J. Shi, C. Kumar/ Materials Science and Engineering 4250(1998)194-208 Table I Details of finite element unit cell models Smooth interface Three wave interface Ten wave interface 30 wave interface ber of elements 1382 4142 ber of nodes 1524 30wave long -O owave rad ◇…10 wave rad 。-3 wave rad 0.8 Strain(%) Fig. 3. Effect of interface roughness(0.I um) on stress-strain curves. number of elements in the model is decided by the The fibre is constrained radially at the left hand number of points required to represent a sine wave vertical side and axially at the bottom side, whereas the ccurately. To save computer time and memory matrix is constrained at the bottom axially but at the each full sine wave has the minimum number of nine right hand vertical side it is constrained in such a way nodes. Consequently there are four finite element mod- that it remains vertical sponding to the straight interface, three, ten and Exactly the same thermal and mechanical loads and 30 wave interface models(see Fig. 2). The sizes of these models are indicated in Table 1. The three wave and boundary conditions were applied as in Ref [5].After an initial thermal step, representing the cooling down from large roughness model represents fibres of long wave- manufacturing temperature, the unit cell is loaded in the length and high undulations, while the 30 wave and fibre direction. It is then unloaded and loaded again. At small undulation model mimics fibres of short wave- the top surface of the fibre, pressure is applied.The length and small undulations, as reported in Ref. [3] To avoid the confusion caused by round-off errors in magnitude (1.57 X 10-3 N um-2) is equivalent to a deciding overclosure, an artificial gap of 0.00015 um composite remote stress of 550 MPa. The temperature between the fibre and the matrix is introduced in the drops from I000° to room temperature(20°Cto finite element model. The artificial gap is so small that simulate the thermal residual stress induced in manu- it does not affect the results. A surface to surface finite facturing. The higher thermal expansion coefficient sliding option in ABAQUS is invoked, and friction is of the matrix leads to a clamping pressure at the described by the classical Coulomb law interface196 J. Shi, C. Kumar / Materials Science and Engineering A250 (1998) 194–208 Table 1 Details of finite element unit cell models Smooth interface Three wave interface Ten wave interface 30 wave interface Number of elements 1382 462 462 4142 Number of nodes 524 524 1524 4526 Fig. 3. Effect of interface roughness (0.1 mm) on stress–strain curves. number of elements in the model is decided by the number of points required to represent a sine wave accurately. To save computer time and memory size, each full sine wave has the minimum number of nine nodes. Consequently there are four finite element mod￾els, corresponding to the straight interface, three, ten and 30 wave interface models (see Fig. 2). The sizes of these models are indicated in Table 1. The three wave and large roughness model represents fibres of long wave￾length and high undulations, while the 30 wave and small undulation model mimics fibres of short wave￾length and small undulations, as reported in Ref. [3]. To avoid the confusion caused by round-off errors in deciding overclosure, an artificial gap of 0.00015 mm between the fibre and the matrix is introduced in the finite element model. The artificial gap is so small that it does not affect the results. A surface to surface finite sliding option in ABAQUS is invoked, and friction is described by the classical Coulomb law. The fibre is constrained radially at the left hand vertical side and axially at the bottom side, whereas the matrix is constrained at the bottom axially but at the right hand vertical side it is constrained in such a way that it remains vertical. Exactly the same thermal and mechanical loads and boundary conditions were applied as in Ref. [5]. After an initial thermal step, representing the cooling down from manufacturing temperature, the unit cell is loaded in the fibre direction. It is then unloaded and loaded again. At the top surface of the fibre, pressure is applied. The magnitude (1.57×10−3 N mm−2 ) is equivalent to a composite remote stress of 550 MPa. The temperature drops from 1000°C to room temperature (20°C) to simulate the thermal residual stress induced in manu￾facturing. The higher thermal expansion coefficient of the matrix leads to a clamping pressure at the interface