Elastic-plastic fracture analysis of anisotropy effect on AA2050-T84 alloy at different temperatures: A Numerical Study

The third generation Al-Li alloy AA2050-T84 is widely used in aircraft applications due to its lightweight and significant mechanical properties. The anisotropic variations of tensile and compression properties of this alloy at various temperatures are substantial. In this work, the variations of the J-integral, CTOD, and Plastic Zone Size (PZS) due to anisotropy of a 4-inch thick AA2050-T84 plate at ambient and cryogenic temperatures were studied numerically by using Compact Tension (C(T)) specimen. The material anisotropy resulted in fracture and constraint parameter variation for Mode-I constant load. Numerical results indicated a decrease in crack driving forces and a constraint parameter with the decrease in temperature at the plate surface and central location. Plate surface locations appear to be isotropic for both temperatures under elastic-plastic fracture analyses as crack driving forces were almost identical. The temperature effect is more on constraint as the normalized PZS values at ambient temperature have been twice that of cryogenic temperature. The isotropic behavior of a plate under sub-zero temperature makes the plate suitable for cryogenic temperature applications.

The effect of surface free energy on the fracture behaviors of nanoparticle-reinforced composites

By considering the surface free energy effect, an analytical investigation on the fracture behaviors of nanoparticle-reinforced composites was performed in this study. The plastic zones ahead of the crack tips based on the Irwin model were introduced in our analysis, which has a significant influence on the fracture toughness of inelastic structures, especially for polymer and metal matrix composites. Take copper and aluminum nanoparticles as examples, comprehensive parametric studies were conducted to investigate the interaction between a Griffith crack and the nearby nanoparticle. It was found that for nanoparticles with the radius of less than 10 nm, apart from the mechanical property of the nanoparticle, the surface free energy effect plays a dominant role in determining the fracture behaviors of the nanoparticle-reinforced composites. Moreover, taking the surface free energy into account, a decrease in the plastic zone size is obtained, particularly for the crack tip nearer the nanoparticle.

A Methodology to Determine the Effective Plastic Zone Size Around Blunt V-Notches under Mixed Mode I/II Loading and Plane-Stress Conditions

The determination of the ductile failure behavior in engineering components weakened by cracks and notches is greatly dependent on the estimation of the plastic zone size (PZS) and, particularly, the effective plastic zone size (EPZS). Usually, time-consuming complex elastic–plastic analyses are required for the determination of the EPZS. Such demanding procedures can be avoided by employing analytical methods and by taking advantage of linear elastic analyses. In this sense, this work proposed a methodology for determining the PZS around the tip of blunt V-notches subjected to mixed mode I/II loading and plane-stress conditions. With this aim, firstly, existing approximate mathematical expressions for the elastic stress field near round-tip V-notches reported in the literature are presented. Next, Irwin’s approach (fundamentally proposed for sharp cracks) and a yield criterion (von Mises or Tresca) were applied and are presented. With the aim of verifying the proposed methodology, elastic–plastic finite element analyses were performed on virtual AISI 304 steel V-notched specimens. It was shown that the analytical formulations presented cannot estimate the complete shape of the plastic zone. However, the EPZS, which is crucial for predicting the type of ductile failure in notched members, can be successfully estimated.

Estimation of Welding-Induced Plastic Zone Size and Residual Stress Levels: Linear Heat Input Approximation

Welding is a highly nonlinear temperature distribution process, where the presence of high-temperature gradients leads to the development of significantly high residual stress levels, up to and/or beyond the material yield strength magnitude and localized plastic deformation. To achieve the desired dimensional accuracy, determination of plastic zone size, shape, and location is critically important in reducing or controlling final distortions, decreasing the residual stress according to length scale, and defining the optimum sequence of the welding process. The plastic zone caused by welding has been found to be directly proportional to linear heat input, defined in (J/mm). The use of actual linear heat input in the estimation of welding-induced residual stress in finite element models often results in an overestimation of heat transferred to the fusion zone of the metal. This manuscript highlights the importance of estimating plastic zone, developed during thermal processes like welding, and its role in mitigating final distortion by using a 3-bar model for the determination of final residual stresses. In the second part, previously developed analytical linear heat input solution for 2D residual stress models is discussed and further demonstrated using examples from open literature. Lastly, a sequentially uncoupled thermal and thermo-mechanical finite element analysis (FEA) is performed, using a generalized plane strain element, and concluded by validation of the numerically developed plastic zone size with analytically developed solutions.

Collaborative Mining Sequence Optimization for Multiple Stopes under Intensive Mining

The optimization of a mining sequence not only reduces stress concentration in surrounding rock but also prevents underground debris flows, significantly improving safety. Firstly, the 870–898 m level of the eastern mining area in the Tiaoshuihe phosphate mine was divided into 25 ore blocks, and six different mining sequences were designed for this area. Then, it was calculated that five ore blocks must be processed simultaneously to reach the annual production output. The distances between the five simultaneously mined ore blocks will inevitably affect the efficiency of the equipment for any scheme. So, a collaborative model considering both the area stability and production capacity was established by combining the distance between the centers of the five ore blocks as an index. Differences in stability, deformation, and plastic zone size between the schemes are compared. The calculation results show that a mining scheme with a convex stepped shape produces the best results. These results provide a general method for entropy-based mining sequence optimization and an optimal solution for the Tiaoshuihe phosphate mine.

Plastic zone size at notch tip in mode I fracture using the modified Irwin’s model and volumetric approach

At crack tip the stress distribution has singularities (i.e the stress intensity is infinite) which is physically impossible. Irwin realised that the stresses at crack tip are finite and subsequently introduced the Stress Intensify Factor(SIF). This factor is used to determine this plastic zone size. The crack is a special case of the notch. Around the notch, the fracture needs a volume to develop according to the volumetric approach. This volume is characterised by the distance effective Xeff, the stress effective σeff and the stress intensity factorKρI. In This paper a new proposed formula called “Modified Irwin’s Model” based on Irwin’s model can be used to determine the plastic zone size. This new formula will be verified using numerical finite element simulation and validated using the Von-Mises and Tresca Criteria. The Modified Irwin’s Model can be an alternative way to estimate the fracture elaboration zone from the plastic zone.