Question

The structure consists of a very large steel plate they will be used to transfer an in plane tensile stress. You have information from the company that performed a non-destructive testing technique if there are any flaws inside the plate. This non-destructive testing technique is based on ultrasonic wave transmission and will only detect a crack if it is bigger than 2.5 mm. No flaws were detected in the plate. You decided to pull some samples from a similar plate and you determined that the KIC value of these plates are 40 MPa*m0.5.
Required:
Estimate the maximum in plane tensile stress that you would suggest that this plate should carry.

Answer 1

Answer:

$\mathbf{\sigma_{max} =638.308 \ MPa}$

Explanation:

For any large steel plate with an infinite length and width and a center through the crack under tension, the stress intensity factor can be expressed as:

$K_I = \sigma \sqrt{\pi a}$

where;

a = 2.5 mm/2

a = 1.25 mm

a = 1.25 × 10⁻³ m

Therefore; the maximum stress in tension capacity can be computed as;

$\sigma_{max} = \dfrac{K_{I_C}}{\sqrt{\pi a_c}}$

$\sigma_{max} = \dfrac{40}{\sqrt{\pi \times 1.25 \times 10^{-3}}}$

$\mathbf{\sigma_{max} =638.308 \ MPa}$