Indentation size effect of germanium single crystal with different crystal orientations

In order to study the indentation size effect(ISE)of germanium single crystals,nano-indentation experiments were carried out on the(100),(110)and(111)plane-orientated germanium single crystals.The true hardness of each crystal plane of germanium single crystals was calculated based on the Meyer equation,proportional sample resistance(PSR)model and Nix-Gao model,and the indentation size effect(ISE)factor of each crystal plane was calculated.Results show that,the germanium single crystals experience elastic deformation,plastic deformation and brittle fracture during the loading process,and the three crystal planes all show obvious ISE phenomenon.All three models can effectively describe the ISE of germanium single crystals,and the calculated value of Nix-Gao model is the most accurate.Compared with the other two crystal planes,Ge(110)has the highest size effect factor m and the highest hardness,which indicates that Ge(110)has the worst plasticity.

Nanoindentation Size Effect on Type 316 Stainless Steel

Nanoindentation size effect was investigated under very low loads on type 316 stainless steel. Nanoindentation measurements were carried out on the samples surfaces with a Berkovich pyramidal diamond indenter applying loads in the range of 25-1000μN. Simultaneously, AFM images of the sample surface were recorded before and after indentation process .For type 316 stainless steel, the indentation size effect was found. The results were discussed in the terms of the model of geometrically necessary dislocations proposed to interpret the indentation size effect.It can be seen that the square of the nanohardness, H 2, vs the inverse of indentation depth, 1/h, is linearly dependent on the indented depth in the range of 25-150nm,which is a good qualitative agreement with the predictions of the model. However, for shallow indents, the slope of the line severely changes.Some possible mechanisms for this change were proposed.

Effect of indentation size and grain/sub-grain size on microhardness of high purity tungsten

Hardness of materials depends significantly on the indentation size and grain/sub-grain size via microindentation and nanoindentation tests of high-purity tungsten with different structures.The grain boundary effect and indentation size effect were explored.The indentation hardness was fitted using the Nix-Gao model by considering the scaling factor.The results show that the scaling factor is barely correlated with the grain/sub-grain size.The interaction between the plastically deformed zone（PDZ） boundary and the grain/sub-grain boundary is believed to be the reason that leads to an increase of the measured hardness at the specific depths.Results also indicate that the area of the PDZ is barely correlated with the grain/sub-grain size,and the indentation hardness starts to stabilize once the PDZ expands to the dimension of an individual grain/sub-grain.

A new approach for determining GND and SSD densities based on indentation size effect:An application to additive-manufactured Hastelloy X

Dislocation plays a crucial role in controlling the strength and plasticity of bulk materials.However,determining the densities of geometrically necessary dislocations(GNDs)and statistically stored dislocations(SSDs)is one of the classical problems in material research for several decades.Here,we proposed a new approach based on indentation size effect(ISE)and strengthening theories.This approach was performed on a laser powder bed fused(L-PBF)Hastelloy X(HX),and the results were verified by the Hough-based EBSD and modified Williamson-Hall(m-WH)methods.Furthermore,to better understand the new approach and essential mechanisms,an in-depth investigation of the microstructure was conducted.The distribution of dislocations shows a clear grain orientation-dependent:low density in large<101>preferentially orientated grains while high density in fine<001>orientated grains.The increment of strengthening in L-PBF HX is attributed to a huge amount of edge-GNDs.Planar slip is the main operative deformation mechanism during indentation tests,and the slip step patterns depend mostly on grain orientations and stacking fault energy.This study provides quantitative results of GND and SSD density for L-PBF HX,which constructs a firm basis for future quantitative work on other metals with different crystal structures.

Indentation Size Effect inβCuAlBe and Cu-2Be Alloys

The indentation size effect(ISE)was studied by instrumented nanoindentation and Vickers hardness measurements on polycrystalline copper,βCuAlBe pseudoelastic and age-hardenable CuBe alloys.Variations in the load-depth curves at different loads would suggest a change in the behavior of the materials as the load increases.Nanohardness was estimated at different loads taking into account the pile-up in each case,which was estimated from the images of the topography obtained by atomic force microscopy(AFM).The effect of the microstructure of Cu-2Be(wt%)samples on the ISE was also studied.For each copper alloy,the Nix and Gao model was applied to the hardness-depth curves,and significant differences were found for the parameters obtained.Cu is in the constant nanohardness regime for depths below 500 nm,while microhardness exhibits the ISE effect.The behavior of the nanohardness and the plastic strain with the depth is almost inverse.CuAlBe presents the lowest values of plastic strains due to the pseudoelastic effect,while Cu presents an almost constant value around 8%,which corresponds to the highest plastic strain obtained.

A NUMERICAL STUDY OF INDENTATION WITH SMALL SPHERICAL INDENTERS

The finite element method for the conventional theory of mechanism-based strain gradient plasticity is used to study the indentation size effect. For small indenters （e.g., radii on the order of 10μm）, the maximum allowable geometrically necessary dislocation （GND） density is introduced to cap the GND density such that the latter does not become unrealistically high. The numerical results agree well with the indentation hardness data of iridium. The GND density is much larger than the density of statistically stored dislocations （SSD） underneath the indenter, but this trend reverses away from the indenter. As the indentation depth （or equivalently, contact radius） increases, the GND density decreases but the SSD density increases.

Microstructure Characterization and Indentation Hardness Testing Behavior of Mg-8Sn-xAl-1Zn Alloys

The influence of Al content on microstructure characterization and indentation hardness testing behavior of Mg-8Sn-x Al(x=1 wt%, 2 wt%, 3 wt%)-1Zn alloys was investigated by optical microscope, Pandat software, X-ray diffraction, scanning electron microscope, differential scanning calorimetry and a microhardness testing equipment. The results can be summarized as follows: when the Al content is 1 wt%, the alloy is composed of α-Mg and Mg2 Sn phases; while the new phase of Mgx(Al Zn)1-x can be observed and the morphology of Mg2 Sn phase transfers from the semi-continuous network to the dispersed particles with further addition of Al content to 2 wt% and 3 wt%. The dendrite arm spacing(DAS) deceases firstly and then slightly increases with the increase of Al content. The micro-hardness of Mg-8Sn-x Al(x=1 wt%, 2 wt%, 3 wt%)-1Zn also increases with increasing of Al content. Moreover, the indentation size effect(ISE) in Vickers hardness for Mg-8Sn-1Al-1Zn alloy was observed with the applied test load ranging from 0.490 to 4.903 N.

Influence of alloying elements on microstructure and microhardness of Mg-Sn-Zn-based alloys

The phase evolution in （88%-91%）Mg-8%Sn-l%Zn-X （X=A1, Mn and/or Ce） system was analyzed via CALPHAD method and simulations were used in precise selection of the chemical composition. The influence of the addition of different alloying elements such as A1, Mn and Ce on the microstructure and microhardness of Mg-8%Sn-l%Zn-based alloys was investigated. Combined addition of A1 and Mn shows features distinct from separate addition of A1 or Mn. Additions of l%AI and l%Mn to base alloy result in the formation of massive A1-Mn phase in a-Mg matrix grains. Addition of Ce element can refme the second eutectic precipitates and form intermetallic compounds with Sn. Fine rod-like Sn-Ce phase presents mainly on the grain boundaries and plays a role in inhibiting grain growth. The effects of alloying elements on Vickers microhardness and indentation size effect of base alloy were examined.

Factors Resulting in Micron Indentation Hardness Descending in Indentation Tests

Some factors that affect the experimental results in nanoindentation tests such as the contact depth,contact area,load and loading duration are analyzed in this article. Combining with the results of finite element numerical simulation,we find that the creep property of the tested material is one of the important factors causing the micron indentation hardness descending with the increase of indentation depth. The analysis of experimental results with different indentation depths demonstrates that the hardn...

Mechanical properties of hot-pressed high-entropy diboride-based ceramics

High-entropy ceramics attract more and more attention in recent years.However,mechanical properties especially strength and fracture toughness for high-entropy ceramics and their composites have not been comprehensively reported.In this work,high-entropy(Ti0.2Zr0.2Hf0.2Nb0.2Ta 0.2)B2(HEB)monolithic and its composite containing 20 vol%SiC(HEB–20SiC)are prepared by hot pressing.The addition of SiC not only accelerates the densification process but also refines the microstructure of HEB,resulting in improved mechanical properties.The obtained dense HEB and HEB–20SiC ceramics hot pressed at 1800℃exhibit four-point flexural strength of 339±17 MPa and 447±45 MPa,and fracture toughness of 3.81±0.40 MPa·m1/2 and 4.85±0.33 MPa·m1/2 measured by single-edge notched beam(SENB)technique.Crack deflection and branching by SiC particles is considered to be the main toughening mechanisms for the HEB–20SiC composite.The hardness Hv0.2 of the sintered HEB and HEB–20SiC ceramics is 23.7±0.7 GPa and 24.8±1.2 GPa,respectively.With the increase of indentation load,the hardness of the sintered ceramics decreases rapidly until the load reaches about 49 N,due to the indentation size effect.Based on the current experimental investigation it can be seen that the room temperature bending strength and fracture toughness of the high-entropy diboride ceramics are within ranges commonly observed in structure ceramics.