Using dilatometer experiments, numerical data can be collected during the sintering process and used to develop a constitutive model for shape changes during sintering. The dilatometer chamber is closed and small compared to a normal industry oven used for sintering. Depending on the final application of the sintered product, different temperatures and heat cycles may be used during the process. It is therefore important for a constitutive model to be robust, giving valid results even when changes are made to the sintering procedure. This is done by optimizing the constitutive parameters with respect to different sintering cycles. Variations of initial density after compaction has also been considered in the constitutive model. The deviatoric part of the model is investigated for experimental results in nonhomogeneous sintered specimens to complete the constitutive model. The model presented is for the full sintering process and relevant physical aspects have been accounted for.

Powder metallurgy is used in the manufacturing of cutting tool inserts to achieve the desired material properties. Tungsten carbide, WC, mixed with a metallic binder, such as Cobalt, Co, is a common cemented carbide used for cutting tool inserts. In large scale production, the powder is pressed and sintered. During the manufacturing process, the volume of the cutting tool significantly decreases. During the sintering process, very little can be done to change the final shape, and the shrinkage during sintering must be accounted for during pressing. This thesis will investigate the mechanical modeling of shrinkage that occurs in the sintering process.

The constitutive model at issue can capture the isothermal stage in the sintering process and can be adjusted to a specific powder. To increase its usability, a sensitivity analysis was performed in Paper A to determine if all parameters must be determined when using a new powder mixture. It was found that some of the parameters were more sensitive than others when optimizing parameters using experimental results. The less sensitive parameters could be constant, reducing the number of necessary experiments to determine all adjustable parameters. 

The different stages of sintering were also investigated in Paper A, where the model had difficulty describing the shrinkage both in the initial stage and in the liquid phase, where the Cobalt starts to melt. The latter was expected, since the constitutive model was explicitly developed for the solid stage of sintering.

To evaluate the model, all the experiments were performed on a specific WC-Co powder blend. For adherence to match the industrial process for cutting tools made from this powder, the debinding phase was included early in the sintering cycle. This was not done in the previous development of the sintering model. The influence of the debinding process was experimentally investigated in Paper B, where it was shown that the shrinkage, as well as the final microstructure, is influenced by the exclusion of the debinding stage. 

In Paper C, multiple dilatometer and sintering furnace experiments were performed to further develop the model. Complements to the initial stage and liquid phase were introduced, and the effect of changing the initial density, post-compaction, was investigated. Different sintering cycles were used to ensure the robustness of the constitutive parameters of the model. The deviatoric influence was tuned with bending experiments. 

To verify the model, Paper D compares simulations to experiments. This was done using two different press dies, where the same amount of powder was pressed to different heights. The powder blanks were sintered to different maximum temperatures and measured. The compaction and sintering process was simulated and compared to the experimental values, showing that the sintering model captured the process well. A sintering furnace was used, where one of the sintering cycles was representative of the industrial production of cutting tools.  

Pulvermetallurgi används vid tillverkning av vändskär för att uppnå de önskade materialegenskaperna. Volframkarbid, WC, blandat med ett metalliskt bindemedel, som exempelvis Kobolt, Co, är en vanlig hårdmetall att tillverka skär av. Vid storskalig produktion är pressning och sintring vanliga, och vid dessa tillverkningsprocesser sker en signifikant volymminskning. Under sintringssteget är möjligheten att påverka den slutgiltiga formen begränsad varför man redan vid pressning behöver ta hänsyn till den krympning som kommer att ske under sintringen. I denna avhandling kommer modellering av krympning under sintring att undersökas.

Den utvalda konstitutiva modellen kan fånga isotermiska delar av sintringsprocessen och har parametrar som går att anpassa för specifika pulversammansättningar. För att förenkla användningen av modellen utfördes en känslighetsanalys i Artikel A. Denna visade att när anpassningsbara parametrar ska justeras till en ny pulversammansättning kan vissa av de mindre känsliga hållas konstanta för att förenkla optimering.

Sintringens olika stadier undersöktes också i Artikel A. Modellen hade svårigheter att fånga krympningen både under den initiala fasen av sintring, samt i smältfassintringen. Det sistnämnda var förväntat, eftersom den konstitutiva modellen från början var specifikt utvecklad för fastfassintring.

För att begränsa osäkerheter vid modellutvärderingen utfördes alla experiment för en specifik sammansättning av WC-Co pulver. För att bättre representera det industriella förloppet vid skärtillverkning med detta pulver inkluderades även avdrivning (då pressmedlet avdunstar) i experimentet. Detta var inte inkluderat i den ursprungliga konstitutiva modellen, och effekten av avdrivningssteget i sintringsprocessen undersöktes experimentellt i Artikel B. Här visades att både krympningen och den slutgiltiga mikrostrukturen påverkas av att inte inkludera avdrivningen i sintringscykeln.

I Artikel C utfördes ytterligare experiment, både med dilatometer och i sintringsugn, för att vidareutveckla modellen. Kompletteringar gjordes både för att ta hänsyn till avdrivning i sintringens initiala fas, samt i smältfasen. Vidare undersöktes effekten av att förändra pulvrets initiala densitet, efter pressning. För att öka modellens robusthet användes olika sintringscykler vid framtagandet av modellens konstitutiva parametrar. Inflytandet av deviatorisk spänning justerades med hjälp av böjexperiment.

För verifiering av modellen jämfördes i Artikel D simuleringar med experiment för olika geometrier. Detta gjordes med två olika pressformar, som pressade samma mängd pulver, men till olika höjder. Dessa sintrades till olika temperaturer och mättes därefter. Kompakterings- och sintringsprocessen simulerades och jämfördes med experimentens resultat, med mycket god överensstämmelse. En sintringsugn användes, där en av sintringscyklerna efterliknande vad som används vid industriell sintring. 

By performing a dilatometer experiment, measured shrinkage can be used to determine the adjustable parameters in a constitutive model for sintering. While the dilatometer machine is excellent at collecting data, its conditions differ from those in an industrial sintering oven. Therefore, the constitutive model must be robust and in the present study, different sintering time cycles have been used to optimize the adjustable parameters in the model. Investigations on initial density has also been performed to better understand the sintering process. Before sintering of particles begins, during the debinding process, densification can be detected, which is dependent on the initial density. The constitutive model for sintering was improved to include this phenomenon by adding particle rearrangement based on the theoretical packing of spheres.

During sintering, a green body of powder particles is heated to high temperatures, fusing the particles together. In cemented carbide production, the sintering process generally results in substantial densification of the material. By using a dilatometer, shrinkage during the sintering process can be measured. For a green body of lower density, early particle rearrangement has been observed. This is investigated here using different initial densities using the same powder, leading to a suggested addition to the constitutive model. The environment in the dilatometer and the sintering furnace differs, especially with respect to heating and temperature during holding. This effect can be minimized by creating robustness in the model, making it independent of the heating cycle. Here, this is done by optimizing the constitutive parameters towards four heating cycles for a specific powder.

The densification of cemented carbides during sintering was studied using an existing constitutive model based on powder particle size and material composition. In the present analysis, we study how well the constitutive model can capture the experimental results of a dilatometer test. Three experiments were performed, where the only difference was the transition between the debinding and sintering process. From magnetic measurements, it is concluded that the carbon level in the specimen is affected by changes to the experimental setup. It is shown, using parameter adjustments, that the constitutive model is more suited for a certain experimental setup and carbon level, which is a limitation of the model. In order to capture the mechanical behaviour under different experimental conditions, further constitutive modelling relevant to the carbon level is recommended.

From a previously developed constitutive model for cemented carbide, the powder size- and configuration can be used to simulate the densification during the sintering process. However, small differences in experimental execution cannot be accounted for in the simulation, making the model sensitive. Here, we study how well the developed constitutive model can capture the experimental results of a dilatometer test. Three different experiments were performed where the only difference was the transition between the debinding and sintering process. From parameter adjustments, it is seen that the constitutive model is more suited for a certain experimental setup, which is a limitation of the model.

This study focuses on an inverse modelling approach, using FEM to simulate the sintering of WC-Co powder using a continuum model. From a previously developed constitutive model of cemented carbide, the dependency of the material parameters is investigated in a sensitivity study. A value of sensitivity is assigned to all the material parameters and calculated at different steps in the sintering process, which represent its importance for capturing the shrinkage during sintering. The approach is that only the more sensitive parameters should be fitted when changing experimental setup or material composition, leaving the less important parameters constant, resulting in fewer tests and iterations. This approach is tested in an optimization of WC-Co powder sintering cycle, where the shrinkage curve is experimentally determined. It is concluded that some of the material parameters play a minor role in the modelling and could be set as constants in an optimization. The constitutive material model alone is unable to capture all features that appeared in the shrinkage curve during the experiment. Improvements of the model are discussed. An additional investigation, performed without heating rate dependency, shows that the remaining material parameters could compensate for the omitted heating rate for a known sintering cycle without losing accuracy.

In the development process of new cutting tools, accurate simulations reduce both time to market and resources. In this paper, previously developed constitutive models of compaction and sintering are used to simulate the manufacturing process. Multiple variations of compaction heights and maximum temperatures in the sintering cycle are used, and simulated results are compared to actual experiments. The results confirm that good prediction of the spatial distribution of relative density is possible even for complicated geometries. The simulations can also be used to predict changes in the press heights' effect on the final product.