Experimental investigation of subsequent yield surfaces using the Moiré method

Abstract

An initial and three subsequent yield surfaces were investigated for aluminium 6061-T 651. The study was approached using theory of plates rather than thin-walled tubes because it was desired to investigate the entire two-dimensional space. The oblique shadow moiré method was employed to measure the deflexions of plates and the equipment used was simple, reducing considerably the scatter in the results. Since the plate thickness was a variable as far as strength criteria were concerned the study was limited to the relative shape of yield surfaces. Combinations of various ratios of bending moments were obtained in the second and fourth quadrants of the two-dimensional bending moment space by using rhomboid plates loaded anticlastically. The first and third quadrants were investigated using a superposition of a square plate supported at the four corners and loaded at the centre, and a square plate supported at two diagonally opposite corners and loaded at the centre. This approach produced combinations of various ratios of bending moments in plates loaded synclastically. To establish the initial yield surface for comparing it to subsequent yield surfaces, a series of specimens were loaded anticlastically, synclastically or subjected to uniaxial bending. The principal bending moments M 1 and M 2 at yielding were plotted in the two dimensional bending moment space. The shape of the initial locus fell between the Tresca and Mises loci. A first subsequent yield surface was established by pre-loading a series of plates anticlastically into the plastic region with M 1 = − M 2. A second subsequent yield surface was defined in the same manner as the first subsequent surface except that the direction for pre-bending into the plastic range was such that M 1 ≈ − 1 2 M 2. A third partial subsequent yield surface was found in the fourth quadrant only. The pre-loading path in this case was the same as in the first subsequent surface ( M 1 = − M 2), the only difference being that the pre-loading was advanced further in the plastic region and it was followed by a recovery of the plates for three months at room temperature. The initial and the three subsequent yield surfaces were compared and important features of the behaviour of metals subjected to any type of biaxial loading and to any straining history were disclosed.