Viscoelastic Material Models of Polypropylene for Thermoforming Applications

Polypropylene (PP), a semi-crystalline material, is typically solid phase thermoformed at temperatures associated with crystalline melting, generally in the 150° to 160°Celsius range. In this very narrow thermoforming window the mechanical properties of the material rapidly decline with increasing temperature and these large changes in properties make Polypropylene one of the more difficult materials to process by thermoforming. Measurement of the deformation behaviour of a material under processing conditions is particularly important for accurate numerical modelling of thermoforming processes. This paper presents the findings of a study into the physical behaviour of industrial thermoforming grades of Polypropylene. Practical tests were performed using custom built materials testing machines and thermoforming equipment at Queen′s University Belfast. Numerical simulations of these processes were constructed to replicate thermoforming conditions using industry standard Finite Element Analysis software, namely ABAQUS and custom built user material model subroutines. Several variant constitutive models were used to represent the behaviour of the Polypropylene materials during processing. This included a range of phenomenological, rheological and blended constitutive models. The paper discusses approaches to modelling industrial plug-assisted thermoforming operations using Finite Element Analysis techniques and the range of material models constructed and investigated. It directly compares practical results to numerical predictions. The paper culminates discussing the learning points from using Finite Element Methods to simulate the plug-assisted thermoforming of Polypropylene, which presents complex contact, thermal, friction and material modelling challenges. The paper makes recommendations as to the relative importance of these inputs in general terms with regard to correlating to experimentally gathered data. The paper also presents recommendations as to the approaches to be taken to secure simulation predictions of improved accuracy.

Constitutive model for localized Lüders-like stress-induced martensitic transformation and super-elastic behaviors of laser-welded NiTi wires

The application of the shape memory alloy NiTi in micro-electro-mechanical-systems (MEMSs) is extensive nowadays. In MEMS, complex while precise motion control is always vital. This makes the degradation of the functional properties of NiTi during cycling loading such as the appearance of residual strain become a serious problem to study, in particular for laser micro-welded NiTi in real applications. Although many experimental efforts have been put to study the mechanical properties of laser welded NiTi, surprisingly, up to the best of our understanding, there has not been attempts to quantitatively model the laser-welded NiTi under mechanical cycling in spite of the accurate prediction required in applications and the large number of constitutive models to quantify the thermo-mechanical behavior of shape memory alloys. As the first attempt to fill the gap, we employ a recent constitutive model, which describes the localized SIMT in NiTi under cyclic deformation; with suitable modifications to model the mechanical behavior of the laser welded NiTi under cyclic tension. The simulation of the model on a range of tensile cyclic deformation is consistent with the results of a series of experiments. From this, we conclude that the plastic deformation localized in the welded regions (WZ and HAZs) of the NiTi weldment can explain most of the extra amount of residual strain appearing in welded NiTi compared to the bare one. Meanwhile, contrary to common belief, we find that the ability of the weldment to memorize its transformation history, sometimes known as ‘return point memory’, still remains unchanged basically though the effective working limit of this ability reduces to within 6% deformation.

1-D constitutive model for evolution of stress-induced R-phase and localized Lüders-like stress-induced martensitic transformation of super-elastic NiTi wires

NiTi alloys have been widely used in the applications for micro-electro-mechanical-systems (MEMS), which often involve some precise and complex motion control. However, when using the NiTi alloys in MEMS application, the main problem to be considered is the degradation of functional property during cycling loading. This also stresses the importance of accurate prediction of the functional behavior of NiTi alloys. In the last two decades, a large number of constitutive models have been proposed to achieve the task. A portion of them focused on the deformation behavior of NiTi alloys under cyclic loading, which is a practical and non-negligible situation. Despite of the scale of modeling studies of the field in NiTi alloys, two experimental observations under uniaxial tension loading have not received proper attentions. First, a deviation from linearity well before the stress-induced martensitic transformation (SIMT) has not been modeled. Recent experiments confirmed that it is caused by the formation of stress-induced R phase. Second, the influence of the well-known localized Lüders-like SIMT on the macroscopic behavior of NiTi alloys, in particular the residual strain during cyclic loading, has not been addressed. In response, we develop a 1-D phenomenological constitutive model for NiTi alloys with two novel features: the formation of stress-induced R phase and the explicit modeling of the localized Lüders-like SIMT. The derived constitutive relations are simple and at the same time sufficient to describe the behavior of NiTi alloys. The accumulation of residual strain caused by R phase under different loading schemes is accurately described by the proposed model. Also, the residual strain caused by irreversible SIMT at different maximum loading strain under cyclic tension loading in individual samples can be explained by and fitted into a single equation in the proposed model. These results show that the proposed model successfully captures the behavior of R phase and the essence of localized SIMT.

Review of visco-plastic soil models for predicting the performance of embankments on soft soils

A number of constitutive models that account for creep or secondary compression and rate dependent behaviour of soil have been reviewed in terms of their strengths and weaknesses. Some results of numerical analysis of some embankments have been discussed and an effort has been made to find out their strengths and limitations.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

Shape memory and elastoplastic materials: from constitutive and numerical to fatigue modeling

Shape memory materials (SMMs) represent an important class of smart materials that have the ability to return from a deformed state to their original shape. Thanks to such a property, SMMs are utilized in a wide range of innovative applications. The increasing number of applications and the consequent involvement of industrial players in the field have motivated researchers to formulate constitutive models able to catch the complex behavior of these materials and to develop robust computational tools for design purposes. Such a research field is still under progress, especially in the prediction of shape memory polymer (SMP) behavior and of important effects characterizing shape memory alloy (SMA) applications. Moreover, the frequent use of shape memory and metallic materials in biomedical devices, particularly in cardiovascular stents, implanted in the human body and experiencing millions of in-vivo cycles by the blood pressure, clearly indicates the need for a deeper understanding of fatigue/fracture failure in microsize components. The development of reliable stent designs against fatigue is still an open subject in scientific literature. Motivated by the described framework, the thesis focuses on several research issues involving the advanced constitutive, numerical and fatigue modeling of elastoplastic and shape memory materials. Starting from the constitutive modeling, the thesis proposes to develop refined phenomenological models for reliable SMA and SMP behavior descriptions. Then, concerning the numerical modeling, the thesis proposes to implement the models into numerical software by developing implicit/explicit time-integration algorithms, to guarantee robust computational tools for practical purposes. The described modeling activities are completed by experimental investigations on SMA actuator springs and polyethylene polymers. Finally, regarding the fatigue modeling, the thesis proposes the introduction of a general computational approach for the fatigue-life assessment of a classical stent design, in order to exploit computer-based simulations to prevent failures and modify design, without testing numerous devices.

Discrete element methods for asphalt concrete : development and application of user-defined microstructural models and a viscoelastic micromechanical model

As an important Civil Engineering material, asphalt concrete (AC) is commonly used to build road surfaces, airports, and parking lots. With traditional laboratory tests and theoretical equations, it is a challenge to fully understand such a random composite material. Based on the discrete element method (DEM), this research seeks to develop and implement computer models as research approaches for improving understandings of AC microstructure-based mechanics. In this research, three categories of approaches were developed or employed to simulate microstructures of AC materials, namely the randomly-generated models, the idealized models, and image-based models. The image-based models were recommended for accurately predicting AC performance, while the other models were recommended as research tools to obtain deep insight into the AC microstructure-based mechanics. A viscoelastic micromechanical model was developed to capture viscoelastic interactions within the AC microstructure. Four types of constitutive models were built to address the four categories of interactions within an AC specimen. Each of the constitutive models consists of three parts which represent three different interaction behaviors: a stiffness model (force-displace relation), a bonding model (shear and tensile strengths), and a slip model (frictional property). Three techniques were developed to reduce the computational time for AC viscoelastic simulations. It was found that the computational time was significantly reduced to days or hours from years or months for typical three-dimensional models. Dynamic modulus and creep stiffness tests were simulated and methodologies were developed to determine the viscoelastic parameters. It was found that the DE models could successfully predict dynamic modulus, phase angles, and creep stiffness in a wide range of frequencies, temperatures, and time spans. Mineral aggregate morphology characteristics (sphericity, orientation, and angularity) were studied to investigate their impacts on AC creep stiffness. It was found that aggregate characteristics significantly impact creep stiffness. Pavement responses and pavement-vehicle interactions were investigated by simulating pavement sections under a rolling wheel. It was found that wheel acceleration, steadily moving, and deceleration significantly impact contact forces. Additionally, summary and recommendations were provided in the last chapter and part of computer programming codes wree provided in the appendixes.

Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects

This paper presents an overview of depth averaged modelling of fast catastrophic landslides where coupling of solid skeleton and pore fluid (air and water) is important. The first goal is to show how Biot-Zienkiewicz models can be applied to develop depth integrated, coupled models. The second objective of the paper is to consider a link which can be established between rheological and constitutive models. Perzyna´s viscoplasticity can be considered a general framework within which rheological models such as Bingham and cohesive frictional fluids can be derived. Among the several alternative numerical models, we will focus here on SPH which has not been widely applied by engineers to model landslide propagation. We propose an improvement, based on combining Finite Difference meshes associated to SPH nodes to describe pore pressure evolution inside the landslide mass. We devote a Section to analyze the performance of the models, considering three sets of tests and examples which allows to assess the model performance and limitations: (i) Problems having an analytical solution, (ii) Small scale laboratory tests, and (iii) Real cases for which we have had access to reliable information

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

Numerical simulation of railway track supporting system using finite-infinite and thin layer elements under impulsive loads

The present study deals with two dimensional, numerical simulation of railway track supporting system subjected to dynamic excitation force. Under plane strain condition, the coupled finite-infinite elements to represent the near and far field stress distribution and thin layer interface element was employed to model the interfacial behavior between sleepers and ballast. To account for the relative debonding, slipping and crushing that could take place in the contact area between the sleepers and ballast, modified Mohr-Coulomb criterion was adopted. Furthermore an attempt has been made to consider the elasto-plastic material non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and supporting materials. Based on the proposed physical and constitutive modeling a code has been developed for dynamic loads. The applicability of the developed F.E code has been demonstrated by analyzing a real railway supporting structure.

Numerical modeling of railway track supporting system using finite–infinite and thin layer elements

The present contribution deals with the numerical modelling of railway track-supporting systems-using coupled finite-infinite elements-to represent the near and distant field stress distribution, and also employing a thin layer interface element to account for the interfacial behaviour between sleepers and ballast. To simulate the relative debonding, slipping and crushing at the contact area between sleepers and ballast, a modified Mohr-Coulomb criterion was adopted. Further more an attempt was made to consider the elasto plastic materials’ non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and other supporting materials. It is seen that during an incremental-iterative mode of load application, the yielding initially started from the edge of the sleepers and then flowed vertically downwards and spread towards the centre of the railway supporting system.

Ratcheting and wear behavior of Australian rail steel: Experimental investigation of material properties and sampling method

To The ratcheting behavior of high-strength rail steel (Australian Standard AS1085.1) is studied in this work for the purpose of predicting wear and damage to the rail surface. Historically, researchers have used circular test coupons obtained from the rail head to conduct cyclic load tests, but according to hardness profile data, considerable variation exists across the rail head section. For example, the induction-hardened rail (AS1085.1) shows high hardness (400-430 HV100) up to four-millimeters into the rail head’s surface, but then drops considerably beyond that. Given that cyclic test coupons five millimeters in diameter at the gauge area are usually taken from the rail sample, there is a high probability that the original surface properties of the rail do not apply across the entire test coupon and, therefore, data representing only average material properties are obtained. In the literature, disks (47 mm in diameter) for a twin-disk rolling contact test machine have been obtained directly from the rail sample and used to validate rolling contact fatigue wear models. The question arises: How accurate are such predictions? In this research paper, the effect of rail sampling position on the ratcheting behavior of AS1085.1 rail steel was investigated using rectangular shaped specimens. Uniaxial stress-controlled tests were conducted with samples obtained at four different depths to observe the ratcheting behaviour of each. Micro-hardness measurements of the test coupons were carried out to obtain a constitutive relationship to predict the effect of depth on the ratcheting behaviour of the rail material. This work ultimately assists the selection of valid material parameters for constitutive models in the study of rail surface ratcheting.

Characterisation of head-hardened rail steel in terms of cyclic plasticity response and microstructure for improved material modelling

Stress- and strain-controlled tests of heat treated high-strength rail steel (Australian Standard AS1085.1) have been performed in order to improve the characterisation of the said material׳s ratcheting and fatigue wear behaviour. The hardness of the rail head material has also been studied and it has been found that hardness reduces considerably below four-millimetres from the rail top surface. Historically, researchers have used test coupons with circular cross-sections to conduct cyclic load tests. Such test coupons, typically five-millimetres in gauge diameter and ten‐millimetres in grip diameter, are usually taken from the rail head sample. When there is considerable variation of material properties over the cross-section it becomes likely that localised properties of the rail material will be missed. In another case from the literature, disks 47 mm in diameter for a twin-disk rolling contact test machine were obtained directly from the rail sample and used to validate ratcheting and rolling contact fatigue wear models. The question arises: How accurate are such tests, especially when large material property gradients exist? In this research paper, the effects of rail sampling location on the ratcheting behaviour of AS1085.1 rail steel were investigated using rectangular-shaped specimens obtained at four different depths to observe their respective cyclic plasticity behaviour. The microstructural features of the test coupons were also analysed, especially the pearlite inter-lamellar spacing which showed strong correlation with both hardness and cyclic plasticity behaviour of the material. This work ultimately provides new data and testing methodology to aid the selection of valid parameters for material constitutive models to better understand rail surface ratcheting and wear.

Experimental Studies on the Mechanics of Cohesive Frictional Granular Media

The mechanical behaviour of cohesive-frictional granular materials is a combination of the strength pervading as intergranular friction (represented as an angle of internal friction - Phi), and the cohesion (C) between these particles. Most behavioral or constitutive models of this class of granular materials comprise of a cohesion and frictional component with no regard to the length scale i.e. from the micro structural models through the continuum models. An experimental study has been made on a model granular material, viz. angular sand with different weights of binding agents (varying degrees of cohesion) at multiple length scales to physically map this phenomenon. Cylindrical specimen of various diameters - 10, 20, 38, 100, 150 mm (and with an aspect ratio of 2) are reconstituted with 2, 4 and 8% by weight of a binding agent. The magnitude of this cohesion is analyzed using uniaxial compression tests and it is assumed to correspond to the peak in the normalized stress-strain plot. Increase in the cohesive strength of the material is seen with increasing size of the specimen. A possibility of ``entanglement'' occurring in larger specimens is proposed as a possible reason for deviation from a continuum framework.

Role of Crosslinking and Entanglements in the Mechanics of Silicone Networks

The goal of this study is to investigate the applicability of different constitutive models for silicone networks using comprehensive multiaxial experimental tests, including non-equibiaxial mechanical tests which introduce differential constraints on the networks in the two orthogonal directions, on samples prepared using various crosslinking densities. Uniaxial stress-strain experiments show that a decrease in crosslinker amounts used in the preparation of silicone networks lead to more compliant material response as compared to that obtained using higher amounts of crosslinker. Biaxial data were used to obtain fits to the neo- Hookean, Mooney-Rivlin, Arruda-Boyce and the Edward-Vilgis slip-link constitutive models. Our results show that the slip-link model, based on separation of the individual contributions of chemical crosslinks and physical entanglements, is better at describing the stress-strain response of highly crosslinked networks at low stretches as compared to other constitutive models. Modulus obtained using the slip-link model for highly crosslinked networks agrees with experimentally determined values obtained using uniaxial tension experiments. In contrast, moduli obtained using coefficients to the other constitutive models underpredict experimentally determined moduli by over 40 %. However, the slip-link model did not predict the experimentally observed stiffening response at higher stretches which was better captured using the Arruda-Boyce model.