polymer-engineering

name	polymer-engineering
description	Polymer engineering — viscoelasticity, creep, stress relaxation, time-temperature superposition, injection molding DfM, failure modes, polymer selection, polymer properties table, Arrhenius degradation.
metadata	{"priority":7,"promptSignals":{"phrases":["polymer","plastic","viscoelastic","creep","injection molding","thermoplastic","thermoset","rubber","elastomer","polymer selection"],"minScore":3}}

Polymer Engineering — Complete Skill

Polymer Classification

Thermoplastics vs. Thermosets

Thermoplastics: linear/branched chains; melt on heating; recyclable Thermosets: crosslinked network; char/degrade; higher temperature resistance; no remelt Elastomers: highly crosslinked rubber; large reversible deformation (>100%)

Crystallinity: Amorphous: random chain arrangement; transparent; T_g controls properties Semi-crystalline: ordered + amorphous regions; opaque; T_m (melt) + T_g (amorphous phase)

Glass Transition Temperature (T_g)

Below T_g: glassy, brittle, high modulus (1-4 GPa) Above T_g: rubbery, compliant, low modulus (1-10 MPa for amorphous; higher if crystalline)

Fox equation (copolymers): 1/T_g = w₁/T_g1 + w₂/T_g2 (w = weight fractions)

Polymer Properties

Common Engineering Polymers

Polymer	T_g [°C]	T_m [°C]	E [GPa]	Sy [MPa]	Su [MPa]	Notes
HDPE	-130	130-140	0.8-1.5	20-30	25-40	Semi-cryst, chemical resistant
PP	-10	160-170	1.3-2.0	30-40	30-50	Low density, fatigue resistant
LDPE	-120	105-115	0.1-0.3	8-15	10-18	Flexible, packaging
PVC (rigid)	87	—	2.4-4.2	40-60	45-80	Amorphous, fire retardant
PET	78	260	2.5-4.5	55-70	55-80	Semi-cryst, packaging, fibers
Nylon 66	57	265	2.5-3.5	75-90	80-100	Water absorbing, good fatigue
Nylon 12	-65	178	1.6-2.0	45-55	50-65	Low moisture absorption
PC	147	—	2.3-2.4	55-65	55-65	High impact, optical clarity
ABS	105	—	2.0-2.6	40-50	40-60	Rubber-toughened PS
PEEK	143	343	3.6-4.0	90-100	100-115	High temperature, biocompat
PTFE	-110	327	0.5	10-20	20-30	Chemical inert, low friction
Epoxy	120-200	—	3-5	60-100	60-90	Thermoset, brittle, adhesive

Filled polymers: 30% glass fiber → E ×3-4, Sy ×2, lower CTE

Viscoelasticity

Linear Viscoelastic Behavior

Time-dependent response: stress depends on strain history Maxwell model (spring + dashpot in series): dε/dt = (1/E)dσ/dt + σ/η Stress relaxation: σ(t) = σ₀ × e^(-t/τ) (τ = η/E = relaxation time)

Kelvin-Voigt model (spring + dashpot in parallel): σ = E ε + η dε/dt Creep: ε(t) = (σ₀/E)(1 - e^(-t/τ)) (retardation time τ = η/E)

Standard linear solid (SLS): better representation of real polymers Maxwell in parallel with spring: captures both creep recovery and stress relaxation

Storage and Loss Moduli (DMA)

E*(ω) = E'(ω) + iE''(ω) E' = storage modulus (elastic component) E'' = loss modulus (viscous component) tan δ = E''/E' = loss factor (damping)

Peak in tan δ occurs near T_g (shifts to higher T at higher frequency) DMA measures T_g more accurately than DSC for engineering purpose

Time-Temperature Superposition (TTS)

Master curve: E' vs. frequency at reference T, using shift factor a_T WLF equation (near T_g): log(a_T) = -C₁(T-T_ref) / (C₂ + (T-T_ref)) Universal: C₁ = 17.44, C₂ = 51.6 K (with T_ref = T_g)

Arrhenius (above T_m for crystalline): log(a_T) = E_a/(2.303 R) × (1/T - 1/T_ref)

Application: long-term creep prediction from short-time high-temperature tests

Creep

Creep Behavior

Three stages: primary (decelerating), secondary (steady-state), tertiary (accelerating → fracture)

Power law (steady-state creep): ε̇ = A × σⁿ × exp(-Q/RT) n = stress exponent (2-8 for polymers) Q = activation energy, A = material constant

Creep compliance: J(t) = ε(t)/σ₀ [Pa⁻¹] (increases with time) D(t) = J(t) for tensile; J(t) = compliance in shear

Isochronous stress-strain curve: stress vs. strain at constant time (t = 100 hr, 1000 hr) Used for design: select allowable stress from creep curve at design life

Design rule: for stressed plastic parts, use allowable stress = σ at 1-2% creep strain at design life time from isochronous curve

Stress Relaxation

σ(t) = σ₀ × E_r(t)/E_0 E_r(t) = relaxation modulus [Pa]

Practical consequence: Bolted joints: bolt preload relaxes over time → retighten or use spring washer Snap fits: design load must account for reduced modulus at end of life

Injection Molding — Design for Manufacturability (DfM)

Wall Thickness

Recommended nominal thickness: 1.5-4 mm (most materials) Maximum: limit by: cooling time ∝ t², warpage, sink marks Minimum: limited by fill pressure, flow length/thickness > 150-200 → incomplete fill

Uniform wall thickness: avoid thick-to-thin transitions; thick sections → sink marks, voids Rib design: t_rib = 0.5-0.7 × t_wall (prevents sink marks on opposite face) Rib height: ≤ 3 × t_wall; fillet radius r ≥ 0.25 × t_wall at base

Draft Angles

Standard: 1-2° per side (minimum for release) Textured surfaces: 3-5° (deeper texture → more draft) Ribs inside: 0.5-1° minimum

Gates, Runners, Venting

Gate: locating at thickest section (last to solidify = avoids shrinkage there) Vent: 0.025-0.05 mm deep at parting line, opposite gate Balanced runners: minimize pressure drop variation

Shrinkage and Warpage

Shrinkage: 0.5-2% (amorphous) to 1-4% (semi-crystalline, direction dependent) Warpage: from differential shrinkage (asymmetric walls, anisotropic fiber orientation) Control: uniform cooling channels, symmetric part geometry, fiber orientation control

Flow Length and Fill

Flow length limit: L/t < 200 (semi-crystalline) to < 300 (amorphous) Gate size: 50-80% of wall thickness (thin gate → high shear heating → degradation)

Failure Modes in Polymers

Crazing: surface micro-cracks perpendicular to tension; precursor to fracture; PC, PS, PMMA Environmental stress cracking (ESC): chemical + stress → crack formation; most common plastics failure mode Fatigue: S-N curves exist but hysteretic heating can dominate (especially in elastomers) UV degradation: photooxidation → embrittlement; use UV stabilizers (HALS, UV absorbers) Thermal degradation: Arrhenius: log(life) ∝ 1/T → 10°C rule of thumb (life halves per 10°C) Hydrolysis: polyesters (PET, PBT) and nylons absorb water → chain scission → strength loss

Material Selection Guide

Application	Recommended Polymer
Chemical tanks	HDPE, PP, PVDF, PTFE
Structural under load	PEEK, PEI, Nylon GF30
High temperature (> 150°C)	PEEK, PPS, PAI, PTFE
Optical/clear	PC, PMMA, PS
Flexible hose/seal	NBR, EPDM, FKM (Viton)
Gear/bearing	Nylon 66, POM (acetal), PEEK
Outdoor UV exposure	ABS+UV stab, ASA, PVDF
Food contact	PP, HDPE, PC (BPA-free), PETG
Flame retardant	V-0 rated: PPS, PAI, FR-ABS

Output

Provide: polymer recommendation for application, key properties (E, Sy, T_g, T_max), creep strain at design life [%] from isochronous curve, T_g check vs. service temperature, injection molding wall thickness [mm], draft angle [°], shrinkage allowance [%], ESC/UV degradation risk assessment.