Discrete Stress-strength Interference Model of Reliability Analysis under Multi-operating Conditions

The conventional stress-strength interference（SSI） model is a basic model for reliability analysis of mechanical components. In this model, the component reliability is defined as the probability of the strength being larger than the stress, where the component stress is generally represented by a single random variable（RV）. But for a component under multi-operating conditions, its reliability can not be calculated directly by using the SSI model. The problem arises from that the stress on a component under multi-operating conditions can not be described by a single RV properly. Current research concerning the SSI model mainly focuses on the calculation of the static or dynamic reliability of the component under single operation condition. To evaluate the component reliability under multi-operating conditions, this paper uses multiple discrete RVs based on the actual stress range of the component firstly. These discrete RVs have identical possible values and different corresponding probability value, which are used to represent the multi-operating conditions of the component. Then the component reliability under each operating condition is calculated, respectively, by employing the discrete SSI model and the universal generating function technique, and from this the discrete SSI model under multi-operating conditions is proposed. Finally the proposed model is applied to evaluate the reliability of a transmission component of the decelerator installed in an aeroengine. The reliability of this component during taking-off, cruising and landing phases of an aircraft are calculated, respectively. With this model, a basic method for reliability analysis of the component under complex load condition is provided, and the application range of the conventional SSI model is extended.

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

Reliability Assessment Method Based on Interference Variable for Stress-Strength Model

Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are all unknown.A new assessment method of interference reliability is proposed and the estimates of the distribution parameters are accordingly given.The lower confidence limit of interference reliability with given confidence can be obtained with the method even though the parameters are all unknown.Simulation studies and an engineering application are conducted to validate the method,which suggest that the method provides precise estimates even for sample size of approximately.

Reliability Bounds based on Universal Generating Function and Discrete Stress-strength Interference Model

A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method

Stress-Strength Structural Reliability Model with a Stochastic Strength Aging Deterioration Process

A stress-strength structural reliability model was proposed with a stochastic strength aging deterioration process. In structural engineering,the deterioration of structure's strength should be the total of the deterioration owing to continual wear, fatigue,corrosion,etc.,and the abrupt deterioration as a result of randomly variable loads. The deterioration of structure's strength should be influenced by both the internal deterioration owing to direct wear and the external deterioration due to randomly variable loads.Meanwhile,the load process was given as Poisson square wave process. The reliability was derived using stress-strength interference theory. In particular,the reliability was also given when random variables followed the normal distribution.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions

Strength Model of Soda Residue Soil Considering Consolidation Stress and Structural Influence

Soda residue(SR)is a type of industrial waste produced in the soda process with the ammonia-soda method.Applying SR to backfilling solves the land occupation and environmental pollution problems in coastal areas and saves material costs for foundation engineering.The strength characteristics of soda residue soil(SRS)under different consolidation conditions are the key points to be solved in the engineering application of SRS.Triaxial compression tests were performed on the undisturbed SRS of Tianjin Port.The shear properties of SRS under different consolidation conditions were then discussed.Meanwhile,a structural strength model(SSM)based on Mohr-Coulomb theory was proposed.SSM reflects the influence of soil structure on undrained strength(Cu)and divides the Cu into the following two parts:friction strength(C_(uf))and original structural strength(C_(u0)).C_(uf)characterizes the magnitude of friction between soil particles,which is related to the consolidation stress.Meanwhile,C_(u0)represents the structural effect on soil strength,which is related to the soil deposition and consolidation processes.SSM was validated by the test data of undisturbed soils.Results reveal that the undisturbed soil generally had a certain C_(u0).Therefore,the SRS strength model was established by combining the experimental law of SRS with SSM.Error analysis shows that the SRS strength model can effectively predict the Cu of undisturbed SRS in Tianjin Port under different consolidation conditions.

Study on Strength and Life of Anisotropic Single Crystal Blade - Part I: Crystallographic Constitutive Models and Applications

The single crystal blade is one of the key technologies for improving the performance, durability and reliability of aero-engines and ground gas-turbine engines. However, the anisotropic mechanical properties of the single crystal material makes a great deal of difficulties on the development and the application of the single crystal blade, which is a challenge for the engineering application of the single crystal superalloy and the theoretic bases of the application. Some researches on the strength analysis and the life prediction of the anisotropic single crystal blade were carried out by the authors' research team. They are as follows. The crystallographic constitutive models for the plastic and the creep behaviors and the method of the rupture life prediction were established and verified. The tensile or the creep experiments for DD3 single crystal alloy with different orientations under different temperatures and different tensile rates or under different temperatures and different stress levels were carried out. The experimental data and the anisotropic properties at intermediate and high temperatures revealed by the experiments are significant for the application of the single crystal alloy. In addition, the experimental research for a kind of single crystal blade was also made. As the application of the researches the strength analysis and the life prediction were carried out for the single crystal blade of a certain aero-engine. In this part, the constitutive models and their applications are described, and the experimental research work will be described in part II.

Triaxial creep damage characteristics of sandstone under high crustal stress and its constitutive model for engineering application

The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone under high crustal stress,this study constructed nonlinear creep damage(NCD)constitutive mode based on the triaxial graded loading‒unloading creep test of sandstone in the Yuezhishan Tunnel.A numerical NCD constitutive model and a breakable lining(BL)model were developed based on FLAC3D and then applied to the stability analysis of the Yuezhishan Tunnel.Based on the creep test results of sandstone,a power function of creep rate and stress level was constructed,by which the long‐term strength was solved.The results show that the long‐term strength of the red sandstone based on the related function of the steady‐state creep rate and stress level is close to the measured stress value in engineering.The NCD model considering damage factors reflects the instantaneous and viscoelastic plasticity deformation characteristics of the red sandstone.The numerical NCD constitutive model and the BL model can reflect surrounding rock deformation characteristics and lining failure characteristics in practical engineering.The research results provide theoretical references for long‐term stability analysis of rock engineering and the deformation control of surrounding rock under high crustal stress.

Mode-I-crack compression modeling and numerical simulation for evaluation of in-situ stress around advancing coal workfaces

The relatively high stress probably leads to generation of a fractured or even instable area around a working coalface. Also, the generated weak area often evolves into an easy-infiltrating field of water/gas to greatly increase probability of accident occurrence. To reveal the distribution of high stress around working faces, we put forward the mode-I-crack compression model. In this model, the goaf following a working face is regarded as a mode-I crack in an infinite plate, and the self-gravity of overlaying strata is transformed into an uniform pressure applied normal to the upper edge of the model crack. Solving this problem is based on the Westergaard complex stress function. For comparison, the software RFPA-2D is also employed to simulate the same mining problem, and furthermore extendedly to calculate the stress interference induced by the simultaneous advances of two different working faces. The results show that, the area close to a working face or the goaf tail has the maximum stress, and the stress is distributed directly proportional to the square root of the advance and inversely proportional to the square root of the distance to the working face. The simultaneous advances of two neighboring working faces in different horizontals can lead to extremely high resultant stress in an interference area.

Shear strength criteria for rock,rock joints,rockfill and rock masses:Problems and some solutions

Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.

Assessment of composite failure and ultimate strength without experiment on composite

This paper attempts to estimate the ultimate strength of a laminated composite only based on its con- stituent properties measured independently. Three important issues involved have been systematically addressed, i.e., stress calculation for the constituent fiber and matrix materials, failure detection for the lamina and laminate upon the internal stresses in their constituents, and input data determination of the constituents from monolithic measurements. There are three important factors to influence the accuracy of the strength prediction. One is the stress concentration factor （SCF） in the matrix. Another is matrix plasticity. The third is thermal residual stresses in the constituents. It is these three factors, however, that have not been sufficiently well realized in the composite community. One can easily find out the elastic and strength parameters of a great many laminae and laminates in the current literature. Unfortunately, necessary information to determine the SCF, the matrix plasticity, and the thermal residual stresses of the composites is rare or incomplete. A useful design methodology is demonstrated in the paper.

Dynamic recrystallization behavior and kinetics of high strength steel

The dynamic recrystallization behavior of high strength steel during hot deformation was investigated.The hot compression test was conducted in the temperature range of 950-1150 °C under strain rates of 0.1,1 and 5 s-1.It is observed that dynamic recrystallization(DRX) is the main flow softening mechanism and the flow stress increases with decreasing temperature and increasing strain rate.The relationship between material constants(Q,n,α and ln A) and strain is identified by the sixth order polynomial fit.The constitutive model is developed to predict the flow stress of the material incorporating the strain softening effect and verified.Moreover,the critical characteristics of DRX are extracted from the stress-strain curves under different deformation conditions by linear regression.The dynamic recrystallization volume fraction decreases with increasing strain rate at a constant temperature or decreasing deformation temperature under a constant strain rate.The kinetics of DRX increases with increasing deformation temperature or strain rate.

Bonding stress—slip constitutive behavior between bars and grout concrete

To establish bonding stress—slip constitutive model between bars and grout concrete,13 test specimens were employed to study the bonding behavior and the force transfer of bars adhered to grout concrete. The bonding stress development of bars adhered to grout concrete was analyzed. The local bonding stress—slip curve was obtained. Based on the test results,a new bonding stress— slip constitutive model between bars and grout concrete was proposed. The results show that the maximum bonding stress is not influenced by the bar bond length,but it is strengthened when the splitting strength of grout concrete is increased. The model matches the experimental results well,and the regressing coefficient equals 1.7.

Analysis of complete plasticity assumption for solid circular shaft under pure torsion and calculation of shear stress

The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding, the applicability of complete plastic model assumption and the shear stress formula were researched. Based on the shear stress formula of circular shaft under pure torsion in elastic stage, the formula of torque in elastic stage and the definition of yield, it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship, and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension. The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section. The distribution of shear stress is still linear with the maximum shear stress ts. The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion. The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory （LSEST）. The traditional yield stress formula for plastic shaft under torsion is reasonable. The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.

Modification of B3 Model for Sealed Concrete with Additives Based on Experimental Observations

Thirteen specimens were tested out of which nine were for creep of sealed concrete and four for shrinkage test,for a period of 700 d under controlled temperature condition.The experimental results for creep and shrinkage were compared with creep and shrinkage computation model B3 and distinct discrepancies between observed and calculated creep and shrinkage strains were observed.Based on regression analysis,modification on B3 model has been formulated which will be applicable at least for concrete of characteristics strength of C40 and C50 with additives.Besides,on the basis of observation on identical specimens with varied stress strength ratio,a function is generated which accounts effect of stress strength ratio on creep.Finally,Civil Engineering community is suggested not to follow the creep prediction models without correction at least for modern concrete,as they do not account the effect of additives on its compliance function.

Consistent constitutive modeling of metallic target penetration using empirical, analytical, and numerical penetration models

Historically, there has been little correlation between the material properties used in(1) empirical formulae,(2) analytical formulations, and(3) numerical models. The various regressions and models may each provide excellent agreement for the depth of penetration into semi-infinite targets. But the input parameters for the empirically based procedures may have little in common with either the analytical model or the numerical model. This paper builds on previous work by Riegel and Anderson(2014) to show how the Effective Flow Stress(EFS) strength model, based on empirical data, can be used as the average flow stress in the analytical Walker–Anderson Penetration model(WAPEN)(Anderson and Walker,1991) and how the same value may be utilized as an effective von Mises yield strength in numerical hydrocode simulations to predict the depth of penetration for eroding projectiles at impact velocities in the mechanical response regime of the materials. The method has the benefit of allowing the three techniques(empirical, analytical, and numerical) to work in tandem. The empirical method can be used for many shot line calculations, but more advanced analytical or numerical models can be employed when necessary to address specific geometries such as edge effects or layering that are not treated by the simpler methods. Developing complete constitutive relationships for a material can be costly. If the only concern is depth of penetration, such a level of detail may not be required. The effective flow stress can be determined from a small set of depth of penetration experiments in many cases, especially for long penetrators such as the L/D = 10 ones considered here, making it a very practical approach. In the process of performing this effort, the authors considered numerical simulations by other researchers based on the same set of experimental data that the authors used for their empirical and analytical assessment. The goals were to establish a baseline with a full constitutive model and to determine if the EFS could be estimated from a standardized constitutive model. We were unable to accomplish this.Several papers detailing simulations using the Johnson–Cook(JC) constitutive model were located and used as a basis for comparison. The authors were somewhat surprised to find that the JC parameters employed in those studies were not actually developed for the target materials that were evaluated experimentally. More disconcerting was the fact that a number of different sets of JC parameters were published for presumably the same material. Although not intended to be a critique of the JC model, this research raises a serious concern regarding the manner in which the model has been applied to terminal ballistics problems. The details of the study are included in this paper because the authors believe it helps put the discussion of EFS into proper context.

Adjustment of B3 model for drying concrete with additives based on experimental data

All currently avalable concrete creep predicting models cannot describe well the creep of a concrete structure because they all leave the effects of additives out of consideration. The purpose of this work was to modify model B3 for overcoming this deficiency. We tested thirteen specimens of C40 and C50 concrete with additives, out of which nine were for creep and four for shrinkage tests over a 700 d period under controlled temperature. We compared the experimental results for creep and shrinkage with those obtained by using model B3, and derived modification terms through regression analysis. Based on the experimental results of identical specimens under varied stress levels, we also derived a function considering the effect of stress level on creep. It is suggested that the creep prediction models without adjustment should not be used for modem concrete with a variety of additives.

复合磨损套管爆裂失效机理及剩余强度预测

超深井、水平井、大位移井等复杂油气井服役工况异常恶劣,套管复合磨损严重,将对井筒完整性构成巨大威胁,且磨损套管剩余强度难以精准预测。为此,基于塔里木盆地塔中北坡顺南区块501井套管磨损数据及P110管材应力—应变本构关系,建立了充分考虑钻杆本体和接头联合造成的磨损模式、夹角、磨损重叠深度及磨损深度的复合磨损套管有限元力学模型,并开展了多种复合磨损模式下套管弹塑性变形、屈服、裂纹萌生、扩展及爆裂行为模拟,得到了不同复合磨损套管应力分布、剩余抗内压屈服强度及爆裂强度。研究结果表明:(1)月牙夹角在0°~90°时,应力干涉削弱应力集中,月牙夹角在90°~180°时,应力干涉增强应力集中,这种交互作用机制导致磨损套管剩余强度随着月牙夹角增加而先增加后降低;(2)裂纹萌生并起始于等效应力最大的位置即磨损月牙中心,并垂直于最大环向应力沿径向从套管内壁向外壁扩展,且裂纹一旦萌生,裂纹将迅速扩展并发生爆裂失效;(3)灰色关联度分析确定了复合磨损套管剩余强度对磨损深度、月牙夹角、复合磨损形式、月牙重叠深度的敏感性,分析结果表明磨损深度是决定套管剩余强度的主控因素。结论认为,该认识为套管强度设计与优化提供了技术参考,并对准确预测复合磨损套管剩余强度和确保井筒安全及完整性具有重要意义。

增压器钛铝涡轮过盈连接结合强度研究

轻质钛铝(TiAl)涡轮能够显著提高涡轮增压发动机的动力性能,而TiAl涡轮与K418过渡体之间的过盈连接失效问题对增压器安全运行有重要影响。考虑了TiAl涡轮和K418过渡体材料非线性、损伤准则,建立了TiAl涡轮过盈连接强度有限元模型,通过拉伸试验验证了该模型的准确性。在此基础上,构建了接触应力与摩擦系数的关系公式,并探索了温度和高温条件下转速对TiAl涡轮过盈连接强度的影响。结果表明:在400~700℃时,随着温度上升,结构过盈界面接触应力衰减呈上升趋势,过盈连接强度下降幅度增加;在高温条件下,转速越大,过盈连接强度下降幅度越大。