Temperature and Rate effects in Finite Viscoplasticity of Glassy Polymers at Different Deformation Modes: Experiments and Simulations

The non–linear inelastic response of glassy polymers is highly influenced by the three–dimensional deformation state, the temperature and the strain rate at which they are deformed. The contribution presents new experiments for different deformation modes which are carried out at different temperatures and rates on commercial bis–phenol A polycarbonate. Emphasis is put not only on the experimental results by themselves but also on the setup and the technique employed in the obtention of the data. The effect of temperature on the velocity with which the neck propagates along the gaged section of a flat specimen under tension is studied means a facility based on photogrammetry. From the homogeneous compression experiments a single set of material parameters appearing in a constitutive model based on the distributed free volume theory under the frame work of additive kinematics will be identified. The inhomogeneous experimental results serve then as a validation for 3–D simulations since the non–uniform strain distribution on the surfaces of both, simulations and experiments, can be compared. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Simulation of Spot-Weld Joints under Crash Loading

This paper compares FE simulations of spot-weld joints for dual-phase steel under different load cases by using damage models of Gurson-Tvergaard-Needleman (GTN) and its two extensions, GTN-Johnson-Cook and GTN-Hutchinson. Spot-weld specimens have three zones depending with different material properties: Base material, heat-affected zone and fusion zone. The characterization of the base material is straightforward. The other two zones are characterized with specifically heat-treated specimens. For each zone, flat smooth tensile, flat notched tensile and Iosipescu-shear specimen are used in order to obtain the damage behavior for different triaxiality values. GTN damage model parameters are calibrated with the help of smooth and notched flat tensile specimens. The parameters of the above mentioned extensions of GTN damage model are identified with the help of Iosipescu-shear specimen. Finally, the calibrated material models are used in the FE simulation of the spot-weld specimens under quasi static-load case (10 mm/min) for loading directions of 0°, 30°, 60°, 90°. The numerical force-displacement results are in good agreement with experimental results. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermomechanical and adhesive properties of radiation-modified polymer composites for thermosetting products

Gamma-irradiated blends of polyethylene (PE) with ethylene-propylene-diene copolymer (EPDM) and a thermotropic liquid-crystalline polymer (LCP) are investigated at absorbed radiation doses not exceeding 150 kGy (10 kGy=1 Mrad). The temperature dependences of elastic moduli, tension diagrams at a temperature above the melting point of the crystalline phase of PE, and long-term strain recovery curves for oriented test specimens are presented. The kinetics of thermal relaxation and shrinkage stresses in previously oriented composite specimens upon their heating and cooling is investigated. Data on the influence of LCP additions on the adhesive interaction of the compositions with steel are obtained. The peculiarities of thermomechanical and adhesion properties of these composites are discussed taking into account the morphologic and calorimetric data obtained. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 379–394, May–June, 2000.     

Investigation of the deformation and failure of polypropylene under indenters of different shapes

In order to study the residual strain distribution in a nontransparent polymer (polypropylene) under identers of various shapes (sphere, cone, cylinder) multilayer colored specimens with a predetermined distribution of the layers were used. By cutting along selected planes it was possible to estimate the residual strains in the interior of the specimen, both qualitatively and quantitatively. By this means we investigated the relations between the reversible and residual strains in polypropylene as a function of the indenter penetration depth and, moreover, the relations between the deformed and failed volumes of polymeric material under indenters of different shapes. It was shown that a change in indenter shape may produce a considerable change (by a factor of 3 or more) in the relations between the penetration, strain propagation, and failure volumes, which should be taken into account both in determining the hardness of polymeric materials by different methods and in selecting the shape of sealing elements.     

A cellular automaton model for boundary friction of PEEK and PEEK6

Nowadays a common material for journal bearings is PEEK (Polyetheretherketon) which is increasingly used under boundary friction. A Cellular Automaton model is developed to describe the boundary layer dynamics of PEEK and its composite PEEK6 sliding against a steel surface. Whereas PEEK is a homogeneous synthetic material, PEEK6 contains also carbon fibres for stability and fillers working as solid lubricants. The automaton shows a representative area of the real surface. The processes in the interface are described by a set of rules based on physical assumptions and measurements. Based on these rules the simulations show the dependency of friction and wear on the load spectrum. The discrete simulation allows to observe the topographic development of the PEEK and PEEK6 surface as well as the build-up of a transfer film on the steel surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro‐Mechanical Modelling of the Constitutive Behaviour of NiTi Shape Memory Alloys

The superelasticity and shape memory effect in NiTi alloys are examined on the basis of micromechanics within the energy minimization framework. We describe the behaviour of polycrystalline shape‐memory alloys via orientation‐distribution of the various martensite‐variants (domains) present in the material. Stress‐strain curves are presented and special attention is payed to the volume fraction of martensite for specific NiTi alloys (Nitinol) specimen under uniaxial tension. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical and experimental analysis of stress concentration in notched multilayered composites with finite outer boundaries

A solution method for stress concentration problems of fibre- and textile-reinforced multilayered composites with account of the influence of a circular or elliptical cut-out and of the finite outer boundary of a composite plate is presented. The method is based on complex-valued displacement functions and conformal mappings in combination with the boundary collocation and least squares methods. This allows a layer-by-layer calculation of full stress, strain, and displacement fields in a generally multilayered anisotropic plate. To verify the calculation model, extensive experimental studies have been carried out. For all the combinations of multilayered GF/PP plates, laminate lay-ups, and notch and specimen dimensions investigated so far, a very good agreement between the analytical calculations and experimental results is found to exist.     

Estimation of the macroscopic stress-strain curve of a particulate composite with a crosslinked polymer matrix

The main focus of the present paper is the estimation of the macroscopic stress–strain behavior of a particulate composite. A composite with a cross-linked polymer matrix in a rubbery state filled with an alumina-based mineral filler is investigated by means of the finite-element method. The hyperelastic material behavior of the matrix is described by the Mooney–Rivlin material model. Numerical models on the basis of unit cells are developed. The existence of a discontinuity (breaking) in the matrix at higher loading levels is taken into account to obtain a more accurate estimate for the stress–strain behavior of the particulate composite investigated. The numerical results obtained are compared with an experimental stress–strain curve, and a good agreement is found to exist. The paper can contribute to a better understanding of the behavior and failure of particulate composites with a polymer matrix.     

Raman spectroscopy investigation of stiffness change and residual strains due to matrix cracking

The matrix cracking models developed for cross-ply composite laminates have been poorly extended in the past to more complex geometries used in practice, and they are still under development. In this paper, a new detailed analysis of the effect of matrix cracking on the behaviour of cross-ply and [0/45]_s laminates under uniaxial tension is attempted. The model used in this work is applicable both to cross-ply laminates and unbalanced systems. It gives exact closed-form expressions for all thermomechanical properties of a general symmetric laminate with cracks in arbitrary layers. The theoretical approach is backed by experimental data obtained by microscopic strain-state variation measurements within a specimen, with using the technique of laser Raman spectroscopy. Glass-fibre-reinforced epoxy systems were investigated. Embedded aramid fibres-sensors within the 0° ply and near the 0°/θ ° interface were necessary due to the poor Raman signal of glass. Using experimental Raman data, the residual strain and the stiffness reduction are determined as functions of increase in crack density. The stiffness reduction is predicted with a high accuracy, whereas the measured residual strains are larger than predicted. The good results for the reduction in the elastic modulus show that the basic assumption of the model is accurate. The difference is explained by the viscoelastic-viscoplastic behaviour of the off-axis layer in shear, which in creases the “apparent” residual strain. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 771–786, November–December, 2006.     

Deep Drawing Simulations Based on Microstructural Data

For the optimization of process chains in sheet metal forming it is required to accurately describe each partial process of the chain, e.g. rolling, press hardening and deep drawing. The prediction of the thickness distribution and the residual stresses in the blank has to be of high reliability, since the subsequent behavior of the semi-finished product in the following subprocesses strongly depends on the process history. Therefore, high-quality simulations have to be carried out which incorporate real microstructural data [1,2,3]. In this contribution, the ferritic steel DC04 is analyzed. A finite strain crystal plasticity model is used, for the application of which micro pillar compression tests were carried out experimentally and numerically to identify the material parameters of DC04. For the validation of the model, a two-dimensional EBSD data set has been discretized by finite elements and subjected to homogeneous displacement boundary conditions describing a large strain uniaxial tensile test. The results have been compared to experimental measurements of the specimen after the tensile test. Furthermore, a deep drawing process is simulated, which is based on a two-scale Taylor-type model at the integration points of the finite elements. At each integration point, the initial texture data given by the aforementioned EBSD measurements is assigned to the model. By applying this method, we predict the earing profiles of differently textured sheet metals. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of mass entrainment of heat-insulating materials from the deformation of stressed casings

A method has been developed for the determination of mass entrainment and reinforcing layer boundaries of stressed casings subjected to erosion and thermal degradation. The method is based on the determination of the stresses acting on the casing and the measurement of casing deformation by means of tensometers (strain gages), installed on the external surface. Results obtained in the experimental verification of the method by model tests carried out on glass-plastic single and double-layer casings are presented.Deceased.P. I. Baranov Central Institute of Aeroengine Design, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 824–828, September–October, 1972.     

Parameter identification for rubber materials with artificial higher dimensional data

In general, laboratory test render only a limited number of experimental data. Consequently, the prediction of material behaviour becomes a difficult task and, moreover, a statistical analysis with a statistically based approach is almost impossible. As a remedy to increase the number of data, artificial data are generated by stochastic simulation. As a consequence an arbitrary number of data is available and the process of parameter identification can be analysed statistically. Here, the special challenge is the consideration of spatial and inhomogeneous problems. In this work artificial data are generated for a elastomer strip with hole under tension. The inhomogeneous stress/strain fields are optically measured with an Aramis/GOM system and have to be fitted to a stochastic model in order to generate artificial data. B-Splines are applied to fit the geometry of the test specimen and the measured data in space as well as in time. Parameter identifications applied and the resulting material parameters are statistically analysed. In the example, a statistical analysis of an Ogden model is performed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recrystallization behavior of a Nb-microalloyed steel during hot compression

Using a Thermecmastor-Z hot simulator, dynamic recrystallization (DRX) and static recrystallization (SRX) behavior of a Nb-microalloyed steel was investigated by single-hit compression tests and double-hit compression tests, respectively. The experimental results show that DRX will more easily occur at higher deformation temperature and lower strain rate. The deformation activation energy and stress exponent for the Nb-microalloyed steel are calculated to be 379.29 ± 23.56 kJ/mol and 5.76 in temperature range of 950 °C to 1100 °C by regression analysis, respectively. Furthermore, a semi-empirical model is developed to identify the peak stress and strain for DRX. It is found that SRX kinetics follows Avrami’s law, and the softening fraction predicted by the model agrees well with experimental results.     

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.     

A phenomenological method of calculating the residual stresses and plastic deformations in a hollow surface-hardened cylindrical sample

A phenomenological method is proposed for calculating the residual stress and plastic deformation fields in a hollow surface-hardened cylindrical sample. Versions of the hardening are considered that lead to isotropy and anisotropy in the plastic deformations in the surface layer. A hardening anisotropy parameter is introduced that relates the axial and circumferential components of the residual plastic deformation tensor. The experimentally determined axial and/or circumferential components of the residual plastic stress tensor are used as the initial information. The tensor fields of the residual stresses and deformations are constructed assuming the hypothesis of surface hardening anisotropy and the absence of secondary plastic compression deformations and that the tangential components of the residual stress tensor and the plastic incompressibility of the material are small. A technique is developed for identifying the parameters of the proposed method. The adequacy is checked using experimental data for test pieces of type 45 and 12X18H10T steels hardened by hydro-shot blasting treatment and of type 45 steel hardened by treatment with a roller. Good agreement is observed between the calculated and experimental results. It is noted that the anisotropic hardening procedure leads to a substantial difference between the circumferential and axial components of the residual stresses in the hardened layer, unlike the case of isotropic hardening where they are practically identical.     

Hysteresis Behaviour of 51CrV4 and Viscoplastic Modeling Aspects

In this work we investigate the material behaviour of steel 51CrV4 in classical uniaxial strain controlled tension tests of different strain rates interposed by relaxation steps, in which the equilibrium stress observed is significantly smaller than the stresses seen in slowest strain rate test. Also, some cyclic experiments with different strain rates and amplitudes were done to analyze the hysteresis behaviour of the material. Against this background of experimental data the modeling possibilties of two models are explored: the Lion model and the Chaboche model with kinematic hardening ansatz. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Experimental investigations on PP-PE foil specimens

In the present work, we present an experimental characterization of a thermoplastic copolymer made out of Polypropylene and Polyethylene (PP-PE); a polymer that is, for example, used as a core material for layered sandwich composites. The rate-dependence and the temperature-dependence were investigated by means of tensile tests within the large deformation range and by shear tests. The experiments were monitored using a Digital Image Correlation (DIC) system. The main goal of the experimental campaign is related to the development of a constitutive model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)