Development of a multi-scale model for the description of the fracture behaviour of nodular cast iron GJS-400

Project Manager

Prof. Dr.rer.nat.habil. Meinhard Kuna, i.R.

Consultant

Dr.-Ing. Geralf Hütter

Motivation

In comparison to steel cast iron with nodular graphite exhibits a considerable more complex fracture behaviour at low temperatures. The reasons therefor are to be searched in the pronounced heterogeneity of the microstructure of cast iron. Until now concepts for the reliable evaluation of fracture safety just as material models adequately involving the specific properties of cast iron in the mentioned range of application are missing.

Fracture surface of cast iron with spherical graphite at different temperatures (from Rehmer, B.: Diss., TU Bergakademie Freiberg , 1992)

Objective

Through the coupling of micromechanical models describing ductile and brittle fracture, a multi-scale model is to be developed in the frame of this project, which permits the numerical simulation of crack initiation and propagation in samples made of ferritic cast iron with spherical graphite (GJS-400) in the whole range of ductility, consisting of brittle, ductile and transition regions. Besides statements concerning the influence of various microstructural parameters on the fracture behaviour, perceptions allowing the definition of appropriate fracture mechanical parameters as well as their experimental determination are expected. Finally the results of the project shall serve for prediction of crack initiation and propagation in structural parts made of GJS-400 under complex loading.

Methods

The evolution of the damage is simulated by means of a combined model, which accounts for ductile as well as brittle softening in the process zone. Simulations with a discretely resolved microstructure substantiate the understanding of the underlying mechanisms and allow conclusions regarding the choice of macroscopic material parameters.

Results

In the micromechanical models the microstructure in the process zone at the crack tip is resolved discretely. The material behavioMicromechanical simulation with discrete 2D voidsr outside this zone is incorporated in a homogenised way. The micromechanical finite element simulations with discrete voids show first with a 2D model that the geometrical softening of the ligaments between the voids after the plastic collapse is sufficient to induce crack growth without necessitating material separation, Figure 2. Initiation and evolution of the local geometrical softening depend strongly on the plastic hardening behavior of the matrix material. Thus, this strong dependency applies to the computed crack growth resistance curves, too. In addition, the arrangement of the voids relative to each other and to the crack tip has a considerable effect. In addition, the simulations show that voidMicromechanical simulation with discrete 3D voids growth outside the actual process zone shields the latter thus retarding fracture initiation. This behavior is especially relevant for materials with a high void volume fraction like ductile cast iron. These findings apply qualitatively as well to the three-dimensional simulationens with more realistic spherical voids, Figure 3. However, the 3D model predicts a higher crack growth resistance. 

 

 

Comparison of computed R-curves with experimental data (from [7])The comparison of the computed crack growth resistance curves with experimental results from literature in Figure 4 shows that the model allows quantitative predictions of the ductile crack growth. Thereby, the curves computed with the idealized void arrangements cp-0 and bcc-45 span a range around the experimental data.

 

 

Micromechanical 2D simulations of the ductile-brittle transitionA cohesive zone model is incorporated to account for cleavage in the model. Regarding the modelling of cleavage a cohesive zone model combines two main features: firstly the softening initiates (in the considered case of pure mode-I loading) when the maximum normal stress reaches a critical value, the cohesive strength. This maximum normal stress is equal to the maximum principal stress. Evaluating possible cleavage initiation with a maximum principal stress criterion is well established. In addition, the cohesive work of separation is the minimum work required for crack propagation which is necessary for separating the crystallographic planes. The crack initiation simulated with such a model is shoMicromechanical 2D simulations of the ductile-brittle transition (from [21]))wn in Figures 5 and 6 for the upper ductile-brittle transition region. Here, considerable crack tip blunting preceedes cleavage initiation. This model allows the simulation of crack initiation and propagation in the complete temperature region, from pure cleavage up to purely ductile failure. However, regarding the computed crack growth resistances, 2D and 3D simulationen exhibit a considerable difference: While the ligaments are separated one after another in the 2D model  (Figure 5), a front of cleavage crack propagation is formed in the 3D case. The crack front propagates continously along the crack plane with increasing loading (Figure 6).

Our recent review article [20] summarizes the knowledge from literature and the findings of the present project on micromechanical modelling of nodular cast iron.

In the macroscopic model the microstructure is not resolved but incorporated in a homogenised way. In particular the void growth is accounted for by different modifications of the Gurson model. Firstly, the modification by Tvergaard and Needleman (GTN-model) is coupled with a quasi-brittle damage model. Simulations of a Charpy test show the typical transition from the initial ductile mode to cleavage during the test, Figure 7. FE-simulation of the Charpy test: model and remaining damage in the ligament However, as with all damage models formulated within the framework of simple material theory, the FE-simulations do not converge towards a physically reasonable solution if the mesh is refined. For this reason a non-local extension of the GTN-model is employed. Such an approach introduces an intrinsic material length scale which is related to the mean void distance of the material. Cleavage is incorporated again by means of the cohesive zone model. Here, the cohesive material parameteres reflect the homogenised behavior. Figure 8 shows that this macroskopical model can describe the material failure within the complete temperature range. This applies especially to the unstable crack crack initiation in the lower ductile-brittle transition region, the crack arrest (a so-called pop-in) in the upper transition region up to the completely ductile failure at higher temperatures.

 

Crack growth resistance curves (from [8])

Financial Support

Deutsche Forschungsgemeinschaft 2008 - 2010 and 2011 - 2013

Monographs

  • G. Hütter: Multi-scale simulation of crack propagation in the ductile-brittle transition region, Dissertation, TU Bergakademie Freiberg, 2013, ISBN: 978-3-86012-463-5, URN: urn:nbn:de:bsz:105-qucosa-121281
  • M. Kuna, U. Mühlich, G. Hütter: Abschlussbericht zum DFG-Vorhaben KU 929/14

Publications

  1. G. Hütter, U. Mühlich, M. Kuna: Simulation of local instabilities during crack propagation in the ductile-brittle transition region, European Journal of Mechanics - A/Solids, 30 (2011), 195-203 pdf
  2. G. Hütter, L. Zybell, U. Mühlich, M. Kuna: Ductile Crack Propagation by Plastic Collapse of the Intervoid Ligaments, International Journal of Fracture, 176 (2012), 81-96 pdf
  3. T. Linse G. Hütter, M. Kuna: Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain, Engineering Fracture Mechanics, 95 (2012), 13-28
  4. S. Roth, G. Hütter, U. Mühlich, B. Nassauer, L. Zybell, M. Kuna: Visualisation of User Defined Finite Elements with Abaqus/Viewer, GACM Report, Summer (2012), 7-14 pdf
  5. G. Hütter, T. Linse, U. Mühlich, M. Kuna: Simulation of Ductile Crack Initiation and Propagation by means of a Non-local GTN-model under Small-Scale Yielding, International Journal of Solids and Structuctures 50 (2013),  662-671
  6. U. Mühlich, L- Zybell, G. Hütter, M. Kuna: A first-order strain gradient damage model for simulating quasi-brittle failure in porous elastic solids, Archive of Applied Mechanics 83 (2013), 955-967
  7. G. Hütter, L. Zybell, U. Mühlich, M. Kuna: Consistent Simulation of Ductile Crack Propagation with Discrete 3D Voids, Computational Materials Science (80) 2013, 61-70
  8. G. Hütter, T. Linse, S. Roth, U. Mühlich: A Modeling Approach for the Complete Ductile-brittle Transition Region: Cohesive Zone in Combination with a Non-local Gurson-model, International Journal of Fracture, 185 (2014),  129-153 pdf
  9. L. Zybell, G. Hütter, T. Linse, U. Mühlich, M. Kuna: Size effects in ductile failure of porous materials containing two populations of voids , European Journal of Mechanics - A/Solids, 45 (2014), 8-19
  10. G. Hütter, L. Zybell, M. Kuna: Size Effects due to Secondary Voids during Ductile Crack Propagation, International Journal of Solids and Structures, 51 (2014), 839-847
  11. G. Hütter, T.Linse, U. Mühlich, M. Kuna: Simulation of Crack Propagation under Small-Scale Yielding by means of a Non-local GTN-Model, Proceedings in Applied Mathematics and Mechanics, 11 (2011), 157-158
  12. L. Zybell, G. Hütter, T. Linse, U. Mühlich, M. Kuna: Nichtlokale Modellierung des duktilen Versagens von Gusseisen mit Kugelgraphit, DVM-Bericht 244, 2012, 47-56
  13. A. Burgold, G. Hütter, L. Zybell, U. Mühlich, M. Kuna: Mikromechanische Simulation des duktilen Risswachstums durch plastischen Kollaps, DVM-Bericht 244, 2012, 191-200
  14. G. Hütter, L. Zybell, U. Mühlich, M. Kuna: 2D and 3D Simulation of Ductile Crack Propagation by Plastic Collapse of Micro-ligaments, Proceeding of the 19th European Conference on Fracture, 2012 pdf
  15. G. Hütter, T. Linse, U. Mühlich, M. Kuna: Integrated Damage Mechanics Approach to Brittle and Ductile Crack Propagation, Proceeding of the 13th International Conference on Fracture, 2013
  16. G. Hütter, T. Linse, U. Mühlich, M. Kuna: Simulation der Rissausbreitung im gesamten spröd-duktilen Übergangsbereich, DVM-Bericht 245, 2013, 49-58
  17. L. Zybell, G. Hütter, U. Mühlich, M. Kuna: Mikromechanische Simulation der duktilen Rissinitiierung in Gusseisen mit Kugelgraphit, DVM-Bericht 245, 2013, 243-252
  18. G. Hütter, L. Zybell, M. Kuna: Mikromechanische Simulation der Rissausbreitung in Gusseisen mit Kugelgraphit im gesamten spröd-duktilen Übergangsbereich, DVM-Bericht 246, 2014, 177-186
  19. G. Hütter, L. Zybell, M. Kuna: Micromechanical Modeling of Crack Propagation with Competing Ductile and Cleavage Failure, Procedia Materials Science, 3C (2014), 428-433
  20. G. Hütter, L. Zybell, M. Kuna: Micromechanisms of fracture in nodular cast iron: From experimental findings towards modeling strategies – A review, Engineering Fracture Mechanics, 144 (2015), 118-141 pdf
  21. G. Hütter, L. Zybell, M. Kuna: Micromechanical modeling of crack propagation in nodular cast iron with competing ductile and cleavage failure, Engineering Fracture Mechanics, 147(2015), 388-397 PDF
  22. G. Hütter, L. Zybell, M. Kuna: Micromechacal simulation of crack initiation and propagation in ductile cast iron (in German), Giesserei-Praxis, 11(2015), 521-526