Interactive software for calculating the principal stresses of compacted cohesive powders with the Warren-Spring equation

The Unconfined Yield Stress (σc) and Major Consolidation Stress (σ1) of a cohesive powder′s compact are found by constructing two Mohr semicircles that are tangential to the Yield Loci Curve (YLC); the first passing through the origin (0,0) and the second at the consolidation conditions (σ0,τ0). When the YLC can be described by the Warren-Spring equation (τ/C)n = (σ + Τ)/Τ or an alternative algebraic expression, this translates into finding the solution of two pairs of simultaneous equations that set the conditions for the tangential YLC and corresponding Mohr semicircles to have the same value and slope at their respective contact points. Once the Mohr semicircle′s equation that corresponds to the consolidation conditions has been found, the Effective Angle of Internal Friction (δ) is calculated in a similar manner. The numerical calculation procedure has been automated in a freely downloadable program posted on the web as a Wolfram Project Demonstration. It allows the user to choose and adjust the values of C, T, n and σ0, and the plot′s scales, by moving sliders on the computer screen. The program calculates and displays the corresponding values of σc, σ1 and δ, and plots the YLC, two Mohr semicircles and the line that defines δ. Since a linear YLC is just a special case of the model where n = 1, the program can be used with input parameters originally obtained by linear regression. But although the program can render reasonable estimates of the principal stresses σc, σ1 and δ in this case too, the physical meaning of C, and especially T, is unclear when calculated by extrapolation instead of being determined experimentally.

The Unconfined Yield Stress (σc), Major Consolidation Stress (σ1) and Effective Angle of Internal Friction (δ) of a compact that obeys the Warren-Spring equation are calculated with a Wolfram Demonstration. The Yield Loci Curve′s C, T, n and σ0 are adjusted with sliders to display the σc, σ1 and δ values and plot the Mohr semicircles and ‘friction line’.Figure optionsDownload as PowerPoint slide