Question

Question 5 (a)(i) What theories of failure are used for? Ductile of materials and Brittle of materials? (2marks)

(ii) List at least two factors that promote the transition from ductile to brittle fracture? (2marks)

(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? (4marks)

(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.

please answer all.clearly written.thank you.

Answer 1

i) Theories of failure used for ductile and brittle materials:

For Ductile materials, the failure mainly happens due to the shear stress (which is the main root cause for the yielding in ductile materials). The max shear stress criteria or Tresca criteria is used for a ductile material. Because in ductile the failure happens in the plane where the max shear stress acting effectively and Von mises criteria also used for these materials but the Tresca criteria is more simple compared to Von mises criteria.

Tresca Criteria: Yielding occurs when the difference between the maximum and minimum normal stresses reaches a critical value or Yielding occurs when the maximum shear stress reaches a critical value.

(or)

Von mises Criteria: Yielding occurs when the second invariant of the stress deviator J2 exceeds a critical value.

For Brittle materials: The Rankine criteria fits a brittle metal like Gray cast iron quite well. According to this the Cleavage fracture occurs when cleavage strength is reached before yield stress.

ii) Two factors which promote the transition from ductile to brittle fracture:

1. Low temperature: This means the temperature below Ductile to Brittle Transition Temperature(DBTT) so that material changes from ductile to brittle nature.
2. High Strain rate or rapid rate of loading
3. Presence of Stress Concentrated Region

iii) Hume Rothery Rules:

A solid solution is a phase where two or more elements are completely soluble in each other. There are two types of solid solutions 1) Substitutional solid solutions 2) Interstitial solid solutions.

There are rules which govern the formation of solid solutions:

1. Crystal Structure Factor: For complete solubility of two elements they should have same type of crystal lattice.
2. Relative Size Factor: The atoms of solute and solvent should have the same atomic size approximately or the difference between atomic radii of two elements is less than 15%.
3. Chemical Affinity Factor: The elements should have less chemical affinity otherwise the formation of compounds instead of solid solutions happens.
4. Electronegativity: Higher the electronegativity; greater is the chance of forming an intermediate phase rather than a solid solution.
5. Relative Valence Factor: Both metals should have same valency and it can be noticed that the metal with lower valency tends to dissolve more of metal of higher valency.

b) Eutectic Diagram:

Eutectic diagram, it mainly represents a eutectic reaction where liquid phase can split into two solid phases.

(L-->+). And the above diagram represents the limited solid solubility on both sides (A-Side and B-side), due to this limited solid solubility two solubility lines formed which represents the maximum amount of solute in solid solution at that particular temperature. (The lines surrounded both alpha and Beta phases below eutectic temperature are called as solvus lines which represent the solubility limits at all the temperatures ).