Objective Tubular composites are widely used in petrochemical, construction, aerospace and other fields. The traditional processing method is winding fiber or fabric and curing after resin impregnation. Because the interlayer is only bonded by resin, it is easy to cause delamination. If the tube wall is made of three-dimensional (3-D) woven fabric, the material's ability to resist delamination would be enhanced. In order to improve the design efficiency based on normal looms, a design method and matrix model of 3-D tubular woven fabric are proposed on the basis of combining the weaving rules of tubular and 3-D woven fabrics.
Method The weaving method of 3-D tubular woven fabric is "flattening-weaving-restoring". First, the weaving process takes the fabric as a two-layer 3-D woven fabriclinked at both selvedges, and then opened up to form a tubular section after removal from the loom. The weave diagram is divided into three steps. Firstly, the face weave diagram is obtained by selecting 3-D woven fabrics such as orthogonal, angle-interlocking and stitched multi-layer as the tube wall. Secondly, the back weave diagram is obtained by method called "negative and flip". Finally, according to the method of layered weaving, the weave diagram of 3-D tubular woven fabric is determined.
Results To verify the feasibility of the proposed method, a design example on 3-D tubular woven fabric based on weft through-thickness type orthogonal weave is given (Fig. 3). Firstly, the arrangement ratio of yarn is determine, for example, face warp∶back warp=1∶1, face weft∶back weft=1∶1, then number of warp and weft in a unit of 3-D tubular woven fabric Rgj=12 and Rgw=12. Secondly, the face weave (Fig. 3(a)) is entered at the intersection of odd columns and odd rows and the back weave(Fig. 3(b)) is input at the intersection of even columns and even row. Finally, according to the method of layered weaving, the intersection of the odd columns and even rows is indicated by "⚪" (Fig. 3(c)). The example shows that the proposed method is feasible. Other examples, 3-D tubular woven fabrics using warp through-thickness type angle-interlock weave (Fig. 4) and stitched multilayer type weave (Fig. 5) can both prove the effectiveness of the proposed method
In order to speed up the design efficiency, a matrix model of 3-D tubular woven fabric is proposed. The elements "1" and "3" represent the floating point of warp and weft of face and back weave, element "0" represents the floating point of warp and weft of face and back weave, and element "5" represents the lifting point of face warp when weaving back weft. Replace the elements of the face weave matrix and adjust the order of the columns of the matrix through the MatLab function to obtain the back weave matrix, then the Kronecker product operation is used to realize the proportional embedding of the face weave matrix in the back weave matrix and the assignment of the lifting point elements in the face warp, so as to obtain the matrix of 3-D tubular woven fabric.
In order to prove the effectiveness of the proposed matrix model, the following example is given (Fig. 6). Firstly, matrix B (face weave) with 6 rows and 6 columns. The element "0" is replaced by "3" through the find function of the MatLab program, and then the element "1" is replaced by "0" to complete the "negative" effect. Secondly,the fliplr function of the MatLab program is used to realize the left and right order adjustment of the matrix columns to complete the "flip" effect, and the matrix L (back weave) of 6 rows and 6 columns can be obtained. Thirdly, to generate a matrix C with 6 rows and 6 columns, to set elements are all "5", then matrix K1, K2, K3. Finally, according to Equation (1), through the Kronecker product operation of the matrix, the matrix W of 3-D tubular woven fabric can be obtained.
According to the plotting functions of the MatLab program, different matrix elements print different symbols, such as the elements "1", "3", "5", and "0" are printed "■", "×", "⚪", "□" respectively, which can realize the automatic drawing of the weave diagram.
Conclusion The design method on weave diagram of 3-D tubular fabric is proposed. Firstly, the 3-D woven fabric is selected as the face weave. Secondly, the back weave is obtained according to the "negative and flip" method. Finally, according to the layered weaving method, the weave diagram of 3-D tubular woven fabric can be constructed. The matrix model of 3-D tubular woven fabric weave is established, which uses different matrix elements to represent the floating point of warp and weft of face and back weave, lifting point of face warp when weaving back weft. Matlab function is used to realize the matrix generation of 3-D tubular woven fabric, that is, through element replacement, sequence adjustment of matrix to realize "negative and flip", matrix Kronecker product operation, and automatic drawing of weave diagram.