Fiber Tensile Strength Simulator: Stress-Strain Analysis

simulator intermediate ~10 min
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Break force = 0.126 N for a 20 µm fiber at 400 MPa

A 20 µm diameter fiber with 400 MPa yield strength breaks at 0.126 N. With 15% elongation, the toughness is approximately 30 MJ/m³.

Formula

σ = E × ε (Hooke's law, elastic region)
F_break = σ_yield × π × (d/2)²
Toughness ≈ ½ × σ_yield × ε_break (triangular approximation)

Pulling Fibers Apart

Tensile testing is the most fundamental characterization of any textile fiber. A single filament is gripped at both ends, stretched at constant rate, and the force-elongation response is recorded. This simple test reveals everything about a fiber's mechanical personality — stiffness, strength, extensibility, and toughness. The resulting stress-strain curve is the fiber's mechanical fingerprint.

The Stress-Strain Curve

In the elastic region, stress is proportional to strain (Hooke's law). The slope is Young's modulus — a measure of intrinsic stiffness. At the yield point, permanent deformation begins as molecular chains slip past each other or crystalline domains break apart. Beyond yield, the curve may strain-harden (as chains orient) or neck (as localized thinning concentrates stress), eventually reaching the breaking point.

From Fiber to Fabric

Individual fiber properties propagate to yarn and fabric performance, but not linearly. A woven fabric's tensile strength depends on fiber strength, yarn twist (which converts axial fiber stress to helical stress), weave structure (which distributes load across interlaced yarns), and friction between fibers. Understanding the single-fiber starting point is essential for predicting and engineering fabric-level behavior.

High-Performance Fibers

Modern engineering fibers push the boundaries of the stress-strain envelope. Aramid fibers (Kevlar) combine high strength (3 GPa) with high modulus (70-130 GPa). Carbon fibers achieve even higher modulus (230-700 GPa). Ultra-high-molecular-weight polyethylene (Dyneema/Spectra) offers the highest specific strength of any commercial fiber. Each represents a different optimization of the molecular architecture visualized in this simulation.

FAQ

What determines fiber tensile strength?

Fiber tensile strength depends on molecular chain orientation, degree of crystallinity, molecular weight, and defect density. Highly oriented, crystalline polymers like ultra-high-molecular-weight polyethylene (Dyneema) achieve strengths exceeding 3 GPa — stronger per unit weight than steel.

What is the stress-strain curve of a fiber?

The stress-strain curve plots applied stress (σ = F/A) against resulting strain (ε = ΔL/L). The initial linear slope is Young's modulus (stiffness). The curve then yields (plastic deformation begins) and eventually the fiber breaks. The area under the curve represents toughness — total energy absorbed before failure.

What is tenacity in textiles?

Tenacity is specific strength — breaking force per unit linear density (g/denier or cN/tex). It normalizes for fiber thickness, allowing comparison across different fiber types. High-tenacity nylon (8-9 g/denier) is used for tire cords, while regular nylon textile fiber is 4-5 g/denier.

Why does fiber diameter matter?

Breaking force scales with cross-sectional area (proportional to d²), so doubling the diameter quadruples the force needed to break the fiber. However, thinner fibers are more flexible (bending stiffness scales with d⁴), which is why microfibers (d < 10 µm) produce softer, more drapeable fabrics.

Sources

Embed

<iframe src="https://homo-deus.com/lab/textile-engineering/fiber-strength/embed" width="100%" height="400" frameborder="0"></iframe>
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