Multiaxial Fatigue Analysis

In Uniaxial Fatigue Analysis, HyperLife converts the stress tensor to a scalar value using user-defined combined stress method (von Mises, Maximum Principal Stress, and so on). In Multiaxial Fatigue Analysis, OptiStruct uses the stress tensor directly to calculate damage. Multiaxial Fatigue Analysis theories discussed in the following sections are based on the assumption that stress is in the plane-stress state. In other words, only free surfaces of structures are of interest in Multiaxial Fatigue Analysis in OptiStruct. For solid elements, a shell skin can be generated in the FEA.

The stress-life method works well in predicting fatigue life when the stress level in the structure falls mostly in the elastic range. Under such cyclical loading conditions, the structure typically can withstand a large number of loading cycles; this is known as high-cycle fatigue. When the cyclical strains extend into plastic strain range, the fatigue endurance of the structure typically decreases significantly; this is characterized as low-cycle fatigue. The generally accepted transition point between high-cycle and low-cycle fatigue is around 10,000 loading cycles. For low-cycle fatigue prediction, the strain-life (E-N) method is applied, with plastic strains being considered as an important factor in the damage calculation.

The Dang Van criterion is used to predict if a component will fail in its entire load history. The conventional fatigue result that specifies the minimum fatigue cycles to failure is not applicable in such cases. It is necessary to consider if any fatigue damage will occur during the entire load history of the component. If damage does occur, the component cannot experience infinite life.

Uniaxial Load

Models with uniaxial loads consist of loading in only one direction and result in one principal stress.

Figure 1. Uniaxial Load

Proportional Biaxial Load

In models with proportional biaxial loads, principal stresses vary proportionally; however, still in one direction. Typically, in-phase loading of stress components is known as proportional biaxial load. Therefore, a fatigue subcase where a single static subcase is referenced is always a proportional biaxial load.

Figure 2. Proportional Biaxial Load

Figure 3. In-Phase Load

In models with non-proportional biaxial loads, principal stresses can vary non-proportionally, and/or with changes in direction. Typically, out-of-phase loading of stress components is known as non-proportional multiaxial load.

Non-Proportional Multiaxial Load

Figure 4. Non-Proportional Multiaxial Load

Figure 5. Out-of-Phase Load

In HyperLife Multiaxial Fatigue Analysis, non-proportional multiaxial loads are considered.

Non-proportional Cyclic Loading and Non-Proportional Hardening

Non-proportional cyclic loads typically generate additional strain hardening, which is not observed in the proportional loading environment. The additional strain hardening is called non-proportional hardening and is caused by interaction of slip planes. As a result of the rotation of the principal axes (Figure 6), multiple sliding planes are active, and hardening can accumulate at a certain point, while the direction of the slip plane changes.

Figure 6. Interaction Between Slip Planes, Due to Non-Proportional Loading

The plasticity model used in Multiaxial Fatigue Analysis will take care of non-proportional hardening, if applied load is non-proportional.