Direct cyclic and low-cycle fatigue analyses

This problem contains basic test cases for one or more Abaqus elements and features.

The tests in this section verify the direct cyclic analysis procedure and the low-cycle fatigue procedure using the direct cyclic approach for structures subjected to different types of cyclic loadings, which include distributed forces, concentrated forces, displacements, and temperatures. The direct cyclic and low-cycle fatigue procedures are also verified when they are preceded or followed by other procedures in a single analysis or in a restart analysis.

This page discusses:

A simple cube
A simple sheet with a circular hole
A round notch bar

ProductsAbaqus/Standard

A simple cube

Elements tested

C3D8 C3D10

Features tested

A simple cube subjected to different cyclic loadings.

Problem description

The model in each test consists of twelve tetrahedral elements or one brick element. All the nodes at one end ( $z = 0$ ) are constrained along the z-axis. Cyclic distributed loads, concentrated loads, or displacements are applied in the z-direction to the nodes at the other end ( $z = 1$ ). Both kinematic hardening plasticity models and two-layer viscoplasticity models are used.

Results and discussion

The results obtained using the direct cyclic procedure are compared with those obtained using the classical approach, which involves applying cyclic loadings repetitively to the model in multiple steps using the static or quasi-static procedures. The shapes of the stress-strain curves in a stabilized cycle obtained using both approaches are consistent.

Input files

dircyclic_cload_ffouri_ftinc.inp: Cyclic concentrated loadings with fixed number of Fourier terms and fixed time incrementation.
dircyclic_cload_ffouri_ftinctp.inp: Cyclic concentrated loadings with fixed number of Fourier terms and fixed time incrementation used with the TIME POINTS option.
dircyclic_cload_vfouri_ftinc.inp: Cyclic concentrated loadings with varying number of Fourier terms and fixed time incrementation.
dircyclic_cload_vfouri_ftinctp.inp: Cyclic concentrated loadings with varying number of Fourier terms and fixed time incrementation used with the TIME POINTS option.
dircyclic_cload_ffouri_vtinctp.inp: Cyclic concentrated loadings with fixed number of Fourier terms and automatic time incrementation used with the TIME POINTS option.
dircyclic_precload.inp: Static pre-loading step.
dircyclic_cload_ffouri_ftinc_r.inp: Restart of dircyclic_precload.inp. Cyclic concentrated loadings with fixed number of Fourier terms and fixed time incrementation.
dircyclic_cload_ffouri_ftinc_rs.inp: Restart of dircyclic_cload_ffouri_ftinc_r.inp. Cyclic concentrated loadings with fixed number of Fourier terms and fixed time incrementation.
dircyclic_cload_ffouri_ftinc_ps.inp: Post output of dircyclic_cload_ffouri_ftinc_r.inp.
dircyclic_cload_ffouri_ftinc_ms.inp: Multiple direct cyclic analysis steps in a single analysis. Cyclic concentrated loadings with fixed number of Fourier terms and fixed time incrementation.
dircyclic_dload_ffouri_ftinc.inp: Cyclic distributed loadings with fixed number of Fourier terms and fixed time incrementation.
dircyclic_disp_ffouri_ftinc.inp: Cyclic displacement loadings with fixed number of Fourier terms and fixed time incrementation.
dircyclic_cloadc_vfouri_ftinc.inp: A general static step with contact followed by a direct cyclic step involving cyclic concentrated loadings with varying number of Fourier terms and fixed time incrementation.

A simple sheet with a circular hole

Elements tested

CPE4R

Features tested

A simple sheet with a circular hole subjected to different cyclic loadings.

Problem description

The undeformed square sheet is 1.5 mm thick and is 7.5 mm on each side. It has a centrally located internal hole of radius 0.25 mm. The body is modeled with 128 plane strain reduced-integration elements (element type CPE4R). The symmetry conditions at $x = 0$ and at $y = 0$ are imposed with a boundary condition. The edges parallel to the x-axis are restrained from stretching in the y-direction. Cyclic concentrated forces or cyclic distributed forces are imposed on the right-hand edge of the mesh in the x-direction. For the case where cyclic thermal loadings read from the results file of a heat transfer analysis are imposed, the right-hand edge is also constrained in the x-direction. Both kinematic hardening plasticity models and two-layer viscoplasticity models are used.

Results and discussion

The results (stress-strain curves) obtained using the direct cyclic procedure are compared with those obtained using the classical approach, which involves applying cyclic loadings repetitively to the model in multiple steps using the static or quasi-static procedures. The shapes of the stress-strain curves in a stabilized cycle obtained using both approaches are consistent. In the case where cyclic concentrated forces are applied to the model, plastic ratcheting occurs in which the shape of the stress-strain curve does not change but the mean value of the strains keeps shifting. This behavior is predicted by using both the direct cyclic approach and the classical approach.

Input files

dircyclic_heat.inp: Heat transfer analysis.
dircyclic_temp_ffouri_ftinc.inp: Cyclic thermal loadings with temperatures read from the results file of the heat transfer run (dircyclic_heat.inp).
dircyclic_rtemp_vfouri_ftinc.inp: Cyclic thermal loadings with temperatures read from the results file of the heat transfer run (dircyclic_heat.inp) and ramped up to their initial condition values.
dircyclic_dload_vfouri_ftinc.inp: Cyclic distributed loadings with varying number of Fourier terms and fixed time incrementation.
dircyclic_cload_vfouri_vtinctp.inp: Cyclic concentrated loadings with varying number of Fourier terms and automatic time incrementation used with the TIME POINTS option.
dircyclic_cload_vfouri_vtinc_ps.inp: Post output of dircyclic_cload_vfouri_vtinctp.inp.

A round notch bar

Elements tested

CAX4

Features tested

A round notch bar subjected to a cyclic loading.

Problem description

The undeformed round notch bar is 75 mm long, with a 2 mm notch radius and a section diameter of 10 mm. The body is modeled with 672 4-node bilinear axisymmetric quadrilateral elements (element type CAX4). The symmetry conditions at $y = 0$ are imposed with a boundary condition. The edges parallel to the x-axis are subjected to displacement loadings in the y-direction. A static step with a displacement loading of 0.25 mm is followed by a low-cycle fatigue step. A sinusoidal cyclic displacement loading between 0.375 mm and 0.125 mm is applied to the low-cycle fatigue step with a time period of 80 seconds. Linear kinematic hardening plasticity model is used.

Results and discussion

The results (scale stiffness degradation, SDEG) obtained using the low-cycle fatigue procedure are compared with those available in the literature (see Pirondi, 2003). As the cycling proceeds, damage accumulation at the notch root continues to increase. When the cycle number reaches 50, SDEG is equal to 0.74, similar to the result obtained in Pirondi (2003).

Input files

directcyclic_fatigue_rnb.inp: A static step followed by a low-cycle fatigue step subjected to cyclic displacement loadings.
directcyclic_fatigue_rnb_rest.inp: A low-cycle fatigue step restarted from the low-cycle fatigue step in directcyclic_fatigue_rnb.inp.
directcyclic_fatigue_rnb_rest2.inp: A low-cycle fatigue step restarted from the static step in directcyclic_fatigue_rnb.inp.
directcyclic_fatigue_rnb_ps.inp: Post output of directcyclic_fatigue_rnb.inp.

References

Pirondi, A., and N. Bonora, “Modeling Ductile Damage under Fully Reversed Cycling,” Computational Materials Science, vol. 26, pp. 129–141, 2003.