WSU-TFREC/Postharvest Information Network/Elastic Modulus: What Is It?
Elastic Modulus: What Is It?
The elastic modulus is the key material property in both approaches. The elastic modulus is defined as the change in stress with an applied strain. Imagine two objects, similar in size and shape, one made of rubber and one of metal. Under the same load, the metal, with a larger elastic modulus, will deflect less than the rubber. Elastic modulus is not the same as strength; a 12 x 12 mm concrete block has a much higher elastic modulus than the same size block of Douglas fir, but the concrete is weaker than the wood in tension. Figure 1 is a graph of stress vs. strain for apple and potato tissue. The slope of the curve is the elastic modulus of the two materials. A few observations of the differences in the curves will illustrate some of the challenges facing nondestructive apple firmness sensor designers. Note the straightness of the potato tissue curve from initial loading to failure (where the curve suddenly drops to zero). The elastic modulus (the slope of this curve) does not change with increasing strain (deformation). The apple tissue in comparison shows a definite upward curvature in the stress vs. strain curve, followed by a downward curvature as the curve reaches the first peak. The first peak is the amount of strain (deformation) that causes a bruise, making the first peak the dividing point between nondestructive and destructive deformation. Because the stress vs. strain curve for apple tissue is not a straight line, apple tissue elastic modulus changes with the amount of strain the tissue undergoes. The question is, which values of elastic modulus are related firmness?
The impact energy approach avoids measuring a particular elastic modulus by measuring the amount of energy the apple tissue absorbs. The absorbed energy can be computed from the stress vs. strain curve as the area under the curve. By measuring the area, the effect of the changing elastic modulus is minimized, but the sensor must measure both the amount of energy absorbed by the tissue and the amount the tissue has been strained in the impact. There is a final point about the stress vs. strain curve. The MTPT measures the peak force needed to insert the probe tip into the apple. Although the insertion force is a complex combination of crushing and shearing forces, the MTPT value for an apple is closely related to the higher of the two peaks on the stress vs. strain curve.
Marvin Pitts and Ralph Cavalieri(1), Steve Drake(2), and John Fellman(3)
(1)Biological Systems Engineering, WSU
(2)USDA-ARS Tree Fruit Research Laboratory, Wenatchee, WA
(3)Horticulture and Landscape Architecture, WSU
Tree Fruit Postharvest Journal 8(4):23