Delamination of Grain-Interfaces in Silicon Nitride

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microsopic Simulation of Thermally-Induced 2nd Order Eigenstresses in AlSi-Alloys

Due to the different coefficients of thermal expansion of aluminium and silicon, high residual stresses of second order occur in Al-Si alloys depending on the cooling rate during the molding process. In products as for example crank cases made of Al-Si alloys these residual stresses may cause microcracks. In the work at hand measurements of the eigenstresses in the single phases (i.e. residual stresses of second kind) performed via neutron diffractometry are compared to numerical simulations for a specific cooling rate. To this end a three-phase model is presented, which considers the α aluminium, the eutectic aluminium, and the silicon particles. The presented model is able to predict the residual stresses in the single phases within an elastoplastic framework. The simulation of tensile loadings of these structures are compared to experiments. The numerical computations are carried on stochastic geometry models by using a fast solver [1] for the Lippmann-Schwinger integral equation, which is based on the fast Fourier transformation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The study of structure optimization of blast furnace cast steel cooling stave based on heat transfer analysis

The three-dimensional mathematical model of temperature and thermal stress field of cast steel cooling stave in a blast furnace has been modeled. Kinds of the parameters optimization of cast steel cooling stave in a blast furnace are proposed based on the heat transfer analysis. The results indicate that the values of the parameters optimization for a cast steel cooling stave are 200 mm for cooling channels interdistance, 25 mm for inner radius of the water channel, 180 mm for thickness of the cooling stave body, 70 mm for thickness of inlaid brick and 1.5 m/s for speed of cooling water. Reducing the water temperature would be uneconomical. The water temperature can be chosen according to the local conditions. The best choice for lining material is silicon nitrogen bond silicon carbide brick or silicon carbide brick.     

Residual stress on the run out table accounting for multiphase transitions and transformation induced plasticity

The development of harder and thinner new steel grades requires computationally efficient numerical simulations of forming processes in order to optimize industrial conditions through parametric studies. Within this general framework, the present contribution deals with one particular process, namely the run out table. Thus, this paper focuses on the evolution of residual stresses of thin strips during cooling on the run out table. Due to the fact that the complete problem is a nonlinear multiphysics process, it is known that simulating such processes with fully coupled numerical procedures leads to high computational costs. Therefore, a simplified numerical strategy has been developed. This procedure consists of three steps: (i) solving the thermal problem coupled with multiphase transitions; (ii) computing thermal expansion, metallurgical deformation and transformation induced plasticity and (iii) solving the associated mechanical problem. Residual stress profiles through the strip thickness are also computed in order to evaluate classic flatness defects such as crossbow and longbow. A post-processing is also included in order to quantify out of plane displacements that would take place if the strip was cut off the production line. The post-processing consists in computing at finite strain the relaxation of residual stresses when the tension applied by the coiler is released. The proposed numerical strategy has been tested on common industrial conditions.     

Macroscopic damage modeling for silicon nitride

Modeling the damage of brittle materials is of great importance considering a variety of structural components. Prominent examples are high strength engineering ceramics. The present work is concerned with silicon nitride, a material with increasing relevance in industrial applications. In the sense of a hierarchical model structure, effective properties of micromechanical simulations were applied to macroscopic, phenomenological damage models for monotonous and cyclic loading. In the following, both models are introduced and the application of the cyclic damage model to a four point bending test is discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic fuzzy reliability models of degraded hold-down structures for folded solar array

The hold-down structures are of considerable importance to the launch of solar array. Due to the difficulties in obtaining sufficient load specimen, it is imprecise to construct the stress as random variables. Therefore, dynamic fuzzy reliability models are developed in this paper, which resolve the problems in dealing with the interaction between the fuzzy stress process and the stochastic strength process. Even for a deterministic fuzzy stress process, the influences of material statistical properties on reliability can be affected by the level α of fuzzy stress. Meanwhile, the level α relates to investment in the collection of information about the fuzzy stress on hold-down bar. Hence, the models can be used for the economic analysis and optimal design of hold-down bar. Finally, key fuzzy parameters of stress, which have significant influences on both the reliability behavior and the effects of material statistical properties on reliability, are identified and some suggestions for the reliability enhancement of hold-down bar are provided in this paper.     

Numerical analysis of micro-stress evolution in dual phase polycrystals

Diffraction methods gain much attention in nondestructive residual stress analysis. While the determination of macroscopic residual stresses is of main interest, the presence of microscopic residual stresses arising from microstructural characteristics of the material can influence the analysis of the acquired data. The residual stress measurements by neutron diffraction on IN718 pancake forgings are analyzed in this work. We present a simple mechanical model supporting the hypothesis that the phase average of the microscopic residual stress accumulated during the forging process is anisotropic causing anisotropy of the macro stress free reference lattice parameter. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Residual stress-strain state of a steel disk under thermal pulsed irradiation

The residual stress-strain state of a disk caused by the action of a laser pulse or an electron beam is investigated within the framework of the dynamic statement of the coupled problem of thermomechanics. The axially symmetric problem is solved numerically using the thermodynamically consistent theory of the inelastic behavior of the material involving the finite-element method and taking into account temperature dependences of physical and mechanical characteristics of the material. The response of the material to thermal irradiation followed by gradual cooling is studied, and the possibility of formation of surface profiles with the use of only thermal treatment is considered. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 157–168, January–March, 2008.     

Progressive thermal stress distribution around a crack under Joule heating in orthotropic materials

Stress intensity factor and stress distribution at crack tips are classical problems in solids, which are closely related to the failure and reliability of materials. A crack in a nonlinearly coupled anisotropic medium, on the other hand, is much more difficult to analyze. Using the generalized complex variable method, the thermal stress problem of a crack embedded in an orthotropic medium has been analyzed, and the progressive thermal stress distributions have been obtained in closed-forms. The analysis shows that the thermal stress intensity factors are linear functions of remote thermal flux while are nonlinear functions of remote current; the thermal stress distributions under produced by thermal flux and Joule heating are similar, but not identical; the thermal stress intensity factors are linear functions with respect to the thermal expansion coefficients; with the increase of crack length, the thermal stress intensity factor caused by Joule heat increases rapidly; the thermal stress intensity factors are directly proportional to the temperature difference between the upper and lower crack surfaces and the left and right half crack surfaces divided by the square root of the crack length, and the ratios are only determined by the material parameters. These results provide a powerful tool for the failure and reliability analysis of conductive materials, and suggested that thermal stress analysis may be localized.     

Calculation of the residual stresses and strains in wound reinforced-plastic products

A method is proposed for determining the residual stresses and strains in wound glass-reinforced plastic products. The fabrication process is divided into five stages: winding, heating polymerization, cooling, and removal from the mandrel. The initial stresses that develop during winding and the subsequent stress increment associated with heating are taken into account. Polymerization is treated as a process during which the mechanical and thermophysical properties of the material change. Chemical shrinkage of the resin and its filtration through the fiberglass are disregarded. Equations are derived for the residual radial and peripheral stresses in the finished product, for the residual change in inside diameter, and for the temperature at which the product is released from the mandrel during the cooling process. The experimental data relating to two types of wound products are discussed. The results of a computation of the residual stresses and the residual changes in inside diameter are compared with the experimental data.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 134–139, January–February, 1969.     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

Finite-length mask effects in the isolation oxidation of silicon

Author to whom all correspondence should be addressed A moving-boundary problem modelling the two-dimensional isolationoxidation of silicon is analysed in the limit of reaction-controlledoxidation for a finite-length nitride mask. Encroachment underthe mask caused by silicon oxidation then occurs from both sidesto produce two ‘bird's beaks’, and it is the interactionbetween these beaks on which attention is focused. This effect,termed ‘bird's beak punchthrough’, is currentlyof interest in submicron silicon-isolation technologies.     

Modeling and simulation of the microstructural behaviour in thermal sprayed coatings

The purpose of the current work is the investigation of the mechanical behavior of thermal sprayed coatings to predict the influence of the application of compaction on the coatings. Due to the porosity and the poor surface quality of thermal sprayed coatings, an additional process step is necessary to compact the coating and to increase the surface quality, though leading to a complex deformation behavior of the coating. In a first step the microstructural evolution is investigated. Due to the fact that the experimental determination of the mechanical properties of a coating is quite complicated and cost-intensive, a general procedure is developed which generates the desired quantities for different coating composites from microstructural images which are compared to analytical mean-field homogenization solutions for elastic material behavior. The discussed thermal sprayed coatings are multiphase systems consisting of a metal-matrix composite with pores. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of material data input on accuracy of fatigue assessments for beam weldments

This numerical study investigates the effects of fatigue material data and finite element types on accuracy of residual life assessments under HCF conditions. The bending of cross-beam connections is simulated in ANSYS Workbench for three different combinations of beam profiles. The weldments are made of the high-strength steel grades C350LO and C450LO according to AS3678. The stress analysis of weldments is implemented with solid and shell elements using linear material and geometry consideration. The stress distributions are transferred to the embedded fatigue code nCode DesignLife. For both variants of FE-mesh, the nominal stress in the weld toes is extracted by splitting the total stress into membrane and bending components and filtering out non-linear component. Considering the effects of bending, size and mean stress, failure locations and fatigue life are predicted using the Volvo method and rules from ASME BPV Code. Three different pairs of experimental S-N curves (stiff and flexible) are used as material data input for fatigue analysis. The obtained numerical predictions are compared to the experimental results for shell FE-models. The predictions using the S-N curves for an equivalent steel demonstrate the best accuracy proving the fact that specific material data input is more effective than a generic data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cryogenic mechanical response of multilayer satin weave CFRP composites with cracks

We deal with the thermomechanical response of multilayer satin weave carbon-fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties subjected to tensile loading at cryogenic temperatures. The composite material is assumed to be under the generalized plane strain. Cracks are located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. A finite-element model is employed to study the influence of residual thermal stresses on the mechanical behavior of multilayer CFRP woven laminates with cracks. Numerical calculations are carried out, and Young’s modulus and stress distributions near the crack tip are shown graphically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 479–492, July–August, 2008.     

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.For Pt. 1, see [1].Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 200–214, March–April, 1997.     

Finite element analysis of thermoelastic field in a rotating FGM circular disk

This study focuses on the finite element analysis of thermoelastic field in a thin circular functionally graded material (FGM) disk subjected to a thermal load and an inertia force due to rotation of the disk. Due to symmetry, the FGM disk is assumed to have exponential variation of material properties in radial direction only. As a result of nonuniform coefficient of thermal expansion (CTE) and nonuniform temperature distribution, the disk experiences an incompatible eigenstrain which is taken into account. Based on the two dimensional thermoelastic theories, the axisymmetric problem is formulated in terms of a second order ordinary differential equation which is solved by finite element method. Some numerical results of thermoelastic field are presented and discussed for an Al₂O₃/Al FGM disk. The analysis of the numerical results reveals that the thermoelastic field in an FGM disk is significantly influenced by temperature distribution profile, radial thickness of the disk, angular speed of the disk, and the inner and outer surface temperature difference, and can be controlled by controlling these parameters.     

热荷载作用下薄板的优化设计

板壳结构是一大类广泛使用的结构元件.在热荷载作用下,当热膨胀受到约束时,板壳结构产生内力及挠度,严重时影响结构的正常服役.由于热荷载的特殊性,简单地均匀加大板壳结构的厚度并不能有效地减少热变形和热应力,热结构设计因此特别困难.该文研究在给定材料体积的条件下,通过优化板壳结构的厚度分布来减少弹性薄板结构在热载荷下的变形.以结构的变形能为优化目标,在给定材料体积的条件下,建立了设计板壳结构厚度分布的优化问题列式,并采用变分法,推导出优化准则,给出了修改厚度的迭代公式.应用商用有限元软件的热结构分析功能,对程序进行二次开发,从而实现该优化算法.算例结果表明,采用该方法优化弹性薄板的厚度分布,可以大幅度地减小结构热变形,是一种有效的热结构设计方法.     

The Sensitivity of Residual Stresses of Cross-Ply Laminates to Manufacturing and Material Parameters

By using a finite-element model elaborated, the sensitivity of residual stresses of polyester/glass cross-ply laminates to manufacturing and material parameters is investigated. The development of residual stresses in the laminates and the significance of the parameters for the problem are discussed. It is found that the main attention in calculating residual stresses should be focused on the properties of resin, which must be measured with care. The most important parameters related to the resin are, of course, its stiffness, thermal expansion, and chemical shrinkage, while the properties of fibers can be obtained from material handbooks with a sufficient accuracy. In curing a thin laminate in an autoclave, the simulation of chemical reactions and the parameters needed in thermal analysis are quite insignificant, because, in practice, the autoclave temperature and the properties of the mold determine the laminate temperature history.