Material Strength Basics

The Tensile Test

The standard material test pulls a specimen to failure while recording load and elongation. The resulting stress-strain curve reveals all key mechanical properties:

Where:

• σ (sigma) = engineering stress (force / original area)
• ε (epsilon) = engineering strain (change in length / original length)

Key Material Properties

Elastic Modulus (Young's Modulus, E)

The slope of the initial linear portion of the stress-strain curve:

This is a measure of stiffness — how much material deflects under load. Values are essentially constant within a material class, regardless of strength grade:

Yield Strength (σ_y or F_y)

The stress at which plastic (permanent) deformation begins. For materials with a distinct yield point (most carbon steels), it is the stress at the upper yield point. For materials without (stainless, aluminum), use 0.2% offset yield strength: stress where a line parallel to E at 0.002 strain intersects the curve.

Design stresses are typically 40-66% of yield for static loading, lower for dynamic.

Ultimate Tensile Strength (σ_u or F_u)

Maximum stress the material withstands before fracture:

Yield is the design limit for ductile materials; ultimate is the design limit for brittle materials (cast iron, ceramics).

Ductility (% Elongation)

How much plastic deformation before fracture:

• Ductile materials (>10% elongation): steel, aluminum, copper — give warning before failure
• Brittle materials (<5%): cast iron, glass, ceramics — fail suddenly without warning

Hardness

Resistance to indentation/penetration. Several scales:

Toughness

Toughness = energy absorbed before fracture (area under stress-strain curve). Two common measures:

• Charpy V-notch (CVN): Pendulum strikes notched specimen; energy absorbed measured in joules (ft-lb). Measures notch toughness at temperature.
• Izod: Similar test, different specimen orientation (UK standard).

Materials transition from ductile (high CVN energy) to brittle (low energy) at a ductile-to-brittle transition temperature (DBTT):

Fatigue Strength

Materials fail at stress levels well below yield strength under repeated/cyclic loading. This is fatigue — responsible for ~80-90% of mechanical failures.

The S-N curve plots stress amplitude (S) vs cycles to failure (N):

• Endurance limit (ferrous metals only): stress below which failure never occurs (≈ 0.5 × UTS for steel)
• Fatigue strength at N cycles: stress for failure at specific life

Factors Affecting Fatigue Life

Creep

At temperatures above ~0.4 × T_melt (absolute), materials slowly deform under constant stress over time — this is creep:

• Carbon steel: significant above ~400°C
• Stainless steel: above ~550°C
• Aluminum alloys: above ~200°C

Creep has three stages: primary (decreasing rate), secondary (steady-state — design basis), tertiary (accelerating — failure imminent).

Design for creep:

• Use allowable creep stress at temperature (ASME II-D tables)
• Consider stress rupture (time to failure at stress/temp)
• Chrome-moly steels (1¼Cr-½Mo, 2¼Cr-1Mo) and stainless for high temperature

Allowable Stress Design

Design codes specify allowable stresses as fractions of material strengths:

Common Material Property Tables

Steel (Room Temperature Reference)

Aluminum Alloys

Summary

Yield strength determines design load for static applications; ultimate strength for brittle fracture. Young's modulus is stiffness and is constant within material classes (E = 200 GPa for all steels). Fatigue causes 80-90% of mechanical failures — avoid stress concentrations and consider surface finish. Toughness (Charpy) matters for low-temperature service. Creep limits service life above 0.4 T_melt. Design codes apply factors of safety (typically 1.5 on yield, 3.5 on ultimate) to establish allowable stresses. Higher strength steel does NOT mean stiffer steel — stiffness comes from geometry (moment of inertia) and E.