Calculating the damage tolerance of the material

[Fra Ser Mur Chie]

Homework Statement

An alloy has a fracture toughness of 62 MPam^1/2

and its ultimate tensile strength is 164 MPa.

Calculate the damage tolerance of the material in the unit of mm.

Relevant Equations

Kic = Yrc sqrt pi * a

Kic = Y Oa sqrt pi * ac

so I have quickly gone over this, but feel that I am not going in the right direction.

I am assuming Y = 1 so,

62 = 164 sqrt Ka

given UTS = 164 Mpa
K_ic = 62 Mpa m^1/2

therefor,

working for ac, (the damage tolerance of the material)

Oa = UTS = 164 Mpa
Kic = Y Oa sqrt ac
62 = 1 * 164 * sqrt ac

there is a symbol in square root for the equation ^ I didn't understand it properly,

I have attached tutorials I have done earlier in the picture with the symbol in the square root.

what i would like some advice on would be the full equation.

 

[LightHero]

The equation for ac (the damage tolerance of the material) is:Kic = Y Oa sqrt ac where Kic is the Ultimate Tensile Strength (UTS), Y is a constant, Oa is the material's ultimate tensile strength, and ac is the material's damage tolerance.Thus, to solve for ac, you can rearrange the equation as follows:ac = (Kic / (Y * Oa))^2Substituting in the values given in the question, we get:ac = (62/(1*164))^2ac = 0.0088