Rate-dependent Material Model Research Articles

Mechanical Testing and Material Modeling of Thermoplastics: Polycarbonate, Polypropylene and Acrylonitrile-Butadiene-Styrene

AbstractThe work presents some results of an ongoing research program aimed at building a material database and material models for specific types of polymers. Results for three thermoplastics are the focus of the present article: polycarbonate, polypropylene, and acrylonitrile-butadiene-styrene. Uniaxial compression / tension tests at room temperature and different strain rates have been performed to characterize their mechanical response. A rate-dependent material model has been developed and implemented in a finite element code to predict such mechanical behavior. The model predictions have shown good agreement with the tests results.

INVESTIGATION OF SIZE-EFFECTS IN MACHINING WITH GEOMETRICALLY DEFINED CUTTING EDGES

The miniaturization of cutting processes shows process specific size-effects like the exponential increase of the specific cutting force k c with decreasing depth of cut h. Experiments were carried out in an orthogonal turning process. The influence of different process parameters on the results was investigated separately to identify process specific size-effects. Two materials were studied: a normalized steel AISI 1045 and an annealed AISI O2. To complement the experiments, parameter variations were performed in two-dimensional, thermo-mechanically coupled finite element simulations using a rate-dependent material model and analyzed by similarity mechanics. The influence of rounded cutting-edges on the chip formation process and the plastic deformation of the generated surface were determined numerically. The complex physical effects in micro-cutting were analyzed successfully by finite element simulations and compared to experiments.

Iso-strain rate material behaviour curves applied to the finite element impact simulation

Tensile impact tests on polypropylene (PP) samples are simulated by a finite element method. A previously proposed characterisation method is applied to obtain the impact properties, and a simple elastic with rate-dependent plasticity material model is used to describe the material behaviour. Impacts at different energy levels are simulated, and a good force–time curve correlation is obtained between experimental and simulated results. The minimum sample rupture energy level is also predicted. However, non-negligible deviations are found between experimental and simulated displacement–time curves, the simulated plastic deformation being greater than the experimental one. This can be associated with the non-strain rate dependence of the elastic modulus and yield strength in the material model. A revision of the high-rate characterisation method and the use of alternative constitutive models that take into account this dependence should be the guidelines in order to achieve a better correlation between displacement–time curves of simulated and experimental tensile impact tests.

Strain Rate Model for Dynamic Analysis of Reinforced Concrete Structures

A strain rate dependent material model for concrete has been proposed for analysis of three-dimensional reinforced concrete structures under transient dynamic loading. The model takes into account the pressure sensitivity in three-dimensional loading situations and strain rate sensitivity in dynamic loading situations. The cracking in tension has been modeled using the smeared cracking approach. The strain rate sensitivity has been considered at two levels: the failure surface is made strain rate dependent as is also the fluidity parameter. The tension stiffening effect observed in reinforced concrete structures has also been considered.

Characterizing rate-dependent material behaviors in self-learning simulation

Structural testing, where inhomogeneous stress distribution is introduced within the test specimen, contains far richer information on the material behavior than the conventional material testing with uniform state of stress. We present a methodology that extracts rate-dependent material behavior using load–displacement measurements from the structural test. Self-learning capability of the rate-dependent neural network material model previously proposed by the authors is used in conjunction with the methodology. Unlike other parameter optimization methods, no prior knowledge of the material is required. The model is also capable of improving its performance as further test data become available. As an illustrative example, the method is applied to capture non-linear creep behavior of superalloy.

Neural network constitutive model for rate-dependent materials

Neural network (NN) constitutive model adjusts itself to describe given stress and strain relationship. It is capable of capturing complex material behavior, using stress and strain sets from experiments. This paper presents a rate-dependent NN constitutive model formulation and its implementation in finite element analysis. The proposed NN model is verified for a standard solid viscoelasticity model. The model is then applied to analysis of time-dependent behavior of concrete. The proposed model has potential of capturing any rate-dependent material models, provided enough data sets are given. The issue of what constitutes a sufficient data set to train a neural network constitutive model must be addressed in future research.

Similarity considerations on the simulation of turning processes of steels

Abstract In order to investigate size effects occurring in the miniaturization of turning processes a complete dimensional analysis using a materials model for high-speed deformation was performed. The derived dimensionless similarity numbers were used to guide the parameter variation in simplified two-dimensional finite-element simulations for orthogonal cutting. The rate-dependent material model leads to size effects like an increase of the specific cutting force while reducing the cutting depth. A counter-intuitive dependence of the cutting force on cutting velocity is explained using a shear-plane model. The derived dependencies on single input parameters are used to predict output values while simultaneously changing several input parameters.

Non-linear strain rate dependent micro-mechanical composite material model for finite element impact and crashworthiness simulation

The present study aims at implementation of a strain rate dependent, non-linear, micro-mechanics material model for laminated, unidirectional polymer matrix composites into the explicit finite element code LSDYNA. The objective is to develop an accurate and simple micro-mechanical, rate dependent material model, which is computationally efficient. Within the model a representative volume cell is assumed. The stress–strain relation including rate dependent effects for the micro-model is derived for both shell elements and solid elements. Micro-failure criterion is presented for each material constituent and failure mode. The implemented model can deal with problems such as impact, crashworthiness, and failure analysis under quasi-static loads. The developed material model has a wide range of applications such as jet engine jackets, armor plates, and structural crashworthiness simulation. The deformation response of two representative composite materials with varying fiber orientation is presented using the described technique. The predicted results compare favorably to experimental values.

Strain-rate effects on elastic and early cell-collapse responses of a polystyrene foam

The compressive behavior of a polystyrene foam was investigated at strain rates from 0.001 to 950/s. A hydraulically driven test machine was used for the quasi-static tests, and a modified split Hopkinson pressure bar (SHPB) was utilized for the dynamic tests. The shape of the incident pulse in the SHPB was carefully controlled so that the resulting stress–strain curves are valid starting from a small value of strain in the elastic region until past the initiation of cell-crushing. The collapse stress of the foam is found to increase nearly linearly with the logarithm of the strain rate, and the elastic modulus is seen to increase with strain rate. A rate-dependent phenomenological material model is employed to describe the experimental results.

Numerical modelling of lap joints bonded with a rate-dependent adhesive

This work focuses on modelling the rate-dependent response of adhesively bonded structures. An experimental study undertaken in parallel with this has provided material data defining both the tensile and shear response of the adhesive system. In addition, instrumented data for a range of single lap joints was also available. Three different rate-dependent material models have been assessed as part of this work. Whilst the rate-dependent von Mises material model was easiest to implement, it was found that it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive. Difficulty was experienced in obtaining a converged solution for the rate-dependent hydrostatic stress-sensitive material model provided by ABAQUS. However, an overstress-based visco-plastic model developed in a previous programme was able to model both the tensile and shear data correctly. Two of these models were then used to simulate the various single lap joints tested and it appeared that the von Mises model gave closer predictions than the visco-plastic model. A possible reason for this was damage within the joint that was not modelled but this aspect was not pursued. Finally, it was shown that a rate-independent strain-based failure criterion appeared to give good predictions of joint strength in most of the configurations considered.

Crystal plasticity simulation of the hydrostatic bulge test

In this article the finite–strain deformation of a membrane under hydrostatic pressure is investigated using a rate-dependent polycrystal plasticity formulation based on Taylor assumptions, where each material point in the sheet is considered to be a polycrystalline aggregate of a large number of grains. A finite element program is developed for arbitrary die aperture geometries and numerical results are generated for a circular specimen using parallel computing features. The plane stress assumption is invoked at the macro level, since the sheet thickness is small compared to the surface dimensions of the specimen. The deformation gradient is computed with the requirement that the two shearing strains along the sheet normal are explicitly enforced to be zero. The effect of deformation induced anisotropy is examined for a single crystal as well as for different polycrystalline materials, with and without initial orthotropy. Using the maximum stress criterion for the rate-dependent material model employed, the onset of instability for the membrane is examined for succesive localization modes. First, the onset and development of biaxial straining localized around the pole, and then the onset of an instability at this region involving localized necking (similar to the forming limit diagrams), are demonstrated and discussed from numerical examples.

Rate Dependent Multicontinuum Progressive Failure Analysis of Woven Fabric Composite Structures under Dynamic Impact

Marine composite materials typically exhibit significant rate dependent response characteristics when subjected to extreme dynamic loading conditions. In this work, a strain-rate dependent continuum damage model is incorporated with multicontinuum technology (MCT) to predict damage and failure progression for composite material structures. MCT treats the constituents of a woven fabric composite as separate but linked continua, thereby allowing a designer to extract constituent stress/strain information in a structural analysis. The MCT algorithm and material damage model are numerically implemented with the explicit finite element code LS-DYNA3D via a user-defined material model (umat). The effects of the strain-rate hardening model are demonstrated through both simple single element analyses for woven fabric composites and also structural level impact simulations of a composite panel subjected to various impact conditions. Progressive damage at the constituent level is monitored throughout the loading. The results qualitatively illustrate the value of rate dependent material models for marine composite materials under extreme dynamic loading conditions.

Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loading

As a direct extension of the asymptotic spatial homogenization method we develop a temporal homogenization scheme for a class of homogeneous solids with an intrinsic time scale significantly longer than a period of prescribed loading. Two rate-dependent material models, the Maxwell viscoelastic model and the power-law viscoplastic model, are studied as an illustrative examples. Double scale asymptotic analysis in time domain is utilized to obtain a sequence of initial-boundary value problems with various orders of temporal scaling parameter. It is shown that various order initial-boundary value problems can be further decomposed into: (i) the global initial-boundary value problem with smooth loading for the entire loading history, and (ii) the local initial-boundary value problem with the remaining (oscillatory) portion of loading for a single load period. Large time increments can be used for integrating the global problem due to smooth loading, whereas the integration of the local initial-boundary value problem requires a significantly smaller time step, but only locally in a single load period. The present temporal homogenization approach has been found to be in good agreement with a closed-form analytical solution for one-dimensional case and with a numerical solution in multidimensional case obtained by using a sufficiently small time step required to resolve the load oscillations.

Modeling torsional split Hopkinson bar tests at strain rates above 10,000 s−1

Finite element analysis is used to study experiments with the torsional split Hopkinson bar technique in which strain rates on the order of 10 4 s −1 are reached by using specimens with a very short gage length. Time-dependent analysis with a viscoplastic constitutive model for the specimen material is used to analyze the whole apparatus (elastic bars and specimen). Results from modeling tests with 1100-O aluminum show that the waves in the elastic bars can be modeled accurately when a significant increase is the flow stress at strain rates of 10 4 s −1 is assumed in the constitutive model of the material. The calculated stresses, strain rates, and strains in the specimen's gage section show that the state is not exactly of pure and homogeneous shear as assumed when the experimental stress strain curve is determined from the measured waves on the elastic bars, and that the plastic zone extends beyond the gage length. Even with these discrepancies the results show that the experimental curve provides a good estimation to the true material response. A time-independent analysis with rate-dependent material model is also used to analyze only the specimen and a short section of the adjacent flanges. The results show that this analysis can also be used to determine the validity of the assumed constitutive model of the material.

Estimation of Parameters in Viscoplastic and Creep Material Models

Estimation of parameters in time and rate dependent materials is frequently performed by least squares regression. Time and rate dependent material models are represented mathematically by systems of differential equations. As predictions of dynamical systems are history dependent, the residuals produced by regression estimators are dependent random variables and the estimates may therefore be biased. A new approach using time series analysis methods, which offers a way to circumvent the problems related to dependent residuals, is presented. In the new approach, the residuals are obtained via a continuous-discrete time Kalman filter. A simulation study, with models suitable for both high temperature creep and transient loading, has been performed. A comparison between the proposed methods and standard least squares regression shows that the model parameters are estimated with up to 40% higher precision. An analysis of the residuals clearly shows that the residuals of the newestimator form an independent sequence of random variables. The results also indicate that the proposed estimator remains unbiased whereas the regression estimator may be biased when the excitation increases.

Development of rheological models for forming flows and picture-frame shear testing of fabric reinforced thermoplastic sheets

The flow of fabric reinforced polymer sheets during sheet-forming processes is dominated by shearing along fibre directions. The goal of this work is to develop models which describe the reheological behaviour of commercially available fabric reinforced thermoplastic sheets. Isotropic and anisotropic models which feature viscous and viscoelastic behaviour and which are suitable for describing processes involving large deformations are developed. Kinematic constraints of fibre inextensibility are used to represent the extremely high resistance to deformation in the reinforcement directions. The suitability of this approach for modelling planar flows of fabric reinforced polymer melts is established by the interpretation of experiments involving two commercially available material systems using a specially developed picture-frame shearing experiment. Shearing flow is imposed on pre-consolidated laminates via a four bar linkage which is loaded by a test machine. The picture-frame apparatus is housed in an environmental chamber and experiments are reported at temperatures in the materials processing range. Force versus displacement data is available for experiments conducted at different actuator displacement rates, and stress relaxation behaviour is also considered. Methods are presented for interpreting the response of two glass fabric reinforced PA-12 materials in terms of a number of continuum models, including Newtonian models, power law viscous models and shear rate dependent Kelvin type material models, all of which feature inextensible fibre directions.

Effect of Time-Dependent Matrix Behavior on the Evolution of Processing-Induced Residual Stresses in Metal Matrix Composites

The usefulness of load-relaxation experiments in investigating the need for rate-dependent matrix material models for predicting the processing-induced residual stresses in metal matrix composites (MMCs) is examined in this study. The experimental data is used in the selection of the appropriate constitutive equations for modeling the cooling process after composite consolidation. Boron/Al-2024 MMC is chosen as the model material system. Bodner-Partom unified model and a classical creep-plasticity model based on the relaxation experiments are used to represent the rate-dependent behavior of Al-2024. The results show that conventional B-P model based on purely monotonic strain-rate tests is not able to capture the inelastic strain variations under practical cooling conditions. The classical creep-plasticity model has been shown to be an effective alternative for this purpose as it considers load-relaxation data while deriving the material constants for the constitutive equations.

Time Dependent Fracture and Cohesive Zones

This presentation is concerned with the fracture response of materials which develop cohesive or bridging zones at crack tips. Of special interest are concerns regarding crack stability as a function of the law which governs the interrelation between the displacement(s) or strain across these zones and the corresponding holding tractions. It is found that for some materials unstable crack growth can occur, even before the crack tip has experienced a critical COD or strain across the crack, while for others a critical COD will guarantee the onset of fracture. Also shown are results for a rate dependent nonlinear material model for the region inside of a craze for exploring time dependent crack propagation of rate sensitive materials.