**Effects of Non-Associated Flow on Residual Stress Distributions in Crankshaft Sections Modeled as Pressure-Sensitive Materials under Fillet Rolling**

*Shin-Jang Sung, Jwo Pan, Yusuf Ali (Ford), Jagadish Sorab (Ford) and Cagri Sever (Ford)*

The evolution equation for the active yield surface during the unloading/reloading process based on the pressure-sensitive Drucker–Prager yield function and a recently developed anisotropic hardening rule with a non-associated flow rule is presented. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into the commercial finite element program ABAQUS with consideration of finite deformation. A two-dimensional plane strain finite element analysis of a crankshaft section under fillet rolling was conducted. After the release of the roller, the magnitude of the compressive residual hoop stress for the material with consideration of pressure sensitivity typically for cast irons is smaller than that without consideration of pressure sensitivity. In addition, the magnitude of the compressive residual hoop stress for the pressure-sensitive material with the non-associated flow rule is smaller than that with the associated flow rule. The computational results indicate that without consideration of pressure sensitivity and the non-associated flow rule, the residual stresses in crankshaft sections under fillet rolling are overestimated.

Figure 1. A portion of the crankshaft section.

Figure 2. A two-dimensional finite element model consisting of a portion of the crankshaft section, a primary roller and a secondary roller.

Figure 3. The definitions of the cylindrical coordinates for the crankshaft fillet. The thick line indicates the location where a crack occurred in the bending fatigue test.

Figure 4. The angular distributions of the residual hoop stress σ_{θθ}, the residual radial stress σ_{rr}, and the residual shear stress σ_{rθ} along the fillet surface based on the Mises yield function and the Drucker-Prager yield function with *µ* = 0.03 and different flow rules when the roller is released.

- S.-J. Sung, J. Pan, M. Y. Ali, J. Sorab and C. Server, 2015, “Effects of Non-Associated Flow on Residual Stress Distributions in Crankshaft Sections Modeled as Pressure-Sensitive Materials under Fillet Rolling,” SAE International Journal of Materials and Manufacturing
**8**(2), pp. 487-493. DOI: 10.4271/2015-01-0602. (SAE 2015-01-0602)