First Topic - Fracture

**Practice HW and the Exam-HW on Fracture**

This the Practice HW for the First Part of the Course-Fracture

Practice HW-I (Fracture)This the Exam-(Take Home) HW -I on Fracture

HW-Exam I on Fracture**Links to Notes and Papers on Fracture**

Discussion of Principal Stresses and Strains

Notes-Principal Stresses and StrainsThe following two notes relate the enthalpy of formation to the elastic modulus. After all the elastic properties are related to stretching of bonds. Bonds when stretched to about 15% strain break. Therefore the work of fracture must be related to the enthalpy of formation - that is, the transition from a gas phase where the atoms do not interact to the phase where they form bonds with their neighbors. Thus the work done to break the bonds is related to the enthalpy of formation. Higher enthalpy of formation implies a higher bond stiffness, and therefore, a higher elastic modulus.

Relationship between the enthalpy of formation and the elastic modulusThe position of the element in the periodic table is also a guide to its enthalpy of formation. Atoms in the middle of the periodic table have a higher valency than the atoms in the left columns, and therefore form more bonds, and therefore have a higher enthalpy of formation, and along with that a higher elastic modulus.

Relationship between the enthalpy of formation and the position in the periodic tableThe following three links give notes to fracture mechanics. The first just below are hand written notes for the derivation of the relationship between the work of fracture and the fracture toughness.

Derivation of the relationship between the work of fracture and the critical stress intensity factorThis second link gives equations for the stresses and displacements at the crack tip in terms of the stress intensity factor.

Stresses and Displacements at the Crack TipThis third link gives a "map" that shows the relationship between fracture toughness and the elastic modulus for different classes of materials.

Map showing the relationship between fracture toughness and elastic modulusThis paper, on tool steel, shows the deformation at crack tips, and how the crititcal value of the crack tip opening displacement then leads to a mechanistic description of the critical stress intensity factor, and then to the work of fracture

Local Yielding at the Crack TipThis paper is related to slow crack growth or sub-critical crack growth, which occurs below the critical stress intensity. In this case time dependent crack growth in silica glass in different corrosive environments is considered and shown that the threshold stress intensity factor below which slow crack growth essentially stops, depends on the crack tip opening displacement being at least as large as the size of the corrosion molelcule.

Michalske and Bunker paper from Scientific American