In creating automotive structures, larger section sizes are desired to provide a stiffer body, yet wall thickness is typically decreased to offset the increase in mass. There is a temptation to throw as strong a material as possible into the design to compensate for this strength compromised structure. In compression-dominated members, any local buckling of the surface will reduce load-carrying capability. They are further compromised by the myriad holes and features needed for integration reasons, shown here :
By calculating the critical buckling stress for the section, we can better refine our choice of material parameters. Shown below is the equation to determine the critical buckling stress of a simple section. Please note that in this equation, geometry is the main factor with no influence of material strength.
First, the edge boundary conditions and the aspect ratio (a/b) of the compression surface(s) are needed to determine the buckling coefficient kc.
Using the buckling coefficient chart
we observe that as the aspect ratio (a/b) approaches 2, the buckling coefficient (kc) can be considered constant for a defined edge boundary condition.
Depending on the section, the edge boundary conditions can fall between fully constrained (Curve A) and simply supported (Curve C). For this example we will assume a balance between simple supported (kc = 4) and fixed (kc = 7), so kc will be 5.5
Assuming Poisson’s Ratio for steel is 0.3 and Young’s modulus of elasticity is 29.6×106 psi, the critical buckling stress is:
By plotting the critical stress against the t/b ratio we can then narrow down our material parameters. For a given t/b ratio, there is a critical stress above which
the material is no longer effective in resisting local buckling. Increasing the material grade will get you very little performance as the structure is “geometry-limited”.
Any improvements will need to be focused on section shape before reconsidering material grade.
Another way to interpret is to consider the typical yield strengths of common steel grades. For a t/b ratio that falls to the right of the critical stress curve, a material upgrade could improve performance. However, for those ratios that fall to the left of the curve, the shape of the section (compression side) will drive performance.
A t/b ratio of 0.02 is a likely ratio in automotive structures (such as a 1.2mm thick surface (t) with a width of 60mm (b)). Using Figure 6, for 0.02, the critical buckling stress is approximately 420MPa. A BIW engineer could specify up to a DP780 material and be confident the material is working efficiently. Anything more than that will fall to the left of the critical stress curve and provide little strength benefit.