The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A53D45298E14F73B86495BBC056E16DC/S0884291400017039a.pdf/div-class-title-an-improved-technique-for-determining-hardness-and-elastic-modulus-using-load-and-displacement-sensing-indentation-experiments-div.pdf

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments

Monolayer molybdenum disulfide (MoS2) is a two-dimensional direct band gap semiconductor with unique mechanical, electronic, optical, and chemical properties that can be utilized for novel nanoelectronics and optoelectronics devices. The performance of these devices strongly depends on the quality and defect morphology of the MoS2 layers. Here we provide a systematic study of intrinsic structural defects in chemical vapor phase grown monolayer MoS2, including point defects, dislocations, grain boundaries, and edges, via direct atomic resolution imaging, and explore their energy landscape and electronic properties using first-principles calculations. A rich variety of point defects and dislocation cores, distinct from those present in graphene, were observed in MoS2. We discover that one-dimensional metallic wires can be created via two different types of 60° grain boundaries consisting of distinct 4-fold ring chains. A new type of edge reconstruction, representing a transition state during growth, was als...

Intrinsic Structural Defects in Monolayer Molybdenum Disulfide

A mechanism-based theory of strain gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of strain gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of strain gradient plasticity in which the Taylor model is adopted as a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.

Mechanism-based strain gradient plasticity— I. Theory

Single-layered molybdenum disulphide with a direct bandgap is a promising two-dimensional material that goes beyond graphene for the next generation of nanoelectronics. Here, we report the controlled vapour phase synthesis of molybdenum disulphide atomic layers and elucidate a fundamental mechanism for the nucleation, growth, and grain boundary formation in its crystalline monolayers. Furthermore, a nucleation-controlled strategy is established to systematically promote the formation of large-area, single- and few-layered films. Using high-resolution electron microscopy imaging, the atomic structure and morphology of the grains and their boundaries in the polycrystalline molybdenum disulphide atomic layers are examined, and the primary mechanisms for grain boundary formation are evaluated. Grain boundaries consisting of 5- and 7- member rings are directly observed with atomic resolution, and their energy landscape is investigated via first-principles calculations. The uniformity in thickness, large grain sizes, and excellent electrical performance signify the high quality and scalable synthesis of the molybdenum disulphide atomic layers.

Vapour phase growth and grain boundary structure of molybdenum disulphide atomic layers

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

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J. P. Hirth

Papers

Theory of Dislocations (2nd ed.)