PROPERTIES RELATED TO STRENGTH

 Strength is the ability of a material to resist applied forces without yielding or fracturing.  Strength of a material may change considerably with respect to the way it is deformed.  Mode of stress, type of stress & rate of stress application may affect the strength of a material.  Strength data are usually obtained from lab. Tests which are performed under strictly standardized specimens under controlled conditions. These tests also serve for obtaining σ-ε relationships.

 σ-ε curves can be grouped into three as: Ductile Materials → exhibit both elastic & plastic behavior Ductile Materials → exhibit both elastic & plastic behavior Brittle Materials → exhibit essentially elastic behavior Brittle Materials → exhibit essentially elastic behavior Viscoelastic Materials → exhibit large elastic deformation Viscoelastic Materials → exhibit large elastic deformation

SPECIAL FEATURES OF STRESS-STRAIN DIAGRAMS σ PL σEσE σYσY σFσF σUσU A B C D E

Point A (Proportional Limit): The greatest stress (σ PL ) that can be developed in the material without causing a deviation from the law of proportionality of stress to strain. In other words it is the stress upto which the material responds following Hooke’s Law. Point B (Elastic Limit): Maximum stress (σ E ) that can be developed in a material without causing permanent deformation. In other words it is the stress upto which the deformations are recoverable upon unloading.

Point C (Yield Point): The stress at which the material deforms appreciably without an increase in stress. Sometimes it can be represented by an upper and lower yield points. σ Y,U represents the elastic strength of the material and σ Y,L is the stress beyond which the material behaves plastically. Point D (Ultimate Strength): It is the maximum stress that can be developed in a material as determined from the original X-section of the specimen.

Point E (Fracture Strength): The stress at which the material breaks, fails.

 In an engineering σ-ε plot the original area (A 0 ) & length (l 0 ) are used when determining stress from the load and strain from deformations.  In the true σ-ε plot instantaneous area & length are used.  The true values of stress & strain for instantaneous area & length of the specimen under tension will differ markedly, particularly close to the breaking point where reduction in cross-section & elongation of the specimen are observed.

& Engineering &True

For ε eng ≤ 0.1 → ln(1+0.1) ≈ 0.1 For ε eng ≤ 0.1 → ln(1+0.1) ≈ 0.1  For small strains ε true ≈ ε eng & If you assume no volume change:

DUCTILITY & BRITTLENESS  Ductility can be defined as strain at fracture.  Ductility is commonly expressed as: a) Elongation b) % reduction in cross-sectional area  A ductile material is the one which deforms appreciably before it breaks, whereas a brittle material is the one which does not.  Ductility in metals is described by:  If %R A > 50 % → Ductile metal

TOUGHNESS & RESILIENCE  Toughness is the energy absorption capacity during plastic deformation.  In a static strength test, the area under the σ-ε curve gives the amount of work done to fracture the specimen.  This amount is specifically called as Modulus of Toughness.  It is the amount of energy that can be absorbed by the unit volume of material without fracturing it.

σ ε T (Joule/m 3 ) σuσu σfσf σ PL εuεu εfεf ε PL  The area under the σ-ε diagram can be determined by integration.  If the σ-ε relationship is described by a parabole.

 Resilience is the energy absorption capacity during elastic deformation. R ε PL ε σ PL σ Since If you assume σ PL = σ y

YIELD STRENGTH  It is defined as the maximum stress that can be developed without causing more than a specified permissible strain.  It is commonly used in the design of any structure.  If a material does not have a definite yield point to measure the allowable strains, “Proof Strength” is used.  Proof strength is determined by approximate methods such as the 0.2% OFF-SET METHOD.  At 0.2% strain, the initial tangent of the σ-ε diagram is drawn & the intersection is located.

DETERMINATION OF E FROM σ-ε DIAGRAMS  For materials like concrete, cast iron & most non- ferrous metals, which do not have a linear portion in their σ-ε diagrams, E is determined by approximate methods. 1. Initial Tangent Method: Tangent is drawn to the curve at the origin 2. Tangent Method: Tangent is drawn to the curve at a point corresponding to a given stress 3. Secant Method: A line is drawn between the origin & a point corresponding to a given stress

3 2 1 ε σ

HARDNESS  Hardness can be defined as the resistance of a material to indentation.  It is a quick & practical way of estimating the quality of a material.  Early hardness tests were based on natural minerals with a scale constructed solely on the ability of one material to scratch another that was softer.  A qualitative & somewhat arbitrary hardness indexing scheme was devised, temed as Mohs Scale, which ranged from 1 on the soft end for talc to 10 for diamond.

1. Talc 2. Gypsum 3. Calcite 4. Fluorite 5. Apatite 6. Orthoclase 7. Quartz 8. Topaz 9. Corundum 10. Diamond HARDER An unknown material will scratch a softer one & will be scratched by harder one. EX: Fingernail-(2.5) Gold, Silver-(2.5-3) Iron-(4-5) Glass-(6-7) Steel-(6-7)

 The hardness of a metal is determined by pressing an indenter onto the surface of the material and measuring the size of an indentation.  The bigger the indentation the softer is the material.  Common hardness test methods are:  Brinell Hardness  Vicker’s Hardness  Rockwell Hardness

1. Brinell Hardness Load P is pressed for 30 sec. and the indentation diameter is measured as d. Load P is pressed for 30 sec. and the indentation diameter is measured as d. P D d Brinell Hardness = (kgf/mm 2 )

2. Rockwell Hardness Instead of the indentation diameter, indentation depth is measured. Instead of the indentation diameter, indentation depth is measured. However, the surface roughness may affect the results. However, the surface roughness may affect the results. So, an initial penetration is measured upto some load, and the penetration depth is measured with respect to this depth. So, an initial penetration is measured upto some load, and the penetration depth is measured with respect to this depth. ΔH = H 2 – H 1 P1P1 Initial load H1H1 P2P2 Final load H2H2

3. Vickers Hardness Instead of a sphere a conical shaped indenter is used. Instead of a sphere a conical shaped indenter is used. P Top View Indentation d2d2 d1d1 (kgf/mm 2 ) Vicker’s Hardness =