E3 Matrix-Reinforcement Interface

Topic

In this model, the quality of the bond between the matrix and the reinforcement determines how effectively load is transferred between the two constituents; this bond quality is measured by the interfacial shear strength. According to the Kelly-Tyson model, the magnitude of this interfacial shear strength directly influences the resulting critical fiber length.

When the composite is loaded, the load is transferred from the matrix to each reinforcing fiber via shear stress acting along the interface over the fiber's embedded length; the longer the fiber section subject to this shear stress, the greater the load transferred into the fiber. Higher interfacial shear strength makes this load transfer more efficient per unit length, thereby reducing the critical fiber length required to transfer the fiber's maximum load-bearing capacity; conversely, lower interfacial shear strength necessitates a greater critical fiber length to achieve the same complete load transfer.

If a fiber's length equals or exceeds this critical length, the "long fiber" condition is met: the fiber reaches its maximum tensile strength in its central section—even before the interface fails at the ends—thereby fully transferring its share of the load. Meeting this long-fiber condition allows the fiber to function as if it were continuous in terms of composite reinforcement.

Conversely, if the fiber length is less than the critical length, the opposite occurs: the fiber lacks sufficient length to accumulate the load required to reach its maximum tensile strength via interfacial shear stress, resulting in debonding before the fiber itself fractures. The fact that this fiber is shorter than the critical length causes the bond between the fiber and the matrix to fail before the fiber itself exhausts its load-bearing capacity.

Consequently, this model—characterized by the interfacial shear strength and critical fiber length established at the outset—relates to another model in the set: the one describing the physical shear-lag mechanism that governs, in detail, that very load transfer between matrix and fiber. Because this model predicts a specific critical fiber length, a separate model within the set can verify it experimentally by comparing the average pull-out length observed on the fracture surface with that critical fiber length.

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