# OS-V: 0270 Torsional Creep of Circular Shaft

This benchmark illustrates the structural response of a power law creeping material in a geometrical configuration subjected to pure torsion. OptiStruct examines strain at the edge of the shaft.

The model examines the torsional creep in circular shaft with 2 variations:

- Relaxation at constant twist
- Forward creep at steady twist rate

## Relaxation at Constant Twist

Twist is applied to the shaft and remains constant from 0 to 100 s. Total strain and
creep strains then analyzed.

### Model Files

Before you begin, copy the file(s) used in this problem
to your working directory.

### Benchmark Model

Four 20-noded brick elements, plus one 16-noded wedge are used. All nodes on lower
face are fixed in X, Y, Z.

- X, Y displacements given at all nodes of front face using cylindrical system: 0.002 mm
- Rotation is given at mid-side nodes: 0.001 radians

Uniform twist of 0.01 radians/unit length is held constant in time from 0 to 100 s.

Twist is instantaneously applied to the shaft and then maintained constant. The
initial response is elastic and subsequently the structure response with a
progressive accumulation of creep strain. Stress reduces (relaxes) slowly till 100 s
due to creep.

**Material Properties****Value**- Young's modulus
- 10 GPa
- Poisson's ratio
- 0.3
- Creep law equation
- ${\dot{\epsilon}}_{eq}=1000\text{}{\sigma}^{5}{}_{eq}$

Where,

- ${\dot{\epsilon}}_{eq}$
- Equivalent creep strain rate
- ${\sigma}_{eq}$
- Equivalent stress (Mises)

### Nonlinear Static Analysis Results

An implicit visco-elastic solution method was used. Displacement, total strain and
creep strain results are analyzed at the edge of the shaft at 100 s.

OptiStruct | NAFEMS | Normalized Target Value | |
---|---|---|---|

Total Strain (*10^{-3}) |
5.46 | 5.77 | 0.95 |

Creep Strain (*10^{-3}) |
4.85 | 4.77 | 1.01 |

Comparison of strain plots.

## Forward Creep at Steady Twist Rate

A steadily increasing twist is applied at constant rate to the shaft.

The stresses increase from zero to steady value. The loads, which cause this steady-state behavior are referred as “primary” loads.

This model is the same as used in Relaxation at Constant Twist; except the boundary
conditions.

### Model Files

Before you begin, copy the file(s) used in this problem
to your working directory.

### Benchmark Model

Four 20-noded brick elements, plus one 16-noded wedge are used. All nodes on lower
face are fixed in X, Y, Z.

- X, Y displacements given at all nodes of front face using cylindrical system: 0.004 mm/unit time
- Rotation is given at mid-side nodes: 0.002 radians/unit time

Uniform twist of 0.02 radians/unit time is steadily increating with time from 0 to
1.5 applied using table curve.

**Material Properties****Value**- Young's modulus
- 10 GPa
- Poisson's ratio
- 0.3
- Creep law equation
- ${\dot{\epsilon}}_{eq}=1000\text{}{\sigma}^{5}{}_{eq}$

Where,

- ${\dot{\epsilon}}_{eq}$
- Equivalent creep strain rate
- ${\sigma}_{eq}$
- Equivalent stress (Mises)

### Nonlinear Static Analysis Results

An implicit visco-elastic solution method was used. Displacement, total strain and
creep strain results are analyzed at the edge of the shaft at 1.5s.

OptiStruct | NAFEMS | Normalized Target Value | |
---|---|---|---|

Total Strain (*10^{-2}) |
1.62 | 1.7321 | 0.94 |

Creep Strain (*10^{-2}) |
1.27 | 1.1693 | 1.094 |

Comparison of strain plots.

### Reference

NAFEMS R0026 - Selected Benchmarks for Material Non-Linearity- Volume 1