How to Calculate Elastic Modulus and Tensile Properties per ASTM D638

A tensile test gives you two columns of numbers: force and displacement (or extension). Everything else —Young’s modulus, yield strength, tensile strength, elongation at break and toughness— is calculated from them. This guide explains how to do it correctly for plastics according to ASTM D638, with a numerical example and the mistakes that most often distort the results.

Before you calculate: specimen and test conditions

Results are only comparable if the specimen and test follow the standard. For the most common specimen, ASTM D638 Type I (thickness up to 7 mm):

Dimension	Value
Overall length	165 mm
Width of narrow section	13 mm
Length of narrow section	57 mm
Gauge length (L₀)	50 mm
Distance between grips	115 mm
Thickness	3.2 ± 0.4 mm

Other key points:

• Conditioning: 23 ± 2 °C and 50 ± 10 % relative humidity for at least 40 h (ASTM D618), and testing under the same conditions.
• Speed: the lowest speed allowed by the standard that produces rupture within 0.5–5 minutes. For rigid plastics with a Type I specimen this is usually 5 mm/min.
• Number of specimens: at least 5 for isotropic materials (10 for anisotropic ones: 5 in each direction).
• Measure every specimen: actual width and thickness of the narrow section, not the nominal mould dimensions.

Step 1: from force to stress

Engineering stress is force divided by the initial cross-sectional area of the narrow section:

σ = F / A₀        A₀ = width × thickness

Example (PLA specimen): width 13.0 mm and thickness 3.2 mm → A₀ = 41.6 mm². With F in newtons and A₀ in mm², σ comes out directly in MPa (1 N/mm² = 1 MPa).

Step 2: from displacement to strain

ε = ΔL / L₀

This is the most common source of error. If ΔL is the machine’s crosshead displacement, it also includes the deformation of the grips, load cell and frame, plus specimen slippage in the grips. The result is an inflated strain and therefore a substantially lower modulus than the real one.

• For the elastic modulus, measure strain with an extensometer over the gauge length (L₀ = 50 mm for Type I).
• If you only have crosshead data, the standard allows a nominal strain referred to the grip separation (115 mm). It is fine for elongation at break, but a modulus obtained this way is not comparable with datasheet values.

Step 3: elastic modulus (Young’s modulus)

The modulus is the slope of the initial linear region of the stress–strain curve:

E = Δσ / Δε

Worked example. In the linear region of the PLA curve we take two points measured with an extensometer:

Point	Force	Stress	Strain
A	200 N	4.81 MPa	0.10 % (0.0010)
B	700 N	16.83 MPa	0.45 % (0.0045)

E = (16.83 − 4.81) / (0.0045 − 0.0010) = 12.02 / 0.0035 ≈ 3,434 MPa ≈ 3.4 GPa

A value consistent with PLA. In practice, instead of two points you fit a linear regression to all the data in the linear region and check the R² (ideally > 0.99).

Details that change the result:

• Toe region: the specimen settling in the grips produces an initial low-slope segment that is not a material property. ASTM D638 describes a toe compensation: extend the straight line of the linear region down to zero stress and use that point as the strain origin.
• ASTM D638 vs ISO 527: ISO 527 defines the modulus as the chord slope between ε = 0.05 % and ε = 0.25 %. For the same material the two methods can give somewhat different values — always state which one you used.
• Sampling rate: if the linear region contains only a few points, the fit is unstable. Increase the data acquisition rate.

Step 4: yield strength

• Materials with a yield point (curve with a local maximum, typical of PP, PE or nylon): yield strength is the stress at the first point where the slope becomes zero (dσ/dε = 0).
• Materials without a clear yield point: use the offset method — draw a line parallel to the modulus line, shifted by a fixed strain (commonly 0.2 %), and take the stress where it intersects the curve.

Step 5: tensile strength and elongation at break

Tensile strength:      σ_max = F_max / A₀
Elongation at break:   ε_break = ΔL_break / L₀ × 100 %

Example: F_max = 2,450 N → σ_max = 2,450 / 41.6 ≈ 58.9 MPa. If the extensometer reads 2.9 mm at break → ε_break = 2.9 / 50 = 5.8 %.

To detect the break automatically, look for the sudden force drop (for example below a percentage of F_max) rather than using the last recorded point.

Step 6: toughness

Tensile toughness is the energy absorbed per unit volume up to failure — the area under the stress–strain curve. With discrete data, integrate with the trapezoidal rule:

U = Σ (σᵢ + σᵢ₊₁) / 2 · (εᵢ₊₁ − εᵢ)

With σ in MPa and dimensionless ε, U is in MJ/m³ (1 MPa = 1 MJ/m³). Use strain as a fraction, not a percentage, or the result will be 100 times too large.

Batch statistics

For each property report the mean and standard deviation and, when comparing groups, the coefficient of variation or a confidence interval. Also:

• Discard specimens that break outside the narrow section or at a visible flaw, and test replacements (the standard itself requires this).
• To compare formulations or processing routes, use a statistical test (Student’s t-test or ANOVA) rather than eyeballing the means.

Common mistakes

1. Calculating modulus from crosshead displacement and comparing it with datasheet values measured with an extensometer.
2. Using nominal dimensions instead of those measured on each specimen.
3. Including the toe region in the linear fit, which lowers the modulus.
4. Mixing units: strain in % in a formula that expects a fraction.
5. Comparing ASTM D638 and ISO 527 results without stating method, specimen and speed.
6. Not conditioning moisture-sensitive materials (nylon, PLA, biopolymers), which noticeably changes their stiffness and ductility.

Formula summary

Property	Formula	Unit
Stress	σ = F / A₀	MPa
Strain	ε = ΔL / L₀	– or %
Elastic modulus	E = Δσ / Δε (linear region)	MPa or GPa
Tensile strength	σ_max = F_max / A₀	MPa
Elongation at break	ΔL_break / L₀ × 100	%
Toughness	Area under σ–ε	MJ/m³

MIND4SCE-Tensile runs this whole process automatically: it detects the force, extension and time columns in your Excel or CSV file, applies the ASTM D638 specimen geometry, calculates every property with its modulus fit and R², and compares groups statistically.