Chapter IV. Microstructural Fracture Analysis
4.5 Results and discussion
4.5.4 Effect of the pores on the transverse tensile response
In this chapter, the effect of a void on the micro-fracture behavior is investigated using RVE 1.
When the chemical vapor infiltration (CVI) process is employed, some areas closed by fibers may remain as pores in the end because the reactive gas cannot reach the region for the matrix deposition on the fiber surfaces. In the RVE 1 model, such an isolated area that can be evolved into a pore exists. The closed area of the RVE 1 model is the largest among those of other RVE models. The void volume fraction of the RVE 1 model is measured to be 1.7%. Figure 56 compares the RVE 1 model with and
without the pore. The same tensile loading as defined in Section 4.5.2 is applied to the RVE 1V model and its mechanical response is examined.
Figure 56 Configurations of RVE 1 and RVE 1V.
Figure 57 compares the stress-strain curves of the RVE 1 and RVE 1V models. Figure 58 shows final fracture patterns of the two models. The red regions indicate fully developed cracks. The final fracture patterns are similar between the RVE 1 and RVE 1V models. When the cracks grow into the final fracture pattern, a load drop occurs in the stress-strain curve. In Figure 57, the load drop for the RVE 1V model come earlier that of RVE 1 because less strain energy is required to fully grow the cracks due to the void. As a result, the fracture toughness of the RVE 1V model is smaller than that of RVE 1.
Figure 57 Stress-strain curves for tension tests of RVE 1 and RVE 1V.
Figure 58 Final fracture patterns of RVE 1 and RVE 1V.
Hereafter, based on the crack progression, the detailed responses of the RVE models at particular steps will be investigated. Figure 59 shows the distribution of the principal stresses of the RVE 1 model in the linear region of the stress-strain curve. As shown in Figure 59(a), stresses are concentrated in the narrow matrix region. Figure 59(b) isolate the coating layers, in which the stress concentrations occur at the left and right sides of the fiber. This is because the stiffnesses of the fiber and matrix material is more than 10 times stronger than that of the coating. Based on the loading direction, the coatings placed between fibers or fiber and matrix material exhibit stress concentrations.
Figure 59 Maximum principal stress at linear stage for RVE 1.
Figure 60 shows relative magnitudes of principal stresses in simple fiber/coating models subjected to transverse loading. In Figure 60(a), the fibers are placed along the loading direction. High stresses are observed in the coating regions between the fibers and between the fiber and matrix material. In Figure 60(b), the fibers are vertically aligned with the loading direction. High stresses are also observed in the coating regions between the fiber and matrix material. For the matrix phase, the stress concentrations are commonly found in the top and bottom sides of the fiber. Because the coating stiffness is lower than the matrix one, the stress concentration in the matrix phase occur at the locations corresponding to its tip based on its geometric shape.
Figure 60 Simple two-fiber models to observe stress concentration. (a) parallel case, (b) perpendicular case.
Figure 61 shows the distribution of the principal stresses in the RVE 1V model at the same strain as Figure 59. (a) represents the entire region and (b) displays the coatings only. Because the coating regions adjacent to the void do not have traction, low stresses are developed while stress concentrations occur more significantly at the sharp tips. Although the sharp tip areas of the coating layers are already damaged because the stresses exceed the strength (50 MPa), the locations of the stress concentrations do not alter greatly compared to the original RVE 1 model. From these observations, it can be confirmed that the stress concentrations at this loading step is a local phenomenon.
Figure 61 Maximum principal stress at linear stage for RVE 1V
Figure 62 compares the principal stress and damage distributions of the RVE 1 and RVE 1V models just before the slopes of their stress-strain curves begin to decrease. Commonly, damage is initiated because the stresses in the stress concentrated areas in the coating layers reach the strength before the matrix material. Especially, in the RVE 1V model, the damage of the coating layers located near the sharp tip around the void grow faster than the other coating regions. However, because the coatings carry less loading and stresses are smaller than the fiber and matrix material, the effects of the coating damage on the global stress-strain curve is not greatly noticeable.
Figure 62 Before strain-stress curve stiffness reduction, (a) maximum principal stress for RVE 1, (b) damage for RVE 1, (c) maximum principal stress for RVE 1V, (d) damage for RVE 1V.
Figure 63 compares the principal stress and damage distributions of the two RVE models just after the slopes of the stress-strain curve decrease. Commonly, in the stress concentrated area in the matrix phase, damage begins to initiate because stresses reach the strength (200 MPa). Because these regions play an important role to carry loading at the corresponding cross sections, stiffnesses are degraded upon damage initiation, resulting in the reduction of the slopes in the global stress-strain curves.
Because the stress relaxations at this time occur differently, other areas in the matrix phase reveal stress concentrations. These regions exist at the locations inter-connecting damages occurring in the coating layers. Because of this, one side of the coating damage occurred on the right and left sides of the fiber in the beginning is enhanced, and the entire crack from the top and bottom sides of the RVE model is starting to shape.
Figure 63 After strain-stress curve stiffness reduction, (a) maximum principal stress for RVE 1, (b) damage for RVE 1, (c) maximum principal stress for RVE 1V, (d) damage for RVE 1V.
Figure 64 illustrates post-peak damage growth and crack propagation behaviors with the S-S curves.
After the matrix damage is initiated at A point, as its area gradually increases and is divided into both sides, when the maximum stress is reached at B point, one of the damages on both sides evolves into a complete fracture. The reason for the damage division is probably because the damage concentration location is adjusted due to the stress relaxation occuring as the coating damages are actively connected.
After the matrix is fractured, the matrix damage is propagated to the coating layer and the complete crack starts form. For the case of the RVE 1 model, from B point to C point, while the bottom half is being fractured, the stress gradually drops in the S-S curve, and in the end, a significant load drop occurs because the middle region surrouding the fiber is fractured. Similarly, for the case of the RVE 1V model, in the same order, the matrix damage is propagated to the coating layer and the crack is formed.
However, on the contrary to the RVE 1 model, because the middle region is empty due to the void, while the bottom half is being fractured at C point, the RVE loses load-carrying capability and the significant load drop occur much earlier.
Figure 64 Damage propagation in RVE 1 and RVE 1V during crack growth.