Novel Microtensile Method for Monotonic and Cyclic Testing of Freestanding Copper Thin Films

This paper presents the results of new microtensile tests conducted to investigate the mechanical properties of submicron-thick freestanding copper films. The method, used in this study, allows the observation of materials response under uniaxial tensile loads with measurements of stress at strain rates up to 5.5 × 10⁻⁴/s. It also facilitates tension–tension fatigue experiments under a variety of mean stress conditions at cyclic loading frequencies to 20 Hz. The sample processes involve fabrication of a supporting frame with springs and alignment beams all made of electroplated nickel. Electroplating took place on top of a previously deposited sample rather than creating a structure by subtractive fabrication. Tensile sample loading is applied using a piezoelectric actuator. Load was measured using a capacitance gap sensor with a novel mechanical coupling to the sample. Tension–tension fatigue experiments were carried out with feedback to give load control. Fatigue tests were conducted on sputter-deposited 500 and 900 nm copper films with grain sizes ∼50 nm. Fatigue life reached 10⁵ cycles at low mean load, which decreased with an increase in the mean load. The results indicate decreasing plasticity with increasing mean load.     

Measurement method of complex viscoelastic material properties

A measurement technique of viscoelastic properties of polymers is proposed to investigate complex Poisson’s ratio as a function of frequency. The forced vibration responses for the samples under normal and shear deformation are measured with varying load masses. To obtain modulus of elasticity and shear modulus, the present method requires only knowledge of the load mass, geometrical characteristics of a sample, as well as both the amplitude ratio and phase lag of the forcing and response oscillations. The measured data were used to obtain the viscoelastic properties of the material based on a 2D numerical deformation model of the sample. The 2D model enabled us to exclude data correction by the empirical form factor used in 1D model. Standard composition (90% PDMS polymer + 10% catalyst) of silicone RTV rubber (Silastic^® S2) were used for preparing three samples for axial stress deformation and three samples for shear deformation. Comprehensive measurements of modulus of elasticity, shear modulus, loss factor, and both real and imaginary parts of Poisson’s ratio were determined for frequencies from 50 to 320 Hz in the linear deformation regime (at relative deformations 10^?6 to 10^?4) at temperature 25 °C. In order to improve measurement accuracy, an extrapolation of the obtained results to zero load mass was suggested. For this purpose measurements with several masses need to be done. An empirical requirement for the sample height-to-radius ratio to be more than 4 was found for stress measurements. Different combinations of the samples with different sizes for the shear and stress measurements exhibited similar results. The proposed method allows one to measure imaginary part of the Poisson’s ratio, which appeared to be about 0.04–0.06 for the material of the present study.     

预静态加载后的混凝土动态受压特性试验

进行了混凝土在应变速率分别为10-5/s、10-4/s、10-3/s的条件下,经历极限抗压强度分别为0、40%、60%、75%和85%的单调荷载作用的动态单轴压缩试验,在此基础上分析了经历不同单调加载历史和应变速率下混凝土的峰值应力、峰值应变和弹性模量的变化规律。试验结果表明,随着应变速率的提高,动态单轴抗压强度明显增加;当单调加载应力水平高于某一应力阈值时,混凝土极限抗压强度明显降低;混凝土弹性模量随着应变速率的提高而增加,随着单调加载幅值的增加表现出先增大后减小的趋势;混凝土峰值应变随着应变速率的提高而增加,随着单调加载幅值的增加而减少。     

Wave propagation in transversely impacted composite laminates

An experimental investigation was conducted to determine wave-propagation characteristics, transient-strain distributions and residual properties for unidirectional and angle-ply boron/epoxy and graphite/epoxy laminates impacted with silicon-rubber projectiles at velocities up to 250 ms^?1 (820 ft/s). Tests were conducted at normal and 45-deg oblique impact. Strain signals obtained from surface and embedded strain gages were recorded and analyzed to determine the types of waves, propagation velocities, peak strains, strain rates and attenuation characteristics. The predominant wave is a flexural on propagating at different velocities in different directions. The flexural wave velocity is higher in the higher-modulus direction. In general, measured wave velocities were higher than theoretically predicted. The amplitude of the in-plane wave is less than ten percent of that of the flexural wave. Peak strains and strain rates in the transverse to the (outer) fiber direction are much higher than those in the direction of the fibers. Strain rates up to 640 s^?1 were measured. Under oblique 45-deg impact, the flexural wave is still the predominant one. Peak strains under this oblique impact range between 36 and 56 percent of those under normal impact of the same velocity. Residual elastic properties and strength were measured around the point of impact. The most significant result was a reduction in the transverse strength of the unidirectional laminates. The dynamics of impact were also studied with high-speed photography. The projectile is completely flattened within 50–70 μs and the total contact time is of the order of 300 μs.     

A weakened form of Ilyushin's postulate and the structure of self-consistent Eulerian finite elastoplasticity

From a general standpoint in terms of internal variables, we formulate a general theory of self-consistent Eulerian finite elastoplasticity based on the additive decomposition of the Eulerian strain rate, i.e., D=D^e+D^p, as well as two consistency criteria. In this theory, the elastic behaviour is characterized by an exactly integrable elastic rate equation for D^e with a general form of complementary elastic potential. It is assumed that the yield function depends in a general manner on the Kirchhoff stress and the internal variables. Moreover, the plastic rate equation for D^p and the evolution equation for each internal variable are allowed to assume general forms relying on the just-mentioned variables and the stress rate. It is indicated that two consistency criteria, i.e., the self-consistency for the elastic rate equation and Prager's yielding stationarity, lead to the unique choice of objective rates, i.e., the logarithmic rate.The structure of the above theory is further studied and examined by virtue of a weakened form of Ilyushin's postulate. In a spinning frame defining the logarithmic rate, we introduce the notion of standard elastoplastic strain cycle, which starts at a point not on but inside a yield surface and incorporates only one infinitesimal plastic subpath. We show that this type of strain cycle is always possible. Then, by ruling out strain cycles starting at points on yield surfaces we propose a weakened form of Ilyushin's postulate, which says that the changing rate of the stress work done along every standard strain cycle should be non-negative, whenever the incorporated plastic subpath tends to vanish. By virtue of simple, rigorous procedures, we demonstrate that this weakened form of Ilyushin's postulate is adequate to ensure direct results concerning the normality rule and the convexity of the yield surface in the context of the foregoing Eulerian finite elastoplasticity theory. Specifically, with an exactly integrable elastic rate equation defining D^e, we prove that, in the space of the Kirchhoff stresses, the difference (D−D^e) is just the gradient of the yield function multiplied by a plastic multiplier, and thus bears the very kinematical and physical feature of plastic strain rate. Furthermore, we prove that, in the space of the Kirchhoff stresses, the elastic domain bounded by each yield surface should be convex. The main results are derived in a self-contained manner within the context of an Eulerian theory of finite elastoplasticity, without involving issues concerning how to define intermediate stress-free states and plastic strains, etc.     

Stress Wave Analysis and Optical Force Measurement of Servo-Hydraulic Machine for High Strain Rate Testing

Based on fundamental mechanical principles, a force measurement method for a servo-hydraulic tensile machine at strain rates from quasi-static up to 10³/s is proposed in this paper. Analytical and numerical stress wave analyses were performed at first to understand the principles of the force signal oscillation. The result of this FEM simulation indicates that the elastic vibration within the tensile specimen has a higher frequency and much lower amplitude than at the piezoelectric force sensor of the test machine. Based on this finding, a noncontact optical force measurement method was developed, which provides a fast and reliable force measurement directly on the specimen with little disturbance from the system ringing effect at strain rates up to 10³/s.     

Evaluation of the Material Properties of an OFHC Copper Film at High Strain Rates Using a Micro-Testing Machine

The material properties of an oxygen-free high thermal conductivity (OFHC) film with a thickness of 0.1 mm were evaluated at strain rates ranging from 10⁻³/s to 10³/s using a high-speed material micro-testing machine (HSMMTM). The high strain-rate material properties of thin films are important especially for an evaluation of the structural reliability of micro-formed parts and MEMS products. The high strain-rate material testing methods of thin films, however, have yet to be established to the point that the testing methods of larger specimens for electronics, auto-body, train, ship, and ocean structures are. For evaluation, a new type of HSMMTM was developed to conduct high-speed tensile tests of thin films. This machine is capable of testing at a sufficiently high tensile speed with an electromagnetic actuator, a novel gripping mechanism, and an accurate load measurement system. The OFHC copper film shows high strain-rate sensitivity in terms of the flow stress, fracture elongation, and strain hardening. These measures increase as the tensile strain rate increases. The rate-dependent material properties of an OFHC copper film are also compared with those of a bulk OFHC copper sheet with a thickness of 1 mm. The flow stress of an OFHC copper film is relatively low compared to that of a bulk OFHC copper sheet in the entire range of strain rates, while the fracture elongation of an OFHC copper film is much larger than that of a bulk OFHC copper sheet. A quantitative comparison would provide material data at high strain rates for the design and analysis of micro-appliances and different types of micro-equipment.     

Application of a discrete polycrystal model to the analysis of cyclic straining in copper

A discrete polycrystal model, designed to simulate a metal aggregate macro-element, is applied to the study of cyclic straining in copper. The numerical method of solution (an adaptation of the “finite element method”) incorporates a convergent discrete Green's function within the constrained minimum principle which governs the (crystallographic) plastic shear increments at each load step. Isothermal elastic moduli of copper crystals and Taylor's hardening rule with constant hardening modulus are used in the calculations. Numerical results are obtained for macroscopic elastic properties, cyclic stress-strain curves (which indicate the contribution of aggregate heterogeneity to macroscopic hardening), macroscopic plastic work, and residual (latent) strain energy through four loading cycles between fixed macrostrain limits. Other estimates for elastic properties also are included, and all results are compared, both qualitatively and quantitatively, with published experiments. The predictions of the model are in general satisfactory.     

玻纤增强复合材料高应变率拉伸实验研究

利用爆炸膨胀环实验技术,对玻璃纤维增强复合材料(GFRC)进行了高应变率(104s-1)下力学性能研究。实验中使用铜丝汽化引爆装药的方法对驱动环进行能量加载,并采用激光速度干涉仪(VISAR)测量试样环自由膨胀的质点速度,实现了玻璃纤维增强复合材料在104应变率下的一维拉伸破坏,并获取了该材料的速度时间曲线。经过计算得到了材料的应力应变关系,最后与该材料在准静态下、中高应变率下实验得到的数据进行了比较。     

Elastic modulus measurements of vertically aligned multi walled carbon nanotubes carpets by using the nanoindentation technique

Electrical, thermal and mechanical properties of Vertically Aligned Multi Walled Carbon NanoTubes (VA-MWCNT) make them an ideal candidate to replace some of conventional materials in micro and nano-electronic components. Integrating this material in micro components requires a good knowledge of their properties. As the electrical and thermal properties, the MWCNT mechanical properties are difficult to assess. Several techniques have been developed to estimate the CNT Young's modulus and the obtained results cover a large range of scale. In this study, we propose an indirect technique for MWCNT carpet Young's modulus measurements by using the nanoindentation technique. Nanoindentation tests are performed on a metallic film deposited on MWCNT. The measured equivalent reduced modulus takes into account the elastic properties of the metallic thin film and those of the MWCNT substrate. Bec et al. model, introduced in 2006, is used to separate elastic properties, and thus determine the MWCNT reduced Young’s modulus which is estimated between 329 and 352 GPa. Knowing the indenter mechanical properties, we estimate the Young’s modulus in the 461 to507 GPa range.     

A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials

This paper presents a split Hopkinson pressure bar technique to obtain compressive stress-strain data for rock materials. This technique modifies the conventional split Hopkinson bar apparatus by placing a thin copper disk on the impact surface of the incident bar. When the striker bar impacts the copper disk, a nondispersive ramp pulse propagates in the incident bar and produces a nearly constant strain rate in a rock sample. Data from experiments with limestone show that the samples are in dynamic stress equilibrium and have constant strain rates over most of the test durations. In addition, the ramp pulse durations can be controlled such that samples are unloaded just prior to failure. Thus, intact samples that experience strains beyond the elastic region and postpeak stresses can be retrieved for microstructural evaluations. The paper also presents analytical models that predict the time durations for sample equilibrium and constant strain rate. Model predictions are in good agreement with measurements.     

Second strain gradient elasticity of nano-objects

Mindlin's second strain gradient continuum theory for isotropic linear elastic materials is used to model two different kinds of size-dependent surface effects observed in the mechanical behaviour of nano-objects. First, the existence of an initial higher order stress represented by Mindlin's cohesion parameter, b₀, makes it possible to account for the relaxation behaviour of traction-free surfaces. Second, the higher order elastic moduli, c_i, coupling the strain tensor and its second gradient are shown to significantly affect the apparent elastic properties of nano-beams and nano-films under uni-axial loading. These two effects are independent from each other and allow for separated identification of the corresponding material parameters. Analytical results are provided for the size-dependent apparent shear modulus of a nano-thin strip under shear. Finite element simulations are then performed to derive the dependence of the apparent Young modulus and Poisson ratio of nano-films with respect to their thickness, and to illustrate hole free surface relaxation in a periodic nano-porous material.     

Experimental investigation of the transverse mechanical properties of a single Kevlar® KM2 fiber

A new experimental setup is developed to investigate the transverse mechanical properties of Kevlar^® KM2 fibers, which has been widely used in ballistic impact applications. Experimental results for large deformation reveal that the Kevlar^® KM2 fibers possess nonlinear, pseudo-elastic transverse mechanical properties. A phenomenon similar to the Mullins effect (stress softening) in rubbers exists for the Kevlar^® KM2 fibers. Large transverse deformation does not significantly reduce the longitudinal tensile load-bearing capacity of the fibers. In addition, longitudinal tensile loads stiffen the fibers' transverse nominal stress–strain behaviors at large transverse deformation. Loading rates have insignificant effects on their transverse mechanical properties even in the finite deformation range. An analytical relationship between transverse compressive force and displacement is derived at infinitesimal strain level. This relation is used to estimate the transverse elastic modulus of the Kevlar^® KM2 fibers, which is 1.34 ± 0.35 GPa.     

An analysis of metal fatigue based on hysteresis energy

Halford's plastic-energy concept for lowcycle fatigue is extended to the medium- and high-cycle ranges. The resulting equations are compared with 74 sets of data in the medium- and high-cycle ranges. The difference in stress between theory and experimental data is less than ±5 percent. The plastic-hysteresis-energy analysis for fatigue is shown to be consistent with the octahedral shear-stress theory. In addition, an improvement is presented for Manson's correlation for the total strain amplitude at 10⁴ cycles.     

基于应变率阶跃测试的晶体铜压入应变率敏感性研究

纳米压入测试可以原位获取材料的诸多力学性能,包括弹性模量,硬度,屈服应力,应变率敏感指数等。本文利用应变率阶跃测试技术对多晶铜试样的应变率敏感性进行测试分析,硬度-位移曲线表明压头下方所存在的变形梯度对各阶跃应变率下的硬度值存在明显影响;采用基于晶体细观机制的塑性应变梯度理论对压入变形梯度效应予以修正,比较了修正与未修正数据所得的应变率敏感指数,在有效剔除压入变形梯度影响的基础上,应变率阶跃测试可实现单次压入下材料应变率敏感性的测试表征。     

BUCKLING ANALYSIS OF ELASTIC FILM BONDED ON SMP SUBSTRATE1)

形状记忆聚合物具有形状变化后在特定条件下可恢复的特点,因此作为一种柔性基底材料在柔性电子中得到广泛应用。对于形状记忆聚合物基底和弹性薄膜组成的双层结构,当 基底收缩时,其表面的弹性薄膜可以形成屈曲波形。针对基底收缩过程中波形的变化, 本文实验测得形状记忆聚合物材料在不同温度下的 属性,结合一维应变恢复函数,利用柔性基底表面薄膜屈曲波形参数(波幅、波长等)表达式,求解得到了在基底收缩的过程中,弹性薄膜屈曲波形的变化规律,和实验结果吻合很好。     

Consequences of the dissipative restrictions in finite anisotropic elasto-plasticity

The paper is devoted to the dissipation postulate in anisotropic finite elastoplasticity, properly formulated in terms of the total strain histories, on small cycles only. The equivalence between the dissipation postulate and the existence of the stress potential together with the dissipation inequality is proved. The modified flow rules compatible with the dissipation postulate follow as a necessary condition. The convexity and normality properties can be treated as an equivalent issue of the dissipation postulate only within the framework of Σ models. We identify such classes of Σ-models based on the pre-image theorem. The difficulties arise from the non-injectivity of the Mandel's stress measure, as dependent on the elastic strain. We define the yield stress function and the admissible elastic stress range in Σ-space. The equivalence is achieved only if it possible to construct the elastic range in strain space, having just the topological properties originally assumed as a basis of the dissipation postulate. The normality to the admissible elastic stress range does not mean an associative flow rule. The results are exemplified for transversely isotropic elasto–plastic materials as well as for models with small elastic strains.     

The development and use of a torsional Hopkinson-bar apparatus

A technique is described by means of which torsional waves of large, essentially constant amplitude can be generated in an elastic bar. Waves with rise times of order 25 μs and maximum angular velocities of order 10³ rad.s^?1 have been achieved and used to test tubular specimens at shear-strain rates up to 15×10³ s^?1. Results are presented for mild steel tested at 2×10³ s^?1, and it is shown that the flow stress correlates well with the trend found at lower rates using conventional methods. The measured drop of stress at yield, however, was considerably smaller in the present tests than in earlier work; this is attributed to the generation of flexural waves which reach the specimen at the same time as the torsional wave.     

Role of elasticity in elastic–plastic fracture: Analytical bi-linear crack-tip fields and finite element analysis

A solution for Model-I plane strain crack tip fields in a bi-linear elastic–plastic material is presented. The elastic–plastic Poisson's ratio is introduced to characterize the influence of elastic deformation on the near tip constraint. Attention is focused on the distribution of elastic/plastic strain energy in the sensitive region of the forward sector ahead of a crack tip. The present study shows that the elastic strain energy can be higher than the plastic strain energy in this sensitive sector while large amount of the plastic strain energy develops outside this sector around the crack tip. The effect of elastic deformation in this sensitive region on the structure of crack-tip fields is considerable and the assumption in some important solutions for crack-tip fields reported in literature that the elastic deformation is small and can be ignored is therefore not physically reasonable. Besides, finite element analysis is carried out to validate the analytical solution and good agreement between them is found. It is seen that the present solution with T-stress can properly describe the crack-tip fields under various constraints for different specimens and an analytical relation is established between the critical value of J-integral, J_c, and T-stress for elastic–plastic fracture.     

An analytical solution for a linear viscoelastic layer loaded with a cylindrical punch: Evaluation of the rebound indentation test with application for assessing viability of articular cartilage

A general closed-form solution for the so-called rebound indentation test’ is obtained for a cylindrical flat-ended punch indenting a linear viscoelastic layer lying on a rigid substrate. Under the assumption of time-independent Poisson's ratio, we derive closed-form analytical expressions for the contact force (in a displacement controlled regime) and for the indentation displacement (in a load-controlled regime) and we consider in detail the case of standard viscoelastic solid. Our results indicate that the rebound displacement (in other words the indentation displacement in the load-controlled stage) is independent of the relaxed elastic modulus and Poisson's ratio, and also of the layer's thickness. Our analytical solution can be used for layered samples of arbitrary materials exhibiting viscoelastic properties; however, since the rebound indentation test has been recently suggested for assessing the viability of biomedical materials, we have applied our theoretical framework to the identification of materials parameters from experiments on articular cartilage. In this context, we have found a pretty good agreement for the rebound deformation, even until the strain becomes relatively large.