Determination of Mechanical and Fracture Properties of Silicon Single Crystal from Indentation Experiments and Finite Element Modelling

It is well-known that cracks are observed around the impression during indentation of brittle materials. The cracks inception depends on load conditions, material and indenter geometry. The paper aims to use experimental micro-indentation data, FE simulations with cohesive zone modelling, and an optimisation procedure to determine the cohesive energy density of silicon single crystals. While previous studies available in the literature, which use cohesive zone finite element techniques for simulation of indentation cracks in brittle solids, tried to improve methods for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, this study focuses on the evaluation of the cohesive energy density 2Γ from which the material toughness can be easily determined using the well-known Griffith-Irwin formula. There is no need to control the premise of the linear fracture mechanics that the cohesive zone is much shorter than the crack length. Hence, the developed approach is suitable also for short cracks for which the linear fracture mechanics premise is violated.

Theory of Narrow U-Shaped Notches in Linear Fracture Mechanics

On the basis of linear fracture mechanics, a complete set of asymptotic formulas is obtained to describe the stress-strain state at the top of a narrow U-shaped notch. This type of defect can be possessed by a crack that has undergone a corrosive effect of the environment, or there can be a crack-like defect in a welded joint, e.g. lack of penetration, undercut, or a narrow slot in the part. To comparatively assess the risk of cracking at the tops of narrow U-shaped notches, and identify the places and directions of fracture initiation, we reveal the possibility of using such energy criteria as the deformation energy density and The previously indicated criteria were proposed by the author of this work for classical cracks-cuts. The purpose of this work was to study, on the basis of singular solutions of linear fracture mechanics, the stress-strain state in terms and near the tops of extremely narrow U-shaped notches, i.e., blunt cracks, in comparison with classical cracks-cuts

Nominal Stress-Based Estimation of Fatigue Life of Welded Joints

The paper presents methods for determining the fatigue life of welded joints with particular emphasis given to typical joints. In addition, the article presents various possible nominal stress-based ways enabling the calculation of stresses, including structural stresses and involving the most complex linear fracture mechanics. The paper also discusses recommendations by the International Institute of Welding related to the determination of the fatigue life of welded joints in flat elements exposed to tension-compression conditions. The work is focused on assessing the fatigue life of welded joints (selected types) in accordance with the guidelines specified in related recommendations issued by the International Institute of Welding and taking into consideration the analysis concerned with the safety of such structures.

Stochastic modelling of fatigue crack growth

The article deals with the influence of the skewness of quasi-constant stress range on the fatigue resistance of a steel bridge member subjected to multiple repeated loading. It is shown that it is necessary to know the statistical characteristics and type of probability density function relatively accurately in the case of quasi-constant stress range, otherwise the estimation of the fatigue resistance may be inaccurate. The fatigue resistance is studied using linear fracture mechanics. The random characteristics of the steel member are simulated using the Latin Hypercube Sampling method. The results of experimental research on calibration functions used in linear fracture mechanics are applied in this study. The calibration function for pure bending, which is presented on an extended domain of relative crack length, is applied. Non-parametric rank-order correlation identifies a strong influence of the quasi-constant stress range on the fatigue resistance. A detailed comparison of three variants of fatigue resistance as output random variables is performed. The results show that the probabilistic assessment of reliability may be burdened with greater or lesser epistemic uncertainty, which can distort the estimates of the remaining service life of the load bearing bridge member.