1.2 Normal Stress
Definition: Stress is internal resistance per unit area offered by material against deformation. It is induced when the motion of the body or bar is restricted by some force or reaction. Stress can be Tensile or Compressive depending upon the nature of load.
A₀ = original cross-sectional area (constant). Used for most engineering design calculations.
Aₐ = actual area at any time of loading = A₀ ± ΔA (+ve for compression, −ve for tension).
- Tensile stresses = +ve | Compressive stresses = −ve
- Stress is induced only when motion of bar is restricted by some force or reaction
- In tension: True stress > Engineering stress (area decreases)
- In compression: True stress < Engineering stress (area increases)
- Pressure has same unit but is a different physical quantity — acts on external surface
1.3 Strain
The elongation or shortening in an axially loaded member per unit length is known as strain. Represented by ε. Strain is a dimensionless quantity.
L₀ = original length of member
Lₐ = actual length at loading = L₀ ± ΔL
(+ for compression, − for tension)
1.4 Tension Test — Stress-Strain Curve for Mild Steel
Specimen: Solid cylindrical rod | Gauge length = 2.0″ | Dia = 0.5″ | L/D ratio = 4.0. Test conducted on Universal Testing Machine (UTM). ASTM guidelines followed.
Fig. 1.1 — Tensile Stress-Strain Diagram for Mild Steel. σ_y (lower yield) = 250 N/mm². Plastic strain (CD) = 10–15 × elastic strain. Fracture strain ≈ 25% for mild steel.
| Point | Name | Description from Source |
|---|---|---|
| A | Limit of Proportionality | Beyond A, linear variation ceases. Hooke’s law valid only in region OA. For mild steel, B is very near A. For other metals (e.g. rubber), B may be greater than A. |
| B | Elastic Limit | Maximum stress up to which a specimen regains its original length and dimension on removal of applied load. |
| C’ | Upper Yield Point | Magnitude of stress depends on cross-sectional area, shape of specimen, and type of equipment used. Has no practical significance. |
| C | Lower Yield Point (σ_y) | Also called actual yield point. Stress at C = yield stress σ_y = 250 N/mm² (typical MS). Yielding begins at this stress. Used for design. |
| CD | Perfectly Plastic Region (Yield Plateau) | Continuous deformation with NO increase in stress. Strain at D ≈ 0.12% for MS; plastic strain = 10–15 times elastic strain. |
| DE | Strain Hardening Region | Further addition of stress gives additional strain. Material changes in atomic and crystalline structure → increased resistance. NOT used for structural design. |
| E | Ultimate Stress Point (σ_u) | Corresponding strain ≈ 20% for mild steel. σ_u = ultimate stress. After E, necking begins — area of cross-section drastically decreases. |
| F | Fracture Point | Breaking stress; strain at F = fracture strain ≈ 25% for mild steel. Region E-F is necking region where cross-section drastically decreases. |
- In compression, engineering stress-strain curve lies above actual stress-strain curve
- MS has yield stress in compression σ_y = 263 N/mm² (slightly greater than tension)
- All grades of steel have the same Young’s modulus (E)
- Among all steel grades, HTS is more brittle; mild steel is more ductile
- The divergence between tension and compression results is called Bauschinger effect
- With increase in % carbon: fracture strain reduces; yield stress and ultimate stress increase
1.5 Properties of Metals
Property by which material can be stretched. Large deformations possible before fracture. Post-elastic strain >5%. Examples: Mild steel, Aluminium, Copper, Lead, Nickel, Brass, Bronze.
Lack of ductility. Fracture immediately after elastic limit with small deformation. Post-elastic strain <5%. Examples: Cast iron, Concrete, Glass. Brittle materials are hard.
Property by which a piece of metal can be converted into a thin sheet by pressing. High degree of plasticity. Used in forging, hot rolling, drop stamping.
Resistance to scratch or abrasion. Measured by: Scratch (Mohr’s test) or Indentation (Brinell, Vickers, Rockwell, Knoop methods).
1.6 Creep & 1.7 Stress Relaxation
Creep is permanent deformation recorded with the passage of time at constant loading. Total creep deformation continues to increase with time asymptotically.
- Magnitude of load
- Type of loading (static or dynamic)
- Time or Age of loading
- Temperature — at higher temperature, greater deformation occurs. Temperature at which creep becomes very appreciable = half the melting point temperature (absolute scale) → called homologous temperature
If a wire of metal is stretched between two immovable supports with initial tension σ₀, the stress in the wire gradually diminishes, eventually reaching a constant value. This is called stress relaxation — a manifestation of creep.
This is why electric wires sag after long time
1.8 Elasticity · Proof Stress · Elasto-Plastic Behaviour
1.8 Elasticity and Resilience
The property by which original dimensions can be recovered after unloading is called elasticity. The total strain energy stored and released is called Resilience.
1.8.1 Proof Stress
Some ductile metals — Aluminium (Al), Copper (Cu), Silver (Ag) — do not show a clear yield point. Design stress is calculated by the offset method.
- Mark 0.2% permanent plastic strain on x-axis
- Draw a straight line parallel to initial portion of stress-strain curve from the 0.2% offset point
- Intersection of this line with the stress-strain curve = Proof Point
- Corresponding stress = Proof Stress (σ_p)
1.8.2 Elasto-Plastic Behaviour
If material is loaded beyond elastic limit (B) to point P, then unloading follows path PC (parallel to initial elastic portion). When entirely unloaded, residual strain OC remains = permanent set. Only CPD strain energy is recovered; OPC is lost = inelastic strain energy.
1.8.3 Types of Material Behaviour
1.9 Toughness & 1.10 Fatigue
1.9 Toughness
Property enabling material to absorb energy without fracture. Very desirable for cyclic/shock loading. Ductile materials are tough.
1.10 Fatigue
Material behaves differently under static and dynamic loading. In cyclic/reverse cyclic loading, if total accumulated strain energy exceeds toughness → fracture failure.
- Loading condition
- Frequency of loading
- Corrosion
- Temperature
- Stress concentration
Examples: Crashing of aircraft (crack in turbine blade), failure of fly wheels, breaking of wire due to cyclic bending.
1.11 Failure of Materials in Tension and Compression
Fig. 1.2 — Four failure modes. Ductile in tension → cup-and-cone at 45° (shear failure). Brittle in tension → flat at 90° (separation). Ductile in compression → bulging at 90°. Brittle in compression → diagonal shear at 45°.
Chapter 1: Properties of Materials — Strength of Materials · MADE EASY Postal Study Package 2019
All technical data from source material only