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Proposal of New Criteria for Celestial Mechanics. Date: November 11, Date: June 27, Jeffrey M. McKenzie, Donald I. Siegel, Laura K. Lautz, Martin H. Otz, James Hassett, Ines Otz. Date: January 5, Why Us? The specific interface microstructure will exhibit different physical and chemical properties, such as wettability, chemical bond, and van der Waals force; thus the interface bond strength is changed to improve the performance of interfacial load transfer.
At present, the fiber surface modification can be used to get appropriately bonded interface, but the physicochemical mechanisms that are how to affect the interfacial micromechanical properties as well as how to control the interfacial stress transfer have been concerned. Although a variety of interface theories in fibrous composites have been proposed, such as wettability theory, chemical bond theory, and friction theory, there is no perfect theory to explain all phenomena of interface [ 2 ].
If the interface strength of fibrous composites is too low, the fiber is easy to debond, pullout, break, and fail. On the contrary, if the interface strength is very high, the stress between the fiber and matrix cannot be relaxed and the brittle fracture would occur at the interface. Therefore, the interface design can be optimized by considering the best comprehensive mechanical properties.
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The interfacial mechanical properties and geometrical parameters are regarded as design variables, and then certain optimization method such as genetic algorithm combines with the finite element analysis to find the best design variables. This is the fast optimization path of interface mechanical performance in fibrous composites.
However, the design variables of composite interface microstructure are not continuous so that the derivative-type optimization method will fail in the case. It is also noted that the uncertainty of initial value limits the capacity of optimization method converging to the global optimum. In addition, the existing mechanical models are imperfect to describe the micromechanical behavior of the composite interface.
The mechanical properties of interface layer, residual stress, and stress singularity are the difficulties to constrain the numerical computation [ 12 , 13 ]. At present, a lot of works are still to seek the appropriate computing optimization methods to solve such problems. It is inevitable and reasonable way for the computation optimization to perfectly combine with the interface evaluation tests, fine interface characterization techniques, and interface mechanical models.
The macroscopic damage and failure criteria for fibrous composites do not consider the micromechanical properties of interface, such as fiber stress distribution, stress concentration, shear strength, and frictional shear stress on the debonding interface. In addition, there is still lack of a common understanding about the influence of interfacial microstructural parameters and physicochemical properties on the interface micromechanical properties.
Currently, the research on microscale experimental mechanics characterization of the interface failure is not only the most difficult and crucial problem but also the important content of interface mechanical evaluation in fibrous composites, as shown in Figure 3. Evaluation tests and characterization methods for micromechanical properties of interface.
The important parameter can be obtained by single fiber micromechanical testing experiments. One kind of these experiments is realized by applying the external load to single fiber, such as fiber pullout test [ 15 ], microbond test [ 21 ], microdroplet tension test [ 14 , 22 ], and fiber push-out test [ 23 ].
The other is finished by applying the external load to the resin matrix, such as fiber fragmentation test [ 12 , 13 ] and Broutman test [ 24 ]. During the implementation and application of these interface evaluation tests for the characterization of micromechanical properties, it is difficult to ensure the integrity, repeatability, and consistency of the interface evaluation. The experimental results of fiber pullout test, fiber fragmentation test, and fiber push-out test vary widely at the same external conditions. Even using the same test method, the experimental results among different laboratories still have differences [ 25 ].
Further studies suggest that this difference comes from the stress singularity at the fiber end [ 26 ], so the reevaluation of these test methods and the development of new, more appropriate test methods are concerned [ 27 ].
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However, the deeper reason is that the differences of many conditions i. The testing specimens employed in the different interface evaluation methods have different geometric parameters, such as the droplet contact angle and the embedded fiber length in the microdroplets tension test. Even with the same specimen preparation procedure, it is difficult to ensure that all samples have a uniform geometry and dimension size, which affects the repeatability and consistency of the interface micromechanical parameters characterized by the interface evaluation test.
The latest research of microdroplet tension test shows that the microdroplet conformations with different contact angles affect the interfacial shear stress distribution and stress transfer efficiency [ 28 ]. By optimizing the design of interface geometry to reduce or even eliminate the stress singularity, the mechanical behavior of fibrous composites can be upgraded [ 29 ]. Therefore, the further research on the interface geometry and physicochemical properties affecting the interfacial stress transfer behavior will benefit to optimize the interfacial stress distribution and reduce the stress concentrations.
Commonly, the interfacial shear strength obtained by the interface evaluation tests is used as an important characteristic parameter in the interface failure models and is an average value for characterizing the interface bonding properties. It cannot completely describe the details of the interfacial stress transfer and interfacial debonding failure processes. However, most studies are lacking in the integrity of mechanical description for the procedures of the interfacial stress transfer and interfacial debonding failure. A very important reason is the lack of suitable microscale stress-strain measurement techniques and full-field observation means.
The testing methods having the ability to carry out the microscale fine characterization, including MRS and digital photoelasticity, digital image correlation, and speckle interferometry. These methods are most likely the first application to completely characterize the micromechanical properties of fiber reinforced composites. When the fiber is under deformation, it causes the movement and deformation of Raman spectrum [ 14 , 15 ], as shown in Figure 4 a. Raman shift has a linear relationship with the strain or stress of aramid fibers [ 15 ], as shown in Figure 4 b. Therefore, it is a potential method of microscale experimental mechanics, and it has recently been used to study the interfacial micromechanical behaviors in fibrous composites, such as fiber stress distribution, stress concentration, and interface integrity.
The interfacial stress transfer behavior between the fiber and matrix in fibrous composites is a major mechanical problem including several successive stages: the interface intact bonding, interface debonding, interface completely debonding, and fiber pullout.
The elastic stress transfer in bonding area and the frictional shear stress transfer in debonded area have been widely recognized. In the process of interfacial debonding and extension, the interface mechanical parameters of bonding shear stress, debonding friction shear stress, and interface debonding length continuously evolve, and the macropulling force or stress is also changed accordingly. At present, the main interface mechanics problems in fibrous composites discussed are as follows: the elastic stress transfer, partial debonding stress transfer, interface failure criterion and fiber bridging, and so on.
One end of single fiber embeds in epoxy matrix, as shown in Figure 5 , an axis tension load pulls the fiber out from the matrix. Single fiber pullout specimen [ 15 ]. The stress distribution along the embedded fiber cannot be obtained by the above equation, so it cannot be used to study the stress transfer between the fiber and matrix.
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It satisfies the relationship as. Piggott's model [ 32 ] is further used to describe the fiber axial stress along the embedded fiber within the elastic stress transfer, so the fiber elastic stress distribution before the interface debonding is written as. Figure 6 a shows the fiber axial stress distribution under different strain levels in fiber pullout test. In the current 1. The interfacial shear stress ISS along the embedded fiber is further given from 2 and 3 as.
Herakovich Mechanics of Fibrous Composites
As shown in Figure 6 b , the ISS distribution increased with the strain levels. The ISS of fiber out of the matrix was zero and reached the maximum at the fiber entry. In the fiber pullout experiment, the aspect ratio n of the embedded fiber is large. This is because the debonding segments of OA and AB exhibit different interface microstructures resulting in unequal shear friction effect.
The interface frictional shear stress accords with the linear distribution assumption on the debonding segments the solid lines in Figure 7 a. Using the simple Cox's shear-lag model, the frictional stress transfer in the debonding interface can be easily analyzed. Assuming a linear distribution of the interfacial friction stress, a two-stage model of the interfacial friction shown in Figure 7 b gives the fiber stress distributions on the debonding interface as. Piggott's model can be used to describe the fiber axial stress at the intact bonding interface Segment BC in Figure 7.
The interface frictional shear stresses on the debonding segments are given by the combination of 2 and 7 as. It can be seen that the frictional shear stress plays the role of stress transfer on the debonding interface and can be described as the multistage constant distribution in this study.
If the load continues to be applied, the interface debonding failure propagates forward. As shown in Figure 8 , when a matrix crack vertically propagated across an embedded fiber without fiber breakage, the bridging fiber with partial debonding was across both sides of the matrix crack.
The formation of bridging fiber can be regarded as two fibers pullout process. The bridging fiber contains three parts: the bonding segment, debonding segment, and bridging segment. The fiber axial stress meets Piggott's model in the bonding segment. It is affected by linear friction shear stress in the debonding segment and remains a constant in the bridging segment. In the following text, the interfacial stress transfer and failure conditions of the bridging fiber are considered to be reloading. Bridging fiber and interfacial debonding during crack opening [ 16 ].
For the case of unloading after the formation of bridging fiber, a reverse slip will occur on the debonding segment and the fiber retraction results in residual interfacial friction stress, as shown in Figure 9 a. When the bridging fiber is reloaded, the partial slip on the debonding segment inverses its sliding direction.
This will cause the different effects of interface friction force on the debonding segment, as shown in Figures 9 b and 9 c. Slip transform for bridging fiber after reloading [ 16 ]. The reverse slip happens on the fiber debonding segment before reloading Figure 9 a , generating the interfacial friction in the opposite direction and resulting in compressive residual stress in the debonding segment. When the load is applied again Figure 9 b , the partial reverse slip on the debonding segment transforms to the forward slip resulting in the reduction of reverse slip length until all reverse slip completely converses to the forward slip Figure 9 c.
The interfacial friction in the forward slip region makes the increase of fiber stress; on the contrary, the reverse slip results in the decrease of fiber stress.