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.

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON’S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.

Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.

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.

Effect of Heat Treatment on High Temperature Stress Rupture Strength of Brazing Seam for Nickel-base Superalloy

In order to enhance the high-temperature stress rupture strength of brazing seam by heat treatment, it was diffusion treated, then solution heat treated, and finally aging treated. The microstructure of brazing seam especially morphology of gamma ' phase and boride was observed and the strength of brazing seam was measured in this process. The results show that heat treatment can enhance high-temperature stress rupture strength by improving the microstructure of brazing seam. The strength of brazing seam after solution heat treatment decreases in comparison with that only after diffusion treatment while aging treatment after solution heat treatment increases the strength of brazing seam.

Nonlinear regression model for peak-failure strength of rockfill materials in general stress space

A nonlinear regression model for peak-failure strength prediction of rockfill materials is proposed. It is based on the relationship between the peak-failure stress ratio and the normalized confining pressure as well as the relationship between the normalized peak-failure stress ratio and the exponent function of the intermediate principal stress ratio. This model can well predict the variations of the peak-failure stress ratio with the initial confining pressure and the intermediate principal stress ratio for different rockfill materials under different general stress paths. Comparisons of the measured and predicted results show that the peak-failure strength under the constant-p' and constant-b path is larger than that under the constant-σ'_3 and constant-b path. The predictive capacity of the proposed model for the peakfailure stress ratio is better than that for the peak-failure friction angle.

EFFECT OF SUBSTRUCTURE AND RESIDUAL STRESS IN STRENGTHENED LAYER ON FATIGUE STRENGTH OF STAINLESS OR LOW CARBON STEEL

In the strengthened layer of stainless steel after shot peening,there are a great amount of deformation microtwins which may act as structural strengthening factor and prevent the gradual relaxation of surface residual stress during fatigue,so as to keep its rather high level of bending fatigue strength.However,in the strengthened surface layer of low carbon steel, dislocation cell structure is so unstalbe during fatigue that its surface residual stress relaxation cannot be retarded.Therefore,the bending fatigue strength of the low carbon steel can not be improred by shot peening.

Mechanical properties of high-strength concrete subjected to high temperature by stressed test

Recently, the effects of high temperature on compressive strength and elastic modulus of high strength concrete were experimentally investigated. The present study is aimed to study the effect of elevated temperatures ranging from 20 ℃ to 700 ℃ on the material mechanical properties of high-strength concrete of 40, 60 and 80 MPa grade. During the strength test, the specimens are subjected to a 25% of ultimate compressive strength at room temperature and sustained during heating, and when the target temperature is reached, the specimens are loaded to failure. The tests were conducted at various temperatures (20-700 ℃) for concretes made with W/B ratios of 46%, 32% and 25%, respectively. The results show that the relative values of compressive strength and elastic modulus decrease with increasing compressive strength grade of specimen.

Delamination strength of HTS tape under transverse tensile stress and its enhancement by using different Ag layer depositing temperatures

For the application of second generation high temperature superconducting coated conductors (CCs) with layered structures, thermal mismatch between different components and electromagnetic force exerted in superconducting layer in a working magnet can cause transverse tensile stress, which would result in delamination behavior. Therefore many research groups have designed experiments to measure the delamination strength and dedicate to improving that. However, the reason of the discrete distribution of measured data has still not get quantitatively studied, besides, there are lack of investigations on the method of changing depositing conditions to improve the delamination strength except by adding an additional metal layer. In this work, we adopt an anvil test device and obtain delamination strengths as 29.6 MPa of YBa2Cu3O7-x (YBCO)/buffer and 114.6 MPa of buffer/substrate by combing energy disperse spectroscopy (EDS) detection. The reason of discretized measurement data on the delamination strength is explained. Moreover, we find that different temperatures during Ag deposition determine the bonding force of Ag and YBCO layer. The Delamination strength between Ag and YBCO layer increases from 4.4 MPa to larger than 114.6 MPa with temperature elevated from 30℃ to 100℃. Hence we present a novel method for improving the delamination strength of YBCO CCs by setting an optimal temperature of Ag deposition.

Influence of pre- plastic deformation on thermal residual stress and yield strength of SiC_w/Al composites

With a micro mechanical model, the feasibility of modification of thermal residual stress of the composites treated by tensile pre plastic deformation was analyzed. The relationship between pre plastic strain and variation of thermal residual stress was established. By using the method of tensile pre plastic deformation, the thermal residual stress in 20%SiC w/6061Al composites was modified. The results show that, with increasing tensile pre plastic strain, the tensile residual stress in the matrix was decreased to zero gradually, and then it was turned into compressive stress. By comparison, it was found that the changing tendency of the test results is similar to that of theoretical analysis. In addition, due to pre plastic deformation, the dislocation density in the matrix was increased, and the yield strength of the composites was improved. The increasing yield strength is mainly due to the decreasing tensile residual stress and the changing of distribution of dislocation in the matrix.

Effect of a novel three-step aging on strength, stress corrosion cracking and microstructure of AA7085

The influence of a novel three-step aging on strength, stress corrosion cracking(SCC) and microstructure of AA7085 was investigated by tensile testing and slow strain rate testing combined with transmission electron microscopy(TEM). The results indicate that with the increase of second-step aging time of two-step aging, the mechanical properties increase first and then decrease, while the SCC resistance increases. Compared with two-step aging, three-step aging treatment improves SCC resistance and the strength increases by about 5%. The effects of novel three-step aging on strength and SCC resistance are explained by the role of matrix precipitates and grain boundary precipitates, respectively.

EFFECT OF DENTIN TUBULES ON THE MECHANICAL PROPERTIES OF DENTIN. PART Ⅰ: STRESS-STRAIN RELATIONS AND STRENGTH CRITERION

As known, there is a large number of dentin tubules in dentin. These tubules have varying radii and are shaped into radially parallel pattern. The anisotropy of microstructure of dentin shows that dentin should be treated as a ma- terial of varying transverse isotropy. In this Part, the elastic stress-strain relations and the quadratic strength criterion are established in the form of having varying transverse isotropy, in the framework of micromechanics to take into account of the effect of the microstructures-dentin tubules. Simplified forms for isotropic and ho- mogeneous cases, as well as the corresponding plane stress form of the stress-strain relations are also given. These theoretical models are very well supported by the experiments shown later in the continued paper (Part Ⅱ).

Stress and Fracture Strength Analysis for Three-Way Pipes

Three-way pipes, T and Y pipes, are very important connecting components in pipeline systems, their strength are related to the safety of pipelines. In the case that crack is not detected in the three-way pipe, ANSYS finite element program version 5.6 is applied to study the stress distribution of the three-way pipe and to obtain the optimum fillet radius in the crotch region of the two pipes. The reasonable intersection angle of the two pipes is also obtained. In the case that a surface crack is detected in the three-way pipe, the maximum stress intensity factor (SIF) near the front of the surface crack is studied.

Stress-deformed state of cylindrical specimens during indirect tensile strength testing

In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe specimen is diametrically compressed by elliptic normal contact stresses. The frictional contactstresses between the specimen and platens are neglected. The analytical solution starts from the contactproblem of the loading jaws of any curvature and cylindrical specimen. The contact width, correspondingloading angle （2 ^0）, and elliptical stresses obtained through solution of the contact problems are used asboundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder issolved using Muskhelishvili＇s method. In this method, the displacements and stresses are represented interms of two analytical functions of a complex variable. In the main approaches, the nonlinear interactionbetween the loading bearing blocks and the specimen as well as the curvature of their surfacesand the elastic parameters of their materials are taken into account. Numerical examples are solved usingMATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on thedistribution of the normal contact stresses as well as on the tensile and compressive stresses actingacross the loaded diameter. Derived equations also allow calculating the modulus of elasticity, totaldeformation modulus and creep parameters of the specimen material based on the experimental data ofradial contraction of the specimen.

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.

Experimental investigation on strength and deformation of plain high-strength concrete under multiaxial stress state

To investigate the strength and deformation behavior of plain high-strength concrete (HSC) under multiaxial stress states,a large static-dynamic true triaxial machine was employed,and multiaxial tests were performed on 100 mm×100 mm×100 mm cubes concrete specimens.Friction-reducing pads were three-layer plastic membranes with glycerine in-between for the compressive loading plane.The tensile loading plane of concrete samples was processed by attrition machine,and then the samples were glued up with the loading plate with structural glue.Failure modes of specimens were described.The principal static compressive strengths,strains at the peak stress and stress-strain curves were measured,and the influence of stress ratios on them was analyzed as well.Experimental results show that the ratio of the compressive strength σ3f over the uniaxial compressive strength fc depends on brittleness-stiffness of concrete besides stress state and stress ratios.The formula of Kupfer-Gerstle's and Ottosen's failure criterion for plain HSC under biaxial compression and multiaxial stress state is proposed respectively.

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.

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

Coupled effects of stress damage and drilling fluid on strength of hard brittle shale

During well drilling process,original stress state of hard brittle shale will be changed due to stress redistribution and concentration,which leads to stress damage phenomenon around the borehole.Consequently,drilling fluid will invade into formation along the tiny cracks induced by stress damage,and then weaken the strength of hard brittle shale.Based on this problem,a theoretical model was set up to discuss damage level of shale under uniaxial compression tests using acoustic velocity data.And specifically,considering the coupled effect of stress damage and drilling fluid,the relationship between hard brittle shale strength and elapsed time was analyzed.

Effect of intermediate principal stress on strength of soft rock under complex stress states

A series of numerical simulations of conventional and true triaxial tests for soft rock materials using the three-dimensional finite difference code FLAC3D were presented. A hexahedral element and a strain hardening/softening constitutive model based on the unified strength theory(UST) were used to simulate both the consolidated-undrained(CU) triaxial and the consolidated-drained(CD) true triaxial tests. Based on the results of the true triaxial tests simulation, the effect of the intermediate principal stress on the strength of soft rock was investigated. Finally, an example of an axial compression test for a hard rock pillar with a soft rock interlayer was analyzed using the two-dimensional finite difference code FLAC. The CD true triaxial test simulations for diatomaceous soft rock suggest the peak and residual strengths increase by 30% when the effect of the intermediate principal stress is taken into account. The axial compression for a rock pillar indicated the peak and residual strengths increase six-fold when the soft rock interlayer approached the vertical and the effect of the intermediate principal stress is taken into account.