The edge crack problem is often observed in engineering applications. It is one of the most prominent factors causing damage and failure of engineering structures, and it is also one of the classical problems in fracture mechanics. Due to the structure heterigenety and the loading conditions complexity, multiple cracks often occur on the edge. The interaction between cracks will affect the crack propagation path and the failure mode of the structure. To study the mechanical properties of multiple edge cracks under different loading conditions is of great engineering significance. Engineers can rationally use the interaction between cracks to improve the life of structures under specific working conditions.
The edge crack problem is often observed in engineering applications. It is one of the most prominent factors causing damage and failure of engineering structures, and it is also one of the classical problems in fracture mechanics. Due to the structure heterigenety and the loading conditions complexity, multiple cracks often occur on the edge. The interaction between cracks will affect the crack propagation path and the failure mode of the structure. To study the mechanical properties of multiple edge cracks under different loading conditions is of great engineering significance. Engineers can rationally use the interaction between cracks to improve the life of structures under specific working conditions.
The research team of the State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences constructed the boundary value problems combining conformal mapping and plane elasticity theory. The complex function is solved by a semi-analytic method, and the corresponding mechanical parameters are calculated. The research team mainly studied double branched cracks (two cracks emanating at the same point at the edge) and Kalthoff-Winkler cracks (two spaced cracks) under far-field uniform tension or concentrated force loading at the boundary. The stress intensity factors, elastic stress fields, and crack opening displacement are calculated. The shielding effect between cracks is investigated. Compared with a single edge crack, the stress intensity factors of a double branched crack decrease due to the shielding effect. The SIFs decay exponentially with decreasing space between the two parallel cracks. KI=KI0-KI1-exp(-a/d)](Fig 1 and 2). The method is universal to study boundary crack problems, and the shielding effect of cracks plays a guiding role in engineering applications.
The above results have been published under the title “Elastic fields of double branched and Kalthoff-Winkler cracks in a half-plane” in the Journal of the Mechanics and Physics of Solids. The first author is doctoral student Yangjian Si. This work is supported by the NSFC Basic Science Center for ‘Multiscale Problems in Nonlinear Mechanics’ (No.11988102).
Fig 1: Normalized SIFs and stress fields of a symmetric double-branched edge crack (a1=a2,?θ1=θ2) subjected to far-field unform tension.
(a) Geometry and loading condition of the crack. (b) Von Mises stress field around the crack tip. (c) Normalized SIFs as a function of θ. Shielding effect between the two branches can be clearly observed.
Fig 2:Normalized SIFs of two parallel edge cracks (following Kalthoff-Winkler experiment) under far-field uniform tension.
(a) Geometry and loading condition of the crack. (b) Normalized SIFs as a function of a/θ. KI*=1.122-0.326[1-exp(-1.8a/d)] ,KII*=0.812[1-exp(-1.2a/d)]. The normalized SIFs converge to those of a single edge crack when d approaches to infinity.
Initial stress affects solid materials through various means such as non-uniform inelastic deformations, phase changes, surface modifications, heating or cooling, chemical reactions, and geological movements. These stresses are non-uniform, traction-free, and in self-equilibrium, making them impossible to eliminate even if all external factors are removed. The initial stress has a significant impact on the material properties and mechanical behavior of the materials. Developing an appropriate hyperelastic constitutive relationship is a challenging task in rational mechanics and a research frontier in engineering sciences.
Professor Ya-Pu Zhao's team at the Institute of Mechanics, Chinese Academy of Sciences, has developed a ground-breaking hyperelastic constitutive relation for soft elastomers with thermally-induced residual stress. The relation is based on Riemann geometry. Their paper, titled “Hyperelastic constitutive relations for soft elastomers with thermally-induced residual stress”, has been published in the prestigious International Journal of Engineering Science. Weiting Chen, a PhD student at the Institute of Mechanics, Chinese Academy of Sciences, is the first author of the paper and Professor Ya-Pu Zhao is the corresponding author.
According to the previously established framework based on Riemannian geometry “Chen, W.T., Zhao, Y.-P., 2022. Thermo-mechanically coupled constitutive equations for soft elastomers with arbitrary initial states. Int. J. Eng. Sci. 178, 103730”, an inhomogeneous free thermal expansion can be induced to compensate for the incompatibility or, more explicitly, the Riemannian curvature brought about by the isothermal release of the given initial stress. On this basis, this study considers material Riemann connections. A compatibility-broken curvature compensation (CBCC) framework based on finite thermoelasticity is established. Such a mechanism indicates the non-local effect of the initial stress, which fundamentally modifies the traditional view that invariant formulations cover all possible functional dependence of the initial stress. More importantly, the governing equations obtained are similar to Einstein's field equation of general relativity. This similarity may deeply imply a standard mechanism concerning the curvature compensation leading to initial stress generation. It opens a new perspective to understand the nature and effects of initial stress and can be extended to other origins of initial stress that have a curvature compensation mechanism.
Links to the papers:
https://doi.org/10.1016/j.ijengsci.2023.103991
https://doi.org/10.1016/j.ijengsci.2022.103730
Figure 1. Diagrammatic sketch of the compatibility-broken curvature compensation framework. (a) Conventional thermoelasticity. (b) The current constitutive theory.
Figure 2. The decomposition of material strains and the associated compatibility-broken curvature compensation framework.
"Structure determines performance" is a classical paradigm followed in solids. However, this paradigm becomes confusing when facing topologically disordered structures such as glass solids. Recently, the research team of Professor Minqiang Jiang at the Institute of Mechanics, Chinese Academy of Sciences has demonstrated that fast relaxation origins from medium-range orders (MROs) structures by the controlled modulation of glass relaxation. The related results are published as "Splitting of fast relaxation in a metallic glass by laser shocks" in Physical Review B 109, 024201 (2024).
Relaxation dynamics of glassy matter is probably one of the deepest and most challenging unsolved problems in condensed matter physics. Metallic glasses (MGs) are considered as simple glasses with dense-packed atoms, thus providing an ideal model for studying glassy relaxation. Recent research has identified an additional fast relaxation below room temperature in MGs, alongside the well-known α and β relaxations. This low temperature relaxation process has lower activation energy and faster characteristic relaxation time than β relaxation and it is closely related to the low-temperature plasticity. Despite numerous research over recent years, the structural origin of fast relaxation remains elusive.
The research team investigate the variation of the fast relaxation in a typical Zr-based MGs by laser shocks and isothermal annealing. The single-peak fast relaxation in the annealed glass is observed to split into two distinct peaks (termed γ and β') after multiple-pulse laser shocks, and this splitting phenomenon disappears after re-annealing. A slight structural rejuvenation of the laser-shocked sample is detected by thermodynamic measurements. The reconfiguration of MROs is captured by HRTEM and high-energy XRD. It turns out that laser shock treatment increases the edge-sharing MROs, which is then recovered by re-annealing. We argue that the fast relaxation originates from the MRO structures, where γ relaxation comes from the edge-sharing type, and the β' relaxation is related to the face-sharing and interpenetrating types. The splitting of fast relaxation is structurally due to the MRO reconfiguration. The simultaneous changes in relaxation dynamics and atomic structure provide solid evidence that fast relaxation originates from the MRO structures. Moreover, the lowest hardness and pile-up of the laser-shocked sample implies that the split fast relaxation improves the RT plasticity of MGs.
The first author of the paper is Cheng Yang, a PhD student of the Institute of Mechanics, class of 2018, and the corresponding author is Professor Minqiang Jiang. This research is supported by the National Outstanding Youth Science Foundation of China under the project of "Mechanics of Amorphous Solids", and by the Foundation's Basic Science Center under the project of "Multiscale Problems in Nonlinear Mechanics".
Fig. 1. Structural origins of fast relaxation: the reversible motion of atoms at the MRO scale.
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