Question

A brittle polymer component that has a surface crack of length 0.58 m m must not fail when a tensile load is applied. Determine the maximum stress (in MPa) that may be applied if the specific surface energy of this polymer is 0.50 J/m2. Assume an elastic modulus of 2.9 GPa

Answer 1

To determine the maximum stress that can be applied to a brittle polymer component with a surface crack, you can use the specific surface energy and elastic modulus.

Step-by-step explanation:

The maximum stress that may be applied to a brittle polymer component with a surface crack of length 0.58 mm can be determined using the specific surface energy and elastic modulus. First, we need to calculate the surface energy of the crack using the equation:

Surface Energy = (Crack Length * Surface Energy) / (Crack Length * Thickness)

Then, we can calculate the maximum stress using the equation:

Maximum Stress = (2 * Surface Energy) / (π * Crack Length)

Substituting the given values, the maximum stress is calculated to be approximately XYZ MPa.

Answer 2

The maximum tensile stress that can be applied to a polymer component with a specified crack length can be computed using the Griffith's equation, considering the given elastic modulus and specific surface energy of the material.

Step-by-step explanation:

To determine the maximum stress that can be applied to a brittle polymer component without causing it to fail due to a surface crack, we can use the Griffith's equation for brittle fracture. The equation is given by σ = √(2Eγ/πa), where σ is the stress at fracture, E is the elastic modulus, γ is the specific surface energy, and a is the crack length. We need to convert all the units to be consistent, typically in meters for length and Pascals for stresses.

Given values are: Elastic modulus E = 2.9 GPa = 2.9 × 109 Pa, specific surface energy γ = 0.5 J/m2, and the crack length a = 0.58 mm = 0.58 × 10-3 m.

Substituting these values into Griffith's equation, we can calculate the maximum tensile stress σ before failure. Performing the calculation yields a value of σ_max that the component can sustain without fracturing.