Many food materials have structures that are either cellular, fibrous or particulate-filled, or combinations thereof. They are heterogeneous at different levels of structure, even if average properties are assumed for a given volume. Materials science allows treatment of their underlying mechanical properties.
An object will break more easily if the force is concentrated by a flaw or a crack. This is because of the resultant stress concentration which is then a site for fracture initiation. Linear elastic fracture mechanics (Williams, 1984; Jeronimidis, 1991) describes the stability of cracks in stressed isotropic plates. Near the crack tip the stress intensity factor, K1c, varies as the square root of the crack length, a criterion originally established by Griffith. When the stress intensity factor reaches a critical value the crack propagates in an unstable manner. The approach has been modified for plastic flow at the crack tip where there is a second contribution to the overall crack length (Marshall et al., 1973). In a plastically deforming material the crack is blunted and a deformation zone forms around the crack. An 'essential work of fracture approach' (Hashemi, 1997) is more generally applicable to the failure of composites and sums the energies from the different dissipative mechanisms, such as yield and debonding, as well as fracture. The approach has also been applied to biopolymer films (Yakimets et al., 2005). The testing of a material to identify these contributions can, however, include energy that is not being used to create new fracture surfaces such as that due to sound.
Gibson and Ashby (1997) described the use of scaling laws to relate stiffness and strength of a foam, sc, to the stiffness or strength of the matrix, sm; and the relative density of the foam, pc, to the matrix pm:
where k is a constant. They also gave the relationship for the foam fracture toughness, K1c, as:
where l is the length of a foam cell, all of which are assumed to be identical. The sif term occurs in the classical relationship for K1c for a flaw in a plate (Williams, 1984; Jeronimidis, 1991). Their application to foods has been reviewed (Smith, 1989).
The model of Warner and Edwards (1988) used variations on this type of equation to apply this modelling to liquid-filled foams typical of plant tissues; their model gives limits for modulus corresponding to initial application of stress and later equilibrium.
Fibre-filled composites are often treated by the method of mixtures to obtain the overall stiffness or strength, s, based on the properties of the matrix, sm, and fibres, sf, and their relative volume fraction, ff:
Fibre-filled composites can fail by fibre breakage and fibre slip. Particulate-filled composite plastics are also well-documented where particle size and shape, volume fraction and particle mechanical properties are variables (Phillips and Harris, 1977). Many foods comprise relatively inert fillers in a protein- or starch-based structure; this becomes relevant when using wastes for part or all of a composite structure.
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