Subcritical crack growth models for static fatigue of Hi-NicalonTM-S SiC fiber in air and steam

Three subcritical crack growth (SCG) laws were used to model strain-rates and failure times for static fatigue of Hi-Nicalon^TM-S SiC fiber tows in air and Si(OH)₄(g)-saturated steam. Models were fit to tow failure times ( t_f ) and steady-state strain rates ( ἑ ) for brittle creep measured at 700 to 1100°C under initial applied stresses ( σ_A ) of 260 to 1260 MPa. A power law, a reaction-rate law, and a bond-energy law were used to describe SCG that caused sequential filament failure, and ultimately tow failure. Two versions of each model were developed. One allowed access of chemisorbed species to flaws throughout the fiber (mode 1) and another only allowed access to flaws at the SiC-SiO₂ interface (mode 2). The stress increase on intact filaments as others fractured and as filaments oxidized, and the increase in stress intensity geometric factors ( Y ) as crack size increased were incorporated in the models. The fits to data were compared for the different models by using both simple regression analysis and orthogonal distance regression (ODR) analysis. Faster convergence and more consistent results were achieved using ODR analysis. Regression analyses found parameters for all models with similar error in data fits, so validity of a model could not be distinguished by regression analysis alone. For all models, the stress dependence of SCG rates was much stronger in steam than in air, and for most models activation energies were between 300 and 420 kJ/mol, regardless of environment. For the steam environment, the bond-length parameter ( δ ) for the bond-energy model was very close to the lattice parameter of β-SiC (.436 nm), but in air it was significantly lower at 0.25-0.26 nm, but still larger than the Si-C bond length of 0.189 nm. Other factors suggest that either a bond-energy based law or a modified version of a reaction-rate law are the best choices for a SCG law. Filament strength distributions initially described by Weibull distributions could not be described by such distributions after application of the models. SCG mechanisms are discussed.     

Strength of adhesive joints with adherend yielding: I. Analytical model

A sandwich element can be isolated in all two-dimensional adhesive joints, thereby simplifying the analysis of strain and stress. An adhesive sandwich model has been developed that accommodates arbitrary loading, a bilinear adherend stress-strain response, and any form of nonlinear adhesive behavior. The model accounts for both the bending deformation and the shear deformation of the adherends. Stress and strain distributions in the adhesive were obtained by solving a system of six differential equations using a finite-difference method. For a sample adhesive sandwich, the adhesive strains and stresses from the new model were compared with those of other models. Finally, the model was coupled with an analytical solution for the detached section of an adhesive joint in peel. The stress and strain distributions in the adhesive and the root curvature of the peel adherend were then compared with finite element results. An accompanying article in this issue uses the model with experimental peel data to investigate the suitability of various adhesive failure criteria.     

Finite element modeling of the time-dependent behavior of nonlinear ductile polymers

A finite element algorithm developed previously has been successfully extended to the study of nonlinear time-dependent problems. Nonlinear viscoelastic and viscoplastic models have been used to study the time-dependent deformation and failure of high density polyethylene (HDPE). Two classes of nonlinear models have been identified; those that allow stress redistribution with time under specified traction boundary conditions, and those that do not. The implications of using viscoelastic vs. viscoplastic models, as well as the specific mathematical form of the constitutive equations selected for use, have been studied. Strains predicted using the FE algorithm have been compared with experimental measurements for (i) a HDPE plate with a hole and (ii) a double edge notch HDPE specimen, both under remote tension. Excellent agreement was obtained between numerical predictions and the experimental values.     

STRENGTH OF ADHESIVE JOINTS WITH ADHEREND YIELDING: I. ANALYTICAL MODEL

A sandwich element can be isolated in all two-dimensional adhesive joints, thereby simplifying the analysis of strain and stress. An adhesive sandwich model has been developed that accommodates arbitrary loading, a bilinear adherend stress-strain response, and any form of nonlinear adhesive behavior. The model accounts for both the bending deformation and the shear deformation of the adherends. Stress and strain distributions in the adhesive were obtained by solving a system of six differential equations using a finite-difference method. For a sample adhesive sandwich, the adhesive strains and stresses from the new model were compared with those of other models. Finally, the model was coupled with an analytical solution for the detached section of an adhesive joint in peel. The stress and strain distributions in the adhesive and the root curvature of the peel adherend were then compared with finite element results. An accompanying article in this issue uses the model with experimental peel data to investigate the suitability of various adhesive failure criteria.     

Estimating time and temperature dependent yield stress of cement paste using oscillatory rheology and genetic algorithms

A controlled shear stress–shear rate rheometer was used to determine the viscoelastic behavior of cement paste incorporating various superplasticizers and subjected to prolonged mixing at high temperature. At a low applied shear stress range, the oscillatory shear strain/stress curve of cement paste was characteristic of a linear elastic solid; while the higher stress range was characteristic of a viscous liquid exhibiting a linear strain increase with increasing applied shear stress. The transition from solid-like to liquid-like behavior occurred over a very narrow stress increment. This transition stress corresponded to the yield stress parameter estimated from conventional flow curves using the Bingham model. The yield stress from oscillatory shear stress tests was estimated using the intersection between the viscous part of the oscillatory shear strain/stress curve and the oscillatory shear stress axis. In this study, equations describing the variation of shear strain versus shear stress beyond the solid–fluid transition for cement pastes incorporating various superplasticizers at different ambient temperatures and mixing times were developed using genetic algorithms (GA). The yield stress of cement pastes was subsequently predicted using the developed equations by calculating the stress corresponding to zero strain. A sensitivity analysis was performed to evaluate the effects of the mixing time, ambient temperature, and superplasticizer dosage on the calculated yield stress. It is shown that the computed yield stress values compare well with corresponding experimental data measured using oscillatory rheology.     

Fatigue strength and failure analysis of weld-bonded joint of stainless steel

Quasi-static tests of spot welded and weld-bonded joints with 1.5 mm-thick SUS304 stainless steel sheets were conducted. Joint weld diameters were measured using scanning acoustic microscopy. Fatigue tests were performed to obtain the fatigue lives of two joint types subjected to different stress levels. The equations of load-life curves were obtained by nonlinear regression using a three parameter power function. Scanning electron microscopy was used to explore fatigue failure mechanisms of the joints. The results illustrate that nugget diameters of weld-bonded joints were smaller than those of spot welded joints. Their shear strength was lower, but weld-bonded joints showed a better fatigue performance than that of spot welded joints. Two fatigue failure modes were observed via testing: eyebrow failure mode and substrate fracture.     

Designing reliable polymer coatings

A method to predict the ultimate adhesion performance of coatings subjected to biaxial, tensile stress is presented. A set of equations is developed to predict the onset of failure when the locus of failure is cohesive in the coating. The equations also have been extended to predict fatigue lifetime when a coating is cycled from a low temperature to room temperature. To test these equations, the Edge Liftoff Test (ELT) was developed. It consists of fabricating coatings of various heights on a rigid substrate and dicing the latter, so that the edges are 90° to the interface. The parts are cooled and the temperature of debonding is recorded. For thermal fatigue validation, cycles at which the first debond is observed are recorded. ELT results have been collected for a typical epoxy for both monotonic and cyclic cooling. The predictions are in agreement with results.     

绝热层流泡状流运动的双流体模型

绝热层流泡状流是泡状流研究中的一个基础范例 .目前描述绝热层流泡状流常采用的双流体模型由于相间作用考虑欠缺而适用性差 .本文结合理论和实验研究结果导出了描述壁面“排斥”作用的表达式 ,并建立了一个封闭的双流体模型 .模型预测值和实验值的比较表明 ,由于相间作用的合理考虑 ,扩大了该模型的适用范围     

Stress analysis of aluminium plates one-sided adhesively bonded reinforced with square composite patches using state space method

Based on state space method, a 2-D model is established for metallic plates with composite patches as reinforcement, the governing equations for the model are derived, and the stress and strain distributions are analyzed. By means of MATLAB, the structure deflection, the adhesive peel stress, and the shear stress under tensile load are figured out. In order to validate the analytical model, the finite element analysis (FEA) is also applied and a FEA model is developed by ABAQUS. Both models give pretty identical results. In the end, using the analytical model, the interlaminar stress and in-plane stress distributions through the thickness of the patch are calculated, which are known to be key contributions to composite failure, and the damage mode is briefly analyzed as well.     

亚格子过滤双流体模型的网格依赖性

基于双流体方程和颗粒动力学理论的计算模型被广泛应用于流化床的气固两相流数值计算,高精度网格是其准确计算流动的必要条件。一些经典的微尺度阻力模型,其网格尺度决定其模拟结果的精度。亚格子过滤双流体模型是一种有效的适用于粗糙网格的计算模型,其包含的气固相间作用力和颗粒相应力本构方程是在高精度网格条件下,以微尺度双流体方程和颗粒动力学理论计算得到的气固流场为基础,对计算结果进行小尺度过滤后得出。使用亚格子过滤双流体模型替换基于颗粒动力学理论的双流体模型,针对同一物理问题,在不同网格尺度下进行了数值计算,结果表明此计算模型相比经典阻力模型具有较好的网格无关特性,并且和实验结果较为一致。同时也对颗粒动力学理论与之相结合进行了尝试,即仅使用亚格子过滤阻力模型,颗粒相应力仍然使用颗粒动力学模型,其计算结果的网格无关性及与实验值的吻合程度优于经典模型。     

Numerical simulation of a polypropylene foam bead expansion process

The production process for expanded polypropylene foam beads (EPP), which consists of steaming, depressurizing, cooling, and ageing operations, was consistently simulated by a set of mathematical models. The models, developed from Yang and Lee's ageing models (Yang and Lee, J. Cell. Plast., 39 , 59 (2003)) for extrusion foam products, were extended in terms of the fundamental aspects of mass and heat transport phenomena. Evaporation and condensation of blowing agents and heat conduction during the steam chest molding and ageing processes were modeled. The governing equations were established by integrating the mass transfer equations of steam and air at the intercellular walls with the constitutive equations of evaporation and condensation in each cell, the equation of heat conduction from the mold to the foam, and the mechanical force balance equation on the cell walls. The models simulate the stress exerted on the steaming chest mold and predict the expansion behavior of cells in the EPP bead‐foam board throughout the ageing process. A sensitivity analysis was also performed by the models to find the key factors which might allow the theoretical determination of the ejection time and shortening of the length of the ageing process. POLYM. ENG. SCI., 48:107–115, 2008. © 2007 Society of Plastics Engineers     

Modeling of fatigue failure for SiC/SiC ceramic matrix composites at elevated temperatures and multi-scale experimental validation

The fatigue failure of ceramic matrix composites at elevated temperatures was predicted using the micromechanics method. Multiple micro-damage models were developed to describe the evolution processes of matrix cracking, interface wear, and fiber fracture during fatigue loading. On this basis, the fatigue life was calculated. To validate the fatigue failure model, multi-scale experiments were conducted. In the macroscale, the S-N curve was obtained by the fatigue test. In the microscale, multiple in-situ measuring methods were developed through which the matrix crack density, the interfacial shear stress, and the percentage of fracture fibers were obtained. Both the macroscale and microscale experimental results were in good agreement with the predicted results. Therefore, the fatigue failure model developed in the present work is accurate.     

Estimation of Fatigue Strength for Adhesively-Bonded Lap Joints Based on Fatigue Failure Criterion Under Multiaxial Stress Conditions

A method for estimation of endurance limits for adhesively-bonded single and single-step double-lap joints was proposed which considers the stress multiaxiality in the adhesive layer. At first, fatigue tests and finite element analysis were conducted for these lap joints. Then, endurance limits of these joints were estimated using their stress distributions and critical regression equations which were obtained from the S-N data of adhesively-bonded scarf- and butterfly-type joints. The results indicate that the endurance limits of these lap joints can be estimated from the regression equation based on the maximum principal stress.     

Mechanical and fracture behavior of an artificially ultraviolet‐irradiated poly(ethylene‐carbon monoxide) copolymer

In this work, 1 wt % carbon monoxide (CO) poly(ethylene‐carbon monoxide) (ECO) copolymer sheets were artificially exposed to ultraviolet (UV) light with a power density of 3 mW/cm² for up to 130 h. A thorough mechanical characterization of the irradiated material was conducted, in which both the stress–strain data and the values of the quasistatic crack initiation and growth toughness were measured and correlated with companion uniaxial tensile tests and single‐edge‐notched fracture tests. Average values of the elastic modulus, failure strain, and failure stress were determined from the tensile tests. The full‐field optical technique of digital image correlation was used to quantify in‐plane deformation (displacements and displacement gradients) during the fracture experiments and to extract values of the crack initiation and growth fracture toughness. The elastic modulus increased monotonically with UV irradiation for the exposure times used in this investigation. In addition, for low irradiation times of less than 5 h, both the failure strain and failure stress of ECO decreased, and this caused a corresponding decrease in the crack initiation and growth toughness. However, for longer irradiation times, the failure strain remained almost invariable, whereas the failure stress increased by about 25% over that of unirradiated ECO. As a result, for longer irradiation times (>5 h), 1 wt % CO ECO became not only stiffer but also stronger and tougher, as quantified by companion fracture experiments. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 139–148, 2004     

Rotated, circular arc models of stress in silos applied to core-flow and vertical rat-holes

Rotated, circular arc geometry models have been developed to describe core-flow and vertical rat-holes in cylindrical hoppers and silos.The conceptual problem of the variation of incremental element thickness has been overcome, resulting in models of greater theoretical rigour.Models have been developed in an average stress and point stress form. Analysis shows that stresses vary with vessel radius through an arc angle parameter, ε, as well as with bed depth.The models indicate that conditions at a rat-hole annulus wall are quite different from the mean stress or wall stress and this has implications for stability and flow.A modified failure criterion, based upon azimuthal stress has been used to assess the stability of deep rat-holes, and a range of rat-hole stability determined, which is dependent upon material properties and vessel diameter.Predicted stress distributions are functions of assumed internal stress distribution relationships. More physical data are required in this area to enable reliable modelling.     

多氯联苯热力学性质的构效关系

通过计算二噁英类化合物多氯联苯（PCBs）217种分子的定位指数和基团对应指数,以这些分子的热力学性质的文献值为建模样本,运用多元线性回归方法建立了多氯联苯的标准熵（S0）、标准焓（H0）、标准自由能（G0）、分子总能量（ET）、热能校正值（Eth）、零点振动能（Ezpv）及恒容热容（Cv0）等热力学性质的定量结构-性质相关方程,相关系数均在0.99以上。这些模型能较好地解释多氯联苯热力学性质的递变规律,而且相关系数高,稳定性好,预测能力强。采用留一法对模型稳健性进行了检验,得到的预测模型对另外一些多氯联苯分子的热力学性质进行预测,预测结果和文献值基本吻合。     

Optimal Shape of Thin Tensile Test Specimen

A tensile test method involving shape optimization of a thin, planar specimen has been developed. The purpose was to reduce the stress concentration in the transition zone between a straight-sided zone and a wider-end zone. Three designs of specimen, including an ISO standard design, were investigated based on finite element analyses. The technological applicability of two of the designs was tested on thin, planar cermets corresponding to the structurally supporting member of a planar anode-supported solid oxide fuel cell (SOFC). Application of optimized shapes appeared as a viable method. The maximum stress in the specimen was reduced to <1.01 times the average stress. The fraction of invalid tests (i.e., specimens failing outside the gauge section) was reduced with the optimized shapes. The tested samples were cut into shape by laser as actual SOFC components. The cutting was seen to generate surface cracks that acted as the main failure initiator.