Hermann Riedel

Numerical simulation of solid state sintering; model and application

A comprehensive model for solid state sintering is presented which combines several previous models for partial aspects of sintering and grain coarsening. Some additional aspects are discussed and the model is extended for external loads several times higher than the sintering stress. Model parameters for a SiC powder are presented. For a face seal made of SiC uniaxial die compaction is simulated and different green density distributions after compaction are obtained for two different pressing schedules. Next, the sintering behavior is simulated using these density distributions as initial conditions. The resulting distortions of the face seal differ significantly for the two pressing schedules. For a special element with average green density the predictions of the sintering model are investigated in more detail. Finally, the shape predictions of the model are compared with a simplified model for solid state sintering.

Finite element simulation of cold isostatic pressing and sintering of SiC components

Abstract Finite element simulations were performed for cold isostatic pressing of SiC powder. To describe the compaction behaviour, the Drucker–Prager–Cap model implemented in ABAQUS/Explicit® computer program was applied. The influence of friction between powder and steel core as well as rubber bag on the density distribution was investigated for compacts with cylindrical and helical cores. Simulations with and without rubber bags were made showing that the effect of the bag on the density distribution is fairly small, at least for thin bags. Due to the presence of the steel core, density gradients develop during compaction, although the outer pressure is hydrostatic. The predicted density variation is consistent with experimental results. After the pressing cycle it may be difficult to remove the helical steel core from the powder compact. The simulation shows that the elastic spring-back leads to residual stresses which may reach the green strength of the powder compact, so that the part may crack during the unloading or removal of the helical core. Investigations of the sintering behaviour predict small shape distortions due to the slightly inhomogeneous density distribution of the green body. However, the differences between the ideal geometry and the predicted outline after sintering are small.

Finite Element Simulation of Die Pressing and Sintering

Numerical simulation of die compaction and sintering is a promising tool for reducing development times and costs or optimizing production cycles. Finite element simulations allow qualitative and quantitative predictions of undesirable distortions after firing. Even qualitative predictions of crack formation are possible.

Densification of sintered molybdenum during hot upsetting : experiments and modelling

Abstract The densification behaviour of sintered molybdenum is investigated experimentally and by modelling using a pressure dependent plasticity model. Therefore the yield condition of Gurson, extended by Tvergaard is used. The uniaxial compression test is applied to determine the evolution of the density as well as the stress–strain curves for the porous metal. Powder metallurgical molybdenum exhibits closed porosity after consolidation due to sintering with nearly spherical shaped pores. The experimental results show that the densification, especially during the first stage of deformation, is different from that of powder compacts or partially consolidated powder materials with open porosity. During hot upsetting, the pores change their size and shape. This behaviour strongly affects the densification rate. For an accurate prediction of the evolution of the density using Gurson’s model, the parameters q1 and q2 introduced by Tvergaard, will be defined as internal variables. The use of internal variables is justified by the fact that the pores change their shape during deformation, although the link between the internal variables and the pore shape is not explicitly established in this paper. If the loading is proportional (which means that the ratio of the stress-components does not change with plastic strain), the pore shape can be associated with the applied plastic strain. With this association the parameters qi can be defined as a function from the invariant quantity equivalent plastic strain, which can be used as the internal variable in the finite element simulation. The influence of the porosity on the flow stress at different levels of plastic strain will also be investigated and is used as a second information to fit both parameters q1 and q2.

Distortions and cracking of graded components during sintering

The aim of the project is to develop methods for predicting distortions and cracking during the fabrication of gradient materials, and to apply them to simple geometries (tubes, beams and plates). Crack formation during sintering is described as the instability of the homogeneous sintering state. It is found that a density disturbance may grow unstably, but only when the material is severly constrained in three dimensions. The equations for describing the distortions of graded beams and plates during sintering are developed. Examples are shown for plates with gradients in grain size, temperature and composition (Mo and ZrO 2 ). If the gradient is carefully balanced, nearly planar plates can be obtained after sintering. Three-dimensional finite element studies of graded circular plates show that the initially axisymmetric mode of deformation becomes unstable in favor of a warping with two symmetry planes (like a potato chip).

Simulation of hot forming processes of refractory metals using porous metal plasticity models

In this work two models for predicting the densification behavior of sintered refractory metals during hot working operations are presented. It is known from experiments and cell model calculations that the pore shape change has a significant influence on the densification behavior. Therefore this effect should be included in a continuum constitutive description. The first model presented is a phenomenological extension of the Gurson model, the second one is the model of Gologanu, Leblond & Devaux, which was implemented as a user material model into the finite element code ABAQUS. The numerical results are compared with the density distribution of a tapered disk made of pure molybdenum after the hot forming operation.

Manufacturing of a gear wheel made from reaction bonded alumina—numerical simulation of the sinterforming process

Sinter forming is a recently developed process for the production of advanced ceramic components. It combines pressure-supported sintering and superplastic deformation, and allows RBAO (Reaction Bonded Alumina) to be sintered without grain coarsening due to the reduction of process time and dwell temperature. Thus, sinterforming can achieve near net shaping and defect free components for highly stressed applications. As many phenomena interact during sinter forming, the process parameters for producing complex shaped parts are difficult to identify without numerical tools. Therefore, a micromechanical model for solid state sintering has been used to investigate the process. The model was extended to consider source controlled diffusion in order to describe the non-linear stress/strain dependence. Several experiments were made in order to determine the material parameters of the model. The model has been implemented as a user subroutine in ABAQUS/Explicit® and is validated by numerical simulations of the accomplished experiments. To show the possibilities of the finite element simulation, the sinter forming process is numerically carried out for a RBAO gear wheel.

A Micromechanical Model for Creep Damage and Its Application to Crack Growth in a 12% Cr Steel

If creep cavities on grain boundaries grow by the constrained diffusive mechanism, partly cavitated boundary facets act mechanically like microcracks. Two cell models, one based on a cylindrical cell and the other on a regular tetrakaidekahedron, are worked out numerically to explore the influence of a distribution of microcracks on the constitutive response of a creeping solid. The results confirm the predictions of analytical estimates based on the differential self-consistent method of Rodin and Parks [5]. The Rodin and Parks model is then combined with the Robinson model [9] to provide a comprehensive model covering primary, secondary, and tertiary creep under arbitrary loading conditions. The combined model is implemented in the finite element code ABAQUS. The model is adjusted to a set of creep curves for a 12% Cr steel (X 20 CrMoV 12 1), and tests on compact specimens are successfully modeled.

Simulation of fatigue crack growth under large scale yielding conditions

A simple mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack-tip opening displacement (ΔCTOD) and the crack growth increment (da/dN). The objective of this work is to compare analytical estimates of ΔCTOD with results of numerical calculations under large scale yielding conditions and to verify the physical basis of the model by comparing the predicted and the measured evolution of the crack length in a 10%-chromium-steel. The material is described by a rate independent cyclic plasticity model with power-law hardening and Masing behavior. During the tension-going part of the cycle, nodes at the crack-tip are released such that the crack growth increment corresponds approximately to the crack-tip opening. The finite element analysis performed in ABAQUS is continued for so many cycles until a stabilized value of ΔCTOD is reached. The analytical model contains an interpolation formula for the J-integral, which is generalized to account for cyclic loading and crack closure. Both simulated and estimated ΔCTOD are reasonably consistent. The predicted crack length evolution is found to be in good agreement with the behavior of microcracks observed in a 10%-chromium steel.

Experimental and Numerical Investigation of Texture Development during Hot Rolling of Magnesium Alloy AZ31

Due to the deformation mechanisms and the typical basal texture rolled magnesium sheets show a significant asymmetry of flow stress in tension and compression. In order to avoid this undesired behavior it is necessary to achieve non-basal texture during rolling, or at least, to reduce the intensity of the basal texture component. The reduction of the anisotropy caused by the basal texture is very important for subsequent forming processes. This project aims at optimizing the hot rolling process with special consideration of texture effects. The development of the model is carried out in close cooperation with the experimental work on magnesium alloy AZ31 .The experimental results are required for the determination of model parameters and for the verification of the model. Deformation-induced texture is described by the visco-plastic self-consistent (VPSC) model of Lebensohn and Tomé. The combination of deformation and recrystallization texture models is applied to hot compression tests on AZ31, and it is found, that the model describes the observed texture and hardening/softening behavior well. In some cases rotation recrystallization occurs in AZ31 which appears to be a possibility to reduce the undesired basal rolling texture.