J Shi, C. Kumar/ Materials Science and Engineering 4250(1998)194-208 U2 rough interface(0.1) --U2 smaller interface(0.01) -x-U2 straight interface -*-U1 rough interface(0. 1) HU1 smaller interface (0.01) ▲U1 straight interface strain(%) Fig 8. The effect of surface roughness magnitude on stress-strain curve the matrix is possible and more material is thus due to the large pulling force applied on the fibre stressed. It can be envisaged that as the surface which made a larger part of the fibre to slide. In the oughness approaches zero, the rough interface results middle part of the fibre the smaller roughness model should approach those of the smooth interface model. gives a higher pressure, whereas for the bottom end moreover, when the surface roughness is reduced, it the two models give the same interface pressure should be easier for the matrix and the fibre to slide When the fibre is unloaded in the third step, much relative to each other. However, any surface rough- of the interface pressure created in the second step is ness significantly smaller than 0.01 um seems to be 'locked-in, even though the external loading becomes not meaningful in practice [3]. Hence no further simu- zero. This is typical for a frictional contact problem lation is performed as illustrated in Fig. 10. The reverse sliding during The interface pressure and shear for the 30 wave unloading is smaller than the forward sliding during model at the end of steps 1, 2 and 3, are given in loading, which has actually resulted in the permanent Fig 9. At the end of the first thermal step, the inter- strain and the hystersis in the stress-strain curve. Be- face pressure is higher for the smaller roughness cause of the smaller reverse sliding and the surface model, as it has a smaller slope. In consequence, the roughness, the matrix remains displaced radially after resistance to sliding resulting from the pressure unloading, and hence the large interface pressure. The smaller. In other words, a larger normal pressure can interface shear plot(Fig. 9f) shows that while the top be tolerated. Despite the fairly uniform pressure dis- 25% of the fibre tends to slide back into the matrix, tortion, the shear stress is concentrated at the matrix the remaining 75% still tries to slide in the opposite crack end. In both cases, about 20% of fibre(matrix) direction. This suggests that the majority of the slid has reached sliding stage, while the rest remains ing damage occurs in this small zone. As the axial ticking state. In the latter part, the shear stresses in loading is zero, it can be seen that the shear stresses both the fibre and the matrix are nearly the same (area under the curve)in the two parts balance each At the end of the second step, in which a mechani- other. Again, the larger roughness model predicts cal load is applied on the fibre to pull it through a higher interface pressure. As shown in [10] the matrix, the interface pressure is higher for the bigger interface shear strongly influences the roughness model at the matrix end. This is mainly timate tensile strength. It can be envisaged thatJ. Shi, C. Kumar / Materials Science and Engineering A250 (1998) 194–208 201 Fig. 8. The effect of surface roughness magnitude on stress–strain curve. the matrix is possible and more material is thus stressed. It can be envisaged that as the surface roughness approaches zero, the rough interface results should approach those of the smooth interface model. Moreover, when the surface roughness is reduced, it should be easier for the matrix and the fibre to slide relative to each other. However, any surface rough￾ness significantly smaller than 0.01 mm seems to be not meaningful in practice [3]. Hence no further simu￾lation is performed. The interface pressure and shear for the 30 wave model at the end of steps 1, 2 and 3, are given in Fig. 9. At the end of the first thermal step, the inter￾face pressure is higher for the smaller roughness model, as it has a smaller slope. In consequence, the resistance to sliding resulting from the pressure is smaller. In other words, a larger normal pressure can be tolerated. Despite the fairly uniform pressure dis￾tortion, the shear stress is concentrated at the matrix crack end. In both cases, about 20% of fibre (matrix) has reached sliding stage, while the rest remains in sticking state. In the latter part, the shear stresses in both the fibre and the matrix are nearly the same. At the end of the second step, in which a mechani￾cal load is applied on the fibre to pull it through the matrix, the interface pressure is higher for the bigger roughness model at the matrix end. This is mainly due to the large pulling force applied on the fibre which made a larger part of the fibre to slide. In the middle part of the fibre the smaller roughness model gives a higher pressure, whereas for the bottom end the two models give the same interface pressure. When the fibre is unloaded in the third step, much of the interface pressure created in the second step is ‘locked-in’, even though the external loading becomes zero. This is typical for a frictional contact problem as illustrated in Fig. 10. The reverse sliding during unloading is smaller than the forward sliding during loading, which has actually resulted in the permanent strain and the hystersis in the stress–strain curve. Be￾cause of the smaller reverse sliding and the surface roughness, the matrix remains displaced radially after unloading, and hence the large interface pressure. The interface shear plot (Fig. 9f) shows that while the top 25% of the fibre tends to slide back into the matrix, the remaining 75% still tries to slide in the opposite direction. This suggests that the majority of the slid￾ing damage occurs in this small zone. As the axial loading is zero, it can be seen that the shear stresses (area under the curve) in the two parts balance each other. Again, the larger roughness model predicts a higher interface pressure. As shown in [10] the interface shear strongly influences the ul￾timate tensile strength. It can be envisaged that