Characterization of short fiber reinforced polymers

This contribution presents ideas, how composite materials can be characterized with respect to experimental testing. The material properties of the investigated short glass fiber reinforced polymer are obtained by providing results from the experiment in order to seperate different material effects, such as elasticity, plasticity, damage, viscoelasticity, compressibility and anisotropy. Therefore, at first, linear uniaxial tensile tests with cyclic loadings have been realized. The application of the material in this work is the machining by a three-dimensional forming process. Hence, multiaxial loadings have to be additionally taken into account matching these conditions. In order to provide more information, biaxial tensile tests have to be realized using a testing device supplying the additional necessary experimental data [1, 2]. A final aim of this work is to develope a verification experiment representing the three-dimensional forming process as realistically as possible, e. g. a Nakajima test [4]. For this case, a three-dimensional optical analysis in order to get the necessary measurement data, is indispensable to realize an inverse method [3] by comparing the information of the complete deformation field as well as the force data of the experiment using a given material model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A RVE-based micro mechanical model for short fiber reinforced plastic materials including matrix damage and fiber fracture

The representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A material model of nonlinear fractional viscoelasticity

Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities. These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one-dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress-strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Parameter Identification by Inverse Modelling of Biaxial Tensile Tests for Discontinous Fiber Reinforced Polymers

In the present article we discuss the characterization of the mechanical properties of long fiber reinforced thermoplastics (LFT) and sheet molding compounds (SMC) with biaxial tensile tests and the inverse parameter identification. The full 3D strain field is measured via digital image correlation (DIC). The anisotropic viscoelastic material properties are identified through inverse modelling by comparison of the heterogeneous experimental and simulated strain fields. A Gauss-Newton type algorithm is used to identify the optimal parameter set [1]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bearing of geometric and material properties to bone strength in bending

Osteoporosis is characterized by decreasing of bone mass and bone strength with advanced age. For characterization of material properties of bone the volumetric bone mineral density is one of the most important contributing factors to bone strength. Often bending tests of whole bone are used to get information about the state of osteoporosis. From an uniaxial test of a bone specimen it is assumed that an elastic region exists up to initial yield stress and a following hardening region. In bending tests beside material properties geometric properties like shape and cortical thickness appropriate the non-linear moment-curvature curve. The aim of this contribution is to show how an elastic-plastic material law including tensile damage influences the global bending behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A comparison of mean field homogenization schemes for short fiber reinforced thermoplastics

Different mean field homogenization methods are applied to a short glass fiber reinforced polybutylene terephthalate. The different models' predictions for the anisotropic effective elastic properties are assessed and compared to experimental data from tensile tests. Additionally, the estimation of fiber stresses and the influence of the fiber length distribution is studied. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New damage evolution model of rock material

As a kind of natural engineering material with original defects, there are distinctly nonlinear and anisotropic mechanical behaviors for rock materials. Nevertheless, the rock damage mechanics can solve this problem well. However, for the complexity of mechanical property of rock material, the mature and applicable model to describe the rock failure process and the method to determine the maximum damage value have not been established very well. To solve this problem, one new damage evolution model for rock material has been proposed. In this model, the least energy consumption principle proposed to describe the fracture process of materials is used. Using the experimental data of granite sample under uniaxial compression and the results of numerical tests under uniaxial tension and uniaxial compression, this model is verified. Moreover, the results of the new model have been compared with the results of the tests (numerical test and real test) and the traditional damage model. The comparison shows that the new model has the higher accuracy and better reflects for the fracture process of the granite sample. Moreover, the released damage energies of the new model and Mazars model are different, and the released damage energy of the new model is slightly less than that of the Mazars model.     

An experimental study towards micro-mechanical modeling of fiber-reinforced aerogels

Fiber-reinforced aerogels are a class of reinforced aerogels characterized by very low thermal conductivity, hydrophobicity and most importantly load bearing capability. In this work, an experimental study describing the damage in these fiber-reinforced aerogels through various uniaxial compression tests is presented. While understanding the damage evolution at the micro-scale, we come across three probable sources contributing towards the damage evolution. They are: (a) matrix cracks, (b) debonding of particles due to fiber sliding, and (c) breakage of fibers. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of a Viscoelastic Material Model in Electro-Mechanics

In this contribution, the numerical modeling of electro-viscoelastic material is considered. The electro-mechanical problem formulated in terms of a symmetrized stress tensor is extended to a viscoelastic material model. For the incorporation of the viscosity model, the logarithmic strain space setting is utilized which mimics the small strain setting. Therefore a rheological model for viscosity from the geometrically linear theory can be used. Numerical examples for a typical uniaxial tensile test show the capability of the method to demonstrate typical relaxation and creep behavior. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite thermo-viscoplasticity of amorphous glassy polymers: Experiments,modeling and simulations

The contribution is concerned with experimental procedures, constitutive modeling and the numerical simulations of finite thermo-viscoplastic behavior of glassy polymers. The experimental study involves both homogeneous and inhomogeneous tests at different temperatures under isothermal conditions. The true stress-true strain curves obtained from compressive homogeneous uniaxial and plane strain experiments are employed in the identification of adjustable material parameters. In contrast to the existing kinematic approaches to finite plasticity of glassy polymers, we propose a distinct kinematic framework constructed in the logarithmic strain space. This leads us to an algorithmically very attractive, additive kinematic structure in R⁶ similar to the geometrically linear theory. The proposed three-dimensional model is implemented into a finite element code. The load-displacement curves acquired from inhomogeneous experiments are compared against the results obtained from finite element analyses where the material parameters identified from homogeneous experiments are used. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental investigation and approximation of the temperature-dependent stiffness of short-fiber reinforced polymers

In order to predict the effective material properties of a short-fiber reinforced polymer (SFRP), homogenization of elastic properties with the self-consistent (SC) scheme and the interaction direct derivative (IDD) method is performed by means of µCT data describing the microstructure of the composite material. Using dynamic mechanical analysis (DMA), the material properties of both, polypropylene and fiber reinforced polypropylene are investigated by tensile tests under thermal load. The measured storage modulus of the matrix material is used as input parameter for the homogenization scheme. The effective properties of SFRP are compared to experimental results from DMA. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and characterization of cyclic relaxation and ratcheting using the distributed-element model

Constitutive modeling of cyclic relaxation and ratcheting (cumulative inelastic deformation) is developed on the basis of the distributed-element model (DEM). Although the original DEM is capable of describing general, elastic–plastic behavior for cyclically stabilized materials, it has the inadequacy of not being able to account for the effect of cyclic relaxation and ratcheting. By introducing the nonlinear kinematic hardening rule proposed by Armstrong and Frederick into element behavior of the DEM, the model becomes effective in characterizing the behavior of cyclic relaxation and ratcheting. Validation of the modified DEM is conducted by simulating cyclic behavior of various metal materials, including CS 1018, heat-treated rail steel, and Grade 60 steel. The results show that the modified DEM demonstrates realistic behavior of materials in both uniaxial and biaxial cyclic relaxation and ratcheting. Furthermore, detailed investigation of element behavior in the model provides us with additional insight into complex behavior and characteristics of materials in cyclic relaxation and ratcheting.     

The effect of overloads on the residual strength and life of laminated GRP

The effect of a short duration cyclic overload on the residual life and strength of laminated glass-fiber reinforced polyester is studied. A uniaxial tensile fatigue loading with the stress ratio 0.1 is considered. The residual life of the composite decreases due to the overload, while the residual strength is almost unaffected. A reasonable agreement of experimental data with the prediction by a residual strength model and by Miner's rule is observed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 701–706, May–June, 1999.     

Thermomechanics of twinning from a parent to a twin with mirror image symmetry

In the paper we develop a modeling with multiple configurations and mirror image of parent crystal in the twinned structure, to describe the behavior of partially twinned structure. In the constitutive framework we take into account that: (1) the untwinned and twinned material have distinct natural configurations by virtue of their miscrostructure being different, (2) the material symmetry groups of the untwinned and twinned structures characterize the peculiar feature that the presence of the mirror image structure is related to the untwinned structure, but it can exist only as a counterpart of the previous one. The partially twinned structure is described by the evolution equations for the growth of twins, characterized by a pair of a deformation like tensorial variable and a scalar field with meaning of the volume fraction for the twins. The capability of the material to twin and untwin at a constant rate of strain in uniaxial compression has been analyzed and the oscillatory behavior predicted by the model reveals qualitative agreement with experimental evidences.     

Optimal Experimental Design to Identify the Average Stress-Strain Response in Short Fiber-Reinforced Plastics

We show how to use optimal experimental design methods for the parameter identification of short fiber reinforced plastic (SFRP) materials. The experimental data is given by computer simulations of representative volume elements (RVE) of the SFRP material. The experiments are designed such that a minimal number of RVE simulations is required and that the model response attains a minimal variance for a class of strains and fiber orientations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mean field homogenization and experimental investigation of short and long fiber reinforced polymers

The effective elastic material properties of short fiber reinforced polypropylen are determined by means of the self-consistent (SC) method and the interaction direct derivative (IDD) method. In order to account for thermoelastic effective material properties, a Hashin-Shtrikman (HS) based two-step homogenization method with variable reference stiffness is used. The influence of the reference stiffness, dependent on a scalar parameter is investigated. Information on the microstructure are derived by computed tomography scans (µCT) and considered within the homogenization schemes. Thermomechanical properties of a long fiber reinforced polymer (LFRP) and a short fiber reinforced polymer (SFRP) are obtained by means of dynamic mechanical analysis (DMA). Simulation results for SFRP are compared to experimental results. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large-scale simulation of arterial walls: mechanical modeling

Biological soft tissues appearing in arterial walls are characterized by a nearly incompressible, anisotropic hyperelastic material behavior in the physiological range of deformations. For the representation of such materials we apply a polyconvex strain energy function in order to ensure the existence of minimizers and in order to satisfy the Legendre-Hadamard condition automatically. When arteries are overstretched, discontinuous damage is observed. For the modeling of this effect we apply a damage model, which basically assumes that the damage occurs mainly in fiber direction. For the numerical simulation we consider an atherosclerotic artery and apply a high internal pressure which is comparable to the pressure applied during a balloon-angioplasty. The 3D-discretization results in a large system of equations, therefore, a parallel algorithm using FETI-DP is applied to solve the boundary value problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)