# Failure Criteria & Safety Factor

## Failure Criteria

For each scenario and iteration a failure criterion is calculated and based on this value the design is formed. Which failure criterion can be used depends on the material properties, manufacturing method and the optimisation intention.

### Von Mises Stress*

The equivalent **von Mises Stress** is the default Failure Criterion. It can be used for all material properties (Isotropic, 3D Transversely Isotropic and 3D Orthotropic). The Stress Goal is calculated with the chosen Safety Factor and the tension strength in axis direction (build direction) of the entered material. For directional dependent stress limits, the **von Mises Stress** is not suitable and one of the following Failure Criteria should be used.

### FFF Thumb Rule

With the **FFF Thumb Rule**, a simplified version of the **directional dependent Tsai-Hill** Failure Criterion can be used to take directional dependencies into account. The **FFF Thumb Rule** can be used in combination with Isotropic material behaviour. Thus, the Tension Strength in build direction can be modified by scaling only this one value. The Shear Strength is calculated automatically with a Thumb Rule [0.6 * Tension Strength]. This is especially useful for manufacturing methods like FFF where the material limit in building direction differs from the transversal in-plane directions.

### Directional Dependency (Tsai-Hill)*

The **directional dependent Tsai-Hill **Failure Criterion allows to set-up different Tension Strength for the build direction (axis) and the In-plane directions as well as the Shear Strength. The FFF Thumb Rule is based on it, in contrast to it the Shear Strength isn’t calculated automatically based on the Thumb Rule.

### Directional Dependency (Tsai-Wu)*

With the **directional dependent Tsai-Wu** Failure Criterion the difference between Tension and Compression Strength can be considered besides the directional dependency.

### Comparison of the different Failure Criteria

von Mises | One Tension Strength for all directions is considered. |

FFF Thumb Rule | The Tension Strength in build direction can be scaled in contrast to the tension strength in in-plane directions. |

Directional Dependency (Tsai-Hill) | The Tension Strength in build direction and in In-plane directions as well as the shear strength can be set up. |

Directional Dependency (Tsai-Wu) | The Tension and Compression Strength in build direction and in In-plane directions and as well as the shear strength can be set up. |

## Safety Factor

The Safety Factor calculates the goal for the optimisation in regard to the material properties. This works for all Failure Criteria (von Mises Stress, FFF Thumb Rule, directional dependent Tsai-Hill and Tsai-Wu). The Tension, Shear and Compression Strength dependent on the direction are scaled with the Safety Factor to define the optimisation goal.

The objective of the optimisation is to load all material with the calculated values from the material properties and the Safety Factor to reach a Failure Criterion value of 1.

In the following an example for the Tsai-Wu Failure Criterion with a Safety Factor of 3 is shown.

Axial Tension Strength | 300 MPa | 3 | 100 MPa |

Axial Compression Strength | 600 MPa | 3 | 200 MPa |

In-Plane Tension Strength | 450 MPa | 3 | 150 MPa |

In-Plane Compression Strength | 900 MPa | 3 | 300 MPa |

Shear Strength | 150 MPa | 3 | 50 MPa |

#### *Failure Criteria Formula

__Von Mises:__

__Von Mises:__

__Directional Dependency (Tsai-Hill):__

__Directional Dependency (Tsai-Hill):__

__Directional Dependency (Tsai-Wu):__

__Directional Dependency (Tsai-Wu):__