Fracture Mechanics Problem

INTRODUCTION

 

The Jigsaw is a mastermind serial killer. Jigsaw is a dying cancer patient who is obsessed with teaching people the value of their own lives. Jigsaw builds deadly traps for his subjects, which symbolize what is missing in the victim’s life. Each trap Jigsaw refers to as “game”, and tells the person the “rules” of the game either by audio or video tape. The rules usually consist of tasks that the victim must adhere too in order to survive.

 

 

 

Richie is a undergraduate student who studied in material engineering department. He always wasting his life just only played video games and did the fun things every day. As a undergraduate student, he’s very lazy. He never get to the course and didn’t do the homework or the exam. Therefore, he was really young boy who didn’t know his true indentity and purpose of his life.

 

 

PROBLEM

One day jigsaw meet Richie and know what person the Richie is. Jigsaw becomes angry after knowing that Richie have been wasting his lives, knowing he will die soon. Jigsaw eventually decides to make Richie appreciate his own lives by forcing him to face with the death. He kidnapped Richie and set the deadly trap for Richie. He told him, if he want to survive/life he should be able to solve the problems which have been made by Jigsaw.

SOLUTION:

From Toperate= 75 oF from figure 4.7, he get:

KIc= 60 ksi√in.
σys= 90 ksi.
σdes.= 1/9 (90) = 10 ksi

Crack is subjected in center of the plate. Which type of the crack is a through thickness and there is a force in the middle of the crack.

Fracture Mechanics problems which is allowed superposition, so the total stress intensity factor at the crack can be considered as the sum of that, due to tensile stress and force in the middle of the crack.

Assumption: – Infinite plate

Through thickness crack
so, the KI equation’s for through thickness crack is:


(2)    Wedge Force
for centrally applied forces in the middle of the crack, the equation for KI is:

Calculated the Superposition:
KI1 = KI2 + KI3            , acr could be determined if KI1 = KIc
So, the calculation is:

From the equations, he can find: acr = 0.125 in.

To prove whether the assumption is true or not, it can be seen from ratio a/b:

Value a/b is too small, so it can be called infinite plate, and the assumption is correct.

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