Numerical Analysis of Strains and Stresses in Stretched Specimens at Microstructure Level

In the paper an incremental methodology was proposed for the determination of the states of stresses and strains in specimens while taking into account the strain history and the strain rate history during a tension stress, and a new methodology to determine mechanical characteristics of metal materials. An equation of motion and deformation of the specimen was introduced while using a variational formulation and the finite element method. The results of numerical simulations which illustrate the methods proposed, were presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress on the interatomic bonds near the surface of a polymer

The stresses on the interatomic bonds in the interior and at the surface of polyethylene terephthalate film in uniaxial tension have been determined by means of infrared transmission and reflection spectroscopy. The stresses are found using the shift in the frequency of the atomic vibrations produced by the application of a mechanical load. It is shown that the stresses on some bonds in the specimen reach 700 kgf/mm², i.e., approach their theoretical strength. The concentration of these bonds in a surface layer 1 µ thick is approximately an order greater than the concentration in the interior of the specimen.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 512–514, May–June, 1976.     

A refined stress-strain analysis in the load transfer zone of flat specimens of high-strength unidirectional composites in uniaxial tension 2. Finite-element parametric analysis

A detailed finite-element analysis of the stress-strain state in the load transfer zone of uneasily tensioned flat test specimens made of a high-strength unidirectional carbon fiber-epoxy composite is carried out with account of the elastoplastic behavior of a structural polyurethane adhesive. Various schemes of introduction of external loads into the specimens are considered. A numerical finite-element analysis of different configurations of specimen tabs allowed us to put forward a technique for significantly reducing the dangerous concentration of operating stresses. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 43–58, January–February, 2007.     

Deformation and Damage Analysis of a Hybrid-Forming Tool under Thermal Shock Conditions

In the hybrid–forming process for gradient structures [1] inhomogeneous cyclic thermo–mechanical stresses and strains lead to higher risks of failure of the forming tool. The main topic of this paper is the validation of finite element calculations for a tool–like specimen under complex thermo–mechanical loadings in order to predict the material behaviour [3]. To this end thermal shock experiments of tool–like specimens are performed. Optical measuring systems are used for three–dimensional digitalisation of the specimens to get a sufficient amount of data. Results of experimental optical measurings and results of finite element calculations are compared. Additionally, damage analysis using the eddy current method is performed to characterize the surface state of the cyclically thermal shocked specimens. This damage analysis provides data for lifetime prediction models under thermal shock conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction and Measurement of Residual Strains for a Composite Bonded Joint

A quasi-isotropic composite laminate/adherend of IM6/3501-6 and a composite bonded specimen were manufactured and tested. The bonded specimen was fabricated by postbonding composite adherends together using a 177°C adhesive resin. Predictions for the residual curing strains in the composite adherends and the adhesively bonded composite specimen were performed using a thermomechanical linearly elastic analysis. The analysis was performed using a computer program based on a polynomial spline displacement approximation method [1]. The residual strains of the specimens were measured using the moiré interferometry technique. Diffraction gratings were replicated at room temperature onto the edges of polished laminated adherends and on the edge of a fully cured adhesively bonded specimen. The specimens were cut through their entire thickness in the middle of the diffraction grating area, resulting in a redistribution of the residual curing stresses, with corresponding changes in the strain field at the edges of the cut. A full-field deformation pattern was obtained in the grating area by analyzing the recorded fringe patterns. The deformation field induced by the cut in the laminated adherends and the adhesive bondline were estimated by the linear thermomechanical analysis. A good agreement between the analysis and the experimental results was obtained.     

Microstructural behaviour of transversal isotropic material

We discuss and simulate transversal isotropic material under tension loading. The preferential direction of the material is inclined under 45 degrees to the direction of the tensile resultant. In this configuration the deformation of a rectangular test specimen differ from the behaviour of isotropic material in the way, that beside Poissons effect additional displacement appear perpendicular to the tension direction. In classical continuum theories, this transverse deformations describe a typical S–shape. By using a non–local continuum theory, the effect of microstructural orientation is incorporated into the numerical model. Then, it depends on a phenomenological parameter of inner structure whether the energetically favoured configuration is classical or contains microstructural behaviour. In the second case, the transverse deformation is not described by the typical S–shape, but with higher forms of it. A simple experimental model will show the connection between the inner structure of the material and the rotational parameters within the non–local continuum theory. It is evident, that these parameters are responsible for the non–classical behaviour and give the possibility to find energetically favoured solutions. The results of the finite–element–analyses can help to understand constitutive parameters for the non–local continuum theory and to apply it to other specimens. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Statistical derivation of the equations of viscoelasticity of rubbery polymers for homogeneous finite deformations

The statistical derivation of the equations of linear viscoelasticity [1, 2] is extended to the slow finite homogeneous deformations of rubbery polymers. It is shown with reference to a Gaussian subchain network model that the time correlation functions of the momentum fluxes (relaxation moduli) in the deformed and undeformed states are the same. The relations previously proposed on the basis of purely phenomenological considerations [15] are obtained for the viscous stresses in uniaxial tension. Comparison with experiment has shown that the proposed relations approximately describe the existing data on the stretching of elastomers in a certain region of finite strains.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 980–986, November–December, 1969.     

Variant of the variable-modulus theory of elasticity

A variant of the variable-modulus theory — a generalization of the ideas of the classical theory of elasticity in which the observed difference in the moduli of elasticity in uniaxial tension and compression and homogeneous shear is taken into account — is considered. Quasilinear expressions are proposed for the stresses in terms of the strains and the strains in terms of the stresses.Tula Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 363–365, March–April, 1969.     

The numerical analysis of the trapezoidal thread rolling process

The thread rolling is difficult technological process. Improve quality and contemporary reduce manufacture cost of the trapezoidal thread requires acquaintances of physical phenomena observed in the contact zone between rolls and deform work-pieces. Therefore, in this paper the physical and mathematical models of deformations (displacements and strains) and stress in the cold process of trapezoidal thread rolling, were developed. The process is considered as a geometrical and physical non-linear, initial as well as boundary value problem. The phenomena on a typical incremental step were described using a step-by-step incremental procedure, with an updated Lagrangian formulation. The state of strains was described by Green-Lagrange's tensor, while the state of stress by the second symmetrical Pioli-Kirchhoff's tensor. The object was treated as an elastic (in the reversible zone) and visco-plastic body (in non-reversible zone) with mixed hardening. The variational equation of motion in three dimensions for this case was proposed. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. The application developed for in the ANSYS programme, which provides a complex time analysis for displacement, strains and stresses occurring in the object. The recommendations concern modeling the trapezoidal thread rolling process, where reduce degrees of freedom in numerical model is very important and provide convergence calculated results for maximum stress and strain values in the thread surface layer, were elaborated. The influence a various process conditions on the states deformation and stress for examples calculations, were presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of wave phenomena in the Zahorski material based on modified library for ADINA software

This paper presents numerical modelling of wave phenomena in simple elastic structures such as rods and shields made of hyperelastic Zahorski material. The main difference between the Zahorski material, which is an elastic material in the Green sense, and the commonly used Mooney–Rivlin material lies in the non-linear term including the constant C₃. Consequently, qualitative and quantitative differences are observed compared to the Mooney–Rivlin material, for example in the values of effective stresses. The extension to the ADINA software developed by the author, which helps create 2D and 3D libraries, significantly facilitates modelling of the Zahorski material. The modification can be used for comparison of wave phenomena that are observed during the propagation of disturbances in the Mooney–Rivlin and Zahorski materials. It should be emphasised that the Zahorski material behaves much better at high strains during the analysis of incompressible rubber and rubber-like hyperelastic materials and can be used in various fields of science wherever the model of Mooney–Rivlin material is successfully applied. The results of numerical computations for both Mooney–Rivlin and Zahorski materials were presented in a graphical form and compared in order to illustrate the differences.     

The Numerical Analysis of the External Round Thread Rolling

The papers [1] describe modeling of the contact problem in the external thread rolling process. This paper shown an application of obtained model for the thread with round outline. The mathematical model of process, were presented. The variational and finite element method, were used. The algorithm of numerical analysis in ANSYS system, were elaborated. Numerical computions of displacements, strains and stresses have been conducted without the necessity to introduce boundary condition in the contact zone – a proper definition of the contact zone by single surface auto 2D. Exemplary results of numerical analysis for various condition of the process realization in the discretized model has been presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

三维变形状态下Ⅰ型裂纹裂尖应力场结构的有限元分析*

本文用ADINA(Automatic Dynamical Incremental Nonlinear Analysis)有限元程序计算了三维变形条件下,幂硬化材料紧凑拉伸(CT)试样的应力应变场,并根据计算结果分析了Ⅰ型裂纹裂尖应力场的结构,发现在厚度方向的任一平面上,裂尖应力场的表达式都可写成r,θ坐标变量分离的形式,从而r的函数部分可展成罗朗级数,且三个正应力分量具有相同的数量级.这两个结论为从理论上求解Ⅰ型裂纹裂尖应力场的数学表达式提供了两个有根据的假设条件,可大大减化求解过程.     

Development and experimental validation of a patient-specific lumbar spine FE model to predict the effects of instrumentations

A lumbar spine model without instrumentations was created using CT data and validated with experimental results of the same specimen. The specimen was loaded with pure moments in a spine test rig. The material parameters were taken from literature and adapted for better simulation of the experiments. The results show that further calibration of the material parameters and the implementation of additional ligamentous structures are necessary to simulate the spine's motion reliably. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anchoring and a Load Transfer Technique in Uniaxial Tension of Unidirectional High-Strength Composites

A simplified analytical method for calculating the stress-strain state in uniaxial tension of unidirectional composite specimens with glued wedges is developed. A numerical analysis of the influence of geometry and mechanical parameters of the specimens on the maximum stresses is carried out. The calculations are refined by finite-element modeling. Tests of the specimens have proved the suitability of the suggested technique of anchoring and load transfer in uniaxial tension of unidirectional high-strength composites.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 319–334, May–June, 2005.     

Experimental and Numerical Study of the Open-Hole Tensile Strength of Carbon/Epoxy Composites

Open-hole tension tests are a part of the qualification process for composite parts that need to be joined to other parts in aircraft structures [1]. With each new material, a new set of tests is required. To reduce costs, it is desirable to develop analysis tools for the prediction of damage and failure in such tests, so that the amount of testing can be reduced and predictions can be made about material behaviour early in the design process. In this paper, an experimental and numerical study is presented on the notched (open-hole) strength of high-strength carbon/epoxy composites (HTA/6376). Open-hole tension tests have been performed on specimens with three different lay-ups — quasi-isotropic, zero-dominated, and cross-ply — in accordance with procedures in available standards. The data observed are being used to develop several methods for predicting the notched strength, and results from one such method using a progressive damage analysis are presented with comparisons with experiments. The predictions of specimen stiffness and failure load were found to agree well with experiments. To gain insight into the failure process, damage progression maps are shown.     

Postbuckling Analysis of Flexible Elastic Frames

completely geometrically nonlinear beam model based on the hypothesis of plane sections and expressed in terms of engineering strains and apparent stresses is applied to the structural analysis of frames. The numerical results are obtained by the Raley–Ritz method with a representation of solutions as a sum of analytical basis functions which were previously proposed by the authors. The convergence of approximate solutions is investigated. High degree of accuracy is demonstrated for both determination of the solution components and the fulfillment of equilibrium equations. It is shown that the limit values of external loads can substantially differ from those predicted by the Euler buckling analysis, which may lead to catastrophic consequences in designing thin-walled structures.     

Effective viscous sintering parameters for heterogeneous plate-like structures using numerical homogenisation

A model to describe the sintering of plate-like structures and the numerical technique to obtain its ingredients from the analysis of a given heterogeneous structure are described. Finite membrane strains are accounted for and numerical creep tests are used to extract suitably defined macroscopic viscosities and generalised sintering stresses for plate-like structures. An example is analysed and compared to a full 3D simulation. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter identification based on multiple inhomogeneous experiments of practical relevance

Existing procedures to identify material parameters are based on experiments with simple specimens. Additionally, the load distribution is approximately homogeneous. But there are only few feasible experiments which produce homogeneous or almost homogeneous load distributions. Furthermore, deviations from homogeneity and their consequences cannot be avoided, but are often ignored. We present a solution algorithm which takes several different experimental results into account. Thereby, the experiments are performed on specimens which respond with inhomogeneous distributions of strains and stresses. The restriction to homogeneous loads is not necessary. Thus, it is possible to use different measured data of multiple load cases on one and the same test specimen. The component-oriented design of the specimen permits to consider the specific properties of product groups, the load types and the effect of the manufacturing process on the final material properties already during the identification process. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)