Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic–plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a “hold” period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and “hold-at-the-maximum-indenter-displacement” for determining the instantaneous modulus using spherical indenters.

Instability Of Crack Propagation In Brittle Bulk Metallic Glass

The instability of the crack tip in brittle Mg-based bulk metallic glass (BMG) is studied. The formation of various fractographic surfaces of the BMG is associated with the instability of the fluid meniscus, which is due to viscous fluid matter being present on the fracture process zone. Depending on the values of the wavelength of the initial perturbation of the fluid meniscus and the local stress intensity factor, different fracture surface profiles, i.e. a dimple-like structure, a periodic corrugation pattern and a pure mirror zone are formed. The fractographic evolution is significantly affected by the applied stress. A decreased fracture Surface roughness is observed under a low applied stress. An increased fracture surface roughness, which has frequently been reported by other researchers, is also observed in the present studies under a high applied stress. Unique fractographic features are attributed to the non-linear hyperelastic stiffening for less softening) mechanism. (C) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Fracture Mechanisms And Size Effects Of Brittle Metallic Foams: In Situ Compression Tests Inside Sem

In situ compressive tests on specially designed small samples made from brittle metallic foams were accomplished in a loading device equipped in the scanning electron microscopy (SEM). Each of the small samples comprises only several cells in the effective test zone (ETZ), with one major cell in the middle. In such a system one can not only obtain sequential collapse-process images of a single cell and its cell walls with high resolution, but also correlate the detailed failure behaviour of the cell walls with the stress-strain response, therefore reveal the mechanisms of energy absorption in the mesoscopic scale. Meanwhile, the stress-strain behaviour is quite different from that of bulk foams in dimensions of enough large, indicating a strong size effect. According to the in situ observations, four failure modes in the cell-wall level were summarized, and these modes account for the mesoscopic mechanisms of energy absorption. Paralleled compression tests on bulk samples were also carried out, and it is found that both fracturing of a single cell and developing of fracture bands are defect-directed or weakness-directed processes. The mechanical properties of the brittle aluminum foams obtained from the present tests agree well with the size effect model for ductile cellular solids proposed by Onck et al. (C) 2008 Elsevier Ltd. All rights reserved.

Deformation Twinning In Bulk Nanocrystalline Metals: Experimental Observations

Deformation twins have been observed in nanocrystalline (nc) fcc metals with medium-to-high stacking fault energies such as aluminum, copper, and nickel. These metals in their coarse-grained states rarely deform by twining at room temperature and low strain rates. Several twinning mechanisms have been reported that are unique to nc metals. This paper reviews experimental evidences on deformation twinning and partial dislocation. emissions from grain boundaries, twinning mechanisms, and twins with zero-macro-strain. Factors that affect the twinning propensity and recent analytical models on the critical grain sizes for twinning are also discussed. The current issues on deformation twinning in nanocrystalline metals are listed.

Comparison Of Shear Banding In Bmgs Due To Thermal-Softening And Free Volume Creation

This paper reports a comparative study of shear banding in BMGs resulting from thermal softening and free volume creation. Firstly, the effects of thermal softening and free volume creation on shear instability are discussed. It is known that thermal softening governs thermal shear banding, hence it is essentially energy related. However, compound free volume creation is the key factor to the other instability, though void-induced softening seems to be the counterpart of thermal softening. So, the driving force for shear instability owing to free volume creation is very different from the thermally assisted one. In particular, long wave perturbations are always unstable owing to compound free volume creation. Therefore, the shear instability resulting from coupled compound free volume creation and thermal softening may start more like that due to free volume creation. Also, the compound free volume creation implies a specific and intrinsic characteristic growth time of shear instability. Finally, the mature shear band width is governed by the corresponding diffusions (thermal or void diffusion) within the band. As a rough guide, the dimensionless numbers: Thermal softening related number B, Deborah number (denoting the relation of instability growth rate owing to compound free volume and loading time) and Lewis number (denoting the competition of different diffusions) show us their relative importance of thermal softening and free volume creation in shear banding. All these results are of particular significance in understanding the mechanism of shear banding in bulk metallic glasses (BMGs).

Ductile To Brittle Transition In Dynamic Fracture Of Brittle Bulk Metallic Glass

We report an unusual transition from a locally ductile to a pure brittle fracture in the dynamic fracture of brittle Mg65Cu20Gd10 bulk metallic glass. The fractographic evolution from a dimple structure to a periodic corrugation pattern and then to the mirror zone along the crack propagation direction during the dynamic fracture process is discussed within the framework of the meniscus instability of the fracture process zone. This work might provide an important clue in understanding of the energy dissipation mechanism for dynamic crack propagation in brittle glassy materials. (C) 2008 American Institute of Physics.

Dynamic Fracture Instability Of Tough Bulk Metallic Glass

We report the observations of a clear fractographic evolution from vein pattern, dimple structure, and then to periodic corrugation structure, followed by microbranching pattern, along the crack propagation direction in the dynamic fracture of a tough Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit.1) bulk metallic glass (BMGs) under high-velocity plate impact. A model based on fracture surface energy dissipation and void growth is proposed to characterize this fracture pattern transition. We find that once the dynamic crack propagation velocity reaches a critical fraction of Rayleigh wave speed, the crack instability occurs; hence, crack microbranching goes ahead. Furthermore, the correlation between the critical velocity of amorphous materials and their intrinsic strength such as Young's modulus is uncovered. The results may shed new insight into dynamic fracture instability for BMGs. (C) 2008 American Institute of Physics.

The Characterization Of Creep And Time-Dependent Properties Of Bulk Metallic Glasses Using Nanoindentation

Viscoelastic deformation and creep behavior of La- and Ce-based bulk metallic glasses (BMGs) with low glass transition temperature are investigated through nanoindentation at room temperature. Creep compliance and retardation spectra are derived to study the creep mechanism. The time-dependent displacement can be well described by a generalized Kelvin model. A modification is proposed to determine the elastic modulus from the generalized Kelvin model. The results are in excellent agreement with the elastic modulus determined by uniaxial compression tests. (c) 2007 Published by Elsevier B.V.

Deformation Behavior Of Fe-Based Bulk Metallic Glass During Nanoindentation

Fe-based bulk metallic glasses (BMGs) normally exhibit super high strength but significant brittleness at ambient temperature. Therefore, it is difficult to investigate the plastic deformation behavior and mechanism in these alloys through conventional tensile and compressive tests due to lack of distinct macroscopic plastic strain. In this work, the deformation behavior of Fe52Cr15Mo9Er3C15B6 BMG was investigated through instrumented nanoindentation and uniaxial compressive tests. The results show that serrated flow, the typical plastic deformation feature of BMGs, could not be found in as-cast and partially crystallized samples during nanoindentation. In addition, the deformation behavior and mechanical properties of the alloy are insensitive to the applied loading rate. The mechanism for the appearance of the peculiar deformation behavior in the Fe-based BMG is discussed in terms of the temporal and spatial characteristics of shear banding during nanoindentation.

Numerical Study Of Pile-Up In Bulk Metallic Glass During Spherical Indentation

Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness, Young's modulus, stress-strain response, etc. Finite element analysis was employed to implement numerical simulation of spherical indentation tests on bulk metallic glass. A new model was proposed to describe the pile-up effect. By using this new model, the contact radius and hardness of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass were obtained under several different indenter loads with pile-up, and the results agree well with the data generated by numerical simulation.

A Modified Free Volume Model For Characterizing Of Rate Effect In Bulk Metallic Glasses

We investigate the plastic deformation and constitutive behaviour of bulk metallic glasses (BMGs). A dimensionless Deborah number De(ID) = t(r)/t(i) is proposed to characterize the rate effect in BMGs, where t(r) is the structural relaxing characteristic time of BMGs under shear load, t(i) is the macroscopic imposed characteristic time of applied stress or the characteristic time of macroscopic deformation. The results demonstrate that the modified free volume model can characterize the strain rate effect in BMGs effectively.

Scaling Functions In Conical Indentation Of Elastic-Plastic Solids

The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young's modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young's modulus E and Poisson's ratio nu are known.

Energy Dissipation In Fracture Of Bulk Metallic Glasses Via Inherent Competition Between Local Softening And Quasi-Cleavage

Compression, tension and high-velocity plate impact experiments were performed on a typical tough Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) bulk metallic glass (BMG) over a wide range of strain rates from similar to 10(-4) to 10(6) s(-1). Surprisingly, fine dimples and periodic corrugations on a nanoscale were also observed on dynamic mode I fracture surfaces of this tough Vit 1. Taking a broad overview of the fracture patterning of specimens, we proposed a criterion to assess whether the fracture of BMGs is essentially brittle or plastic. If the curvature radius of the crack tip is greater than the critical wavelength of meniscus instability [F. Spaepen, Acta Metall. 23 615 (1975); A.S. Argon and M. Salama, Mater. Sci. Eng. 23 219 (1976)], microscale vein patterns and nanoscale dimples appear on crack surfaces. However, in the opposite case, the local quasi-cleavage/separation through local atomic clusters with local softening in the background ahead of the crack tip dominates, producing nanoscale periodic corrugations. At the atomic cluster level, energy dissipation in fracture of BMGs is, therefore, determined by two competing elementary processes, viz. conventional shear transformation zones (STZs) and envisioned tension transformation zones (TTZs) ahead of the crack tip. Finally, the mechanism for the formation of nanoscale periodic corrugation is quantitatively discussed by applying the present energy dissipation mechanism.

Plastic deformation in Ce-based bulk metallic glasses during depth-sensing indentation

The deformation behavior and the effect of the loading rate on the plastic deformation features in (numbers indicate at.%) Ce60Al15Cu10Ni15, Ce65Al10Cu10Ni10Nb5, Ce68Al10Cu20Nb2, and Ce70Al10Cu20 bulk metallic glasses (BMGs) were investigated through nanoindentation. The load-displacement (P-h) curves of Ce65Al10Cu10Ni10Nb5, Ce68Al10Cu2, and Ce70Al10Cu20 BMGs exhibited a continuous plastic deformation at all studied loading rate. Whereas, the P-h curves of Ce60Al15Cu10Ni15 BMG showed a quite unique feature, i.e. homogeneous plastic deformation at low loading rates, and a distinct serrated flow at high strain rates. Moreover, a creep deformation during the load holding segment was observed for the four Ce-based BMGs at room temperature. The mechanism for the appearance of the "anomalous" plastic deformation behavior in the Ce-based BMGs was discussed. (c) 2006 Elsevier B.V. All rights reserved.