A neural-network approach to describe the scatter of cyclic stress–strain curves

In order to predict a product’s durability in the early phases of development it is necessary to know the stress–strain behaviour of the material, its resistance to fatigue and the loading states in the material. These parameters, however, tend to exhibit a considerable degree of uncertainty. Due to a lack of knowledge of the actual circumstances in which the product is used, during the early development phase, simulations based on statistical methods are used. The results of the experiments show that the cyclic stress–strain curves demonstrate not only a large amount of scatter, but also a dependence on the temperature, the size of the cross-section, the content of alloying elements, the loading rate, etc.This article presents a method for modelling cyclic stress–strain curve scatter using a hybrid neural network for an arbitrary selection of the influencing factors. In an example of the measured data for a high pressure die-cast aluminium alloy it is clear that the suggested method is suitable for describing cyclic stress–strain curves. The main advantage of a hybrid neural network in comparison with a conventional method is the neural network’s ability to precisely describe the influence of various factors, and their combinations, based on the form and scatter of the cyclic stress–strain curve families. Defining the model parameters, i.e., training the neural network, is a procedure that does not require any additional user interventions; however, it enables us to gather knowledge that would otherwise require a lot of research. Thus, the trained neural network is a robust tool that can be used to predict cyclic stress–strain curves for random values of influencing factors. The capabilities of the presented method are only limited by the quantity of the measured data used for the neural-network training.     

Determination of S–N curves with the application of artificial neural networks

The present paper describes the application of artificial neural networks for estimating the finite-life fatigue strength and fatigue limit. A comprehensive database with results of single-stage tests on specimens which simulate structural components is evaluated and prepared for processing with the use of neural networks. The available data are subdivided into different classes. A total of six different data classes are specified. The results of the prediction by means of neural networks are superior to those obtained with conventional methods for calculating the fatigue strength. The experimental results are estimated with high accuracy.     

A fuzzy approach for drawing S–N curves in the finite life region

In this work a fuzzy approach has been developed in order to estimate the probability of fatigue failure. In particular, with the proposed method the S–N curves of a material in the finite life region can be drawn. The experimental data are represented in terms of fuzzy sets and are fitted using a fuzzy linear regression. Data scattering and uncertainty in the empirical failure model are reflected in the definition of membership functions. Several examples are shown to illustrate the procedure. Failure probabilities and fatigue curves obtained by the fuzzy method are similar to those obtained by traditional statistical analysis, based on normal distributions of strength with standard deviation that remains constant with different load levels. In particular, the results obtained indicate that the possibilities offered by fuzzy systems are also applicable for estimating the Wöhler curve of a material under fatigue stresses. To evaluate its reliability, the proposed method is compared with the traditional one, with particular attention to the case in which a small amount of experimental data is available. The new fuzzy method is slightly less accurate than traditional statistical analysis to outline S–N curves in the finite life region. This is mainly due to the fact that the method is influenced by the nonuniformity of data dispersion at each level of stress.     

Determination of J–R curves of thermoplastic starch composites containing crossed quasi-unidirectional flax fiber reinforcement

Thermoplastic starch (MaterBi) composites reinforced with quasi-unidirectional flax fiber in cross-ply (CP) arrangement were produced by film stacking followed by hot pressing. These composites, containing various amount of flax, failed ductilely with pronounced crack growth. Therefore, to determine their fracture mechanical behaviour the J-integral resistance curve concept (J–R) was applied. As the crack growth could not be traced, attempt was made to use the located acoustic emission (AE) events for that purpose. It was established that weighting and smoothing the located cumulative AE amplitudes the crack path can be correctly reconstructed. This was proved by collating the AE results with those derived from infrared thermographic (IT) inspection. Knowing the crack propagation at each point of the force–displacement curves the J–R curves could be determined. Both critical or initiation J-integral and tearing modulus went through a minimum with increase of flax content in the composites.     

An improved method for estimation of Ramberg–Osgood curves of steels from monotonic tensile properties

In the present study, first a method for estimating cyclic yield strength is improved and compared using the experimental data of 121 steels from literature. Correlations between cyclic deformation properties (K′ and n′) and monotonic tensile data are then investigated, and a simple method requiring only the monotonic tensile properties is developed for estimation of the Ramberg–Osgood curve. Prediction capability of the proposed method is not only evaluated using the aforementioned 121 steels, but also compared with several commonly used methods that are available in the literature. The proposed correlations are shown to predict the cyclic deformation properties of most of considered steels reasonable well.     

An example of the use of neural computing techniques in materials science—the modelling of fatigue thresholds in Ni-base superalloys

Two adaptive numerical modelling techniques have been applied to prediction of fatigue thresholds in Ni-base superalloys. A Bayesian neural network and a neurofuzzy network have been compared, both of which have the ability to automatically adjust the network’s complexity to the current dataset. In both cases, despite inevitable data restrictions, threshold values have been modelled with some degree of success. However, it is argued in this paper that the neurofuzzy modelling approach offers real benefits over the use of a classical neural network as the mathematical complexity of the relationships can be restricted to allow for the paucity of data, and the linguistic fuzzy rules produced allow assessment of the model without extensive interrogation and examination using a hypothetical dataset. The additive neurofuzzy network structure means that redundant inputs can be excluded from the model and simple sub-networks produced which represent global output trends. Both of these aspects are important for final verification and validation of the information extracted from the numerical data. In some situations neurofuzzy networks may require less data to produce a stable solution, and may be easier to verify in the light of existing physical understanding because of the production of transparent linguistic rules.     

New method for determining P‐S‐N curves in terms of equivalent fatigue lives

A new method for determining the P‐S‐N curves is proposed by the probabilistic analysis of the mixed samples that are composed of the testing fatigue lives and equivalent fatigue lives. The equivalent fatigue lives at each level are converted from all the testing data at all the testing levels according to the equivalent fatigue failure probability, where the life distributions are determined by the medians of logarithmic fatigue lives at respective levels and a unified coefficient of variation. Comparison results of the P‐S‐N curves of 2024‐T3 and A356.0‐T6 alloys with the different methods indicate that the new method can determine the high‐precision P‐S‐N curves with different sample sizes of the S‐N testing data, and can save testing time and improve testing efficiency, especially for the situation of large‐scatter S‐N testing data.     

Predictions of the Joule–Thomson inversion curves for polar and non-polar fluids from the SAFT-CP equation of state

In this work, we calculate the Joule–Thomson inversion curves of some non-polar fluids, including argon, nitrogen, oxygen, carbon dioxide, n-alkanes (C₁–C₄), ethene, acetylene, benzene and toluene and some polar fluids, including hydrogen sulfide, ammonia, acetone and ethyl ether from the SAFT-CP equation of state. Comparisons with correlated experimental data and reference equation of state indicate that this molecular based equation of state gives good prediction for non-polar fluids. For polar fluids, the predictions of the low-temperature branch are satisfied; but, unfortunately, due to lack of isenthalpic data for high-pressure–high-temperature gas condensate, the reliability of model predictions could not be completely verified. In this work, the performance of some cubic equations of state in predicting the Joule–Thomson inversion curves is also compared with SAFT-CP equation of state.     

An improved method of calculating the peak stress distribution for a broad‐band random process

An improved method of fast fatigue life prediction under broad‐band random loading is proposed, which is based on the power spectral density of stress in the critical points of structures and the peak stress distribution of a stationary Gaussian random process. The improved method has higher precision than other existing approximate methods that are based on the peak stress distribution.     

Controllable formation of Er–Yb codoped Al2O3 films by the non-aqueous sol–gel method

1 mol%Er³⁺–10 mol%Yb³⁺ codoped Al₂O₃ thin films have been prepared on thermally oxidized SiO₂/Si(110) substrates by a dip-coating process in the non-aqueous sol–gel method from the hydrolysis of aluminum isopropoxide [Al(OC₃H₇)₃] under isopropanol environment. Addition of N,N-dimethylformamide (DMF) as a drying control chemical additive (DCCA) into the sol suppresses formation of the cracks in the Er³⁺–Yb³⁺ codoped Al₂O₃ thin films when the rare-earth ion is doped with a high doping concentration. Homogeneous, smooth and crack-free Er³⁺–Yb³⁺ codoped Al₂O₃ thin films form at the conditions by a molar ratio of 1:1 for DMF:Al(OC₃H₇)₃. A strong photoluminescence spectrum with a broadband extending from 1.400 to 1.700 µm centered at 1.533 µm is obtained for the Er³⁺–Yb³⁺ codoped Al₂O₃ thin films, which is unrelated to the addition of DMF. Controllable formation of the Er³⁺–Yb³⁺ codoped Al₂O₃ thin films may be explained by the fact that the DMF assisted the deprotonation process of Al–OH at the surfaces of gel particles, resulting in enhancement of the degree of polymerization of sols and improvement of the mechanical properties of gel thin films.     

An efficient method of solving the Navier–Stokes equations for flow control

A new method of solving the Navier–Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen–Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier–Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier–Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier–Stokes equation. © 1998 John Wiley & Sons, Ltd.     

An efficient numerical method for computing the topological sensitivity of arbitrary‐shaped features in plate bending

The objective of this paper is to introduce an efficient numerical scheme to compute the topological sensitivity (TS) of arbitrary‐shaped features in plate bending. The proposed method captures the first‐order change in quantities of interest (example: plate compliance) when an arbitrary‐shaped feature is created within a plate. Both the theory and algorithms are provided to rapidly compute the feature‐specific TS for the classic Kirchhoff–Love plate models. An important application of the proposed method is in design exploration/optimization wherein a designer can explore the impact of including plate features, without recourse to repeated finite element analysis. The proposed method is illustrated and validated through numerical experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

An anisotropic damage model based on microstructure of boom–panel for the fatigue life prediction of structural components

Because of their simplicity, many isotropic damage models have been used to approximately predict the fatigue life of metallic engineering components. However, experimental observations confirm that the anisotropic damage evolves at probable failure sites even for isotropic materials. In this study, a model of microstructure of boom–panel is constructed to simulate a representative volume element (RVE), and the anisotropic damage of the RVE is described by the independent isotropic damage of boom and panel. Firstly, the constitutive equation of the RVE in terms of stiffness of boom–panel is deduced by the principle of deformation and static consistency. Then the expressions of damage‐driving force for boom and panel based on the principle of thermodynamics are introduced, and the damage evolution equations are constructed. The parameters of boom and panel are identified from fatigue test data of uniaxial tension and pure torsion, respectively. Finally, the aforementioned method is applied to predict the fatigue life of two structures: one is Pitch‐Change‐Link, which is a kind of structure in helicopter, and the other is a specimen under tension–torsion. The prediction results all fit well with the experimental data.     

An enhanced cell‐based smoothed finite element method for the analysis of Reissner–Mindlin plate bending problems involving distorted mesh

In this work, an enhanced cell‐based smoothed finite element method (FEM) is presented for the Reissner–Mindlin plate bending analysis. The smoothed curvature computed by a boundary integral along the boundaries of smoothing cells in original smoothed FEM is reformulated, and the relationship between the original approach and the present method in curvature smoothing is established. To improve the accuracy of shear strain in a distorted mesh, we span the shear strain space over the adjacent element. This is performed by employing an edge‐based smoothing technique through a simple area‐weighted smoothing procedure on MITC4 assumed shear strain field. A three‐field variational principle is utilized to develop the mixed formulation. The resultant element formulation is further reduced to a displacement‐based formulation via an assumed strain method defined by the edge‐smoothing technique. As the result, a new formulation consisting of smoothed curvature and smoothed shear strain interpolated by the standard transverse displacement/rotation fields and smoothing operators can be shown to improve the solution accuracy in cell‐based smoothed FEM for Reissner–Mindlin plate bending analysis. Several numerical examples are presented to demonstrate the accuracy of the proposed formulation.Copyright © 2013 John Wiley & Sons, Ltd.     

The two‐shearfield test – A suitable method for the empirical shear capacity design of masonry / Der Zweifeld‐Schubversuch – Eine praxistaugliche Methode zur versuchsgestützten Bemessung der Schubtragfähigkeit von Bestandsmauerwerk

The investigations [1] demonstrate that the two‐shearfield test is a suitable method for the determination of the shear capacity of masonry. The testing equipment is mounted directly on the wall in order to retain realistic boundary conditions like stiffness, load and prior damage. The behaviour factor q and the capacity curves of certain masonry walls can be directly obtained from the experimental results and realistic material behaviour in earthquake design can be represented. In particular, existing masonry can be assessed realistically with methods like the response spectrum, the push‐over and the capacity spectrum by using the two‐shearfield test.