## 1 Introduction  
Non-crimp fabric (NCF) is constituted by a large amount of fairly straight fiber tows that are placed side by side and bounded by warp-knitting [1]. Compared with the unidirectional (UD) pre-preg composites, NCF composites have many advantages, such as lower production cost, higher out-of-plane damage tolerance and fracture toughness. Thus, it is becoming more popular in the manufacture of complex and thicker parts than UD pre-preg composites [2]. The NCF has two main types, open structure and continuous plies [3]. The fiber tows of continuous plies are laid as closely as possible to reduce the waviness of the fiber tows. However, fiber distortion still exists in the plies [4]. Mechanical properties of single lamina are the basic parameters for composites. Many theories and failure criteria are developed based on the assumptions that each lamina of the laminated composites is homogeneous and orthotropic [5]. Since each lamina in the NCF has a unique fiber direction, it can be considered as semi-laminar [6]. For the mechanical analysis of NCF composite structures, the basic mechanical properties of the semi-laminar composites should be known. To obtain the mechanical properties of each lamina of quadriaxial non-crimp fabric (QNCF) composites (the material is supplied with a layer stacking sequence (45\({}^{\circ}\)/90\({}^{\circ}\)/\(-45^{\circ}\)/0\({}^{\circ}\))) through experiment, four kinds of UD specimens need to be produced (one for each fiber direction, including the through-thickness yarn) [7]. This process is very complicated and costly, for it is not very easy to adjust the warp-knitting machine for a small batch production of these UD specimens. Alternatively, the mechanical properties of NCFcomposites can be predicted by using a multiscale analysis approach. However, a complete multiscale analysis is also very time-consuming [6]. An equivalent analysis method was proposed based on semi-laminar considerations [6; 8; 9]. In this method, the mechanical properties of NCF lamina are determined by equivalent UD composite lamina, which is multiplied with knock-down factors to take into consideration the effect of fiber waviness. The effect of fiber waviness on the mechanical properties was studied using different modeling methods in references [10; 11; 12]. The knock-down factor or stiffness reduction in the previous works mainly focused on the out-of-plane fiber waviness of opening structure NCF composites. However, the waviness of continuous plies NCF composites mainly presents in the in-plane direction of the fabrics rather than the out of plane direction. Thus, the effect of in-plane fiber waviness should be considered when evaluating the mechanical performance of this kind of NCF composites. Several researchers have studied the mechanical properties of continuous plies NCF using either experimental or multiscale modeling approach. [PERSON] et al. [13] compared the experimental results of the elastic modulus with that of classical laminate theory (CLT) predictions, and found that the effect of stitching on the stiffness of this material was not significant. However, earlier works [14; 15] claimed that the experimental measurements were about 17% lower than those obtained by the CLT. [PERSON] et al. [16] used acoustic emission (AE) registration and X-ray imaging to detect damage initiation and evolution in quadriaxial laminates under tensile load, and the numerical simulation of the failure process was also carried out. [PERSON] et al. [17] summarized the previous meso-scale model, and set up a meso-scale mechanically representative volume (mRVE), and predicted the effect of stitching on the mechanical properties of non-crimp fabric composite, such as, stiffness, failure initiation, stiffness degradation and strength. The current researches were focused on the performance of a whole continuous plies QNCF layer or laminate, but few studies has been done on the lamina mechanical properties of the materials.