Final answer:
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.