4. The following equation can be used to calculate the fracture energy (Jm-2) of a material:...

 

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4. The following equation can be used to calculate the fracture energy (Jm-2) of a material: T G = 2 -awo ac where is the critical extension ratio, a is the notch length, and Wo is the strain energy density. A is the point during a single-edge notch test (left graph below) where the max stress is reached and a drop in stress is seen as the gel begins to tear. This value of 2 is needed to calculate the area under the curve from the stress strain curve (obtained via a regular tensile test; right graph below), from x = 0 and y = 0 until the point where x = c Stress (kPa) 2 cy Single edge notch test 3wt% tannic acid 10 30 40 Strain (%) The calculated area is the Wo 20 50 60 70 Stress (kPa) 6 5 0 -1 0 10 3wt tannic acid- Stress strain curve 20 30 40 50 Strain (%) g 80 70 80 90 a. Given this data, determine 2 and calculate the fracture energy (G) of this hydrogel, which has a notch length of 1.4 mm and area under the curve (Wo) of 244.91 kPa. Hint: Convert all units to base units and do not convert percentage to a fraction. b. If you increase the amount of crosslinker in the hydrogel, what do you expect will happen to and Ge? Why? Assume that a and Wo remain constant. 4. The following equation can be used to calculate the fracture energy (Jm-2) of a material: T G = 2 -awo ac where is the critical extension ratio, a is the notch length, and Wo is the strain energy density. A is the point during a single-edge notch test (left graph below) where the max stress is reached and a drop in stress is seen as the gel begins to tear. This value of 2 is needed to calculate the area under the curve from the stress strain curve (obtained via a regular tensile test; right graph below), from x = 0 and y = 0 until the point where x = c Stress (kPa) 2 cy Single edge notch test 3wt% tannic acid 10 30 40 Strain (%) The calculated area is the Wo 20 50 60 70 Stress (kPa) 6 5 0 -1 0 10 3wt tannic acid- Stress strain curve 20 30 40 50 Strain (%) g 80 70 80 90 a. Given this data, determine 2 and calculate the fracture energy (G) of this hydrogel, which has a notch length of 1.4 mm and area under the curve (Wo) of 244.91 kPa. Hint: Convert all units to base units and do not convert percentage to a fraction. b. If you increase the amount of crosslinker in the hydrogel, what do you expect will happen to and Ge? Why? Assume that a and Wo remain constant.

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The problem provides the equation for the fracture energy Gc of a material as follows Gc frac2sqrtpi lambdac a w0 where lambdac is the critical extens... View the full answer