9 (a)The introduction of discrete defects into an otherwise elastic solid containing a large sharp crack can either increase or decrease the apparent fracture toughness of the solid.Describe the physical basis common to both effects. (b)What effect will a dislocation withb=10=001]have on the Mode I stress intensity factor of a crack on the (010)plane with crack front parallel to [0011.This dislocation is located directly ahead (=0)of the crack.Given: cos -sin e sin 301 √2πr 2 2 2 e. 0.38 022=- -cos-[l+sin。sin 2πr 2 2 62 K,-sin号cos2co .0030 2πr2 2 2 (c)Ignoring the areal fraction contribution,will an array of small internally pressurized bubbles,uniformly distributed in the matrix,affect the fracture toughness of steel below the NDT?Explain. 10.Discuss the motion of the dislocations shown in each of cases below.Be as quantitative as possible,discussing the particular path of motion the dislocation will take,showing detailed expressions where possible, explaining your steps,and interpreting your results.Assume that the direction of dislocation motion coincides with direction of dislocation motion coincides with the direction of force acting on the dislocation. Hint:The Peach-Koehler equation defining the force exerted on a unit length of dislocation line with direction s and Burgers vector b,due to an external stress fieldo,is: R =(o·b)×5 L Case(a) A specimen of uniform thickness with a dislocation located at position (xl=a, x2=b)from a corner,and defined by b=bes 5=e39. (a) The introduction of discrete defects into an otherwise elastic solid containing a large sharp crack can either increase or decrease the apparent fracture toughness of the solid. Describe the physical basis common to both effects. (b) What effect will a dislocation with , have on the Mode I stress intensity factor of a crack on the (010) plane with crack front parallel to [001]. This dislocation is located directly ahead ( b b [ ] 100 → = ξ [001] → = θ = 0) of the crack. Given: 11 22 33 3 cos [1 sin sin ] 2 2 2 3 cos [1 sin sin ] 2 2 2 3 sin cos cos 2 22 2 I I I K r K r K r 2 2 θ θ θ σ π θ θ θ σ π θθ θ σ π = − = + = (c) Ignoring the areal fraction contribution, will an array of small internally pressurized bubbles, uniformly distributed in the matrix, affect the fracture toughness of steel below the NDT? Explain. 10. Discuss the motion of the dislocations shown in each of cases below. Be as quantitative as possible, discussing the particular path of motion the dislocation will take, showing detailed expressions where possible, explaining your steps, and interpreting your results. Assume that the direction of dislocation motion coincides with direction of dislocation motion coincides with the direction of force acting on the dislocation. Hint: The Peach-Koehler equation defining the force exerted on a unit length of dislocation line with direction ξ and Burgers vector b, due to an external stress fieldσ , is: ( ) F b L = σ ⋅ ×ξ Case (a) A specimen of uniform thickness with a dislocation located at position (x1=a, x2=b) from a corner, and defined by 3 3 ˆ ˆ b be ξ e = =