Comparative study between crack closure model and Willenborg model for fatigue prediction under overload effects

A comparative study is performed between a crack closure model and the Willenborg model, which can calculate the fatigue crack growth rate under the overload effects. The modified virtual crack annealing (VCA) model is briefly reviewed, which is based on the equivalent plastic zone concept. In this method, the retardation phenomenon is explained by the crack closure level variation, which is derived from the interactions between forward and reverse plastic zones ahead of the crack tip. As a comparison, the Forman equation in conjunction with the Willenborg model is also reviewed. The retardation phenomenon is described by directly modifying the stress intensity factor. It is known that the large plastic zone created by the overload can decelerate the fatigue crack growth rate until the crack grows beyond this region. A relationship between the plastic zone and the modified stress intensity factor is developed, which is a mathematical fitting equation instead of physical-based formulation. The experimental data in aluminum alloys are used to val-idate these two models. Overall, good agreement is observed between the model predictions and the testing data. It is noted that the approach based on modified VCA model can give more accurate prediction curves than the Willenborg model.     

GROWTH BEHAVIOR OF SHORT FATIGUE CRACKS FOR ALUMINUM- LITHIUM ALLOY 8090

The growth behaviors of short through cracks (0.2 < △a < 2.2mm) and long cracks are compared using CT type specimens in aluminum-lithium alloy 8090 T651. It is found that the short cracks grow much more than long ones and are observed to grow at the stress intensity ranges far below the long crack threshold. The distinction of growth bahavior between short and long cracks is attributed to the difference of their crack closure effect. The growth behavior of short cracks can be rationalized with that of long ones in terms of effective stress intensity ranges. The upper demarcation value of short through cracks for aluminum-lithium alloy 8090 is presented.     

A new method to predict fatigue crack growth rate of materials based on average cyclic plasticity strain damage accumulation

By introducing a fatigue blunting factor, the cyclic elasto-plastic Hutchinson-Rice-Rosengren (HRR) field near the crack tip under the cyclic loading is modified. And, an average damage per loading-cycle in the cyclic plastic deformation region is defined due to Manson-Coffin law. Then, according to the linear damage accumulation theory-Miner law, a new model for predicting the fatigue crack growth (FCG) of the opening mode crack based on the low cycle fatigue (LCF) damage is set up. The step length of crack propagation is assumed to be the size of cyclic plastic zone. It is clear that every parameter of the new model has clearly physical meaning which does not need any human debugging. Based on the LCF test data, the FCG predictions given by the new model are consistent with the FCG test results of Cr2Ni2MoV and X12CrMoWVNbN 10-1-1. What’s more, referring to the relative researches, the good predictability of the new model is also proved on six kinds of materials.     

Static aeroelastic analysis of very flexible wings based on non-planar vortex lattice method

A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.     

混合型裂纹扩展的动光弹-数值分析

 The K field parameters of K1, KI, and *ox at the crack tip associated with crack high-velocity curving of epoxy resin specimen under impact tension are determined. The parameters obtained are used to construct the theoretical isochromatic fringe patterns fitting the experimental data. The curves of dynamic relation between stress intensity factor and crack length is also given.     

THE COMPLEX-VARIABLE-VARIATIONALMETHOD FOR ANALYSING FINITEINTERNALLY CRACKED PLATESAND ITS APPLICATION

In this paper, a whole field solution to finite internally cracked plates is derived by complex variable method, where the equations of equilibrium and compatibility, the single value condition of displacements and the traction-free condition on crack surfaces are satisfied exactly. The stress intensity factors of finite plates with central crack or eccentric crack or cracks emanating from a hole are calculated by using minimum potential energy principle to treat the boundary conditions excluding those on crack surfaces. As an application of the method to engineering problems, the computation about a finite rivet joint stiffened plate with cracks emanating from a hole is also performed. The numerical results show that the method presented in this paper gives rapid convergence and is much time-saving in computations.     

国产材料疲劳寿命分布参数α的初步估计

 <正> The fatigue-tested data of home-made materials and simple structure data are collected, which consist of 488 groups of 2705 specimens for aluminum alloys ; 313 groups of 1798 specimens for alloy steels) 79 groups of 389 specimens for titanium alloys. The shape parameter a of two-parameter Weibull distribution is estimated with maximum-likelihood estimation method and the preliminary estimation of a is given. In this study, the estimated parameters of home-made materials coincide with the parameters of overseas materials and the parameters a suggested by the literature can be applied to home-made material, too. This work also studies the effects of stress concentration factor ranges of fatigue life and tensile strength of materials on the values of a.     

Residual Strength of Stiffened LY12CZ Aluminum Alloy Panels with Widespread Fatigue Damage

Experimental and analytical investigations on the residual strength of the stiffened LY12CZ aluminum alloy panels with widespread fatigue damage （WFD） are conducted. Nine stiffened LY12CZ aluminum alloy panels with three different types of damage are tested for residual strength. Each specimen is pre-cracked at rivet holes by saw cuts and subjected to a monotonically increasing tensile load until failure is occurred and the failure load is recorded. The stress intensity factors at the tips of the lead crack and the adjacent WFD cracks of the stiffened aluminum alloy panels are calculated by compounding approach and finite element method （FEM） respectively. The residual strength of the stiffened panels with WFD is evaluated by the engineering method with plastic zone linkup criterion and the FEM with apparent fracture toughness criterion respectively. The predicted residual strength agrees well with the experiment results. It indicates that in engineering practice these methods can be used for residual strength evaluation with the acceptable accuracy. It can be seen from this research that WFD can significantly reduce the residual strength and the critical crack length of the stiffened panels with WFD. The effect of WFD crack length on residual strength is also studied.     

Improved uncertainty propagation method of dynamic model for Mars entry spacecraft

In order to research the uncertainty propagation laws of Mars entry dynamic equations for the Mars entry phase,an improved method was presented for analyzing the effect of the initial state uncertainties and uncertainty factor on the system state in the state trajectories.When applying the method to the entry phase of one of the NASA Mars exploration missions,the simulation results agreed well with the Monte Carlo method,especially the flight path angle simulation at least reaching 92%.It is found that the improved method can not only predict the uncertainty propagation laws with high accuracy of at least 92%in flight path angle simulation and large application scope from-0.1degree to 0.1degree,compared with local linearization method,but also save several hours relative to Monte Carlo method.     

Equivalent model of close-packed film cooling holes in nickel-based single crystal cooled blade based on crystallographic theory

The mechanical properties of nickel-based single crystal thin-walled plate with close-packed film cooling holes were studied based on the equivalent solid material concept. The effective plastic parameters inversion method based on crystallographic theory were proposed. A simplification method for close-packed film cooling hole plates with square and triangular penetration patterns was presented. A large number of finite element analysis results covering different ligament efficiencies and penetration patterns were provided to verify the feasibility of the plastic equivalent principle and simplification method. The results show that the stress–strain curve and resolved shear stresses of simplification models are in consistence with the plate models with close-packed film cooling holes. The equivalent errors of yield strength are all within the error band and the values of equivalent errors are all less than 10%. In addition, the equivalent errors of the positions where maximum resolved shear stress occurs are all less than 15°, indicating the accuracy of plastic equivalent model and simplification method.     

Analytical solutions of cracks emanating from an elliptical hole under shear

Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors（SIFs） are provided for the plane problem of two collinear edge cracks emanating from an elliptical hole in an infinite plate under shear. The stress distribution along the horizontal axis is given in graphical forms, which conforms to Saint-Venant＇s principle. The influences of crack length and ellipse shape on the stress intensity factors are evaluated. Comparing the analytical solutions with finite element method（FEM） results shows good coincidence. These numerical examples show that the present solutions are accurate.     

Constructing G~2 Continuous Curve on Freeform Surface with Normal Projection

This article presents a new method for G～2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with prescribed tangent direction and curvature vector,respectively,at every point.First,a G～2 continuous curve is constructed in three-dimensional space.Then the curve is projected normally onto the given surface.The desired interpolation curve is just the projection curve,which can be obtained by numerically solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit case.Several shape parameters are introduced into the resulting curve,which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand.The presented method is independent of the geometry and parameterization of the base surface.Numerical experiments demonstrate that it is effective and potentially useful in numerical control (NC) machining,path planning for robotic fibre placement,patterns design on surface and other industrial and research fields.     

渐变结构系统模糊可靠性灵敏度分析的矩方法(英文)

For a degradable structural system with fuzzy failure region, a moment method based on fuzzy reliability sensitivity algorithm is presented. According to the value assignment of performance function, the integral region for calculating the fuzzy failure probability is first split into a series of subregions in which the membership function values of the performance function within the fuzzy failure region can be approximated by a set of constants. The fuzzy failure probability is then transformed into a sum of products of the random failure probabilities and the approximate constants of the membership function in the subregions. Furthermore, the fuzzy reliability sensitivity analysis is transformed into a series of random reliability sensitivity analysis, and the random reliability sensitivity can be obtained by the constructed moment method. The primary advantages of the presented method include higher efficiency for implicit performance function with low and medium dimensionality and wide applicability to multiple failure modes and nonnormal basic random variables. The limitation is that the required computation effort grows exponentially with the increase of dimensionality of the basic random vari- able; hence, it is not suitable for high dimensionality problem. Compared with the available methods, the presented one is pretty competitive in the case that the dimensionality is lower than 10. The presented examples are used to verify the advantages and indicate the limitations.     

SYNTHETIC STRESS LIFE TESTING OF MECHATRONIC PRODUCTS UNDER VARIABLE STRESS SPECTRUM

Mechatronic products usually endure the variable stress spectrum when they operate in certain operational condition and environmental condition, which obey the Weibull distribution. In accordance with the features of mechatronic product, this paper analyzes the failure mode, its corresponding sensitive stress and the design principles of life testing profiles. Based on the above analyses, this paper presents a synthetic stress life testing method based on the hybrid Weibull distribution and its statistical method under variable stress spectrum to evaluate the reliability and life indices of mechatronic products. Because the mechatronic products have many characteristics such as high price, long life and small testing samples, the synthetic stress life testing method under variable load spectrum can simulate the real various spectra, decrease the life testing time and reduce the testing samples. So it is effective to carry out the life testing to mechatronic products. The application results of hydraulic pumps indicate that this method can easily handle the experimental data under variable amplitude spectrum, obtain the high precision parameters point estimation and confidence interval estimation and reduce the testing cost greatly.     

Numerical simulation and transonic wind-tunnel test for elastic thin-shell structure considering fluid–structure interaction

Aerodynamic force can lead to the strong structural vibration of flying aircraft at a high speed. This harmful vibration can bring damage or failure to the electronic equipment fixed in aircraft. It is necessary to predict the structural dynamic response in the design course. This paper presents a new numerical algorithm and scheme to solve the structural dynamics responses when considering fluid–structure interaction(FSI). Numerical simulation for a free-flying structural model in transonic speed is completed. Results show that the small elastic deformation of the structure can greatly affect the FSI. The FSI vibration tests are carried out in a transonic speed windtunnel for checking numerical theory and algorithms, and the wind-tunnel test results well accord with that of the numerical simulation. This indicates that the presented numerical method can be applied to predicting the structural dynamics responses when containing the FSI.     

DELAMINATION FORMATION AND DELAMINATION PROPAGATION OF COMPOSITE LAMINATES UNDER COMPRESSIVE FATIGUE LOADING

Fatigue tests of the smooth composite laminates and the notched composite laminates under compressive cyclic loading have been carried out. The damage mechanism is discussed and analyzed. Damage evolution is monitored using stiffness decay. From these tests, it is found that the initial delamination occurs at the free boundary of smooth specimens, or the notch boundary of notched specimens, subjected to the compression-compression cyclic load. A point of view in relation to two-phases of compression fatigue delamination of composites is proposed, namely, compression-compression delamination consists of the delamination formation phase and the delamination propagation, and there is a “damage transition point” to separate this two-phases. Furthermore, an empirical modulus degradation formula and its parameters fitting method are presented. According to the test data handling results, it is shown that this formula is univocal and can fit the test data conveniently. In addition, two kinds of new anti-buckling devices are designed for these tests. At last, the E-N curves, the D-N curves and the S-N curve of the smooth carbon fiber reinforced composite laminates of T300/648C are determined to predict the fatigue life of the notched composite laminate. And the E-N curve of the notched specimens at the given load ratio R=10 and minimum load P_min=-0.45　kN is also measured to verify the estimated result of fatigue life.     

A second-order numerical method for elliptic equations with singular sources using local flter

The presence of Dirac delta function in differential equation can lead to a discontinuity,which may degrade the accuracy of related numerical methods.To improve the accuracy,a secondorder numerical method for elliptic equations with singular sources is introduced by employing a local kernel flter.In this method,the discontinuous equation is convoluted with the kernel function to obtain a more regular one.Then the original equation is replaced by this fltered equation around the singular points,to obtain discrete numerical form.The unchanged equations at the other points are discretized by using a central difference scheme.1D and 2D examples are carried out to validate the correctness and accuracy of the present method.The results show that a second-order of accuracy can be obtained in the fltering framework with an appropriate integration rule.Furthermore,the present method does not need any jump condition,and also has extremely simple form that can be easily extended to high dimensional cases and complex geometry.     

THE INFLUENCE OF DEFORMATIONCONDITIONS ON THE FLOW STRESS ANDMICROSTRUCTURE OF ALLOY GH169

In this paper the dependence of flow stress in alloy GH169 on the deformation temperature, strain and strain rate based on the data of hot working simulation test is defined for the first time. Experimental results indicate that for the alloy GH169 the values of flow stress at high temperatures are much higher than those of alloy steel and the work hardening is remarkable. The deformation conditions have significant influence on the flow stress and microstructure of alloy GH169. It is found that under certain conditions fine grain structure can be obtained even though the deformation processes are carried out at high temperatures. This finding is beneficial to the raise of productivity of forming processes. Increasing the cooling rate after deformation is also favourable to the development of fine grain structure. To sum up, the microstructure of alloy GH169 can be controlled effectively through thermomechanical treatment.     

A single-level composite structure optimization method based on a blending tapered model

In order to decrease the number of design variables and improve the efficiency of com- posite structure optimal design, a single-level composite structure optimization method based on a tapered model is presented. Compared with the conventional multi-level composite structure opti- mization method, this single-level method has many advantages. First, by using a distance variable and a ply group variable, the number of design variables is decreased evidently and independent with the density of sub-regions, which makes the single-level method very suitable for large-scale composite structures. Second, it is very convenient to optimize laminate thickness and stacking sequence in the same level, which probably improves the quality of optimal result. Third, ply con-tinuity can be guaranteed between sub-regions in the single-level method, which could reduce stress concentration and manufacturing difficulty. An example of a composite wing is used to demonstrate the advantages and competence of the single-level method proposed.     

Comparison Structure Forms Between Isogrid and Orthogrid of C/ E CompositeTrellis Wound Structure Based on Calculation of Load Carrying

This paper calculated load carrying of isogrid and orthogrid of carbon epoxy composite trellis wound
structure (C/ E CTWS) using non linear finite element method. Based on the analysis, test cases were designed and
tests of axial compression were carried. Analysis result and test result fit well. In order to be used in the project, this
kind of structure cut out repairing was calculated. The method presented in this paper has been proved and can be used
to solve complicated engineering problems. According to calculations and experimental results combined with applica
tion, a principle of choosing wound structure is obtained and principle could be applied to engineering.