Stability Of Warp Knitted Fabrics With The Structure Of Steiner Minimal Tree

In recent years, due to the continual conflicts, warfare and terrorist incidents in various regions of the world, the development and research of the protective materials, such as stab-resistant, bullet-proof and explosion-proof materials, are becoming highly valued. With the good physical and chemical properties, the composite material with textile structure has higher specific strength, specific modulus, aseismicity and shock-absorbent performance than those of the metal materials. What’s more, it is a good momentum absorber without second killing effect. Theory and practice have proved that it is a kind of composite materials with excellent and ideal maintenance.The mechanical properties of composite material with textile structure depend upon not only its material, but also its structure. The knitted fabric has been gradually used as the reinforcement of the composite material with textile structure because of its unique loop structure as well as good energy absorption and out-of-plane mechanical properties. However, the mesh and the loop are inseparable. All kinds of loop structures of the knit fabric have formed a variety of mesh shapes, such as triangles, quadrilateral, hexagon, rotundity, etc. At present, there are few deep researches on the mesh geometry structure of knitted fabrics. This thesis, based on the previous researches, has established the mesh topology structure of the warp knitted fabric and analyzed the stability and economy of this structure. To further investigate the protective property of the fabric with this topological structure, this thesis has mainly studied the warp knitted fabric with quadrilateral and hexagonal meshes.According to their characteristics of quadrilateral and hexagonal meshes of the warp knitted fabric, in this thesis, we have introduced grid and Steiner minimal tree topology structure. For any n given points, by the definition of Steiner minimal tree in graph theory, it is the minimal network. The thesis has applied geometrical inference to the warp knit fabrics with grid and Steiner minimal tree topology structure respectively and come to the following conclusion:when two kinds of fabrics are made of the same material, the fabrics with Steiner minimal tree structure can use the least materials. To compare the mechanical properties of the warp knit fabrics with quadrilateral and hexagonal meshes, this thesis, based on the theory of mechanics of materials, has made an mechanical analysis on the smallest unit of topology structure of this two kinds of fabrics, and drawn this conclusion:Steiner minimal tree topology structure has the better stability. That is, the fabric with Steiner minimal tree topology structure is not vulnerable to be disrupted by an external force.After the quasi-static mechanical analysis of the warp knit fabrics with grid and Steiner minimal tree topology structure, this thesis has made systematically tongue tearing tests in weft or warp direction or in local weft or warp direction, and bursting strength of the two kinds of fabrics respectively. Tearing test results showed that tear direction and partial damage to fabrics make very little difference to the tear property of the warp knit fabrics with Steiner minimal tree topology structure; on the contrary, they have much effect on that of the fabrics with grid topology structure. This test result verified that the Steiner minimal tree topology structure has better stability and fabrics with this structure have stronger mechanical properties from the perspective of dynamical mechanics. In order to simulate the multi-direction load situation of fabrics, this thesis has made a bursting strength test to the knit fabrics with Steiner minimal tree topology structure. The result showed that this kind of fabrics has excellent mechanical properties. In addition, in the course of the tearing and bursting experiment of fabrics, we arrived at a very interesting conclusion:with the size decreasing of the units of Steiner minimal tree topology structure, the mechanical properties are increasing gradually.Owing to the randomness and quantification of the experiments, this thesis tries to get the mechanical model that can generally describe the stability of fabrics with Steiner minimal tree topology structure. Thereupon, this thesis has established the tearing and bursting strength model of the warp knit fabrics with Steiner minimal tree topology structure with parameters obtained from the mechanical property experiment and by the method of dimensional analysis. The tear model is AL=k·r·(π1)α(π2)β where AL is the elongation of fabrics when the first Steiner minimal tree structure cell is destructed, r is the radius of yarns, π1=d/r, and π2=F/E·r2, d is the diameter of inscribed circle of the mesh, E is the elastic modulus of yarns, F is the tearing strength. From the tear model, we can obtain two main parameters determining the tear property of fabrics: geometric parameter π1and mechanical parameter n2. According to these two parameters and their index, we can estimate the tearing property of fabrics. After dimensional analyzing for the tongue tearing test in weft and warp direction and in local weft or warp direction of fabrics with Steiner minimal tree topology structure, we found that to the fabrics with the same size of the minimum structure unit, the gap between the value of αweft,αlocal weft and the value of αwarp,αlocal warp is small, and the value of βweft, βlocal weft agree well with the value of βwarp, βlocal warp; to the fabrics with different size of the minimum structure unit, their tear property is increasing with the decreasing of the size of the minimum structure unit. Therefore, the difference of the tearing forms can not affect the tear property of fabrics. That is, the tear direction of and the local damage to the fabrics have no influence to the overall performance of fabrics. The bursting strength model is F=k·Er2(△L/r)α(d/r)β,in which E is the elastic modulus of yarns, r is the radius of yarns, α and β are undetermined index respectively, AL is the elongation of fabric, d is the diameter of inscribed circle of the mesh. In accordance with the data from the bursting test of fabrics with Steiner minimal tree topology structure, we got α=5.16, β=-1.02. The result shows that the bursting strength of fabrics is increasing with the reduction of the size of Steiner minimal tree topology structure. Through the dimensional analysis on the tearing and bursting process of fabrics with Steiner minimal tree topology structure, we verified that the Steiner minimal tree topology structure is much stable in theory.According to previous researches, we know that Steiner minimal tree is the geometrical foundation of carbon nano-tube which not only has stable structure but also plays an important role in the bullet-proof and explosion-proof areas. Nevertheless, because the preparation of carbon nano-tube fibers is difficult, the carbon nano-tube fibers are so expensive that it is not easy to be popularized in the area of protection. Relatively speaking, the price of the warp knit fabrics is very low. Based on the research of this thesis, Steiner minimal tree is also the geometrical foundation of knit fabrics with hexagonal meshes. From the mechanical research of the warp knit fabrics with Steiner minimal tree topology structure, it is feasible to use this fabric as the wild phase in the composite materials with explosion-proof fabric structure. This thesis, after illustrating the explosion-proof principle of fabrics, optimized the design of the microstructure of explosion-proof fabrics by applying the friction self-locking principle in addition to the stability of Steiner minimal tree topology structure, and put forward the rotatable and hierarchical structure of Steiner minimal tree. Because the mechanical properties of fabrics with Steiner minimal tree topology structure are increasing with the size of the units decreasing, the microstructure of explosion-proof fabrics can be designed as hierarchical and rotatable Steiner minimal tree topology structure in nano/micro scale. The fabric with hierarchical and rotatable Steiner minimal tree topology structure has excellent properties of stab-resistant, bullet-proof and explosion-proof, the minimal cascade in the hierarchical structure can reach as small as nano/micro scale, it can self heal when destroyed, and local destruction or local instability will not affect its whole stability much.The research of this thesis contributes to the understanding of the topology structure of warp knit fabrics and in the meanwhile it has extremely important theoretical value and realistic significance to design and manufacture the fabrics with Steiner minimal tree topology structure and its transmutations to be used for protective fabrics, especially for the production of explosion-proof equipments.