CAE Fidesys 9.0 Documentation

Safety Factor

Staging

Strength criteria are available in FidesysViewer in a separate filter.

For the filter to become active in FidesysViewer, it is necessary in the preprocessor In the output field settings, check the box “Output material properties” (Fig. 1).

Figure 1. Solver Settings

Strength criteria are available in FidesysViewer as a separate filter.

Safety factor (Menu - Filters - Alphabetical - Safety Factor)

Formula for strength criteria.

1. σ_t — uniaxial tensile strength;

   σ_c — uniaxial compressive strength;

   σ_m — von Mises stress;

   c — cohesion;

   φ — angle of friction;

   σ₁ — first principal stress;

   σ₂ — second principal stress;

   σ₃ — third principal stress;

   n — safety factor whose field should be displayed.

1. Calculation according to the first theory of strength

Used in the assumption of brittle fracture. Along isolines σ₁ construct isolines of safety factors n = σ_t / σ_1.

2. Calculation according to the energy theory of strength (Mises stress)

Used in the assumption of ductile fracture or if it is not allowed plastic state.

Isolines of safety factors are constructed using isolines σ_i n = σ_y / σ_m or n = σ_0.2 / σ_m, where σ_y or σ_0.2 – physical or proof strength.

3. Calculation according to the Pisarenko-Lebedev theory

Used for mixed destruction.

Isolines of coefficients are constructed using the fields σ_m and σ₁ safety factor:

, где

4. Calculation according to Mohr's theory, mixed destruction

Safety factor isolines:

5. Third theory of strength Tresca, ductile fracture or avoidance plastic flow

It turns out as a special case from Mohr’s theory with:

6. The Mohr-Coulomb criterion

- normal stress on the plane of destruction

A = c; B = - tanφ

or

If the strength limits σ_c and σ_t are given, then

where a = σ_t + σ_c;

b = σ_t - σ_c < 0 (at b > 0 angle of internal friction becomes negative, which is unacceptable).

Safety factor:

7. Mogi-Coulomb criterion

or

Safety factor

8. Drucker-Prager criterion

Strength criterion:

The strength criterion is met if the following is true:

where

Since the Drucker-Prager yield surface is inscribed in the Coulomb-Mohr yield surface, then in terms of the angle of internal friction and cohesion:

Safety factor:

This criterion evaluates the destruction of the model material under the influence of plastic deformations.

9. Navier criterion

Another name for the Mohr-Coulomb criterion

- the normal stress at failure;

A = c; B = - tanφ;

The disadvantage is explained by the fact that compression should lead to strengthening, and compression correspond to negative values ​​of σ_n

c = - τ_B - shear (torsional) strength, which user input for each material, or cohesion;

10. Hooke-Brown criterion

The Hook-Brown criterion in positive compression stresses:

The strength is maintained at

The Hook-Brown criterion in negative compression stresses:

The strength is maintained at

that is, when