Some Models of Material Behavior During Injection Molding

The overall, macroscopic constitutive behavior of most materials of technological importance such as fiber-reinforced composites or polycrystals is very much influenced by the underlying microstructure. The latter is usually complex and heterogeneous in nature, where each phase constituent is governed by non-linear constitutive relations. In order to capture such micro-structural characteristics, numerical two-scale methods are often used. The purpose of the current work is to provide an overview of state-of-the-art finite element (FE) and FFT-based two-scale computational modeling of microstructure evolution and macroscopic material behavior. Spahn et al. (Comput Methods Appl Mech Eng 268:871–883, 2014) were the first to introduce this kind of FE-FFT-based methodology, which has emerged as an efficient and accurate tool to model complex materials across the scales in the recent years.

The classical theories of continuum mechanics — linear elasticity, viscoelasticity, plasticity and hydrodynamics — are defined by special constitutive equations. These can be understood to be asymptotic approximations of a quite general constitutive model, valid under restrictive assumptions for the stress functional or the input processes. The general theory of material behavior develops systematic methods to represent material properties in a context of physical evidence and mathematical consistency. According to experimental observations material behavior may be rate independent or rate dependent with or without equilibrium hysteresis. This motivates four different constitutive theories, namely elasticity, plasticity, viscoelasticity and viscoplasticity. Constitutive equations can be formulated explicitly as functionals. Then, the particular constitutive models correspond to continuity properties of these functionals, related to convenient function spaces. On the other hand, a system of differential equations may lead to an implicit definition of a stress functional. In this case additional variables are introduced, which are called internal variables. For these variables additional evolution equations must be formulated, specifying the rate of change of the internal variables in dependence on their present values and the strain (or stress) input. In the context of different models of inelastic material behavior the evolution equations have different mathematical characteristics. These concern the existence of equilibrium solutions and their stability properties. Rate independent material behavior is modelled by means of evolution equations, which are related to an arclength instead of the time as independent variable. It can be shown that the rate independent constitutive equations of elastoplasticity are the asymptotic limit of rate dependent viscoplasticity for slow deformation processes.

Modeling of materials behavior at various temperatures of hot isostatically pressed superalloys

A series of out-of-pile quench tests is currently performed at the QUENCH facility of the Karlsruhe Research Center. Due to some non-prototypical features in the fuel rod and bundle design and in the whole test set-up, the results of these tests cannot directly be extrapolated and applied to reactor conditions. Therefore simulations of these quench tests with the help of computer codes are needed to achieve this aim. This led to the development of the bundle code CALUMO. The simulation of the test conditions in the CALUMO code is based on the solution of balance equations for the fuel rod simulators, the shroud, and the coolant. The code calculates also the oxidation of the bundle, the hydrogen production and the steam consumption. Models for the behavior of boron carbide absorber rods have also been implemented, as well as a simple quench model. The main aim of the code was to have a simple tool for the investigation of the oxidation of the claddings and the shroud and the mechanisms leading to temperature escalations in the transient and re-flooding phase. The CALUMO code has been validated in post test calculations for most of the QUENCH tests done so far. In this report results of the triplet of the tests QUENCH-07, QUENCH-08, and QUENCH-09 are presented and compared to results of the test instrumentation and to findings of post test examinations (PTE). The results of the code are in the overall encouraging, although still some improvement of the modeling is needed, especially with regard to relocation of liquid material. One big advantage of the code is the possibility to implement new models for material behavior rather easily and to test different oxidation correlations.

Ingenieurwerkstoffe neigen bei erhöhten Temperaturen zusätzlich zum elastischen Verhalten zum Kriechen oder, mit anderen Worten, man kann neben einer spontanen Werkstoffreaktion auch eine zeitabhängige beobachten. Unter Berücksichtigung der wachsenden Sicherheitsanforderungen für Kraftwerke, Flugzeugkomponenten, chemischen Anlagen usw. ist das zeitabhängige Werkstoffverhalten in den Konstruktionsprozess einzubeziehen. Zahlreiche Bauteile, die unter Kriechbedingungen eingesetzt werden, können als dünnwandig klassifiziert werden. Ihre Analyse ist dann mit drei Problemen verbunden: mit der Auswahl eines geeigneten Werkstoffmodells, mit der Auswahl eines adäquaten strukturmechanischen Modells und mit der Auswahl eines geeigneten numerischen Lösungsverfahrens. Dabei besteht eine enge Verbindung zwischen den drei Problemen. Beispielsweise hat die Auswahl des strukturmechanischen Modells (Balken, Platte, Schale usw.) signifikanten Einfluss auf den numerischen Aufwand. Andererseits wird die Berechnungsgenauigkeit durch das Materialverhaltensmodell beeinflusst, wenn verschiedene Effekte einbezogen oder vernachlässigt werden. Die Kriechmechanik als Zweig der Festkörpermechanik hat eine mehr als einhundertjährige Geschichte. Nach einer kurzen Diskussion der geschichtlichen Entwicklung sowie der Anführung ausgewählter Referenzliteratur werden zwei Modelle zur Beschreibung des Kriechverhaltens eingeführt. Das erste Modell ist dadurch gekennzeichnet, dass die Art des Spannungszustandes keine Rolle bei der Beschreibung des Materialverhaltens spielt, während in die Formulierung des zweiten Modells eine derartige Abhängigkeit eingeht. Ein typisches Beispiel für das zweite Modell ist ein unterschiedliches Zug- und Druckverhalten. Dieses kann beispielsweise im Tertiärkriechbereich vorausgesetzt werden, da eine Schädigung durch Zugbedingungen gefördert wird. Wenn man Druckbedingungen antrifft, können Kriechverzerrungen auftreten, der Schädigungszustand ist jedoch teilweise eingefroren (u.a. kein Auftreten neuer Hohlräume). Der letzte Teil ist strukturmechanischen Modellen gewidmet. Für dünnwandige Strukturen werden in der Regel alle Annahmen in Übereinstimmung mit der “Dünne” der Struktur getroffen. Damit kann man beispielsweise Hypothesen für die Spannungen, Verzerrungen und/oder Verschiebungen in Dickenrichtung einführen, und es werden zu lösende Gleichungen abgeleitet, die bezüglich der Dimension reduziert sind (statt dreidimensionaler Feldgleichungen hat man ein System von zwei- oder eindimensionalen Feldgleichungen). Über die Korrektheit und Genauigkeit dieses Konzepts wird berichtet. In addition to the elastic behavior, engineering materials at elevated temperatures tend to creep or, with other words, a spontaneous and a time-dependent material response can be observed. Due to the increasing safety requirements for power plants, aircraft components, equipment for chemical processes, etc. the time-dependent material behavior should be taken into account in the design process. Since many structural elements working under creep conditions can be classified as thin-walled structures the analysis is connected with the following three items: the choice of a suitable material behavior model, the choice of an adequate structural analysis model, and the choice of a suitable numerical solution technique. All three items are interlinked. For example, the choice of the structural analysis model (beam, plate, shell, etc.) has a significant influence on the numerical effort. On the other hand, the accuracy of the calculations is influenced by the material behavior model taking into account more or less effects. Creep mechanics is a branch of solid mechanics with a history of more than 100 years. After a brief discussion of the historical development and the introduction of some important references two creep behavior models are presented. For the first one the material behavior is not influenced by the kind of stress state while in the second case significant differences in dependence on the kind of the stress state can be observed. A typical example of such behavior is the different behavior in tension and compression. This behavior can be observed, for example, for the tertiary creep characterized by the damage evolution under tensile conditions. If we establish compression conditions, the creep deformations are changing but the damage state is partly frozen (no nucleation of new voids, for instance). The last part is devoted to the structural models. For thin-walled structures all simplifications of the analysis equations are founded on the assumptions with respect to the “thinness” of the structure. In this case, for instance, one can introduce some hypotheses for the stresses, strains and/or displacements in the thickness direction, and with the help of these hypotheses governing equations, reduced with respect to the dimension, can be established (instead of a system of three-dimensional equations we have a system of two- or one-dimensional equations). On the correctness and accuracy of such an approach will be reported.

In a regular extrusion process for thermoplastic specimen, the material behavior in dies and its rheological properties have a major influence on the mechanical properties and the quality of the extruded product. This study outlines the multiphysical model, which has been adapted to address the specific issues associated with polyamide 12 polymer extrusion. A series of numerical simulations, based on the modeling of material behavior, have been conducted using the computational code Comsol Multiphysics®. These simulations have been applied to the study of polymer melt flows through an industrial extrusion die. The objective of this study is to analyze the influence of the imposed extrusion parameters on the physical field distribution and the material displacement within the die. The die swell at the exit of the extrusion die has been investigated as a function of the imposed pressure. The progression of the polymer flow front inside the extrusion tool and the swelling rates have been analyzed. In particular, the phenomenon of delayed swelling at high pressure has been highlighted at high pressure. Highlights Polymer swelling at industrial extrusion die exit is investigated. Polymer melt extrusion within industrial extrusion tool is numerically simulated. Flow front progression and extrudate swell are analyzed. Effect of extrusion pressure on instabilities and die swell is highlighted.

For the installation of a fuel cell stack to convert chemical energy into electricity it is common to apply bipolar plates to separate and distribute reaction gases and cooling agents. For reducing manufacturing costs of bipolar plates a fully automated injection molding process is examined. The high performance thermoplastic matrix material, polyphenylene sulfide (PPS), defies against the chemical setting and the operation temperature up to 200 °C. To adjust also high electrical and thermal conductivity, PPS is highly filled with various carbon fillers up to an amount of 65 percentage by volume. In the first step two different structural plates (one-sided) with three different gate heights and molds are designed according to the characteristics of a bipolar plate. To cope with the approach that this plate should be producible on standard injection molding machines with variothermal mold temperature control, injection molding simulation is used. Additionally, the simulation should allow to formulate a quality prediction model, which is transferrable to bipolar plates. Obviously, the basis for a precise simulation output is an accurate description of the material properties and behavior of the highly filled compound. This, the design of the structural plate and mold and the optimization via simulation is presented, as well. The influence of the injection molding process parameters, e.g. injection time, cycle times, packing pressure, mold temperature, and melt temperature on the form filling have been simulated to determine optimal process conditions. With the aid of the simulation and the variothermal mold temperature control it was possible to reduce the required melt temperature below the decomposition temperature of PPS. Thereby, hazardous decomposition products as hydrogen sulfide are obviated. Thus, the health of the processor, the longevity of the injection molding machine as well as the material and product properties can be protected.

The results of numerical modeling of a Charpy impact test for steel Weldox 460-E with LS-DYNA program using are presented. The simulation carried outfor two widely known models of material behavior at dynamic loading. These are Johnson-Cook and Cowper-Symonds models. The possibility of literarycoefficients using for above-mentioned models without optimization to a necessory loading condition is estimated. The necessity of strain rate accounting in dynamic processes numerical simulation is shown. The accuracy appraisal of design model with usage additional resolution criteria which allows significantly to increase accuracy of solution were carried out. The results of numerical modeling conduction proved its qualitative character. The disarrangement in 39,6% don’t allow us to advise to use experimental characteristics from literature without their optimization in accordance with certain type of load. Although, the difference value is 4,8% in case of introduction of additional resolution criterion with maximum magnitude of strains, that’s point out the necessity of experimental tests of materials and definition of its limit values of resolution under different velocities of deformation and use of these values during performance of numerical modeling. Cowper-Symonds model showed much better convergence while performing modeling of this experiment. It could be related to low values of deformation velocity (level 102 с-1) in experiments on impact strength.

Finite element simulation of explosively-driven plate impact with application to explosive welding

Using the mathematical apparatus of catastrophe theory, the model of material behavior during its degradation is proposed. It is considered what the smallest number of parameters is with which the studied systems can be described, how order and chaos alternate in the space of the parameters that have been taken for use, and how the order of the material microstructure at various scale levels becomes complicated.

Crack propagation and branching are modeled using nonlocal peridynamic theory. One major advantage of this nonlocal theory based analysis tool is the unifying approach towards material behavior modeling - irrespective of whether the crack is formed in the material or not. No separate damage law is needed for crack initiation and propagation. This theory overcomes the weaknesses of existing continuum mechanics based numerical tools (e.g. FEM, XFEM etc.) for identifying fracture modes and does not require any simplifying assumptions. Cracks grow autonomously and not necessarily along a prescribed path. However, in some special situations such as in case of ductile fracture, the damage evolution and failure depend on parameters characterizing the local stress state instead of peridynamic damage modeling technique developed for brittle fracture. For brittle fracture modeling the bond is simply broken when the failure criterion is satisfied. This simulation helps us to design more reliable modeling tool for crack propagation and branching in both brittle and ductile materials. Peridynamic analysis has been found to be very demanding computationally, particularly for real-world structures (e.g. vehicles, aircrafts, etc.). It also requires a very expensive visualization process. The goal of this paper is to bring awareness to researchers the impact of this cutting-edge simulation tool for a better understanding of the cracked material response. A computer code has been developed to implement the peridynamic theory based modeling tool for two-dimensional analysis. A good agreement between our predictions and previously published results is observed. Some interesting new results that have not been reported earlier by others are also obtained and presented in this paper. The final objective of this investigation is to increase the mechanics knowledge of self-similar and self-affine cracks.

Coarse-grained materials, such as sand and gravel, exhibit a significant dependence on particle failure rate, which greatly influences their engineering behavior. This research focuses on the three-dimensional modeling of grain material behavior using the discrete element method (DEM) with PFC3D software and FISH programming language. The specific objective is to model the particle breakage phenomenon and its impact on resistance behavior and deformation. To accurately represent the non-spherical shape of the particles, an interconnected sphere approach was employed. The modeling of grain failure was achieved by establishing a failure criterion that considers two critical conditions: the heterogeneity of contact forces and stress within the particle. The proposed model and criteria were validated through comparison with triaxial experimental results obtained from the Purulia dam gravel. The results demonstrate that the developed model successfully captures the essential aspects of particle failure and its influence on the behavior of the granular environment. The simulations accurately represent the resistance behavior and deformation characteristics observed in the triaxial experiments. This validates the effectiveness of the proposed model in simulating the significant effects of particle failure on the behavior of coarse-grained materials. The findings of this study contribute to a deeper understanding of the complex behavior of coarse-grained materials, particularly in terms of their response to particle failure. The developed DEM model, incorporating the particle breakage phenomenon, provides a valuable tool for accurately predicting and analyzing the behavior of granular materials in various engineering applications.

For the most comprehensive modeling and prediction of materials behavior at the microscale, experimentally measured three-dimensional (3-D) microstructural datasets must be incorporated as initial input into computational models. Although the capability to collect and store large amounts of 3-D microstructural data is advancing continuously, computational resources for the processing and simulation can limit the amount of data that can be analyzed. Depending on the features and properties of interest, several approaches can be applied to optimize processing, reduce the amount of data that needs to be simulated, and increase the efficiency of simulations to maximize the statistical significance of microstructure analyses. This paper presents examples of four such approaches to efficient integration of large 3-D datasets into modeling and simulations of mechanical behavior in an efficient yet statistically significant manner.

Two-scale FE–FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior

Multi-phase transformations at large strains – Thermodynamic framework and simulation