Question

A steel wire with a cross-section area 2.5X10^-3 m2 and a length of 10 m is used to pull a truck on the road. The truck is 10 tons and the friction coefficient between the tires and road is 0.25N/kg. Steel has a Young’s modulus 250MPa.

Suppose this wire contain surface cracks. Determine the largest linear size of the surface crack so that the wire will not fail due to fracture in this application. Kc = 0.1 MPa m^0.5

Answer 1

Given data,

Cross-section area (A) = 0.0025 m² , Length (L) = 10 m , Weight of truck (W) = 10000 kg ,

Friction coefficient () = 0.25 N/kg , Young’s modulus (E) = 250 MPa ,

Fracture toughness (Kc) = 0.1 MPa m^0.5 , Geometry dominated factor for wire (Y) = 1 ,

Crack length (a) = ?

Now, First we need to calculate critical stess value up to which wire will not fail (),

Net force (F) = Frictional force

                   = *W*g

                   = 0.25*10000

              F = 2500 N

Now, = F/A

      = 2500 / 0.0025

   = 1 MPa

Now, Theory of linear elastic fracture mechanics,Fracture toughness formula ,

     K_c = Y**(*a)^0.5

    0.1 = 1 * 1 * (3.14*a)^0.5

   3.14*a = 0.01

   a = 0.00318 m