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Engineering Tensile Stress, Strain & Young’s Modulus

Calculates engineering tensile stress (sigma), strain elongation (epsilon), and Young’s Elastic Modulus (E) per ASTM D638 / ISO 527.

Mathematical Canonical Relation

\sigma = \frac{F}{A_0}, \quad \epsilon = \frac{\Delta L}{L_0}, \quad E = \frac{\sigma}{\epsilon}

Plain Formula: sigma = F / A0, epsilon = DeltaL / L0, E = sigma / epsilon

Live Engineering Parameter Solver

Input your production or test values below for instant, verified output.

Verified Engine

Applied Load Force (N) (N)

F_N

Range: 100 – 20000 N

Initial Area A0 (mm²) (mm²)

A0_mm2

Range: 5 – 200 mm²

Extension DeltaL (mm) (mm)

dL_mm

Range: 0.1 – 20 mm

Gauge Length L0 (mm) (mm)

L0_mm

Range: 25 – 100 mm

Calculated Engineering Result:

E = 1.25 GPa (Sigma = 30 MPa)

Engineering Verification:Calculated per ASTM D638 / ISO 527 standards.

When & Where to Apply

Use when testing polymer dumbbell test bars on a Universal Testing Machine (UTM) to determine tensile yield strength and modulus.

Common Engineering Pitfalls

Using instantaneous deformed area instead of initial area A0 (that would be true stress)
Measuring strain across grip displacement instead of extensometer gauge length L0

Physical Assumptions & Validity Limits

Uniaxial tension in elastic deformation region
Uniform initial cross-sectional area A0
Constant testing crosshead speed

Variable Symbols, SI Units & Dimensional Specifications

Symbol	Variable Meaning	SI Unit	Typical Industrial Range
\sigma	Engineering tensile stress	MPa (N/mm²)	—
\epsilon	Engineering tensile strain	mm/mm (%)	—
E	Young’s Elastic Modulus	MPa (GPa)	—
F	Applied load force	N	1250
A_0	Initial cross-sectional area	mm²	41.6
\Delta L	Gauge length extension	mm	1.2
L_0	Original gauge length	mm	50.0

Worked Industrial Numerical Example: HDPE Injection Molded Dogbone Tensile Test

Problem Statement:

An HDPE dogbone specimen (A0 = 41.6 mm², L0 = 50.0 mm) tested on an Instron UTM reaches 1,250 N force at a 1.2 mm gauge extension in the linear elastic zone. Calculate stress, strain, and Young’s modulus.

Step-by-Step Numerical Solution:

Calculate stress: sigma = 1250 N / 41.6 mm² = 30.048 MPa
Calculate strain: epsilon = 1.2 mm / 50.0 mm = 0.024 mm/mm (2.4%)
Calculate Young’s modulus: E = 30.048 MPa / 0.024 = 1,252 MPa = 1.25 GPa

Final Answer: Sigma = 30.0 MPa, Epsilon = 2.4%, E = 1.25 GPa

💡 Engineering Interpretation: Modulus E = 1.25 GPa falls within standard commercial HDPE injection molding grade specifications (1.1 - 1.4 GPa).

Authoritative Technical Reference & Source Provenance

ASTM D638: Standard Test Method for Tensile Properties of Plastics by ASTM International (ASTM International, 2022), 2022, Page 1-15.

Connected Curriculum Lesson

ASTM D638 Tensile Properties of Plastics

Study Full Lesson