**3. Internal stress state**

The manufacturing of composites with ceramic matrix almost always leads to residual stresses caused by the mismatch of thermal properties of constituent phases. The value of these stresses mainly depends on mechanical properties of constituent phases of the composite and the absolute difference between their CTE's. A large difference in thermal expansion coefficients (CTE's) could introduce to the composite system stresses reaching even more than gigaPascals. Such a phenomenon has to influence mechanical properties of the material. The distribution of residual stresses depends also on the phase arrangement and shape of grains.


**Table 1.** Data necessary for calculation of the residual stresses value.

The thermal expansion coefficient of tungsten carbide (*αWC*) is lower than thermal expansion coefficients of both considered oxide phases (αAl2O3 and αZrO2). It means that in composites with both oxide matrices the internal stress state is similar. Matrices are under tension and carbide inclusions are under compression.

For this chapter results of calculation of stresses in materials was made using the finite elements model (FEM) based on following predictions:


The results of FEM simulations were visualized at Figures 3 and 4. They present the distribution of principal maximal stresses around in the hypothetical composite microstructure. Calculations were made for the same schematic microstructure. Matrix was assumed as zirconia or alumina, respectively. The inclusion phase was WC. Calculations were made for Al2O3/WC and ZrO2/WC composites.

84 Tungsten Carbide – Processing and Applications

**3. Internal stress state** 

and shape of grains.

Phase CTE (*α*),

carbide inclusions are under compression.

and, additionally, in one corner,

principle,

2Al2O3 + 9WC = Al4C3 + 9W + 6CO (6)

Calculations showed that reactions (4 - 6) cannot proceed in the range of potential sintering

reaction is much higher than zero. That results were also confirm by Niyomwas [23], who

The manufacturing of composites with ceramic matrix almost always leads to residual stresses caused by the mismatch of thermal properties of constituent phases. The value of these stresses mainly depends on mechanical properties of constituent phases of the composite and the absolute difference between their CTE's. A large difference in thermal expansion coefficients (CTE's) could introduce to the composite system stresses reaching even more than gigaPascals. Such a phenomenon has to influence mechanical properties of the material. The distribution of residual stresses depends also on the phase arrangement

Young modulus *E*,

GPa Poisson ratio, <sup>ν</sup>

0) of that

temperatures (1400 - 1700C) because of fact that standard free enthalpy (ΔGr

stated that Al2O3/WC system is thermodynamically stable up to 2000C.

10-6C-1

**Table 1.** Data necessary for calculation of the residual stresses value.

elements model (FEM) based on following predictions:


eliminated the stress accumulation at the model edge, - grain boundaries inside constituent phases were omitted,


Alumina 7.9 385 0.250 Zirconia ss. 11.0 210 0.210 WC 5.2 700 0.300

The thermal expansion coefficient of tungsten carbide (*αWC*) is lower than thermal expansion coefficients of both considered oxide phases (αAl2O3 and αZrO2). It means that in composites with both oxide matrices the internal stress state is similar. Matrices are under tension and

For this chapter results of calculation of stresses in materials was made using the finite





**Figure 3.** The principal maximal stresses calculated for ZrO2/WC composite. Dark blue color represents the maximal values of compressive stresses, brown color represents the maximal values of tensile stresses. At this Figure WC inclusions are generally in blue color.

Generally, the maximum value of principal maximal stresses in the zirconia matrix is about 30 % higher than in the alumina one. The tensile stress level near the interphase boundary in the zirconia matrix materials exceeds 1000 MPa all around the inclusion grain (Fig. 3). In the alumina based materials maximum stress values in this area are much lower (Fig. 4).

This fact influences the path of crack in the investigated materials. In zirconia-based composites crack goes along the interphase boundary (Fig. 5). The crack course in composites with alumina matrix is different. It usually goes near the inclusion grains, but it is deflected before it reaches the interphase boundary (Fig. 6). This means that the crack goes through alumina grains.

Tungsten Carbide as an Reinforcement in Structural Oxide-Matrix Composites 87

**Figure 5.** The SEM image of crack path in ZrO2/WC composite.

**Figure 6.** The SEM image of crack path in Al2O3/WC composite.

**Figure 4.** The principal maximal stresses calculated for Al2O3/WC composite. Dark blue color represents the maximal values of compressive stresses, brown color represents the maximal values of tensile stresses. At this Figure WC inclusions are generally in blue color.

The final effect of such crack behaviour for material toughening is summarized in Table 4. As it is clearly visible, the relative fracture toughness increase observed for the aluminabased composites is higher than for the zirconia ones.

This phenomenon should be attributed to the lower stress level in the alumina-based composites. As it can be seen at Figures 3 – 4, the maximum stress values are present in some distance between inclusion grains. Probably the strength of alumina grain is comparable with the strength of interphase boundaries (Al2O3/WC) in composites. Such a situation promotes transgranular cracking of alumina (see Fig. 6), but in a specific way, the crack still wanders around inclusions and crack deflection mechanism is still active and it consumes energy effectively.

In TZP matrix composites the tensile stress acting on the interphase boundary is much higher than in these with alumina matrix. It decrease the amount of energy dissipated during cracking. Additionally, high toughness of the zirconia material causes that the crack does not deflect as in the case of alumina. The crack rather goes to the interphase boundary and deflects directly on it. These observations are only qualitative but they could help to understand the effect of a relatively high level of toughening in the alumina based composites.

**Figure 5.** The SEM image of crack path in ZrO2/WC composite.

86 Tungsten Carbide – Processing and Applications

**Figure 4.** The principal maximal stresses calculated for Al2O3/WC composite. Dark blue color represents the maximal values of compressive stresses, brown color represents the maximal values of

The final effect of such crack behaviour for material toughening is summarized in Table 4. As it is clearly visible, the relative fracture toughness increase observed for the alumina-

This phenomenon should be attributed to the lower stress level in the alumina-based composites. As it can be seen at Figures 3 – 4, the maximum stress values are present in some distance between inclusion grains. Probably the strength of alumina grain is comparable with the strength of interphase boundaries (Al2O3/WC) in composites. Such a situation promotes transgranular cracking of alumina (see Fig. 6), but in a specific way, the crack still wanders around inclusions and crack deflection mechanism is still active and it

In TZP matrix composites the tensile stress acting on the interphase boundary is much higher than in these with alumina matrix. It decrease the amount of energy dissipated during cracking. Additionally, high toughness of the zirconia material causes that the crack does not deflect as in the case of alumina. The crack rather goes to the interphase boundary and deflects directly on it. These observations are only qualitative but they could help to understand the

effect of a relatively high level of toughening in the alumina based composites.

tensile stresses. At this Figure WC inclusions are generally in blue color.

based composites is higher than for the zirconia ones.

consumes energy effectively.

**Figure 6.** The SEM image of crack path in Al2O3/WC composite.
