Force-deformation curve

FIGURE 21.18 Force-deformation curves of local points indicated by open circles in Figure 21.15c. The curve fitting against Hertz model are superimposed on each curve, (a) Carbon black (CB) region (upper circle), 1.01 0.03 GPa, (b) interfacial region (middle circle), 57.3 0.8 MPa, and (c) rubber region (lower circle), 7.4 0.1 MPa. 

FIGURE 21.19 (a) The force-deformation curve at a point between inteifacial and carbon black (CB) regions as indicated by a filled circle in Figure 21.15c. The Young s modulus calculation is conducted by dividing a curve into two parts, (b) the curve fitting within the first part, 4.1 0.1 MPa, and (c) the curve fitting within the second part, 76.3 0.1 MPa. 

An Instron Testing System (Model 1122), fitted with a 10 cm six-wire grid (Ottawa Texture measuring system, OTMS cell) was used to determine rheological properties. A loading rate of 50 mm/min and a chart speed of 500 mm/min resulted in a well defined force-deformation curve. Force at the bioyield point and the area under the curve were calculated. These values were then converted into maximum stress, work and specific work values ... 

Determine Young s modulus of elasticity (E), which is the slope of the linear portion of the stress versus strain curve. Calculate the stiffness of the specimen from the force/deformation curve. 

To correct deformation for an initial curved region of the force/deformation curve (toe region) due to specimen irregularities at the contact surfaces of a specimen with a Hookean... 

Figure H2.1.1 A force/deformation curve illustrating specimen fracture of a banana (2.5 cm length, 3.0 cm diameter, 5 mm/min deformation rate), Cheddar cheese (2.0 x 2.0 x 2.0 cm, 10 mm/min deformation rate), and a seedless grape (2.2 cm length, 1.7 cm diameter, 2 mm/min deformation rate) under uniaxial compression at room temperature.

Ob and Eg are determined from force-deformation curves for materials which exhibit squeezing flow behavior (e.g., peanut butter, processed cheese). 

Figure H2.2.1 Force/deformation curves illustrating three puncture probe tests (50 mm/min deformation rate) of an apple specimen and a cone penetrometer test (10 mm/min deformation rate) of Cheddar cheese, all at room temperature.

Puncture probes are commonly used for fruits and vegetables, and allow for the determination of force at rupture of the cellular structure. The procedure outlined below is adapted from the method of Bourne (1979). Cone penetrometers are commonly employed for determining firmness and yield value for foods such as margarine and butter, which may be a reflection of the product s spreadability. Quite often it is desirable to use a testing system that provides a constant deformation rate. Additionally, a mechanical testing machine allows for production of a force/deformation curve to further analyze the data. 

Figure H2.2.2 A force/deformation curve illustrating the potential difference between the rupture point and the ultimate strength of a food specimen (adapted from Mohsenin, 1970).

Figure H2.2.3 A force/deformation curve illustrating a compression-extrusion test (10 mm/min deformation rate) for canned green peas using a Kramer shear cell (multiblade) at room temperature.

The rupture force may or may not be the represented as the maximum point on the force/deformation curve (see Figure H2.2.2). At rupture the food material begins to flow back up through the annular gap. 

Voisey, P.W. 1977. Interpretation of force-deformation curves from the shear-compression cell. J. Texture Studies 8 19-37. 

Figure 13. Schematic drawing of force - deformation curve for brittle and ductile fracture (adapted from ref. 71).

Typical force-deformation curve for mechanical testing of a brittle food. 

The jagged portion of the force-deformation curve and of acoustic emission data has been assessed by fractal analysis and Fourier transform analysis (Barrett et al., 1992) and by the weighted distribution spectrum of the individual peaks (Vincent, 1998). 

Of several physical parameters derived from the force-deformation curve (three-point bending assay) only the relation of the maximum force at breakage (MFB) of the dried products with water activity will be discussed here (Figure 7.7). At low moisture content, air dried samples showed a lower MFB than the FD sample. This may be because during drying in hot air. 

Figure 6.3 Force-deformation curve for characterizing a polishing pad.3...

Food texture is measured by sensory analysis or by an instrumental method. Using a human inspector for a textural evaluation is subject to some errors because of variations in perception, even when trained panelists are used and a well-defined standard is referenced. However, Katz and Labuza (1981) compared sensory results and cohesiveness values from force-deformation curves for potato chips, popcorn, puffed corn curls as well as saltines, and obtained a good agreement between the two sets of data. A similar comparison was made by van Loon et al. (2007) for the crispness of French fries comparable results were also noted. 

Figure 1 Force-deformation curve for rigid foam.

Figure 10 Force-deformation curve for flexible foam.

FIGURE 2.10.2 Force-deformation curve typical of biological materials. Deformation of the resting state of the material is usually somewhere in the center of the curve where the slope is greatest. 

Figure 2.10.3 shows these resuits, it can be recognized that the iines are curved, simiiar to the initiai section of the generai force-deformation curve in Figure 2.10.2. Because the curves end at the defiection where puncture occurred, the reverse curve at higher forces and defiec-tions is not shown.

Why do you suppose most biological materials have the shape of the force-deformation curve given in Figure 2.10.2 ... 

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