Question

Use Matlab to make a graphical comparison between the maximum shear stress and distortion

energy failure criteria for cases of plane stress, for AISI 1010 HR steel. Plot the contour for the
distortion energy theory and the maximum shear stress theory that separates safe from unsafe loading (in the
σB versus σA plane). Make sure to scale your plot equally in the x- and y-direction(hint: axis equal). Add a
grid and axes labels to the plot. Mark the following stress states in your figure with black markers and explain
whether the failure criteria predict failure or not.
a) σ1= 200 MPa, σ2= 190MPa, σ3= 0
b) σ1= 100 MPa, σ2= 0 MPa, σ3=-30 MPa

Answer 1

To compare the maximum shear stress and distortion energy failure criteria for plane stress in AISI 1010 HR steel, you can use MATLAB to plot the contours in the σB versus σA plane. The critical shear stress and critical distortion energy can be calculated using specific formulas. By marking the given stress states on the plot, you can determine whether the failure criteria predict failure or not.

Step-by-step explanation:

To make a graphical comparison between the maximum shear stress and distortion energy failure criteria in cases of plane stress for AISI 1010 HR steel using MATLAB, you will need to define the stress state by specifying the values of σ1, σ2, and σ3.

For the maximum shear stress theory, the failure criterion states that failure occurs when the maximum shear stress reaches a critical value. The critical shear stress can be calculated using the formula:

τ(max) = (σ1 - σ3) / 2

For the distortion energy theory, the failure criterion states that failure occurs when the distortion energy per unit volume reaches a critical value. The critical distortion energy can be calculated using the formula:

DE = √((σ1 - σ2)^2 + (σ2 - σ3)^2 + (σ3 - σ1)^2) / √2

You can plot the contour for the distortion energy theory and the maximum shear stress theory in the σB versus σA plane, and mark the stress states given in the question to determine whether the failure criteria predict failure or not.