Fracture Specimen To Visualize whether a crack of

Fracture Specimen • • To Visualize whether a crack of given length in a material of known fracture toughness is dangerous, because it will propagate to given stress levels. To visualize the driving force on a crack to characterize the material's resistance to fracture.

Fracture Specimen Fracture • • Fracture – A fracture is the (local) separation of an object or material into two, or more, pieces under the action of stress. The process of Fracture can be considered to be made up of two components – Crack Initialization. – Crack propogation • Fractures are of two types Brittle fracture Ductile fracture • Crack • Fatigue

Fracture Specimen Griffith & Irwin theory of brittle fracture • • • The first Explanation of discrepancy between the observed fracture strength of the crystals and theoritical cohesive strength was proposed by griffith. Griffith proposed that “ A crack will propogate when the decrease in elastic strain energy is at least equal to the energy required to create the new crack surface. Let us consider a elliptical crack of length 2 c subjected to axial tensile load, where tensile stress is given by σ.

Fracture Specimen • • Total energy of the system = u U= ue + us • • • Where • • • When crack extends by δc, the ue = Decreases us = Increases For equilibrium d. U/d. C is= 0; ue = elastic Strain Energy us = Energy in creating new crack surface area.

Fracture Specimen • • • Let us consider a edge crack whose length is a and subjected to tensile loading. As the crack grows longer (a increases), the quadratic dependence of strain energy on a eventually dominates the surface energy, Beyond a critical crack length ac the system can lower its energy by letting the crack grow still longer. Up to the point where a = ac, the crack will grow only if the stress is increased. Beyond that point, crack growth is spontaneous and catastrophic.

Fracture Specimen Critical stress • The value of the critical crack length can be found by setting the derivative of the total energy S + U to zero:

Fracture Specimen As per graffiti : Critical stress expression • For ductile materials the relation ship for Critical stress is given by • Where is critical strain energy release rate

Fracture Specimen The variation of elastic strain energy and surface energy formation of new crack area is presented in the following animation. The parameters of observation are Crack propogation Variation of Elastic strain energy Variation of Surface energy Critical crack length.

Fracture Specimen Fracture Analysis START

Fracture Specimen Fracture Analysis

Fracture Specimen Fracture Analysis

Fracture Specimen Fracture Analysis

Fracture Specimen Fracture Analysis

Fracture Specimen Check Your Understanding • The _____ is a measure of material toughness. • Resistance to crack propagation • Critical stress intensity factor • Geometry of object • All the above Read the question and select the appropriate option by clicking on them. Then click 'Submit’ to verify your answers.

Fracture Specimen Check Your Understanding Important information about crack and its nature is obtained from o Stress strain Curve o Material properties o Physical observation of the object under test o Gross Microscopic Examination of the fracture surface. . Read the question and select the appropriate option by clicking on them. Then click 'Submit’ to verify your answers.

Fracture Specimen Check Your Understanding • If 'a' is crack length and ' ac ' is critical crack length, up to which point the crack will grow only if the stress is increased. • up to any length • Up to ac • Up to the geometric length of the object • Up to half of length. Read the question and select the appropriate option by clicking on them. Then click 'Submit’ to verify your answers.

Fracture Specimen Check Your Understanding • The cohesive strength of silica fiber if E= 95 Gpa and a 0=. 16 nm , surface energy per unit area=1 J/sq, m is ------? • 20 Gpa • 24. 4 Gpa • 35. 6 Gpa • 12. 2 Gpa Read the question and select the appropriate option by clicking on them. Then click 'Submit’ to verify your answers.

Fracture Specimen The crack propogation in brittle materials compared to ductile materials is o Slow o fast o o o Crack propogation is same No comparision

Fracture Specimen Resources Books: Mechanical metalurgy by George E dieter. Reference Links: http: //www. efunda. com/formulae/solid_mechanics/fracture_mechanics/fm_intro. cfm http: //www. dsto. defence. gov. au/publications/1880/DSTO-GD-0103. pdf http: //ecommons. library. cornell. edu/handle/1813/3075 http: //pcwww. liv. ac. uk/rockdef/lectures/3%20 Griffith%20 theory. pdf