- Email: [email protected]
Fatigue (Multiaxial): General
Fatigue (Multiaxial): General A great majority of mechanical\structural components are subjected to cyclic loading during their service life. In most cases the applied loads produce a multiaxial stress state within components or structural members. For example, even if the applied load is uniaxial, the stress state at the root of a notch in a shaft or in a pipe connection would be bi\multi-axial. Furthermore, stress (strain) components may vary either in a proportional or nonproportional (out-ofphase) manner. This could occur when a component is subjected to different sources of loading, e.g., thermal cycles combined with mechanical vibration, etc. Residual stresses arising from cooling process during fabrication are also of a multiaxial nature, owing to thermal gradients. This compound state of stress results in a rather complicated analysis when attempting to assess the fatigue damage and life prediction of components. The search for a suitable damage parameter (or function), which could provide a valid description of the multiaxial fatigue mechanisms and correlate with experimental data, is still under investigation. Here, it will suffice to mention that the plethora of proposed criteria can be grouped under four categories: equivalent-stress, equivalent-strain, critical-plane, and energy-based. The order mentioned above also follows the historic development. Each methodology has certain advantages and limitations.
Fig. 1. This element is then analyzed by subjecting it to three stress states, viz. torsion, uniaxial and equibiaxial. At this stage, it would be useful to specify what is meant by a ‘‘multiaxial’’ stress state. A bar subjected to a uniaxial tension when sectioned at an angle (between perpendicular and parallel to the applied load) would have two stress components, a normal stress and a shear stress. Thus, a multiaxial stress in fatigue analysis is defined with respect to the principal stress components. When there is more than one principal stress component, then a multiaxial stress state exists. Within this definition, a torque applied to a bar produces a biaxial stress state as shown in Fig. 1 (top line). The other two stress states are obtained by adding a tensile stress in the principal direction 2, equal in magnitude to that in the direction 1. In this manner one generates progressively uniaxial and equibiaxial stress states (Fig. 1). The corresponding maximum shear stress planes are shown in the right-hand column of Fig. 1. It is instructive to note that for torsional loading (top line in Fig. 1) the maximum shear stress planes are located on a plane 45m inclined to the principal plane 1–2. For this type of loading, an initiated crack will grow faster along the surface than into the thickness, i.e., it would be a shallow crack. For the uniaxial loading, in addition to the above-mentioned shear planes, there are two maximum shear stress planes inclined 45m with respect to the principal plane 1–3, i.e., an initiated crack would grow deeper into the material. The difference between the uniaxial and
1. Influence of Multiaxial Stress It is well established that the fatigue damage process is a localized phenomenon initiated at a scale of a material’s microstructure. Thus, in an ideal situation, a fatigue crack initiation criterion should be based on the microstructural parameters. However, at this scale the local material response is highly anisotropic, and a direct approach based on microstructural properties would be a difficult task, at present. Therefore, the conventional approach has been to use a continuum theory based on bulk stresses and strains. A further assumption involved here is that the material properties do not degrade appreciably before ‘‘failure.’’ In adopting such an approach one must then ensure that the requirements of the continuum theory are adhered to. (This has not always been the case, particularly with a number of critical-plane-based criteria.) Furthermore, a successful criterion, which could provide a valid extrapolation beyond the data for which it was calibrated, must have an underlying microstructural support. In the absence of gross interior defects, fatigue cracks initiate from the surface of a material where the grains are not fully constrained. To comprehend the influence of multiaxial stresses on the fatigue process, an element near the surface is isolated, as shown in
Figure 1 An element near the surface of a material subjected to shear, uniaxial, and equi-biaxial loading and the corresponding maximum shear stress planes.
1
Fig. 1. This element is then analyzed by subjecting it to three stress states, viz. torsion, uniaxial and equibiaxial. At this stage, it would be useful to specify what is meant by a ‘‘multiaxial’’ stress state. A bar subjected to a uniaxial tension when sectioned at an angle (between perpendicular and parallel to the applied load) would have two stress components, a normal stress and a shear stress. Thus, a multiaxial stress in fatigue analysis is defined with respect to the principal stress components. When there is more than one principal stress component, then a multiaxial stress state exists. Within this definition, a torque applied to a bar produces a biaxial stress state as shown in Fig. 1 (top line). The other two stress states are obtained by adding a tensile stress in the principal direction 2, equal in magnitude to that in the direction 1. In this manner one generates progressively uniaxial and equibiaxial stress states (Fig. 1). The corresponding maximum shear stress planes are shown in the right-hand column of Fig. 1. It is instructive to note that for torsional loading (top line in Fig. 1) the maximum shear stress planes are located on a plane 45m inclined to the principal plane 1–2. For this type of loading, an initiated crack will grow faster along the surface than into the thickness, i.e., it would be a shallow crack. For the uniaxial loading, in addition to the above-mentioned shear planes, there are two maximum shear stress planes inclined 45m with respect to the principal plane 1–3, i.e., an initiated crack would grow deeper into the material. The difference between the uniaxial and
1. Influence of Multiaxial Stress It is well established that the fatigue damage process is a localized phenomenon initiated at a scale of a material’s microstructure. Thus, in an ideal situation, a fatigue crack initiation criterion should be based on the microstructural parameters. However, at this scale the local material response is highly anisotropic, and a direct approach based on microstructural properties would be a difficult task, at present. Therefore, the conventional approach has been to use a continuum theory based on bulk stresses and strains. A further assumption involved here is that the material properties do not degrade appreciably before ‘‘failure.’’ In adopting such an approach one must then ensure that the requirements of the continuum theory are adhered to. (This has not always been the case, particularly with a number of critical-plane-based criteria.) Furthermore, a successful criterion, which could provide a valid extrapolation beyond the data for which it was calibrated, must have an underlying microstructural support. In the absence of gross interior defects, fatigue cracks initiate from the surface of a material where the grains are not fully constrained. To comprehend the influence of multiaxial stresses on the fatigue process, an element near the surface is isolated, as shown in
Figure 1 An element near the surface of a material subjected to shear, uniaxial, and equi-biaxial loading and the corresponding maximum shear stress planes.
1