decreased and then increased. For the 6063 aluminum alloy cylindrical shell, with increasing length–diameter ratio, diameter–thickness ratio, and crack length of the cylindrical shell, the buckling load decreased accordingly. However, concerning the crack inclination, as the crack inclination increased, the buckling load increased accordingly. This indicates that the larger the crack inclination, the higher the load capacity of the cylindrical shell containing cracks. Through finite element simulations of cylindrical shells with cracks, it was found that through compressive mechanical properties, both elastic and elastic–plastic buckling loads yielded results that are closer to the experimental results. Additionally, the inclusion of contact effects in numerical simulations further improved the agreement with the experimental results, and the variation trend of the buckling load in the finite element simulation was consistent with the experimental results. The research findings provide valuable references for the assessment of load capacity in structures containing cracks. [ABSTRACT FROM AUTHOR]

In order to evaluate the reliability of cracked cylindrical shell effectively and reasonably, study the load capacity of cracked structures and understand the failure modes of cracked structures, in this paper the finite element method is adopted for cylindrical shells with mixed mode crack. The finite element models of cylindrical shell with an inclined through crack under external pressure were established by finite element method, the elastic and elastic-plastic buckling loads were calculated. The influences of crack length (c), crack angle (θ), cylindrical shell length-radius ratio (L/R), radius-thickness ratio (R/T), boundary conditions on buckling load were explored. The analysis of cracked cylindrical shells with simple support on buckling load shows that the load bearing capacity of cracked cylindrical shells decreases with the increase of length- radius ratio, radius-thickness ratio and crack inclination angle. The increase of crack length can weaken the bearing capacity of cylindrical shell. The variation of elastic-plastic buckling load is consistent with that of elastic buckling load. Under the clamped support, the variation of buckling load is consistent with the buckling load of cracked cylindrical shell with simple support, and the buckling load of cracked cylindrical shell with clamped support is evidently higher than that of simple support. The post-buckling analysis further shows that the changes of crack inclination angle and crack length do not affect the variation modes of pre-buckling and post-buckling deformation of cracked cylindrical shells, but affect the load capacity. The relationship between buckling load of different boundary conditions (simply supported and clamp-supported) and geometrical parameters (length-radius ratio, radius-thickness ratio, crack length and crack Angle) was obtained by nonlinear regression. The results of solution can predict the buckling load of cylindrical shell with an inclined through crack. [ABSTRACT FROM AUTHOR]

Based on fracture mechanics theory, a finite element method was used to determine the stress intensity factors of the inclined crack on the inner surface of the pipe under axial compression load and external pressure. The effects of different influencing factors on the stress intensity factor along the crack front considering crack closure were systematically explored, which were different to those under internal pressure. The effects of high aspect ratio on KII, the crack inclination asymmetry caused by curvature and the effects of the friction coefficient on the stress intensity factors of the pipe with an inclined inner surface crack under axial compression load and external pressure were explored in this paper. To be fit for defect assessment, the solutions for stress intensity factors KII and KIII were derived, and new correction factors fθ and fμ were proposed in the empirical solutions to accommodate the crack inclination asymmetry and the friction coefficient, respectively. [ABSTRACT FROM AUTHOR]

The in-plane biaxial specimen can well reflect the complex stress state of sheet metal. However, there is no standard for small-sized specimens used in the low-power biaxial fatigue testing machine. The main goal of this paper is to apply the finite element method and orthogonal experiment method to design the cruciform specimen, considering the influence of three main parameters including the diameter of the central semispherical thinning area, the minimum thickness of the center and the arm thickness of the specimen. According to the central strain dispersion coefficient and the strain concentration coefficient proposed in this paper, we ensured that the distribution of strain in the gauge area is uniform and the strain it at its maximum value at the same time. The optimized specimen is verified by a biaxial fatigue test with the digital image correlation (DIC) technique. It is found that the fatigue crack appears in the center region, which proves that the optimized specimen can be effectively used for biaxial fatigue test. [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]

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]

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]

The effect of bend angle on plastic limit loads of pipe bends under different load conditions is presented using three-dimensional non-linear finite element analyses. Based on finite element analysis, the characteristics of deformation, stress and strain were studied and effect of bend angle on the limit load was discussed. The results show that the effect of bend angle on limit load is great both at 0°∼120° range under internal pressure, torsion moment and in-plane bending moment and at 0°∼90° under out-of-plane moment. Then existing expressions of limit load and the finite element results were compared, and the solutions of limit load under single load condition were made. The proposed unified load solutions were obtained by fitting the finite element data under internal pressure, in-plane bending moment, out-of-plane bending moment and torsion moment. The results show that the proposed unified load solutions are consistent and in good agreement with the current finite element results. [ABSTRACT FROM AUTHOR]

This paper is dedicated to providing a detailed plastic collapse load analysis for un-cracked and circumferential through-wall cracked pipe bends under torsion moment by three dimensional FE methods considering geometric nonlinearity. For un-cracked pipe bends results show that radius-to-thickness is the main factors affecting the plastic collapse load. For cracked pipe bends the weakening factor decreases with increasing crack length, and the decreasing rate exhibits three typical stages which performs a similar trend with that in bending case. Although the weakening factor in plastic collapse load shows the similar variation based on geometric nonlinearity with that based on geometric linearity change, the limit load solutions based on geometric linearity fail to be used in prediction for torsion load based on geometric nonlinearity. So estimating limit load solutions by FE method are proposed, which shows a better choice compared with the past solutions. Furthermore the effect of yield strain is considered with the normalized parameter proposed to represent this weakening effect of yield strain on torsion moment. Results show that pipe parameters bend radius-to-radius and crack length have little impact on the weakening parameter, however radius-to-thickness have an obvious impact on the weakening parameter, which increases with decreasing weakening parameter. Results also show that radius-to-thickness has a great impact on the ovality deformation, while bend radius-to-radius hasn't. Therefore geometry effect is significant for a high yield strain value and a high radius-to-thickness value. [ABSTRACT FROM AUTHOR]

In this work, finite element (FE) method is used to determine plastic limit load solutions for pipe bends with circumferential through-wall crack under torsion moment. Both extrados and intrados crack are considered regarding of crack location. Based on FE results estimated solutions are proposed for application, and are also compared with corresponding solutions in previous literatures showing that existing solutions are unfit for prediction of torsion load. The weakening factor W decreases with crack length increasing, and the decreasing rate exhibits three typical stages which performs a similar trend to that with bending moment. Finally a detailed analysis for the mechanical behavior of pipe bends has been conducted which provides some evidence to explain the weaken effect caused by the presence of crack. In torsion mode results show that the non-uniform distributed shear stress is performing symmetric to the profile plane and may have a crucial influence on the weakening factor, while in bending mode the distribution in axial stress and circumferential stress is symmetric to the profile plane and has a decisive influence. Therefore crack is pulled open by in-plane bending load while torn open by torsion load. Some evidence also can be obtained from the Mises stress distribution, where similar variation rule will provide another argument to support such description. [ABSTRACT FROM AUTHOR]

In present paper, 3D finite element (FE) method is used to determine plastic limit load solutions for pipe bends under combined bending and torsion moment. With a detailed analysis and comparison, a common awareness for loading effect is showing which will raise researchers concern. By the way, past solutions are not appropriate to estimate FE results. In this respect of finite element analysis, overall yielding considering the spread process of yield region from crown to the straight pipe shows these promising finite element results. A wide range of non-dimensional parameters for pipe bends are considered and plastic limit load solutions are suggested. The results show that r / t is the main factor affecting the limit loads. Plastic limit load is independent on the loading path and material constants by normalizing. Results show that the circular interaction rule is a great approximation for pipe bends under combined bending and torsion moment. A series of approaches are confirmed in order to validate our finite element method on plastic limit analysis. Based on the finite element results, approximate plastic limit load solutions are proposed. Present work will further improve the limit load solution for pipe bends under complex loading conditions. [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]

Abstract: In this paper, based on the finite element (FE) simulation and the analytical net-section criterion (NSC) solution, the influences of the off-centered angle and the dimension of local wall thinning (LWT) on limit loads of pipes with LWT are systematically investigated. It is interesting that the off-centered angle commonly affects the limit load for all dimensions of LWT. Moreover, the axial length of LWT also plays an important role in the load capacity, which cannot be considered in the analytical NSC solution. In order to improve the prediction accuracy of the NSC analytical solution of pipes with the off-centered LWT, the effects of the off-centered angle and the axial length are considered together in the establishment of the improved NSC solution. It is confirmed by the statistical analysis that the prediction accuracy of the NSC solution can be significantly improved by addressing the effects of two factors together. [Copyright &y& Elsevier]

• 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]