N. I. Tymiak

Plastic strain and strain gradients at very small indentation depths

Abstract Plastic strains and their respective strain gradients produced by nanoindentation have been theoretically interpreted and experimentally measured at shallow indentation depths. Existing data for 〈100〉 tungsten with four different conical tip radii varying from 85 to 5000 nm and new data for four conical tips (R=0.5 to 20 μm) into 〈100〉 aluminum are presented. Theoretical results based on geometrically necessary dislocations and semi-empirical experimental continuum calculations are compared for spherical and wedge indenters. For a sharp wedge, both experimental continuum based and theoretical geometrical approaches suggest strain gradient decreasing with the increasing indentation depth, δ. In contrast, theoretical geometrical analysis for a spherical contact yields a depth independent strain gradient proportional to 1/R and continuum calculations suggest a slight increase of a strain gradient proportional to δ1/4/R3/4. Both single crystals exhibit about a factor of two decrease in hardness with increasing depth, irrespective of either increasing or decreasing average strain gradients. Implications to strain gradient plasticity and indentation size effect interpretations at very shallow depths are discussed.

Nanomechanical probes as new approaches to hydrogen/deformation interaction studies

Abstract Continuous developments into the understanding of hydrogen/deformation interactions have been facilitated by experimental advances and improved computational capabilities. Interactive fracture problems have enjoyed the assistance of fracture mechanics theory and methodology. Regarding hydrogen embrittlement (HE) the current study leans toward a generic hydrogen enhanced decohesion model (HEDE), allowing quantitative engagement with experiments. These include degradation in terms of fracture criteria, subcritical slow crack growth, alternating ductile/brittle transition, threshold values and fine scale fracture surface assessments. In this context the HEDE model remains illuminating, physically based, and experimentally consistent. However, one of the main points of contention, if not confusion, has been the use of thermodynamically based vs. kinetically based arguments to define the threshold and crack growth regimes. We give our view of the general process which we believe to have greater applicability to time-dependent interactive processes. In this context, the description applies to some aspects of stress corrosion cracking and liquid metal embrittlement as well. Following a brief overview regarding HE in the bulk, the paper centers on new avenues of exploring small volume problems. As such this investigation was assisted by nanomechanical testing and high resolution observations. Here, mainly two examples are described in polycrystalline FCC systems. For example, it is shown that hydrogen increases the load onset for dislocation nucleation in a metastable austenitic stainless steel by about a factor of two or more whereupon the yield point recovers to a value near 200 μN after hydrogen outgasses. In a different set of indentation experiments, it is shown that hydrogen decreases both the practical and true works of adhesion at Cu/Ti/SiO2 interfaces by about 50%. Besides evaluating interfacial strengths, the nanomechanical approach should allow additional critical experiments of hydrogen/deformation interactive effects.

Highly localized acoustic emission monitoring of nanoscale indentation contacts

This study evaluated a novel approach for acoustic emission (AE) monitoring of nanoindentation. The technique utilizes a miniature AE sensor integrated into a calibrated diamond indenter tip on a commercial nanoindentation system. The evaluation focused on the yield -point phenomenon in W (100); MgO (100); and sapphire C (0001); R ( 1 012); A (1 2 10); and M (10 1 0) single-crystal surfaces. The minimum amount of elastic energy release sufficient to produce AE signal detectable with the indenter tip sensor was nearly two orders of magnitude lower than the minimum energy level required for conventional AE sensors. Wave forms detected with the indenter tip sensor were independent of sample size. A linear relationship between released elastic energies and the corresponding AE energies was observed for all three evaluated materials. The scaling coefficient of the linear relationship was independent of indenter tip size/shape and indentation depth. The differences between the mechanisms of the initial stages of plasticity for the various crystallographic orientations of sapphire were reflected in the following aspects of AE activity: detection of a specific type of AE wave form that correlated to the presence of linear surface features near the indentation sites; AE signal associated with the yield point, consisting either of one or two distinct wave forms; and presence or absence of AE signals after the yield point. The possibility of plasticity onset in sapphire involving both slip and twinning is discussed.

THE MECHANICAL BEHAVIOR OF A PASSIVATING SURFACE UNDER POTENTIOSTATIC CONTROL

Continuous microindentation has been carried out on an iron–3% silicon single crystal in 1 M sulfuric acid. The ability of the material to support elastic loading is directly linked to the presence of thermally grown oxide films and passive films applied through potentiostatic control of the sample. When the passive film is removed, either by chemical or electrochemical means, the iron alloy can no longer sustain pressures on the order of the theoretical shear strength of iron. Instead, the metal behaves in a traditional elastic-plastic manner when no film is present. The oxide film at the edges of the indentation can sustain applied tensile stresses up to 1.2 GPa prior to failure. Indentation in materials undergoing dissolution must account for the rate of material removal over the remote surface and the resulting plastic deformation around the contact of the indentation.

Initial stages of contact-induced plasticity in sapphire. I. Surface traces of slip and twinning

The present study focuses on the effects of surface orientation on the peculiarities of the earliest stages of nanoindentation-induced plasticity in sapphire (Al2O3) single crystal surfaces. The previous theoretical analyses do not account for all the experimentally observed trends. Additional considerations are required to bridge the gap between experimental results and theoretical predictions. Of key importance are accounting for the sense of twinning shear, the multiplicity of slip and twinning systems involved and an appropriate criterion for the transition from elastic to elastic-plastic regime. The present study supplements a continuum-based stress analysis with the above considerations and compares the resulting theoretical predictions with the experimental results for basal [C, (0001)], rhombohedral [R,(1102)] and prism [A,(1210) and M,(1010)] surfaces. Surface patterns of slip and twining are scrutinized in Part I. Previously unexplained features justified by the results obtained by the present authors include the distribution of the linear surface features ascribed to twinning and the symmetry of indentation pile-up. Part II focuses on the mechanisms of the transition between the elastic and elastic–plastic regimes.

The role of plasticity in bimaterial fracture with ductile interlayers

Evaluation of the plasticity effects in fracture along ductile/brittle interfaces requires appropriate models for plastic dissipation in a ductile component. For thin ductile films, constitutive properties appropriate to the small volumes involved are essential for adequate modeling. Here, yield stress is of primary importance. With nanoindentation, one can obtain both a large strain flow stress as well as the far field yield stress representing the small strain elastic-plastic boundary. Using these to estimate an appropriate plastic strain energy density, the crack tip plastic energy dissipation rates associated with the interfacial crack extension can be estimated for a ductile film. With the preceding analysis, plasticity effects on the interfacial toughness have been evaluated for external measures of strain energy release rates as obtained from indentation tests using the axisymmetric bilayer theory. Comparison involved RF sputtered 200- to 2000-nm-thick Cu interlayers between oxidized silicon and sputtered tungsten. Experimental values for the Cu/SiO2 interface increased with Cu film thickness from 1 to 15 J/m2. This was in qualitative agreement with the theoretical predictions for plastic energy dissipation rates. In contrast, first-order estimates suggest that the observed interfacial toughness increases cannot be attributed to either mode mixity effects or increased intrinsic interfacial fracture energies. As such, crack tip plasticity is identified as the dominant mechanism for increasing interfacial toughness.

Initial stages of contact-induced plasticity in sapphire. II. Mechanisms of plasticity initiation

Part II of the present study focuses on the yield point phenomenon, a discontinuous transition from the apparently elastic to the elastic–plastic regime for basal [C, (0001)], rhombohedral [R, (1 012)] and prism [A, (12 10) and M, (101 0)] planes of sapphire (Al2O3) under spherical contacts. The yield point mechanisms are predicted by supplementing the analysis presented in Part I with a criterion for the yield point transition. The proposed criterion accounts for the low-symmetry structure of sapphire. The resulting theoretical predictions are compared with experimental results. This comparison focuses on the effects of surface orientation and loading rates on the yield point load and on the peculiarities of yield point mechanisms, as reflected in the acoustic emission (AE) signals associated with the yield point. For the C plane, the availability of pyramidal and prism slip is expected to be a limiting factor for the yield point transition. Depending on the loading rate, either basal slip or basal twinning dominates the yield point mechanism for the M plane. For the A plane, the yield point is determined by basal slip. For the R plane, a yield point mechanism involving rhombohedral twinning combined with basal or pyramidal slip is possible. Consistent with the experimental results, the highest and the lowest yield point loads are predicted for C and R planes, respectively.

A brittle to ductile transition (BDT) in adhered thin films

It has been long recognized that the BDT in bulk materials may be associated with enhanced plastic energy dissipation. This can be achieved by either changing the state of stress (plane strain to plane stress) or by raising the test temperature (lowering the yield stress). The situation is somewhat different in thin films where the BDT can be achieved by increasing film thickness or perhaps, even in a limited temperature range, by raising the test temperature. To study the latter we use a superlayer technique with a 1 μm tungsten film on top of thin copper films bonded to SiO 2 /Si wafers. This involves indenting into the superlayer which stores and then releases large amounts of elastic energy into the thin film/substrate interface. Here, preliminary data on 500 nm thick Cu demonstrates more than an order of magnitude increase in fracture energy from about 10 to 200 J/m 2 as the test temperature is raised from 20°C to 130°C. As the amount of plastic energy absorption would appear to be limited by film thickness, this relatively large value was unanticipated. This interfacial fracture energy translates to a stress intensity of 5 MPa-m 1/2 . In context of the highest possible nanocrystalline Cu yield strength, this still represents a plastic zone of nearly 30 μm. This illustrates the quandary associated with explaining such high apparent toughness values as one generally expects plasticity to be truncated by film thickness. Is this associated with: –some artifact of assessing local stresses during nanoindentation at elevated temperature: –extending the plastic zone in the direction of crack growth much further than the film thickness; –a shielding mechanism from an organized dislocation array in a ductile film sandwiched between a brittle substrate and a higher yield strength superlayer; –some plastic energy dissipation in the superlayer; –or by enhanced mode II at higher temperatures? A few of these will be addressed in some detail with a goal of narrowing the field of the most promising candidates.

Microindentation method for in situ stress measurements in precipitated iron sulfate FILMS

Abstract Active-passive potential steps have been applied during continuous microindentation into 300 μ m thick Fe3%Si sheets exposed to 1 M H 2 SO 4 . First, samples were allowed to deflect in the indentation direction whereby the indenter penetration changed due to local metal dissolution and sample deflection resulting from passive film stress induced bending. Samples were then constrained to eliminate stress induced deflection. A distinct difference between the indentation curves for the above two types of tests allowed separation of the effects of film stress and local dissolution. Indenter tip displacement correlated with the current behavior and was consistent with the salt film evolution and resulting electrostrictive film stress. A theoretical model allows estimates of the time dependent film thickness (3.5 μ m at maximum) and electrostrictive film stress (330 MPa at maximum).

Acoustic Emission Monitoring of Nanoindentation-Induced Slip and Twinning in Sapphire

Monitoring with an Acoustic Emission (AE) sensor integrated into an indenter tip was utilized for the evaluation of the earliest stages of indentation-induced plasticity in sapphire single crystal. The evaluated surfaces included basal (C), rhombohedral (R) and two different prismatic orientations (A and M). The differences between the mechanisms of the initial stages of plasticity for the various crystallographic orientations were reflected in the following aspects of AE activity: detection of a specific type of AE waveform that correlated to the presence of linear surface features near the indentation impressions; AE signal associated with the yield point, consisting either of one or two distinct waveforms; and presence or absence of AE signals after the yield point. Moreover, analysis of AE activity revealed loading rate effects on the yield point mechanism for the M plane. The possibility of plasticity onset mechanisms involving both slip and twinning is discussed.