Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: A study by synchrotron and bulge test techniques

We present a systematic study of the mechanical properties of different Cu, Ta/Cu and Ta/Cu/Ta films systems. By using a novel synchrotron-based tensile testing technique isothermal stress–strain curves for films as thin as 20 nm were obtained for the first time. In addition, freestanding Cu films with a minimum thickness of 80 nm were tested by a bulge testing technique. The effects of different surface and interface conditions, film thickness and grain size were investigated over a range of film thickness up to 1 μm. It is found that the plastic response scales strongly with film thickness but the effect of the interfacial structure is smaller than expected. By considering the complete grain size distribution and a change in deformation mechanism from full to partial dislocations in the smallest grains, the scaling behavior of all film systems can be described correctly by a modified dislocation source model. The nucleation of dissociated dislocations at the grain boundaries also explains the strongly reduced strain hardening for these films.     

Size effects on the mechanical properties of thin polycrystalline metal films on substrates

An analysis of the effects of the thickness and grain size of polycrystalline thin films on substrates is presented with the objective of linking the film mismatch stress to the underlying characteristic size scales. The model is predicated on the notion that the relaxation of mismatch strain in the film is accommodated by the introduction of dislocation loops whose population, dimensions and interaction energies are controlled by the film thickness and microstructural dimensions. The model is capable of capturing the combined effects of these size scales by accounting for the interaction energies of the constrained dislocation structure, and provides quantitative predictions of the evolution of film stress during thermal excursions. The predictions of the analysis are compared with available experimental results for polycrystalline films of face-centered cubic materials on Si substrates. It is shown that the model correctly predicts the observed influence of film thickness and grain size on stress evolution during thermal excursions. Aspects of strain hardening in thin polycrystalline films with high dislocation densities are also discussed.     

Bauschinger and size effects in thin-film plasticity

We present an experimental investigation of the effects of surface passivation, film thickness and grain size on the plastic behavior of freestanding Cu thin films. The stress–strain curves of the films are measured using the plane–strain bulge test. Films with a passivation layer on one or both surfaces have an offset yield stress that increases significantly with decreasing film thickness; the yield stress of unpassivated films, by contrast, is relatively independent of film thickness and increases mainly as a result of grain-size strengthening. The stress–strain curves of passivated films show an unusual Bauschinger effect on unloading. This effect is not observed for unpassivated films. Our experimental results suggest that passivation layers prevent dislocations from exiting the films and that they block slip bands at the film–passivation interface. The back stresses associated with these blocked slip bands increase the resistance to forward plastic flow on loading and cause reverse plastic flow on unloading. The effect of the back stresses increases with decreasing film thickness and leads to the observed strengthening of the passivated films. The constraint of a passivating layer on dislocation motion and hence on plastic flow cannot be described by classical plasticity theories, but can be modeled with some strain–gradient plasticity theories. We evaluate the suitability of the strain–gradient plasticity theory developed by Fleck and Hutchinson to describe our experimental results in a continuum framework. Comparison between experimental results and calculations yields very good agreement for the effect of film thickness, but the strain–gradient plasticity model fails to describe the Bauschinger effect observed in passivated films.     

Mechanical properties and microstructures of Al-Cu Thin films with various heat treatments

The relationship between microstructure and mechanical properties has been investigated in Al-Cu thin films. The Cu content in Al-Cu samples used in this study ranges from 0 to 2 wt.% and substrate curvature measurement was used to measure film stress. In thin films, the constraints on the film by the substrate influence the microstructure and mechanical properties. Al-Cu thin films cooled from high temperatures have a large density of dislocations due to the plastic deformation caused by the thermal mismatch between the film and substrate. The high density of dislocations in the thin film enables precipitates to form inside the grain even during a very rapid quenching. The presence of a large density of dislocations and precipitates will in turn cause precipitation hardening of the Al-Cu films. The precipitation hardening is dominant at lower temperatures, and solid solution hardening is observed at higher temperatures in the tensile regime. Pure Al films showed the same values of tensile and compressive yield stresses at a given temperature during stress-temperature cycling.     

Anisotropy and texture in thin copper films—an elasto-plastic analysis

The role of elastic anisotropy on the stress inhomogeneity and effective behavior of columnar grained textured Cu thin films have been analyzed within a continuum framework. The analysis is based on a three-dimensional model of a film/substrate system. The film exhibits a fiber texture with (111), (001) and randomly oriented grains. Mainly two load cases have been considered. Biaxial loading of a film deposited on a silicon substrate and tensile loading of a film deposited on a polyimide substrate. The stress distributions in the (111) and (001) grains were generally found to be very different when subjected to biaxial loading and quite similar when subjected to tensile loading. When plastic behavior is invoked, a structural hardening effect is observed. The plastic behavior differs significantly between biaxial and tensile cyclic loading respectively. A new orientation dependent hardening law is proposed. This hardening law causes the plastic hardening behavior to be orientation dependent and scale with elastic anisotropy. The newly proposed hardening law is demonstrated on a film with small grain aspect ratio.     

Strain gradient plasticity analysis of the strength and ductility of thin metallic films using an enriched interface model

The mechanical response of thin metallic films is simulated using a two-dimensional strain gradient plasticity finite-element model involving grain boundaries in order to investigate the effect of the thickness, grain shape and surface constraint on the strength, ductility and back-stress. The grain boundaries and surface layers are modeled as initially impenetrable to dislocations while allowing for relaxation at a critical stress level. The model captures the variation of the strength with grain size, film thickness, and with the presence or not of constraining surface layers, in agreement with experimental results on Al and Cu films. A decrease in the uniform elongation is predicted with decreasing film thickness due to a loss of strain-hardening capacity and the possible presence of imperfections. These two effects dominate over the stabilizing contribution of the plastic strain gradients. Accounting for the relaxation of the interface constraint affects the magnitude of the back-stress as well as the drop in ductility.     

Thickness effect on shape memory behavior of Ti-50.0at.%Ni thin film

The thickness effect on the shape memory behavior of Ti-50.0at.%Ni thin films was investigated. It was found that the transformation strain and residual strain under a constant stress are very sensitive to the film thickness when the thickness is less than the average grain size, 5 μm. Cross-sectional observation showed that these strains are affected by two kinds of constraints from surrounding grains and surface oxide layers. With decreasing thickness, the former effect becomes weak, but the latter effect becomes strong. As a result, the transformation strain and residual strain show a maximum around a thickness of 1–2 μm. In addition, the transformation temperatures were also found to be affected by surface oxidation if the thickness is less than 1 μm.     

The flow stress in polycrystalline films: Dimensional constraints and strengthening effects

An analytical model is presented in order to derive a general expression for the flow stress in polycrystalline films which encompasses and correlates dimensional constraints and strengthening effects. The model is based on the Thompson approach, which is extended to take into account both different grain aspect ratios and distinct strengthening contributions. It allows an accurate prediction of the growth textures in polycrystalline CdTe thick films when grain growth is driven by strain energy minimization. The model also matches the experimental data concerning the grain size and film thickness dependences of the yield stress in polycrystalline Cu thin films either deposited on a substrate or freestanding. Interestingly, the yield stress is found to be fitted by a modified Hall–Petch relation resulting in a d⁻ⁿ dependence in which the exponent n varies between ½ and 1 as a function of the grain size for a given thickness.     

Evolution of deformation mechanisms of Ti–22.4Nb–0.73Ta–2Zr–1.34O alloy during straining

The plastic deformation behavior of Ti–22.4Nb–0.73Ta–2Zr–1.34O alloy was investigated by compression testing at room temperature. The multi-peak stress oscillations of the true stress–strain curve, characterized by a stress plateau, initial strain-hardening, followed by strain-softening and a second strain-hardening stages, is observed in a titanium alloy for the first time. The experimental results show that the above four-stage plastic deformation behavior is caused by a change in the dominant deformation mechanisms. At the stress plateau stage, the alloy deforms via multiple plastic deformation mechanisms. The initial strain hardening is caused mainly by tangling of dislocations. Subsequent strain softening is due to the formation of kink bands. The second strain hardening corresponds to the formation of shear bands. The above results suggest that the dominant deformation mechanisms of Ti–Nb–Ta–Zr–O alloys are related not only to the stability of the β phase, but also to the extent of plastic deformation.     

Dislocation accumulation and strengthening in Cu thin films

An analysis that addresses the strain-hardening behavior of thin metallic films on substrates is presented. Stress measurements were made on 0.5 μm thick Cu films on Si substrates during thermal cycling, during stress relaxation at room temperature (RT), and after quenching in liquid nitrogen. Significant strengthening was observed in the thermal cycle during cooling. The stress relaxation at RT shows a decrease of the stress from 360 MPa to 290 MPa within 15 months. A theoretical approach to the strengthening phenomenon is made on the basis of the Peach–Koehler dislocation-interaction forces. It shows that adding threading dislocations into a parallel array of dislocations at the film–substrate interface can contribute significantly to the strain hardening of thin films. The calculated strain hardening accounts for a large portion of the observed strengthening.     

Plastic flow characteristics of ultrafine grained low carbon steel during tensile deformation

In order to explain steady-state plastic deformation, i.e. the absence of strain hardening in ultrafine grained low carbon steel during tensile deformation, steel of different ferrite grain sizes was prepared by intense plastic straining followed by static annealing and then tensile-tested at room temperature. A comparison between the ferrite grain size of ultrafine grained steel and the dislocation cell size of coarse grained steel formed during tensile deformation revealed that uniform dislocation distribution with high density and cell formation were unlikely to occur in this ultrafine grained steel. This is ascribed to the fact that the ultrafine grain size is comparable to or smaller than the cell size at the corresponding stress level. In addition, from a consideration of dynamic recovery, it was found that the characteristic time for trapped lattice dislocations to spread into the grain boundaries was so fast that the accumulation of lattice dislocation causing strain hardening could not occur under this ultrafine grain size condition. Therefore, the extremely low strain hardening rate of ultrafine grained low carbon steel during tensile deformation is attributed to the combined effects of the two main factors described above.     

Investigation of Strain Rate Effect by Three-Dimensional Discrete Dislocation Dynamics for fcc Single Crystal During Compression ProcessEI北大核心CSCD

Microelectromechanical systems (MEMS) have become increasingly prevalent in engineering applications. In these MEMS, a lot of micro-components, such as thin films, nanowires, micro-beams and micropillars, are utilized. The characteristic geometrical size of those components is at the same scale as that of grain, the mechanical behavior of crystal materials exhibits significant size effect and discontinuous deformation. In addition, those MEMS are often subjected to high strain rate at work, such collision and impact loading. The coupling deformation characteristics of small scale crystals and high strain rate makes their mechanical behavior more complicated. Accordingly, investigation of the effect of the strain rate on crystal materials at micron scale is significant for both the academia and industry. In this work, a plastic deformation model of fcc crystal under axial compression was developed based on three-dimensional discrete dislocation dynamics (3D-DDD), which considered the influence of externally applied stress, interaction force between dislocation segments, dislocation line tension and image force from free surface on dislocation movement during the process of plastic deformation. It was applied to simulate the plastic deformation process of a Ni single crystal micropillar during compression under different loading strain rates. 3D-DDD and theoretical analysis are carried out to extensively investigate the effect of strain rate on flow stress and deformation mechanisms during plastic deformation process of crystal materials. The results show that the flow stress and the dislocation density increased with the loading strain rate. In the case of low strain rate, the flow stress was dominated by the activation stress of FreakRead (FR) source in plastic deformation. With the increase of strain rate, the contribution of activation stress of FR source to the flow stress decreases and the effective stress gradually dominated the flow stress. Under high strain rate loading, with the increase of the initial FR source, the dislocation density also increased at the same strain correspondingly, which makes it easier to meet the requirement of the loading strain rate, so the flow stress is smaller. In addition, under the low strain rate loading, a few activated FR sources can meet the requirement of the plastic deformation, a single slip deformation come up as a result. While, as the loading strain rate increases, more and more activated FR sources would be needed to coordinate the plastic deformation, the deformation mechanisms of the single crystal micropillar transformed from single slip to multiple slip.     

基于FIB/SEM双束系统的原位、实时观测三点弯曲薄膜测试方法

目的 需要直接测量薄膜的极限形变这一关键参数,来评价某种薄膜在一定服役载荷下的某种基体表面是否能胜任。方法 借助聚焦离子束显微镜/扫描电子显微镜(FIB/SEM)双束显微分析测试系统,提出了一种在微米尺度下、原位进行三点弯曲薄膜测试的方法,同时可以进行实时观测与分析记录。之后,使用磁控溅射技术制备了具有强择优晶体生长取向的CrN薄膜和Cr/CrN多层薄膜,并使用上述三点弯曲测试方法对这两种薄膜进行了弯曲测试。结果 CrN薄膜的极限形变量为(1.8±0.1)%,且其在原位三点弯曲试验中断裂前的变形类型为纯弹性形变,而不是塑性形变或者弹性/塑性混合形变。而Cr/CrN多层薄膜的极限形变达到了9.1%,是纯CrN薄膜的5倍,且对“预裂纹”等缺陷不敏感。结论 将此测试方法与在微米尺度使用FIB测量薄膜残余应力的方法相结合,将可以有效地评估多种薄膜的形变能力及形变特性。所获得的薄膜相关性能数据,对于针对不同基体、不同使用工况(如不同的表面受力状态、变形状态等)的薄膜体系或结构的选择与设计,具有很好的指导意义。     

Effects of nanocrystalline and ultrafine grain sizes on constitutive behavior and shear bands in iron

The mechanical behaviors of consolidated iron with average grain sizes from tens of nanometers to tens of microns have been systematically studied under uniaxial compression over a wide range of strain rates. In addition to the well-known strengthening due to grain size refinement, grain size dependence is observed for several other key properties of plastic deformation. In contrast with conventional coarse-grained Fe, high-strength nanocrystalline and submicron-grained Fe exhibit diminished effective strain rate sensitivity of the flow stress. The observed reduction in effective rate sensitivity is shown to be a natural consequence of low-temperature plastic deformation mechanisms in bcc metals through the application of a constitutive model for the behavior of bcc Fe in this strain rate and temperature regime. The deformation mode also changes, with shear localization replacing uniform deformation as the dominant deformation mode from the onset of plastic deformation at both low and high strain rates. The evolution and multiplication of shear bands have been monitored as a function of plastic strain. The grain size dependence is discussed with respect to possible enhanced propensity for plastic instabilities at small grain sizes.     

Discrete and continuous deformation during nanoindentation of thin films

This paper describes nanoindentation experiments on thin films of polycrystalline Al of known texture and different thicknesses, and of single crystal Al of different crystallographic orientations. Both single-crystalline and polycrystalline films, 400–1000 nm in thickness, are found to exhibit multiple bursts of indenter penetration displacement, h, at approximately constant indentation loads, P. Recent results from the nanoindentation studies of Suresh et al. (Suresh, S., Nieh T.-G. and Choi, B.W., Scripta mater., 1999, 41, 951) along with new microscopy observations of thin films of polycrystalline Cu on Si substrates are also examined in an attempt to extract some general trends on the discrete and continuous deformation processes. The onset of the first displacement burst, which is essentially independent of film thickness, appears to occur when the computed maximum shear stress at the indenter tip approaches the theoretical shear strength of the metal films for all the cases examined. It is reasoned that these displacement bursts are triggered by the nucleation of dislocations in the thin films. A simple model to estimate the size of the prismatic dislocation loops is presented along with observations of deformation using transmission electron microscopy and atomic force microscopy. It is demonstrated that the response of the nanoindented film is composed of purely elastic behavior with intermittent microplasticity. The overall plastic response of the metal films, as determined from nanoindentation, is shown to scale with film thickness, in qualitative agreement with the trends seen in wafer curvature or X-ray diffraction measurements.     

Constitutive model based on dislocation density and ductile fracture of Monel 400 thin sheet under tension

In micro-scaled plastic deformation, material strength and ductile fracture behaviors of thin sheet in tension are quite different from those in macro-scale. In this study, uniaxial tensile tests of Monel 400 thin sheets with different microstructures were carried out to investigate the plastic deformation size effect in micro-scale. The experimental results indicate that the flow stress and fracture strain departure from the traditional empirical formula when there are only fewer grains across the thickness. And the number of dimples on the fracture surface is getting smaller with the decreasing ratio of specimen thickness to grain size. Then, a constitutive model based on dislocation density considering the free surface effect in micro-scale is proposed to reveal the mechanism of the flow stress size effect. In addition, a model is proposed considering the surface roughening inducing the thickness nonuniform and the decrease of micro-voids resulting from the reduction of grain boundary density with the decreasing ratio of specimen thickness to grain size. The interactive effects of the surface roughening and the decrease of micro-voids result in the earlier fracture in micro tension of the specimen with fewer grains across the thickness.     

Rrevealing plastic deformation mechanisms in polycrystalline thin films with synchrotron XRD

Understanding the fundamentals of plastic deformation mechanisms in polycrystalline thin metal films and the associated size effects is crucial to the design and fabrication of microelectronic devices. A combination of in-situ synchrotron diffraction experiments was conducted to investigate two cooperative plastic deformation mechanisms in polycrystalline face-centered cubic thin metal films: conjugate deformation twinning in uniaxially strained polycrystalline thin gold films and subgrain structure rotations in biaxially strained polycrystalline thin silver films. The experimental results demonstrate an increase in the total coverage of (115) oriented deformation twins in the thin gold films upon uniaxial deformation to 2% strain at a macroscopic yield stress of 250 MPa.     

Effect of Bimodal Grain Size Distribution on the Strain Hardening Behavior of a Medium-Entropy Alloy

The evolution of strain hardening behavior of the Fe_(50)(CoCrMnNi)_(50) medium-entropy alloy as a function of the fraction of recrystallized microstructure and the grain size was studied using the Hollomon and Ludwigson equations.The specimens under study were partially recrystallized,fully recrystallized with ultrafine-grained microstructure,and fully recrystallized with coarse grains.The yield strength decreases steadily as the fraction of recry stallized micro structure and grain size increases due to the recovery process and the Hall-Petch effect.Interestingly,the bimodal grain distribution was found to have a significant impact on strain hardening during plastic deformation.For instance,the highest ultimate tensile strength was exhibited by a 0.97 μm specimen,which was observed to contain a bimodal grain distribution.Furthermore,using the Ludwigson equation,the effect of the bimodal grain distribution was established from the behavior of K_2 and n1 curves.These curves tend to show very high values in the specimens with a bimodal grain distribution compared to those that show a homogenous grain distribution.Additionally,the bimodal grain distribution contributes to the extensive L(u|")ders strain observed in the 0.97 μm specimen,which induces a significant deviation of the Hollomon equation at lower strains.     

Creep and stress relaxation in free-standing thin metal films controlled by coupled surface and grain boundary diffusion

An analytical solution is presented that interprets the effects of grain size, surface and grain boundary diffusivities, surface and grain boundary free energies, as well as grain boundary grooving on the creep rate in free-standing polycrystalline thin metal films. The Coble creep in the film plane is also taken into account; this has a significant effect on the creep rate of the film. The effects of diffusion ratio and free energy ratio between surface and grain boundary on film agglomeration are illustrated as well. A closed-form expression for stress relaxation in films under constrained strain conditions is derived from this solution. An exponential decay in stress is found as a function of the film microstructure. Results predicted by the solution are shown to be in agreement with the experiments.     

Three strategies to achieve uniform tensile deformation in a nanostructured metal

In nanostructured metals with grain sizes of the order of 100 nm, dislocation mechanisms remain dominant in controlling plastic deformation. These materials, similar to their coarse-grained counterparts that have been subjected to heavy cold work, can no longer go through the several strain hardening stages of normal metals and are hence susceptible to plastic instabilities such as necking in tension. For processing and applications, it is obviously important and often necessary to control such inhomogeneous plastic deformation. Here we demonstrate three strategies to achieve relatively large stable tensile deformation in nanostructured metals, using the pure Cu processed by equal channel angular pressing as a model. The first approach uses an in situ formed composite-like microstructure, such as a bimodal grain size distribution, to impart strain hardening to the material and attain large uniform tensile strains while maintaining the majority of the strengthening brought forth by nanostructuring. In the second route, deformation is conducted at low temperatures, such as 77 K. The material regains the ability to work harden due to suppressed dynamic recovery. Uniform elongation is achieved as a result, together with an elevated strength at the cryogenic temperature. The third method takes advantage of the elevated strain rate sensitivity of the flow stress of the nanostructured Cu, especially at slow strain rates. Using the stabilizing effects of strain rate hardening on tensile deformation, nearly uniform strains can be acquired in absence of strain hardening. We also discuss the deformation mechanisms involved in these approaches to assess their applicability to nanocrystalline metals with grain sizes well below 100 nm, where normal dislocation activities become severely suppressed.