Posted: August 1st, 2022

Effect of Angle on Gelatin Fracture

Effect of Angle on Gelatin Fracture
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Methodology and Technical Approach Proposed
Fracture toughness is important in design since brittle failure is often catastrophic and can happen at loads below yielding. Plastic deformation substantially increases the energy cost to lengthen a crack in the Griffith equity is not reasonable to use fracture toughness to measure surface energies since very few solids are ideally brittle. The plastic zone is the region around the crack tip within which the stress is high enough to cause plastic deformation
The finite size of the plastic zone extends the effective size of the crack. If the thickness of the specimen is small then the material near the sides yields and the crack changes shape. This change in shape leads to a deviation of the cracks. The Griffith eq can be applied immediately to practical problems and if compared with the stress concentration equation it proved that a sharp crack the Griffith eq sets the lower limit on fracture strength.
The wedge loading test is conducted based on Vincent et al., 1991 wedge fracture test. The test is designed to propagate a crack in a solid material ahead of the tip of the wedge. The mode of fracture that was applied in the test is the tension mode. The tension mode involves applying tensile loads which open and widen the crack, allowing the wedge test measurement to be achieved (Berthaume, 2016). The test applied here is a standard fracture test, whereby the two cleaved parts of the wedge are separated by feeding the strain energy into the sample by a wedge. However, the sample component is only cut once at the beginning of the test to allow the penetration of the wedge sufficient strain energy within the material. The crack obtained through the cut ahead of the tip of the wedge allows the force to be applied to continue pushing the wedge in the material. As the force is applied, the amount of energy drops as the strain energy is used to advance the crack tip, which allows the force to remain constant and the rate of strain energy being fed to become the same as the energy used by the advancing crack.
The figure below illustrates a sequence of events as a wedge enters a fracture test-piece. At point 1 the wedge is just about to enter the specimen. At point 2 the top of the specimen deflects storing elastic energy. At point 3 the wedge cuts into the specimen allowing the elastic energy to be fed into the cut surface and the force to drop. At point 4 the two halves of the specimen are forced apart storing strain energy as the wedge enters further. The small peaks in the curve at point 4 in the figure illustrate that the wedge is cutting through cell walls. Point 5 shows that sufficient strain energy is available to start a free-running crack propagating ahead of the wedge, allowing the force to fall. Point 6 of the figure illustrates that propagation of the crack stabilizes and propagates at the same velocity as the wedge.
THE WEDGE FRACTURE TEXT
The first material for the test used is an apple on an Istron with the use of wedges that were each made from two stiff-backed razor blades glued with epoxy to a wood spacer. The wedges were forced into the specimen at a rate of I mm/min at angles that included 10, 20, or 30 degrees. Another instrument test was performed on cheese using an Overload Dynamics materials testing instrument with the use of polished Perspex wedges with an angle of 10 degrees (Perez, 2016). On the instrumental test on cheese, one of the wedges was attached to the cross-head and pointing downwards while the other pointing upwards was placed at the base, which mimicked the pair of opposite incisors. The cross-head was moved upwards at 1 mm/min allowing the force penetration curve to be recorded and the point at which there was a reduction of force. Overload Dynamics materials testing instrument was also used for simple compression tests within the cross-head speed with the use of cylinders of cheese of 10 mm diameter, 30 m height, and notched test piece.
The sensory test on an apple with four cubes of Cox apple 15 mm on both sides. The orientation of the cubes was to ensure the radical air spaces would either be presented parallel or perpendicular to the direction of biting and a line manifested transversely on the cube top indicating the orientation. To test the force and energy rate, the biting was conducted slowly with incisors on the line with the biting stopping as soon as the force which is being exerted diminishes and the test piece cleaved into two. The penetration distance of the incisors into the sample was also recorded at that point. The sensory test on cheese involved cubes that were 20 mm on both sides of the five pieces of cheese being used to test two samples of each cheese. The distance of the teeth penetration into each sample before the crack could begin to freely propagate was recorded.

References
BERTHAUME, M.A., 2016. Food mechanical properties and dietary ecology. American journal of physical anthropology, 159(Suppl 61), pp. 79-104.
LUCAS, P.W., OATES, C.G. and LEE, W.P., 1993. Fracture toughness of mung bean gels. Journal of materials science, 28(5), pp. 1137-1142.
OATES, C.G., LUCAS, P.W. and LEE, W.P., 1993. How brittle are gels? Carbohydrate polymers, 20(3), pp. 189-194.
PEREZ, N., 2016. Introduction to Fracture Mechanics. Fracture Mechanics. Cham: Springer International Publishing, pp. 53-77.
VINCENT, J.F.V., JERONIMIDIS, G., KHAN, A.A. and LUYTEN, H., 1991. The wedge fracture test: a new method for measurement of food texture. Journal of texture studies, 22(1), pp. 45-57.

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