Materials Engineering 2D: Crystal Lattice Under Stress

Materials Engineering (2D)

Applied stress 0 MPa

Temperature 293 K

Defect density Low

Current stress

0 MPa

Elongation

0.0%

Yield strength

250 MPa

State

Elastic

How it works

This is the 2D cross-section companion to the 3D crystal-lattice simulator: the same simple-cubic lattice of bonded atoms, viewed here as a flat row-and-column slice so the elastic-to-plastic-to-fracture path is easy to read directly against a live stress-strain curve instead of an orbiting scene. Below the yield point, bonds stretch reversibly and strain is proportional to stress (Hooke's law). Past yield, dislocations glide through the lattice — visualized as a slipped block of atoms — and strain grows permanently until bonds snap at the fracture stress.

sigma = E * epsilon         (elastic region, E = Young's modulus)
sigma_yield falls as T rises and defect density rises
fracture when sigma >= sigma_yield * (1 + hardening) and epsilon > eps_crit

Applied stress — the tensile load pulling the lattice apart, in MPa.
Temperature — higher temperature softens bonds and lowers the yield point, mimicking thermal weakening.
Defect density — vacancies and impurities that make dislocations easier to nucleate, lowering yield strength further.
The strip chart below the lattice traces the same run as a stress-strain curve — the straight elastic ramp, the bending plastic region and the vertical drop at fracture.

This elastic to plastic to fracture sequence is exactly what a real tensile-test stress-strain curve captures, and it is the basis for every material safety factor an engineer specifies.