Abstract
Three micromechanical teat methods to measure the interface shear strength in polymer matrix composites are reviewed. The classical pull-out test and the newer push-in test both offer specific advantages, but the actually used analysis schemes are shown to be often too elementary. We present a more complete micromechanical analysis of a third experiment, namely the fragmentation test. It is shown theoretically that, for increasing applied strains, the fibre aspect ratio can reach values which are lower than those predicted by Kelly’s shear-lag model. A method is proposed to estimate the different components of the interface shear strength, i.e. the bond shear strength, the friction strength and the matrix yield strength.
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Abbreviations
- D:
-
fibre diameter (m)
- Ef :
-
fibre Young’s modulus (MPa)
- Em :
-
matrix Young’s modulus (MPa)
- Fdeb :
-
force needed to provoke debonding a t the interface (N)
- Fpo :
-
maximum load applied to the fibre to pull the fibre out of the matrix (N)
- Fpi :
-
maximum load necessary to de bond the fibre completely in the push-in test (N)
- Ffr :
-
maximum load necessary to break the fibre (N)
- Gm :
-
matrix shear modulus (MPa)
- L:
-
fibre length (m)
- Lc :
-
critical fibre length (m)
- m:
-
dimensionless length of the fibre inelastic zone
- n:
-
elastic constant
- r:
-
fibre radius (m)
- s:
-
fibre aspect ratio (LID)
- sc :
-
critical fibre aspect ratio
- T:
-
thickness of the specimen (m)
- Vf :
-
fibre volume fraction
- x:
-
coordinate along the fibre axis
- α:
-
elastic constant, function of the fibre and matrix elastic properties
- ∈1 :
-
strain applied at the specimen (in the fibre direction)
- ∈mr :
-
fracture strain of the matrix
- ∈fr :
-
fracture strain of the fibre
- σfr :
-
tensile strength of the fibre (MPa)
- σf :
-
tensile stress in the fibre (MPa)
- σf, max :
-
maximum tensile stress in the fibre due to elastic stress transfer (MPa)
- τav, po :
-
average interfacial shear strength measured by the pull-out test (MPa)
- τav, pi :
-
average interfacial shear strength measured by the push-in test (MPa)
- τav, fr :
-
average interfacial shear strength measured by the fragmentation test
- τdeb :
-
bond shear strength of the interface (MPa)
- τe :
-
shear stress at the interface (MPa)
- τe, max :
-
maximum shear stress at the interface (MPa)
- τi :
-
constant shear stress at the fibre ends (MPa)
- τi, fr :
-
frictional shear strength of the interface (MPa)
- τmax’ po :
-
maximum average shear strength measured by the pull-out test (MPa)
- τmy :
-
matrix yield strength (MPa)
References
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Verpoest, I., Desaeger, M., Keunings, R. (1990). Critical Review of Direct Micromechanical Test Methods for Interfacial Strength Measurements in Composites. In: Ishida, H. (eds) Controlled Interphases in Composite Materials. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7816-7_60
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DOI: https://doi.org/10.1007/978-94-011-7816-7_60
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