Strength and Structure
Lecture notes for 4LC00 · TU/e Mechanical Engineering
A compression test on a polymer glass, and the model that explains it, built up one chapter at a time. Each step adds one ingredient from the notes and redraws the true stress–strain curve it predicts. Every label on the graph names the chapter that explains that feature, and links to it. Use the arrows or the chapter buttons to step through at your own pace. Behind the scenes the glass is a set of Maxwell elements in parallel (Section 5.5) that share one Eyring viscosity, which rounds off the yield point as in a real polymer. The parameters are illustrative, close to those of polycarbonate.
What you are seeing¶
Yield: stress-activated flow
Stress helps molecular segments over their energy barriers, so the viscosity of the glass collapses above a yield stress. That yield stress grows only with the logarithm of the strain rate, so a hundred times faster adds just a few MPa. See Section 6.1.
Hardening: the chain network
Entangled chains form a rubbery network in parallel with the glass. It is a hundred times softer than the glass, but it stiffens at large strain, so it takes over once the glass flows. The free energy splits into a glassy part and a network part , so their stresses add (Section 7.3).
Softening: ageing, erased
A glass slowly packs more densely over time, which raises its yield stress. Plastic deformation undoes that ageing, so after the peak the stress drops back to that of an unaged glass: strain softening. Ageing and rate dependence are the two time dependencies of Section 8.1.1.
Where to start¶
New to the course? Begin with the Preface, then work through the chapters in order.
Kinematics, force and stress, and the balance laws.
Hyperelasticity, viscoelasticity, viscoplasticity, and their formulation in three dimensions.
The influence and quantification of microstructure, micro-macro coupling, dislocations and polymer composites.
Vector and tensor calculus, and flow and structure.