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What is the stress triaxial ratio? Why is it so important for fracture mechanics?
In continuum mechanics, the stress triaxial ratio is the relative ratio of the horizontal stresses under a given stress state. This concept is usually used as the triaxiality factor (T.F.), which is the ratio of the horizontal stress to the von Mises equivalent stress. For materials science and fracture mechanics, knowing the stress triaxial ratios is crucial to predicting the behavior of a material under a specific stress state.
The increase in the stress triaxial ratio indicates that the stress state is mainly horizontal rather than deviated.
High stress triaxial ratios (> 2-3) generally promote the formation of brittle cracks, which is relatively obvious compared to the formation of ductile cracks. Conversely, lower stress triaxial ratios are usually associated with shear slip, which can lead to greater ductility and generally also results in greater toughness. These phenomena are particularly evident for materials that behave at high strain rates. Many fracture criterion models, such as the Johnson-Cook (J-C) fracture criterion, the Rice-Tracey model, and the J-Q Large deformation models all take into account the stress triaxial ratios.
The concept of stress triaxial ratio was first introduced by Davies and Connelly in 1959. They defined the so-called triaxial ratio factor, which is the ratio of the first principal quantity of the Cauchy stress to the effective stress. Their study showed that negative pressure (spherical tension) has a significant impact on the ductility loss of metals and emphasized the need for a parameter to describe this effect.
The influence of negative pressure attracted the attention of many scholars at that time, which led to the in-depth study of the three-axis ratio factor.
As the research progressed, Wierzbicki and his collaborators proposed a slightly different definition of the triaxial ratio factor and pointed out that in addition to horizontal stress, the Lode angle can also significantly affect the ductility of metals. and other properties. These changes have prompted further exploration of the stress triaxial ratio in applications, particularly in the context of biaxial testing, where unique correlations between the stress triaxial ratio and fluid properties have been discovered.
In material testing, the definition of stress triaxial ratio is not limited to the stress state in a single dimension, but covers a wider range of stress and rheological properties. This enables engineers to more accurately predict how materials will behave under extreme conditions, leading to more reliable design and structural analysis methods.
The stress triaxial ratio is not only the key to understanding material fatigue and failure, but also an indispensable part of the structural design process.
With the advancement of technology, the study of stress triaxial ratio has gradually shifted to numerical simulation and laboratory testing, which enables researchers to gain a deeper understanding of the behavior of materials in different environments. The specific crystal structure, material type and application will affect the actual performance of the stress triaxial ratio, and sometimes it may even become a key indicator for predicting the fracture mechanism.
In short, the stress triaxial ratio is a complex and important concept, which affects fracture mechanics, production technology and material service life. Future research is needed to explore its effects in more nuanced ways to facilitate the development of new materials and improve the performance of existing materials. In this context, we can't help but ask: How will future materials science use stress triaxial ratios to predict and improve material properties?
