WCJ
Geotechnical
- Jun 23, 2012
- 6
I hope I'm doing something fundamentally wrong that somebody can point out!
I looked up published stress-concentration factors (SCF) for a cylindrical rod with a notch in bending only (1) and tried to simulate the same condition with Solidworks Premium's linear CAD and FEM (2). My conundrum is that I'm getting much higher SCFs from Solidworks than published. When computing SCF from Solidworks (SW) results, I'm taking the ratio of the maximum Y Normal stress (the component along the rod, the other components and the von Mises stress being smaller) in the notch to the extreme-fiber value away from the notch. (The latter can, of course, be computed analytically, and SW gives near-perfect agreement.) Is this the correct way to compute SCF?
1) For a single circumferential notch with a cross section equivalent to NF24 threads (having the largest possible notch-bottom radius that's tangent to the thread walls, .0060", and corresponding thread depth, .0256") cut into a rod with the major diameter of a 5/16" bolt, Noda and Takase [1999 -- see attached PDF file] give SCF = 3.54. (For a factor-of-four smaller notch-bottom radius and correspondingly larger thread depth of .0301", SCF = 6.70.) These are complicated calculations from the published formulae; all I can say is that I believe I did them correctly and am able to get agreement with Noda and Takase's Figure 14 for several test cases.
2) In SW I set up a rod of the same diameter with the same notch shape in a case of "pure bending" -- stress in the extreme fiber is uniform along the length. (This was achieved using equal and opposite "Remote Load (Direct transfer) Moments" applied to the opposing faces of the rod, with "Use inertial relief" stabilizing the model -- no fixtures.) The maximum stress in the extreme fiber away from the notch was the same as calculated for pure bending in the absence of a notch (either analytically or with SW). The maximum stress at the bottom of the notch was found to be a factor of 6.1 larger than the pure-bending maximum. This result is quite insensitive to mesh resolution over the four meshes I tried, so I tend to believe it.
I haven't been able to figure out why this SW SCF result of 6.1 is so much larger than the stress-concentration factor of 3.54 predicted by Noda and Takase. [SW also gives an approximately factor-of-two larger SCF than Noda and Takase for the smaller notch bottom radius mentioned in (1).] Any suggestions where I might be going wrong? -- jclarkw
I looked up published stress-concentration factors (SCF) for a cylindrical rod with a notch in bending only (1) and tried to simulate the same condition with Solidworks Premium's linear CAD and FEM (2). My conundrum is that I'm getting much higher SCFs from Solidworks than published. When computing SCF from Solidworks (SW) results, I'm taking the ratio of the maximum Y Normal stress (the component along the rod, the other components and the von Mises stress being smaller) in the notch to the extreme-fiber value away from the notch. (The latter can, of course, be computed analytically, and SW gives near-perfect agreement.) Is this the correct way to compute SCF?
1) For a single circumferential notch with a cross section equivalent to NF24 threads (having the largest possible notch-bottom radius that's tangent to the thread walls, .0060", and corresponding thread depth, .0256") cut into a rod with the major diameter of a 5/16" bolt, Noda and Takase [1999 -- see attached PDF file] give SCF = 3.54. (For a factor-of-four smaller notch-bottom radius and correspondingly larger thread depth of .0301", SCF = 6.70.) These are complicated calculations from the published formulae; all I can say is that I believe I did them correctly and am able to get agreement with Noda and Takase's Figure 14 for several test cases.
2) In SW I set up a rod of the same diameter with the same notch shape in a case of "pure bending" -- stress in the extreme fiber is uniform along the length. (This was achieved using equal and opposite "Remote Load (Direct transfer) Moments" applied to the opposing faces of the rod, with "Use inertial relief" stabilizing the model -- no fixtures.) The maximum stress in the extreme fiber away from the notch was the same as calculated for pure bending in the absence of a notch (either analytically or with SW). The maximum stress at the bottom of the notch was found to be a factor of 6.1 larger than the pure-bending maximum. This result is quite insensitive to mesh resolution over the four meshes I tried, so I tend to believe it.
I haven't been able to figure out why this SW SCF result of 6.1 is so much larger than the stress-concentration factor of 3.54 predicted by Noda and Takase. [SW also gives an approximately factor-of-two larger SCF than Noda and Takase for the smaller notch bottom radius mentioned in (1).] Any suggestions where I might be going wrong? -- jclarkw
