J Shi, C. Kumar/ Materials Science and Engineering 4250(1998)194-208 phenomenon observed in these tests is the load drop in P=157E03N/山m re-seating due to the surface roughness [3, 4 To account for the 3d stress field and to include the frictional effect. finite element models have been devel- ped (see e.g. [5-7D). In particular, a unit cell corre 0.00015m sponding to a unidirectional CMC, with a fully bridged matrix crack and complete matrix-fibre debonding was studied in great detail by Sorensen [5]. A deep FibreMatrix insight was gained into the load transfer between the Fibre E=0.20N/um2 fibre and the matrix. The finite element study [5] was =0.35 based on a smooth fibre-matrix interface. whereas the a=3.0E06/C interface roughness was investigated analytically in [8]. 1267r and it was shown that interface roughness affects the Matrix E=0.098 N/um overall response of CMCs. The analytical solution pro- v=0.3 a=50E06C vides useful qualitative information of the surface roughness effects. However, a quantitative knowledge of these effects is clearly desirable In these investigations only the surface roughness amplitude at most is considered, while surface shape is ignored. Furthermore uniform sliding of the interface has been assumed in analytical models to simplify the analysis. In this paper, the surface roughness is approx 5gm516985μm imated by sinusoidal waves and accounted for explicitly Fig. l. Unit cell model of the composite with fully cracked matrix and by direct finite element modelling. (With the limit of interface memory size and speed for todays computers, unlikely to simulate a true or measured interface com pletely and successfully. The global response, interfa- unit cell is worked out from the volume fraction ratio cial shear and pressure as well as local stress states, of 0.35. The length of the model is 80 um, which hich are not available from an analytical solution, will be examined in detail probably agrees well with the saturated matrix crack spacing. Only fully cracked matrix and interface are modelled and the fibre is assumed to remain intact This suggests that the composite behaviour beyond 2. The unit cell model and its finite element proportional limit, but below ultimate tensile strength is representation studied The general finite element analysis package In this paper, a unit cell(Fig. 1)similar to that of ABAQUS was chosen for its contact modelling Sorensen [5] was used, the only difference being that the capability. Four-noded axisymmetric element was used interface consists of sine waves. to simulate the surface to model the unit cell, as the eight node element gave roughness. The unit cell is made of two concentric strong stress oscillation and hence was not used. The cylinders: the inner one corresponds to the fibre, while he outer one corresponds to the matrix. No attempt has been made to model the interface layer, which is so thin that it does not make any contribution to the composite stiffness, particularly when the interface fully debonded In the present study, the interface is made of three, ten and 30 sine waves the magnitude of which is 0. 1 or 0.01 um. In reality, the surface roughness depends on the manufacturing process and can vary a great deal [3] Further. the in situ interface morphology compared with as fabricated fibre. The surface roughness causes uneven pressure and friction istribution which leads to differential wear and reduc Fig. 2. Finite element model of the unit Tor different types of tion of asperity along the interface. But neither of these interfaces: (a)straight interface: (b)three sine waves: (c) ten sine complications are consideredJ. Shi, C. Kumar / Materials Science and Engineering A250 (1998) 194–208 195 phenomenon observed in these tests is the load drop in re-seating due to the surface roughness [3,4]. To account for the 3D stress field and to include the frictional effect, finite element models have been devel￾oped (see e.g. [5–7]). In particular, a unit cell corre￾sponding to a unidirectional CMC, with a fully bridged matrix crack and complete matrix–fibre debonding, was studied in great detail by Sørensen [5]. A deep insight was gained into the load transfer between the fibre and the matrix. The finite element study [5] was based on a smooth fibre–matrix interface, whereas the interface roughness was investigated analytically in [8], and it was shown that interface roughness affects the overall response of CMCs. The analytical solution pro￾vides useful qualitative information of the surface roughness effects. However, a quantitative knowledge of these effects is clearly desirable. In these investigations only the surface roughness amplitude at most is considered, while surface shape is ignored. Furthermore uniform sliding of the interface has been assumed in analytical models to simplify the analysis. In this paper, the surface roughness is approx￾imated by sinusoidal waves and accounted for explicitly by direct finite element modelling. (With the limit of memory size and speed for today’s computers, it is unlikely to simulate a true or measured interface com￾pletely and successfully.) The global response, interfa￾cial shear and pressure as well as local stress states, which are not available from an analytical solution, will be examined in detail. 2. The unit cell model and its finite element representation In this paper, a unit cell (Fig. 1) similar to that of Sørensen [5] was used, the only difference being that the interface consists of sine waves, to simulate the surface roughness. The unit cell is made of two concentric cylinders: the inner one corresponds to the fibre, while the outer one corresponds to the matrix. No attempt has been made to model the interface layer, which is so thin that it does not make any contribution to the composite stiffness, particularly when the interface is fully debonded. In the present study, the interface is made of three, ten and 30 sine waves, the magnitude of which is 0.1 or 0.01 mm. In reality, the surface roughness depends on the manufacturing process and can vary a great deal [3]. Further, the in situ interface may have a different morphology compared with as fabricated fibre. The surface roughness causes uneven pressure and friction distribution, which leads to differential wear and reduc￾tion of asperity along the interface. But neither of these complications are considered. Fig. 1. Unit cell model of the composite with fully cracked matrix and interface. The fibre diameter is 15 mm, while the diameter of the unit cell is worked out from the volume fraction ratio of 0.35. The length of the model is 80 mm, which probably agrees well with the saturated matrix crack spacing. Only fully cracked matrix and interface are modelled and the fibre is assumed to remain intact. This suggests that the composite behaviour beyond proportional limit, but below ultimate tensile strength is studied. The general finite element stress analysis package ABAQUS was chosen for its good contact modelling capability. Four-noded axisymmetric element was used to model the unit cell, as the eight node element gave strong stress oscillation and hence was not used. The Fig. 2. Finite element model of the unit cell for different types of interfaces: (a) straight interface; (b) three sine waves; (c) ten sine waves; (d) 30 sine waves