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This study analyzes the transmission principle and structural characteristics of a high-speed-ratio compound gear with small tooth difference. On this basis, the finite element meshing characteristic analysis model of the above gear transmission device is established. The model considers the coupling deformation of 3-stage transmission, the specific structure of the cycloid gear, the output disc, the planet carrier and the case. The stress of each key component and the transmission error of the whole machine are simulated and analyzed, and the dynamic process of the multi-tooth meshing of the pin-cycloid transmission is discussed in detail. The results show that during the operation of the reducer, the stress fluctuation range of each component is small, and they are all far below the yield limit of their materials. The two cycloidal gears always bear the load through a rigid zone and a flexible zone simultaneously. The teeth of the rigid zone are the main bearing zone, and the teeth of the flexible zone are less stressed. The total number of meshing gear teeth of the two cycloidal gears is 9-11. The transmission error curve is stable and periodic, without noticeable long waves, and the peak-to-peak value of the transmission error of the whole machine is 46.719 5″. This research provides a theoretical basis for the optimal design of dynamic characteristics and meshing characteristics of the high-speed-ratio compound gear with small tooth difference.

The current work reveals the influence of loading parameters on the crack growth behavior of a Zr/Ti/steel composite plate with a crack normal to the interface by using an experiment and the finite element method. The Chaboche model was first used to study cyclic plastic evolution in composite materials. The results reveal that an increase in Fmax, Fm, and Fa can promote da/dN; meanwhile, an increase in R will reduce da/dN. The plastic strain accumulation results indicate that Fm mainly contributes to the tensile strain and compressive stress after the first cycle. Additionally, Fa increases the stress range and compression stress and greatly improves the plastic strain accumulation degree in subsequent loading cycles. The Fmax can significantly increase the stress amplitude and plastic strain accumulation level. When R increases, the plastic strain accumulation increases a little, but the stress amplitude and compression stress decrease greatly. Furthermore, it is also found that the elastic–plastic mismatch also affects the plastic evolution, that is, strengthening or weakening the effect of the loading parameters. [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]

The influence of pre-strain on the fatigue crack growth behavior of Zr702/TA2/Q345R composite plate is studied by experiments and the finite element method. The crack perpendicular to the interface and the through-wall crack are considered at the same time. For the crack perpendicular to the interface, the monotonic plastic zone and cyclic plastic zone at the crack tip are used to study the influence of pre-strain on the plastic zone. Furthermore, the influence of pre-strain on the evolution of the plastic damage at the crack tip is analyzed in detail by studying the variation in the initial plastic energy and equivalent plastic strain. For the through-wall crack, the effect of pre-strain on the propagation behavior of cracks on both sides and the whole crack is studied systematically. The results show that the strengthening of the cracks on the Zr702 side is significantly higher than that on the Q345R side, so the inhibitory effect of pre-strain on the whole crack of the through-wall specimen is mainly due to the increase in the resistance to crack growth on the Zr702 side. [ABSTRACT FROM AUTHOR]

In this paper, the effects of maximum load, load ratio, and average load on fatigue crack propagation of Zr702/TA2/Q345R composite plate with a crack normal to the interface are studied by experiment and finite element method. When crack propagates to the interface from the compliant material side, the crack growth rate decreases to the minimum at first. After crack penetrates through the interface, the fatigue crack growth rate accelerates continuously. When crack propagates to the interface from the stiff material side, the fatigue crack growth rate generally increases with the crack length. Regardless of the direction of crack growth, the increase of load ratio will weaken the difference of crack growth rate near the interface caused by material property mismatch. Finite element results show that elastic modulus mismatch significantly changes the variation of the stress intensity factor amplitude. All results demonstrate that crack growth rate is dependent on the competition of the stress intensity factor amplitude, the fatigue crack growth rate in the corresponding material, and the interface strength. [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]

The existence of crack groups in structures is objective and inevitable during the process of manufacture and service. In this paper, the interactions between penetrating parallel double cracks are systematically investigated through finite element methods, experimental studies and theoretical analyses, where both the brittle dominant and ductile materials are taken as the research objects. The interactions between cracks are discussed through the interference factors C based on stress intensity factor K , which is related with the relative distance between crack tips. It is found that the fracture behaviors of multiple cracks are associated with all the interference factors at four crack tips. For the alignment double crack, shielding effects at all the crack tips cause the mutually exclusive crack propagations, and then strengthen the critical load of the specimen. For offset double cracks, the inner crack extension directions are attracted to each other, the outer crack extension directions are repelling each other, the critical loads depend on the degree of the attraction or the repelling effect. There exists a relationship between the comprehensive interference factor with all the crack tips included and the loading capacity. For the specimen with multiple surface cracks, the interference effects are also related with the relative distance between crack tips, through which it can be preliminary obtained that the regulations and the effect to the fracture behaviors are similar to those of penetrating cracked specimen, which will be discussed in detail in our next findings. The interference behaviors and critical loads of multiple cracks discussed above also provide an important basis on the coalescence and evaluation of multiple cracks. • Interferences factor based on K is proposed to describe the interference effects at crack tips, which is mainly dependent on the relative distance between crack tips, for specimens with both penetrating cracks and surface cracks. • Cracks' repelling propagations strengthen the critical loading of the specimen, while the cracks' attraction propagations weaken the critical loading, which role in dominant is the main factor determining the final loading capacity of the cracked specimen. • Relationships between the comprehensive interference factor with all the crack tips included and the loading capacity is proposed. [ABSTRACT FROM AUTHOR]

To investigate the optimal cutting depth (Cap) in small incision lenticule extraction from the perspective of corneal biomechanics, a three-dimensional finite element model of the cornea was established using a stromal sub-regional material model to simulate small incision lenticule extraction. The displacement difference P Δ at the central point of the posterior corneal surface before and after lenticule extraction, as well as the von Mises stress at four points of different thicknesses in the center of the cornea, were analyzed using the finite element model considering the hyperelastic property and the difference in stiffness between the anterior and posterior of the cornea. The numerical curves of P Δ -Cap and von Mises Stress-Cap relations at different diopters show that the displacement difference P Δ has a smallest value at the same diopter. In this case, the von Mises stress at four points with different thicknesses in the center of the cornea was also minimal. Which means that the optimal cutting depth exsisting in the cornea. Moreover, P Δ -Cap curves for different depth of stromal stiffness boundaries show that the optimal cap thickness would change with the depth of the stromal stiffness boundary. These results are of guiding significance for accurately formulating small incision lenticule extraction surgery plans and contribute to the advancement of research on the biomechanical properties of the cornea. [ABSTRACT FROM AUTHOR]

In this paper, the through-wall crack of Zr702/TA2/Q345R composite plate is studied by experiment and finite element method. The influence of loading parameters on crack growth rate, stress intensity factor, monotonic plastic zone and interaction effect between component materials are investigated. The elastic mismatch and yield strength between Q345R, TA2 and Zr702 leads to different crack driving force at the crack tip. Although the crack driving force is higher in component material with higher elastic module and yield strength, the crack growth rate of component materials in Zr702/TA2/Q345R composite plate is closely related to the ability of corresponding single material to resist crack propagation and the interaction effect between component materials. In addition, the fatigue crack propagation characteristic and damage mechanism are analyzed, and the effect of complex microstructures near Zr702/TA2 and TA2/Q345R interface on crack propagation behavior is clarified. Besides, it is found that the interface with higher properties mismatch preferentially delaminates. [ABSTRACT FROM AUTHOR]

Lacking specimens is the biggest limitation of studying the mechanical behaviors of human corneal. Extracting stress-strain curves is the crucial step in investigating hyperelastic and anisotropic properties of human cornea. 15 human corneal specimens extracted from the small incision lenticule extraction (SMILE) surgery were applied in this study. To accurately measure the personalized true stress-strain curve using corneal lenticules, the digital image correlation (DIC) method and finite element method were used to calibrate the stress and the strain of the biaxial extension test. The hyperelastic load-displacement curves obtained from the biaxial extension test were performed in preferential fibril orientations, which are arranged along the nasal-temporal (NT) and the superior-inferior (SI) directions within the anterior central stroma. The displacement and strain fields were accurately calibrated and calculated using the digital image correlation (DIC) method. A conversion equation was given to convert the effective engineering strain to the true strain. The stress field distribution, which was simulated using the finite element method, was verified. Based on this, the effective nominal stress with personalized characteristics was calibrated. The personalized stress-strain curves containing individual characteristic, like diopter and anterior surface curvature, was accurately measured in this study. These results provide an experimental method using biaxial tensile test with corneal lenticules. It is the foundation for investigating the hyperelasticity and anisotropy of the central anterior stroma of human cornea. • Biaxial extension test using corneal lenticules. • Effective nominal stress distributes uniformly within study area. • Conversion equation between effective engineering strain and true strain. • Personalized stress-strain curve contains patient individual characteristics. [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]

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]

• 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]