FINITE ELEMENT STUDIES OF CRACK GROWTH IN A WC-Co MULTILIGAMENT ZONE

8/12/2019 FINITE ELEMENT STUDIES OF CRACK GROWTH IN A WC-Co MULTILIGAMENT ZONE

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FINITE ELEMENT STUDIES OF CRACK GROWTH IN A WC-Co MULTILIGAMENT ZONES. SchmauderMax-Planck-Institut fr Metallforschung. Institut fr Werkstoffwissenschaften. Seestr. 92. 7000 Stuttgart 1. FRG

SUMMARY

Crack growth in the system WC-Co was studied. An analysis of the plastic deformation of ductile Co-bridges withina multiligaulent zone has been carried out by means of thefinite element method FEM . An experimentally observed twodimensional crack tip morphology [lJ was used in the calculation. The FEM studies allowed the analysis of the propagation of the plastic region in front of the crack tip underincreasing load. The calculations demonstrated that the ligaments were simultaneously plastically deformed to varyingdegrees. The size of the plastic zone in each ligament didnot exceed a width of about 1 ~m. in agreement withexperimental results. The development of pores inside theligaments was also considered. A stress-controlled voidnucleation criterion could be extracted by comparison ofcalculations with experimental results.INTRODUCTION

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The toughness of WC-Co hardmetals can be qualitativelyunderstood in terms of microstructural parameters such asthe volume content of Co and the mean grain size of WC. However. there are many different interpretations from experiments and calculations concerning the important processes atthe crack tip. Detailed experimental information has beenrare until recently.

It was shown experimentally [lJ that a large amount ofthe crack propagation energy is dissipated during theductile fracture of the Co-binder. Therefore. the crackresistance is mainly dependent on the size of the plasticzone in the binder. Controversy exists concerning the sizeof this plastic region. FEM calculations [2J predicted asize 10 times larger than the experimentally determined one.


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In this paper. crack tip plasticity in a technically

interesting WC-Co-alloy with 10 w cobalt and a coarsegrained microstructure is examined in detail by FEM. Themodel used is different from previous calculations in thatplasticity in the entire process zone is considered.

The predicted plastic deformation in the binder iscompared with the experimental observations of ref. [1] andthe accompanying void formation is accounted for by a stresscriterion in the FEM-calculation.

The size of the plastic zone is the critical parameterin all the existing toughness models. On the other hand.reliable experimental results on the crack-tip region [1]suggest modelling a whole process zone of WC-Co for thefirst time.TRE PROBLEM

Fig. 1 shows a typical structure of a process zone inWC-Co where the crack propagates predominantly in thebrittle carbide phase surrounding the ductile binder region.Such a process zone is called a multi-ligament zone MLZ)[3]. In coarse-grained WC-Co-alloys. the MLZ extends toabout 10 um and typically contains 3 ligaments of theCo-binder phase.

Fig. 1: In WC-Co. the crack propagates preferentially in thebrittle carbide phase. After fracture. Co-ligaments


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9Dimples on the fracture surfaces prove that the liga-

ments fail by the development of pores It has beenexperimentally shown that the location and orientation ofthe surrounding carbide crack determines the fracture pathin the ligaments This is shown schematically in Fig 2

a bFig 2: The location of the carbide crack determines the

fracture path in the ligaments The void density ishigher along carbide/binder phase boundaries thanacross ligaments

It has been experimentally demonstrated that thedensity of voids is higher at WC/Co phase boundaries than atcrack paths which are far away from the interfaces Fig 3shows schematically how the voids grow and how they lead tothe fracture in the ligaments by coalescence

fr tured zone multilig ment zone el sti zone

Fig 3: Schematic idea of crack propagation in WC Co by nu-cleation growth and coalescence of pores in theligaments [1]


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39The methods and the plastic zone sizes predicted by

different investigators for comparable alloys are listed inthe following table. where 2 r 1 is defined as the extensionof the plastically deformed re~~on normal to the cracksurface in mode r loading:

Author(s) Ref.ethodrediction4]odel2r = 5]EN 2rpl > ip1]xperiment2r:~ < iThe experiments in ref. [1] did not show plastic defor

mation of binder regions remote from the crack surfaceswithin a resolution limit of 0.5 of plastic strain. Theplastic zone size and the me an free path in the binder werefound to be 2rpl = 0.6 pm and p = 0.84 pm. respectively.

To the author s knowledge. the first FEM-calculationsof deformation in WC-Co were performed by Sundstrm [6].These calculations were performed with a medium-fine FE-meshunder applied pressure and showed good agreement with theexperimentally determined macroscopic stress-strainrelation. Only small regions suffered plastic strains ofmore than 1 .

This latter result is in agreement with the calculattions performed in ref. [ where external forces were applied on a very coarse FE-mesh. There. it was shown that anincrease in binder yield stress reduces the plastic zonedramatically according to Irwin s relationship

2r 1:::: Kr /0c ywhere Kr is the stress intensity factor and 0 the yieldstress. The size of the plastic zone is not ve~y sensitiveto the strain hardening of the binder. The models of both.[5] and [6]. are coarse. They use low yield stresses of 0 =783 MPa and 0 = 1150 MPa. respectively. and do not accou6tfor the MLZ i6 a realistic manner.THE MODEL

A MLZ model was built according to an experimentallydetermined crack trace on a WC-Co alloy surface. Themicrograph from which the trace was obtained is shown inFig. 4. The unfractured microstructure was also obtainedfrom Fig. 4 assuming that the crack was elastically closedand that the ligaments were undeformed.

Before the FE-mesh was generated. some insignificantchanges had been made. e.g. some WC/Co-boundaries had been


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Fig. 4: Section of the crack trace in a WC-Co alloy.Measurable plastic deformations are restricted tothe ligaments. Binder regions remote from the interface are not plastically deformed.

straightened. The cracked carbide grains had also been modelled. The frame of the modelled structure with ligamentsL1-L3. binder phase regions B. B1-B6. carbide grains K1-K17.crack tip R. and crack tip positions A-F are shown in Fig.5.

Fig. 5: The modelled microstructure after Fig. 4 K carbide grain. L = ligament. B = binder. R = crack tipIA-F crack tip positions .

The parameters of the model and of the real microstruc


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Fig b: Continuum surrounding the MLZ modelled with finiteelements

Fig c: Finite element discretization of the outer con-tinuum shell surrounding the area of Fig b Crackand boundary conditions are also shown

et al [9J were used:


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395segments open with a rectangular profile in agreement withthe experiment Fig. 4 . The development of the plasticdeformation can be seen in Figs. 8-9 plane stress and inFigs. 10-11 plane strain . respectively.

Plastic Zone Kl : 0.33K1ci l o.33K c< Kl : 0.67Klc~ 0.67 Klc < Kl : K1

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FINITE ELEMENT STUDIES OF CRACK GROWTH IN A WC-Co MULTILIGAMENT ZONE