**1. Introduction**

Many engineering structures in use have reached or exceeded their design service life. In combination with changing operational requirements (e.g., increased loads, influence of environmental factors), design, execution, and operational errors can result in numerous failures. Historically, the most famous case of this type was the cracking of the hulls of Liberty tankers in the 20th century. In the following years, cracks in the structures of industrial tanks, gas pipelines, and others were observed many times. As shown by the research and analyses carried out, one of the causes of the damage was the imperfect method of designing and calculating structures that did not follow the rapid technological progress. Extensive research on the explanation of the causes of failures resulted in the establishment of a new field of science, which is the mechanics of fracture. Furthermore today, with the rapid development of material technologies, the importance of this relatively young science continues to grow.

For about 60 years of development, the fracture mechanic has provided models to predict failure of structural components containing defects. The first solutions were developed on the basis of the linear theory of elasticity, gradually developing them in terms of taking into account plasticity and non-linear phenomena. The so-called global approach has proved to be useful in solving engineering problems in which classic material strength methods are not applicable.

Based on the methods of classical fracture mechanics, many engineering procedures have been developed, among which the PD6493 [1], BS7910 [2], R6 [3], FITNET [4], and SINTAP [5] procedures deserve special mention.

The development of material technology and computational methods, mainly numerical ones, which have been progressing in recent decades, has revealed a number of limitations of conventional methods. Their most common disadvantage is their low versatility, because each case of the geometry of a structural element and a defect requires an individual approach. Thus, these procedures are costly and time-consuming [6].

Local methods, developed since the 1980s, are characterized by much wider possibilities, mainly in combination with FEM analysis. The essence of the local approach is the

**Citation:** Wci´slik, W.; Pała, R. Some Microstructural Aspects of Ductile Fracture of Metals. *Materials* **2021**, *14*, 4321. https://doi.org/10.3390/ ma14154321

Academic Editors: Krzysztof Schabowicz and Thomas Niendorf

Received: 9 June 2021 Accepted: 28 July 2021 Published: 2 August 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

analysis of phenomena that take place in a small area of crack initiation and development (called the process zone).

This paper discusses the basic aspects related to the local approach to the analysis of ductile fracture of metals, taking into account changes in the microstructure of the material, namely the development of voids.

#### **2. Mechanisms of Structural Metals Failure**

Two basic mechanisms of metals failure are distinguished, namely cleavage and ductile fracture.

Due to its violent, uncontrolled nature and its consequences, brittle fracture has been the subject of advanced research for many years. The mechanism of brittle failure may take the form of intergranular and transgranular fracture. In most metals, the intercrystalline fracture mechanism is related to the cracking of particles arranged along the grain boundaries. Initiating the fracture process requires breaking the interatomic bonds. The increase in the volume of the resulting void is the result of hydrostatic stresses.

Local stresses, necessary to break the bonds, are characterized by significant values compared to the material strength measured on a macroscopic scale. It follows that the crack initiation takes place around stress concentrators, which are usually geometrical discontinuities at the microscopic level (microvoids, notches, inclusions).

The occurrence of the brittle fracture mechanism in ferritic steels is favored by low ambient temperature and high deformation rates [6]. It should also be emphasized that the process of the brittle fracture largely depends on the microstructural structure of the material (e.g., grain size).

In typical operating conditions of the structure (static character of loading, room temperature), material failure often takes the form of ductile fracture and is preceded by the occurrence of significant plastic deformation. In metals of high metallurgical purity (copper, gold), in the absence of internal stress concentrators, the failure occurs by necking the cross-section up to a complete narrowing (Figure 1a).

**Figure 1.** Ductile failure in metals: (**a**) necking; (**b**) shear; (**c**) development of voids.

The second process is associated with a slip mechanism in which the shear bands are inclined at an angle of approximately 45 degrees to the axis of the main tensile stresses (Figure 1b). However, ductile fracture in technical metals is most often associated with nucleation and the development of internal microvoids (Figures 1c and 2).

**Figure 2.** Phases of void development: (**a**) nucleation of voids; (**b**) growth; (**c**) coalescence; (**d**) rupture.
