Full-Range Compressive Stress–Strain Curves for Cold-Formed 304 Stainless Steel Circular Hollow Sections After Exposure to Vacuum Brazing

With the rapid development of microscale cellular structures, the small-diameter cold-formed welded stainless steel tubes have recently been used for creating the metallic lattice topologies with high mechanical properties. In this paper, to obtain the accurate material properties of the circular hollow section (CHS) under pure compression, a series of concentric compression tests are conducted on the millimeter-scale cold-formed 304 stainless steel circular tubular stub columns after exposure to a vacuum brazing process. The tests cover a total of 18 small-diameter stub tubes with measured thickness-to-diameter ratios (t / D) from 0.023 to 0.201. A generalized three-stage nominal stress–strain model is developed for describing the compressive behavior of the post-brazing CHSs over the full strain range. This mechanical model is especially applicable to computer code implementation. Hence, an interactive computer program is developed to simultaneously optimize three strain hardening exponents \((n_1 ,n_2 ,n_3 )\) in the expression of the model to produce the stress–strain curve capable of accurately replicating the test data. To further reduce the number of the model and material parameters on which this model depends, this paper also develops five expressions for determining the 2.5% proof stress \((\sigma _{p_2 } )\), \(n_2 \), the ultimate compressive strength \((\sigma _{p_3 } )\), \(n_3 \), and the ultimate plastic strain \((p_3 \% )\) for given experimental values of three basic material parameters \((E_0 ,\sigma _{0.01} ,\sigma _{0.2} )\). These expressions are validated to be effective for the CHSs with \(t{/}D\ge 0.027\). The analytically predicted full-range stress–strain curves have generally shown close agreement with the ones obtained experimentally.