Matrix shear strength

But it does not usually do this. We have already seen that, if the length of the fibres is less than 2x, they will not fracture. And if they do not fracture they must instead pull out as the crack opens (Fig. 25.6). This gives a major new contribution to the toughness. If the matrix shear strength is tr (as before), then the work done in pulling a fibre out of the fracture surface is given approximately by... 

Transverse compressive strength of the lamina Shear strength of the lamina Tensile strength of fibres TensUe/compressive strength of matrix Shear strength of matrix... 

A composite material for a car-repair kit consists of a random mixture of short glass fibres in a polyester matrix. Estimate the maximum toughness of the composite. You may assume that the volume fraction of glass is 30% the fibre diameter is 15 pm the fracture strength of the fibres is 1400 MPa and the shear strength of the matrix is 30 MPa. 

Fig. 2. Results of interfacial shear strength measurements of the same fiber/matrix systems using four different micro-mechanical tests during a round-robin program involving 12 different laboratories, (a) Results for untreated, unsized carbon fibers, (b) Results for carbon fibers with the standard level of surface treatment. Redrawn from ref. [13].

Assuming the work of adhesion to be measurable, one must next ask if it can be related to practical adhesion. If so, it may be a useful predictor of adhesion. The prospect at first looks bleak. The perfect disjoining of phases contemplated by Eq. 1 almost never occurs, and it takes no account of the existence of an interphase , as discussed earlier. Nonetheless, modeling the complex real interphase as a true mathematical interface has led to quantitative relationships between mechanical quantities and the work of adhesion. For example, Cox [22] suggested a linear relationship between Wa and the interfacial shear strength, r, in a fiber-matrix composite as follows ... 

Fig. 19. Inlerfacial shear strengths of various fiber/matrix composites as a function of the work of adhesion as determined by IGC. 1, glass fiber-poly (ethylene) 2, carbon fiber-epoxy B 3, carbon fiber-epoxy A and 4, carbon fiber-PEEK. Redrawn from ref. [102].

Flexibilized epoxy resins are important structural adhesives [69]. Liquid functionally terminated nitrile rubbers are excellent flexibilizing agents for epoxy resins. This liquid nitrile rubber can be reacted into the epoxy matrix if it contains carboxylated terminated functionalities or by adding an amine terminated rubber. The main effects produced by addition of liquid nitrile rubber in epoxy formulations is the increase in T-peel strength and in low-temperature lap shear strength, without reducing the elevated temperature lap shear. 

If the matrix in 3.7 was reinforced with the same volume fraction of glass but in the form of randomly oriented glass fibres rather than continuous filaments, what would be the tensile strength of the composite. The fibres are 15 mm long, have an aspect ratio of 1000 and produce a reinforcement efficiency of 0.25. The fibre strength is 2 GN/m and the shear strength of the interface is 4 MN/m". 

Aside from type of claim (fiber dominant or interfacet matrix dominant), the efficiency of surface treatments depends noticeably on the fiber content within the composite. At a fiber content of 30 vol%, tensile strength increases by 10% and shear strength increases by about 100% (Fig. 12). In contrast to modified fibers where shear strength rises with increasing fiber content, the chart, after having reached a maximum, shows a... 

Sf = tensile stress at the fiber, and T = fiber-matrix interfacial shear strength. 

In the push out test [93], the fiber is pushed into the matrix rather than being pulled out. The test allows the measurement of two quantities, Fdcb (the force at which debonding occurs) and F/., (the force needed to push the fiber through the matrix sample if it is thin enough). The bond shear strength Tdeb is calculated using the shear lag theory ... 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

In other words, the critical fiber length is a function of its strength, diameter and the shear strength at the filler-matrix interface. 

As fibers are crushed in the composite, their strength increases. So long as the fibers interact with each other they can stand a load. When, however, the fiber length becomes so small that the shear stresses between the fiber and the matrix become about as low as the shear strength at the interphase the crushing process will stop and fiber fragments will be pulled out of the matrix. 

Equations were obtained in [150] relating alim and the critical length with fiber diameter, adhesion to the matrix (expressed in terms of shear strength) and Weihull distribution parameters ... 

Fig. 18 The strength shear strength r0 for debonding of the chain from the surrounding matrix consisting of secondary bonds... 

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