Question

Question 5

(a)(i) What theories of failure are used for? Ductile of materials

and Brittle of materials?

(ii) List at least two factors that promote the transition from ductile to brittle fracture?

(iii) Often, it is beneficial to know how many materials or components can be combined without producing an additional phase. When alloying elements are added to metal, solid or liquid solutions can be formed.

For example, when we add sugar to water, sugar solution is obtained. When we diffuse a small number of phosphorus (P) atoms into single crystal silicon (Si), we produce a solid solution of P in Si. Furthermore, they display unlimited solubility. Regardless of the ratio of water and sugar, only one phase is produced when they are mixed together. What factors or conditions that must be satisfied before a single phase of solution are realized?

(b) .What is a eutectic phase diagram? Draw a typical equilibrium diagram for a eutectic type of a system with limited solid solubility and explain its important features.

(c) The filament of a 75 W light bulb of my pressing iron may be considered as a black body radiating into a black enclosure at 700 C. The filament has a diameter of 0.10 mm and a length of 5 cm. considering the radiation, determine the filament temperature.

Answer 1

1)

Criteria used to predict the failure of ductile materials are usually called yield criteria. Commonly used failure criteria for ductile materials are:

the Tresca or maximum shear stress criterion

the von Mises yield criterion or distortional strain energy density criterion

the Gurson yield criterion for pressure-dependent metals

the Hosford yield criterion for metals

the Hill yield criteria

various criteria based on the invariants of the Cauchy stress tensor

For brittle materials, some popular failure criteria are:

criteria based on invariants of the Cauchy stress tensor

the Tresca or maximum shear stress failure criterion

the von Mises or maximum elastic distortional energy criterion

the Mohr-Coulomb failure criterion for cohesive-frictional solids

the Drucker-Prager failure criterion for pressure-dependent solids

the Bresler-Pister failure criterion for concrete

2)Presence of surface notches also contributes for brittle nature of ductile material. Due to residual stresses in cold working and quenching, it behaves like brittle. Voids are also one of the factor for brittleness.

3)conditions are:

Atoms or ions must have same size or size difference not more than 15 percent

Should have same electronegativity

Should have same structure

Should have same valency

4)

Q=75 W= 75 J/s

Ts=70+273=343

d=0.1 mm

L=5 cm

Area=πdl

ϵ=1 for black body

Q=σ∈A(T₁^4-Ts^4)

=5.67×10^(−8)×π×0.1×10^(−3)×5×10^(−2)(T1^4−3434)

T1=3029-273=2756℃

4)