Charpy Impact Test - 2D Lab

What the test measures

A pendulum of mass m and arm L is released from angle a. At the bottom it breaks a notched bar and swings up to b on the other side. Energy balance: E = m g L (cos b - cos a). Nothing else is measured, so E is the total work the bar absorbed (elastic and plastic work, new surface, kinetic energy of the pieces and a little friction). This lab uses m = 21 kg, L = 0.82 m, a = 140 deg: capacity 298 J and a striking speed of 5.3 m/s, in the 5-5.5 m/s window of the standard ISO 148 / ASTM E23 tests.

Why steel turns brittle when it is cold

Body-centred cubic metals (ferritic steels) have a yield stress that rises steeply as temperature falls, because dislocation motion needs thermal help to overcome the lattice (Peierls) barrier: sy(T) = sa + sth exp(-beta T) + ky / sqrt(d) + dsig, with grain size d (Hall-Petch term) and any irradiation or precipitation hardening dsig. Cleavage needs a stress that a grain-boundary-limited crack can reach: sF = sF0 + kF / sqrt(d) (Cottrell-Petch), which depends only weakly on temperature. A sharp notch raises the peak tensile stress ahead of it to Q sy (slip-line field: Q about 2.57 for a V-notch in plane strain). The bar yields and tears (ductile) while Q sy < sF; it cleaves when Q sy(T) >= sF. The crossing temperature T* is the transition.

From stress to energy

Each specimen has its own cleavage stress (5 % scatter, an honest stand-in for the weakest-link statistics of real steel). With r = Q sy / sF the energy is E = E_LS + (E_US - E_LS) g(r), where g = 1 for r <= 1 (full ductile upper shelf) and g = exp(-(r-1)/0.07) above, which also gives the share of fibrous (shear) fracture surface. Averaging over the scatter gives the S-shaped curve and the mid-energy temperature E50, a common definition of the ductile-to-brittle transition temperature (DBTT). Face-centred cubic metals (aluminium, austenitic stainless steel) keep a flat, high energy: their yield stress hardly depends on temperature, so there is no transition.

What you can change and why it matters

Finer grains raise sy a little but raise sF more, so T* falls (about 100 K between 20 and 6 micrometres here). Irradiation hardening raises sy and pushes T* up: the reason reactor pressure vessels carry surveillance Charpy specimens. A plain bar has Q = 1 and never cleaves in this model. A larger release angle raises the strain rate slightly (sy ~ v^0.08). A long transfer lets the cold bar warm by Newton cooling, Ts = Ta + (Tbath - Ta) exp(-t/tau) with tau about 350 s for a 10 mm bar in air.

What is simplified

The constants are representative of a mild structural steel, not a measured material: real DBTT depends on composition, microstructure, thickness and loading rate, and E50 is not a design rule. Crack-tip mechanics are reduced to one number Q and one cleavage stress; the pendulum is treated as a point mass on a rigid arm, without windage or bearing friction (which a real machine corrects for). The specimen is drawn three times larger than real so that it is visible.

• Start with the mild steel at 20 C: the bar bends and absorbs about 165 J with a fibrous surface. Drag the bath to -100 C and strike again: a few joules and a bright crystalline surface.
• Press "Run temperature sweep" and watch the S-curve appear. Then pick "Fine grain steel": the whole curve slides left by about 100 K.
• Choose the Liberty-ship plate (coarse grain): it is already brittle at room temperature, the failure mode of those welded wartime ships in cold water.
• Set the bath to -40 C and raise the transfer time to 40 s: the bar warms by about 3 K more and behaves differently. This is why standards cap the transfer at 5 s.
• Select aluminium or stainless steel and sweep from -196 C: no transition at all.