/ME 5463-001 Fracture Mechanics, Homework #18

— David Wagner 2009/11/30 03:38

A CTOD test is performed on the three-point bending specimen aforementioned. If the plastic component, V_p, is known at a load P,

  1. derive an expression for plastic CTOD (delta_p) and the specimen dimensions; and
  2. if V_p and delta_p are known with r_p being undetermined, derive an expression for r_p, in terms of V_p and delta_p the specimen dimensions, assuming the angle of rotation is small.

1. The expression is

delta_p = {r_p(W-a)V_p}/{r_p(W-a)+a}

2.

delta_p = {r_p(W-a)V_p}/{r_p(W-a)+a} = V_p r_p(W-a) 1/{1+a/{r_p(W-a)}}

1/delta_p = {r_p(W-a)+a}/{r_p(W-a)V_p} = {1/V_p} + a/{r_p(W-a)V_p} ⇒ {(W-a)V_p}/a ({1/delta_p} - {1/V_p}) =1/r_p

⇒ r_p = a/{(W-a)V_p} 1/{{delta_p}^{-1} - {V_p}^{-1}} = r_p = a/{(W-a)V_p{delta_p}^{-1} - W+a} =

r_p = 1/{{V_p/delta_p} ({W/a}-1) - {W/a}+1}

Personal Tools