Fracture toughness




Yusuke Onoda


Leaf fracture property is one of the mechanical properties describing leaf’s resistance to fracture.

Terminology and equations

Leaf fracture properties can be measured by shear, punch and tear tests. In all methods, work (J) and/or maximum force (N) are measured to fracture a part of leaf, and the values are typically expressed per unit fracture length or fracture area. Terms are dependent on whether work or force is measured and on the type of tests (shear, punch and tear). Some examples are as follows (Abbreviations: W, work; Fmax, the maximum force; l, fracture length; c, circumference of the punch rod; w, width of lamina strip; t, thickness):

Methods At structure level (per fracture length) At material level (per fracture area )
Calculation Name Calculation Name
Shear W/l [J m-1] Work to shear W/(l x t) [J m-2] Specific work to shear *1
Punch Fmax/c [N m-1] Force to punch Fmax/ (l x c) [N m-2] Specific force to punch *2
Tear Fmax /w [N m-1] Force to tear Fmax/ (w x t) [N m-2] Specific force to tear *3

*1 Also called fracture toughness

*2 Also called shear strength

*3 Also called tensile strength

Measurement approaches

Shearing tests, also called scissor, cutting and guillotine tests, measure the work required to cut a leaf. This method can measure heterogeneity of fracture resistance along a transect of leaf (e.g. veins and lamina).

Punch tests, including punch-and-die and penetrometer tests, which measure the maximum load required for the punch rod to penetrate a leaf (normally lamina).

Tearing method, also called tensile tests, can measure leaf resistance to tensile force. In this test, force is applied parallel to the surface, while in the shearing and punch tests, force is applied perpendicular to leaf.

Ranges of values

The 95% range of leaf fracture properties for woody, herbaceous and grass species. (Onoda et al. unpublished dataset)

Woody Herb Grass
Work to shear (Ws, J m-1) 0.022~0.539 0.033~0.34 0.016~1.12 (*)
Force to punch (Fp, kN m-1) 0.036~1.6 0.029~0.75 0.57~2.1 (*)
Force to tear (Ft, kN m-1) 0.23~11.7 0.14~5.3 0.76~36

* The number of observation is limited (N<10).

Health, safety and hazardous waste disposal considerations

Care in handling samples and measurements as high pressure is applied to samples during measurement.

Anatomy and Microscopy

Tissue Chemistry

Literature references

Aranwela N., Sanson G. & Read J. (1999). Methods of assessing leaf-fracture properties. New Phytologist, 144, 369-383.

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