Analysis of Rectangular and Circular Cross-section Power Hardening Elements Under Pure Bending

Engineering theory of elastic plastic bending is used in solving a grate variety of strength and durability problems. The accuracy of analysis depends on stress-strain curve idealization model. The elastic linear hardening stress-strain relation is simple and frequently used. But the actual stress-strain behaviour of ductile material in plastic region is non-linear and, therefore, elastic power hardening material model is more preferable. Moreover, the properties of monotonic tension and compression as proportional limits and parameters of hardening can differ. In this regard, analytical solution for rectangular and circular cross-section elements loading by monotonic elastic plastic pure bending is presented in the paper. The simple power relation of stress and strain response is used. The equations describing deviation of the stress neutral axis from centroidal axis of an element and dimensionless bending moment are derived.Mechanical properties of majority of ductile materials determined by tensile and compressive testing usually differ. Consequently constants of idealized stress-strain curves (proportional limits and parameters of hardening) are also different. Analysis of pure bending of rectangular and circular cross-section element can be realized with regard to this. The values of dimensionless bending moment can be found directly from presented diagrams or calculated by deduced formulas.