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Yield Criteria for Ductile Materials under Plane Stress01:25

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In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
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The stress-strain relationship in ductile materials such as structural steel or aluminium is intricate and progresses through several stages. When a specimen is loaded, it initially exhibits a linear length increase, depicted by a steep straight line on the stress-strain diagram. It indicates the material is elastically deforming and will return to its original shape once unloaded. However, when a critical stress value is reached, plastic deformation begins. This stage sees substantial...
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Strain-Energy Density01:20

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Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
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Fatigue occurs when materials rupture under repeated or fluctuating loads, even at stress levels far below their static breaking strength. It typically results in brittle failure, even for ductile materials. It is a critical consideration in designing machines and structural components subjected to repetitive or varying loads. The nature of these loadings can range from fluctuating loads like unbalanced pump impellers causing vibrations to repeatedly bending a thin steel rod wire back and forth...
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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
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Related Experiment Video

Updated: Jul 7, 2025

An Available Technique for Preparation of New Cast MnCuNiFeZnAl Alloy with Superior Damping Capacity and High Service Temperature
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Phase-Specific Damage Tolerance of a Eutectic High Entropy Alloy.

Shristy Jha1,2, Rajiv S Mishra1,2, Sundeep Mukherjee1,2

  • 1Department of Materials Science and Engineering, University of North Texas, Denton, TX 76203, USA.

Entropy (Basel, Switzerland)
|December 23, 2023
PubMed
Summary

This study examined how two different phases in a high entropy alloy respond to mechanical stress. The alloy has a microstructure made of L12 and B2 phases. Researchers used a microcantilever bending technique to test each phase separately. The L12 phase showed better strength and deformation resistance, while the B2 phase was more prone to cracking. The study also looked at how the alloy fails at the microscale, finding that the L12 phase behaves in a ductile way, whereas the B2 phase shows brittle fracture. These results help explain how the alloy's performance depends on its phase composition, which could be useful for designing stronger materials.

Keywords:
eutectic systemhigh entropy alloymicro-cantilever bendingmicrocantilever bendinghigh entropy alloysmechanical failure analysisphase-specific deformation

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Area of Science:

  • Materials science of high entropy alloys
  • Microstructural mechanics in advanced alloys

Background:

Understanding the mechanical behavior of high entropy alloys at the microscale remains a challenge. Prior research has shown that these alloys exhibit complex deformation mechanisms due to their multi-phase microstructures. However, the phase-specific damage tolerance of such materials has not been fully characterized. This gap motivated the current investigation into how individual phases within a eutectic high entropy alloy respond to mechanical stress. Existing studies have focused on macroscopic properties, but micro-scale deformation mechanisms remain less explored. The need to distinguish between phase-specific responses is critical for optimizing alloy performance. No prior work had resolved the role of phase boundaries in damage propagation. This uncertainty drove the use of microcantilever techniques to isolate phase-specific behavior. The goal was to clarify the mechanical contributions of each phase in a two-phase system.

Purpose Of The Study:

The study aimed to evaluate the damage tolerance of individual phases in the AlCoCrFeNi2.1 high entropy alloy. The alloy features a lamellar microstructure composed of L12 and B2 phases. The researchers sought to determine how each phase responds to micro-scale mechanical loading. They also aimed to assess the influence of phase boundaries on deformation and failure. The motivation stemmed from the need to improve the mechanical reliability of high entropy alloys. By isolating phase-specific behavior, the team hoped to identify deformation mechanisms unique to each phase. The study focused on microcantilever bending as a method to induce and measure localized damage. The objective was to compare the mechanical performance of the two phases under controlled conditions.

Main Methods:

The researchers employed a microcantilever bending technique to assess phase-specific damage tolerance. Notches were milled into the L12 phase, the B2 phase, and the phase boundary. Each cantilever was subjected to controlled bending to simulate mechanical stress. The dimensionalized stiffness (DS) was measured to evaluate changes in mechanical response. Fractography was conducted after compression tests to analyze failure modes. The L12 and B2 phases were examined separately to isolate their deformation behaviors. The study utilized electron microscopy to observe microstructural changes. The phase boundary's role in crack propagation was also investigated through these methods.

Main Results:

The L12 phase showed higher bending strength and greater strain hardening compared to the B2 phase. Cantilevers made from the L12 phase maintained relatively constant dimensionalized stiffness during loading. This indicated plastic deformation followed by increased stiffness at later stages. In contrast, B2 phase cantilevers experienced a continuous drop in stiffness, suggesting crack propagation. The L12 phase exhibited ductile failure characteristics, including multiple slip planes and shear lips. The B2 phase showed quasi-cleavage fracture with cleavage facets and a river pattern. These differences were confirmed through post-compression fractography. The phase boundary did not significantly alter the mechanical response of either phase.

Conclusions:

The study found that the L12 phase of AlCoCrFeNi2.1 has superior damage tolerance compared to the B2 phase. The L12 phase demonstrated plastic deformation and strain hardening, while the B2 phase failed through crack propagation. These findings suggest that the mechanical performance of the alloy depends on the phase composition. The researchers propose that the L12 phase contributes more to the alloy's overall strength. The B2 phase, however, may be more prone to brittle failure under bending stress. The phase boundary did not influence the mechanical behavior of either phase. The authors suggest that these results could inform the design of high entropy alloys with improved damage resistance. The study highlights the importance of phase-specific analysis in multi-phase materials.

The L12 phase shows superior bending strength and plastic deformation, while the B2 phase experiences crack propagation and lower damage tolerance.

They used microcantilever bending with notches milled into each phase and the phase boundary to isolate mechanical responses.

To track changes in mechanical response, indicating plastic deformation in the L12 phase and crack propagation in the B2 phase.

L12-phase cantilevers showed ductile failure with slip planes and shear lips, while B2-phase cantilevers exhibited quasi-cleavage fracture.

No, the phase boundary did not significantly alter the mechanical response of either the L12 or B2 phase.

The results suggest that phase composition influences mechanical performance, guiding the development of alloys with improved damage resistance.