From Pressure Vessel Design: The Direct Route
The Gross Plastic Deformation Design Check (GPD-DC) deals with
the main failure mode gross plastic deformation and
the secondary failure mode excessive local strain,
with regard to
short-time response, i.e. excluding creep effects, and
single monotonic application of actions.
Figs. 4.1a d show four types of such responses of real structures made of real materials. Fig. 4.1a shows a load versus displacement curve that is typical for experimental results with tensile bars and trusses subjected to axial forces at ambient temperatures, or results for cylindrical or spherical shells under internal pressure, made of mild steel or any other material with pronounced yield point at the testing temperature.
Figure 4.1: (a) Load versus displacement curve, type 1: Three-bar truss made of mild steel ; (b-1) Load versus displacement curves, type 2: Uniformly loaded, simply supported beam, I-shaped cross section, made of mild steel ; (b-2) Load versus displacement curve, type 2: Dished end, internal pressure, made of mild steel ; (c) Load versus displacement curve, type 3: Post buckling of a cylindrical shell under torsion ; (d) Load versus displacement curve, type 4: Three-bar truss made of aluminium .
When the monotonically increasing load reaches the unrestricted plastic flow load A up the rate of change becomes zero, or nearly zero, but the structure can still carry larger loads, up to the ultimate load. The increase in load carrying capacity is mainly due to the strain hardening of the material, possibly enhanced by geometric effects.
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