For Stress- and Strain-Based, High- and Low-Cycle Fatigue Analysis
Fatigue Analysis for Many Different Structures and Applications
When structures are subjected to repeated loading and unloading due to material fatigue, they can fail at loads below the static limit. A virtual fatigue analysis can be performed in the COMSOL Multiphysics environment with the Fatigue Module, an add-on to the Structural Mechanics Module. With the stress-based and the strain-based critical plane methods, you can evaluate the high-cycle and low-cycle fatigue regime. In applications involving nonlinear materials you can use energy-based methods or Coffin-Manson type models to simulate thermal fatigue.
When dealing with variable loads, the accumulated damage can be calculated from the load history and the fatigue limit. The fatigue load cycle can be simulated in solid bodies, plates, shells, multibodies, applications involving thermal stress and deformation, and even on piezoelectric devices. In order to improve computational efficiency when dealing with subsurface or surface initiated fatigue, a fatigue evaluation can be performed on domains, boundaries, lines and in points.
Stress- and Strain-Based Critical Plane Models
Critical plane models search for a plane that is most favorable for crack initiation and propagation where fatigue will take place. These are available in the Fatigue Module for both the stress- and strain-based models. In the high-cycle fatigue domain, where plasticity is very limited, stress-based models are typically used. In the Fatigue Module, they are calculated through the Findley, Normal stress, and Matake criteria, which calculate the fatigue usage factor that is compared to the fatigue limit.
Strain-based models evaluate strains or combinations of strains and stresses when defining a critical plane. Once the critical plane is identified, they predict the number of cycles to failure. The Fatigue Module features the Smith-Watson-Topper (SWT), Fatemi-Socie, and Wang-Brown models. These models are usually used in low-cycle fatigue where the strains are large. The Neuber's rule and the Hoffmann-Seeger method are available to approximate the effect of plasticity in a quick linear-elastic simulation. It is also possible to consider a full elastoplastic fatigue cycle when using the Nonlinear Structural Materials Module.
- High-cycle fatigue analysis for non-proportional loading using critical plane methods.
- The distribution of stress cycles at a certain point as computed by the Rainflow counting algorithm using a Matrix Histogram plot. The mean stresses are shown on the horizontal axis and stress amplitudes are shown on the vertical axis.
- A frame with a central cutout is subjected to a random load consisting of 1000 load events. The stress distribution is calculated with the Rainflow counting algorithm and the damage is estimated using the Palmgren-Miner linear damage rule.
- Solder joint in a surface mount resistor. Life prediction based on the dissipated creep energy in one thermal fatigue cycle.
Material expansions or contractions due to temperature change introduce stress concentrations and strain accumulations that can lead to failure. The Fatigue Module provides a number of tools to address this through thermal fatigue modeling. The thermal load cycle can be simulated utilizing the Thermal Stress and the Joule Heating and Thermal Expansion physics interfaces. Thermal fatigue failure can be evaluated using several fatigue models. For nonlinear materials, this includes the Coffin-Manson model and the energy-based Morrow and Darveaux relations. In addition to the available options for inelastic strains or dissipated energies, the fatigue evaluation models can also be modified by the user to evaluate strain or energy expressions when calculating fatigue.
Cumulative Damage Analysis
Random loads introduce a variety of stresses with different magnitude into a structure. In the Fatigue Module, the Cumulative Damage analysis not only identifies the overall trends in the stress history, but also calculates the accumulated damage from each of them. The stress history can be evaluated through the principle stress or von Mises stress, with a sign determined by principle or hydrostatic stress. The load history is then processed with the Rainflow counting algorithm, and the damage is calculated using the Palmgren-Miner linear damage rule. The effect of the R-value is incorporated through the limiting S-N curve.
When the number of load events is large in a random load analysis, simulation of the load cycle is time-consuming. This can be greatly reduced if the nonlinear effects are not present in the simulation. In that case, the stress cycle can be prescribed with help of superposition, which is selectable in a Cumulative Damage analysis. Utilization of this technique not only saves computational time, but also greatly reduces the size of the model that needs to be stored for fatigue evaluation.
Visualizing Your Fatigue Calculations
The Fatigue Module calculates the number of cycles until failure as well as the fatigue usage factor. In cumulative damage simulations, the stress distribution of the applied random load can be shown together with the relative usage factor. This simulation displays contributions of a specific fatigue load to the overall fatigue usage factor, which in this case is seen as damage. The stress distribution is presented as a function of the stress amplitude and the mean stress.
Thermal Fatigue of a Surface Mount Resistor
A surface mount resistor is subjected to thermal cycling. The difference in the thermal expansion of different materials will introduce stresses in the structure. The solder which connects the resistor with the printed circuit board is seen as the weakest link in the assembly. It responds nonlinearly to changes in both temperature and time. In ...
High-Cycle Fatigue Analysis of a Cylindrical Test Specimen
A benchmark model for the fatigue module. A cylindrical test is subjected to non-proportional loading. Three stress based models: Findley, Matake, Normal stress, are compared to analytical values and to each other. The non-smooth behavior of the Matake model is captured and discussed.
Submodeling of Thermal Fatigue in a Ball Grid Array
In a cooling system, a microelectronic component has been identified as the critical link. Since the power is repeatedly switched on and off, the component is subjected to thermal cycling. As a results a crack grows through a solder joint and disconnects the chip from the printed circuit board so that the component loses its operational ...
Random Load Fatigue in a Frame with a Cutout
A frame with a central cutout is subjected to a random load consisting of 1000 load events. The external load, recorded using three strain gauges, is simulated using superposition of three unit loads. The stress state around the cutout is obtained with the Rainflow cycle counting algorithm. The damage is estimated using the Palmgren-Miner linear ...
Fatigue Analysis of a Car Wheel Rim
A fatigue analysis is performed on a wheel rim. The Findley fatigue criterion is examined. The submodeling technique is utilized performed a detailed study on the critical part of a spike. At first a study of the full model is made. The critical part is identified and a submodel is reanalyzed. The road load, which rotates around the wheel, is ...
Low-Cycle Fatigue Analysis of Cylinder with a Hole
A load carrying component of a structure is subjected to multi-axial cyclic loading during which localized yielding of the material occurs. In this model you perform a low cycle fatigue analysis of the part based on the Smith-Watson-Topper (SWT) model. Due to localized yielding, you can use two methods to obtain the stress and strain distributions ...
Structural and Fatigue Analyses of a Shaft with a Fillet
This benchmark model shows how to perform a high-cycle fatigue analysis for non-proportional loading using critical plane methods.
Notch Approximation to Low Cycle Fatigue Analyis of Cylinder with a Hole
A load carrying component of a structure is subjected to multi-axial cyclic loading during which localized yielding of the material occurs. In this model you perform a low cycle fatigue analysis of the part based on the Smith-Watson-Topper (SWT) model. Due to localized yielding, you can use two methods to obtain the stress and strain ...
Cycle Counting in Fatigue Analysis - Benchmark
A benchmark model of the Rainflow counting algorithm compares results between ASTM and COMSOL fatigue module using a flat tensile test specimen. An extension is made for the cumulative damage calculation following the Palmgren-Miner model and results are compared with analytical expressions.