Multiaxial yield behavior of 1100 aluminum following various magnitudes of prestrain

The multiaxial yield and flow behavior of metals has been of interest for many years. Recently, the experimental work of Phillips & Lee [1979], Shiratori et al. [1979] and Ohashi [1982] has been quite notable in this field. These authors have concentrated their efforts in measuring yield loci after small to moderate prestrains (≤0.06). In this paper we discuss small strain yield loci we have measured after prestrains between 0.03 and 0.05 in torsion. These experiments on 1100 aluminum are in general agreement with the literature. They show a translation, distortion and expansion of the yield loci. A rounded nose forms in the direction of prestrain with the yield locus flattering opposite the prestrain. We observed that the distortions change to match the strain direction after very small reversals in prestrain.The subsequent yield locus has also been measured after a large torsional prestrain of γ=0.5. Using a 5 × 10^?6 offset criterion for yielding, the shape, distortion and translation of the yield locus was very similar to that found after the smaller prestrains. In addition a large-strain yield locus, using a back extrapolation technique, was determined for the same sample. This yield locus exhibited close to von Mises isotropic expansion. The observed deviations, while slight are extremely important. They match those predicted by a polycrystal slip model. Thus, the small-strain yield locus, after a large prestrain, appears to be determined largely from dislocation considerations only, where as the large-strain yield locus is determined by the developing texture. Finally, aluminum sheet was deformed by rolling to larger prestrains ?^{von Mises} = 0.5, 1.0, 1.5, 2.0 and 2.5 and subsequently tested in plane strain compression. Two types of compression experiments were done, one such that there was no deformation mode change from rolling, the other rotating the direction of zero strain by 90° producing a stress path change. The large strain yield and flow behavior of these experiments was again predicted using the relaxed constraint polycrystal model of Kocks & Canova [1981]. For these very large prestrains the experiments and texture theory differ. Micrstructural observations have shown the presence of micro-shear bands which resulted from the rolling prestrain. We speculate that these features are responsible for the deviation from crystal plasticity theory.We believe that this work points to several operative mechanisms of deformation. Small-strain yielding (5 × 10^?6) appears to be controlled purely by dislocation mechanisms and interactions even after relatively large prestrains. Large-strain yielding, on the other hand, is controlled by texture after moderate prestrains (at least to γ = 0.5). After large prestrains, obtained by rolling, the experiments deviate from texture based predictions. This is possibly the result of microstructural deformation mechanisms, for example micro-shear bands, playing a role in the deformation process.     

MECHANICS ANALYSIS OF TWO-DIMENSIONALLY PRESTRAINED ELASTOMERIC THIN FILM FOR STRETCHABLE ELECTRONICS

Various methods have been developed to fabricate highly stretchable electronics. Recent studies show that over 100% two dimensional stretchability can be achieved by mesh structure of brittle functioning devices interconnected with serpentine bridges. Kim et al show that pressing down an inflated elastomeric thin film during transfer printing introduces two di- mensional prestrain, and therefore further improves the system stretchability. This paper gives a theoretical study of this process, through both analytical and numerical approaches. Simple analytical solutions are obtained for meridional and circumferential strains in the thin film, as well as the maximum strain in device islands, which all agree reasonably well with finite element analysis.     

Stretchability and compliance of freestanding serpentine-shaped ribbons

High-performance stretchable electronics have to utilize high-quality inorganic electronic materials such as silicon, oxide or nitride dielectrics, and metals. These inorganic materials usually crack or yield at very small intrinsic strains, for example, 1%, whereas bio-integrated electronics are expected to at least match the stretchability of bio-tissues (20%) and deployable structure health monitoring networks are expected to expand from wafer scale (several centimeters) to cover macroscopic structures (several meters). To minimize strains in inorganic materials under large deformation, metallic and ceramic films can be patterned into serpentine-shaped ribbons. When the ribbon is stretched, some sections of the ribbon can rotate and/or buckle to accommodate the applied displacement, leaving much smaller intrinsic strain in the materials compared to the applied strain. The choice of the shape of the serpentine depends on systematic studies of the geometric variables. This paper investigates the effect of serpentine shapes on their stretchability and compliance through theoretical, numerical, and experimental means. Our closed-form curved beam solutions, FEM results, and experimental measurements have found good agreement with one another. Our results conclude that in general, the narrower ribbon, the larger arc radius and arc angle, and the longer arm length will yield lower intrinsic strain and effective stiffness. When the arm length approaches infinite, the stretchability can be enhanced by several orders. A few unexpected behaviors are found at arc angles that are close to straight bars. With additional practical constraints such as minimum ribbon width and finite overall breadth, the optimal serpentine shape can be accurately determined using our closed-form analytical solution.     

Effect of interfacial stiffness on the stretchability of metal/elastomer bilayers under in-plane biaxial tension

Flexible electronic devices are often subjected to large and repeated deformation, so that their functional components such as metal interconnects need to sustain strains up to tens of percent, which is far beyond the intrinsic deformability of metal materials(～1%). To meet the stringent requirements of flexible electronics, metal/elastomer bilayers, a stretchable structure that consists of a metal film adhered to a stretchable elastomer substrate, have been developed to improve the stretch capability of metal interconnects. Previous studies have predicted that the metal/elastomer bilayers are much more stretchable than freestanding metal films. However, these investigations usually assume perfect bonding between the metal and elastomer layers. In this work, the effect of the metal/elastomer interface with a finite interfacial stiffness on the stretchability of bilayer structures is analyzed. The results show that the assumption of perfect interface(with infinite interfacial stiffness) may lead to an overestimation of the stretchability of bilayer structures. It is also demonstrated that increased adhesion between the metal and elastomer layers can enhance the stretchability of the metal layer.     

Buckling of a stiff thin film on a pre-strained bi-layer substrate

Controlled buckling can impart stretchable mechanics to brittle materials when integrated as thin films on soft, elastomeric substrates. Typical elastomers are permeable to fluids, however, and therefor unable to provide robust barriers to entry of water, for instance, into devices built with the supported thin films. In addition, the mechanical strength of a system dominated by a soft substrate is often unsatisfactory for realistic applications. We show that introduction of a bi-layer substrate yields a robust, high strength system that maintains stretchable characteristics, with a soft layer on top of a relatively stiff layer in the substrate. As a mechanical protection, a soft encapsulation layer can be used on top of the device and the stretchability of the encapsulated system is smaller than that of the system without encapsulation. A simple, analytic model, validated by numerical analysis and FEA, is established for stiff thin films on a bi-layer substrate, and is useful to the design of stretchable systems.     

轴向拉伸下氮化钛纳米杆变形机制及力学性能的分子动力学研究

本文使用分子动力学软件包lammps并采用第二近邻改进型嵌入原子法(2NN MEAM)模拟了单晶氮化钛纳米杆的轴向拉伸破坏过程,分析了分别沿[100]、[111]晶向的不同截面尺寸、不同拉伸应变率、不同温度下的氮化钛纳米杆的力学性能,详细描述了氮化钛纳米杆拉伸变形过程。研究发现, 拉伸晶向、截面尺寸、拉伸应变率及温度均会对TiN纳米杆的拉伸变形过程及屈服强度、弹性模量等力学性能产生不同程度的影响。 沿[100]晶向的拉伸,截面尺寸越大,屈服强度越低;而沿[111]晶向,截面尺寸越大,屈服强度越大。应变率越大,屈服强度及屈服应变越大,但对于弹性模量几乎无影响。温度越高,材料的屈服强度、屈服应变及弹性模量越小,断裂应变越大。不同拉伸条件下的氮化钛纳米杆的拉伸过程均包括弹性变形、塑性变形与断裂阶段。[100]晶向的弹性模量都要高于[111]晶向。     

A parameter for measuring the magnitude of a change of strain path: Validation and comparison with experiments on low carbon steel

Various tension-tension and tension-shear strain sequential experiments have been performed on low carbon steel sheet along different material axes. Owing to the rapid plastic instability that occurs during the reloading in uniaxial tension of prestrained samples, the results are focussed on the evolution of the macroscopic reloading yield stress (back extrapolated stress). For a given prestrain amount, the reloading stress is a function of the magnitude of the strain path change. A parameter is proposed, which allows the comparison of different sequential loading tests: the scalar product of the unit tensors corresponding to the prestrain and to the subsequent strain modes, respectively. For low carbon steel, a single curve is obtained when the reloading stress, normalized by the stress along the monotonic strain path is plotted against this parameter whatever the combination of loading sequences and the material direction of the prestrain.     

A constitutive model of nanocomposite hydrogels with nanoparticle crosslinkers

Nanocomposite hydrogels with only nanoparticle crosslinkers exhibit extraordinarily higher stretchability and toughness than the conventional organically crosslinked hydrogels, thus showing great potential in the applications of artificial muscles and cartilages. Despite their potential, the microscopic mechanics details underlying their mechanical performance have remained largely elusive. Here, we develop a constitutive model of the nanoparticle hydrogels to elucidate the microscopic mechanics behaviors, including the microarchitecture and evolution of the nanoparticle crosslinked polymer chains during the mechanical deformation. The constitutive model enables us to understand the Mullins effect of the nanocomposite hydrogels, and the effects of nanoparticle concentrations and sizes on their cyclic stress–strain behaviors. The theory is quantitatively validated by the tensile tests on a nanocomposite hydrogel with nanosilica crosslinkers. The theory can also be extended to explain the mechanical behaviors of existing hydrogels with nanoclay crosslinkers, and the necking instability of the composite hydrogels with both nanoparticle crosslinkers and organic crosslinkers. We expect that this constitutive model can be further exploited to reveal mechanics behaviors of novel particle-polymer chain interactions, and to design unprecedented hydrogels with both high stretchability and toughness.     

Wave propagation in prestrained polyethylene rods

The influence of prestrain on the propagation of mechanical waves along a slender rod of low-density unoriented polyethylene was experimentally investigated. The investigation consisted of two major parts: first, a uniaxial continuous-wave technique was used to determine the dynamic mechanical properties of the polyethylene in the form of the frequency-dependent phase velocity and damping factor for frequencies spanning the audio spectrum and for levels of uniaxial static prestrain up to 10 percent. A linear incremental dynamic viscoelastic behavior about a state of finite-static prestrain was shown to obtain over the range of strains and frequencies used. In the second part, the propagation of an incremental strain pulse along a slender rod of the same material used in the first part was investigated. With the rod in a state of static prestrain, an incremental impact-induced strain pulse was introduced into the polyethylene rod and monitored at two positions along the rod. Assuming a linear incremental dynamic viscoelastic behavior of the material, the equations necessary to describe the resulting uniaxial strain as a function of time and position along the rod are presented and the solution obtained by Fourier transform methods. The resulting Fourier inverse transform was numerically evaluated, using the material properties determined in the first part. The strain measured at the first position was used as the input boundary condition for computing the strain at the second position. Results of the continuous-wave studies indicate that the phase velocity decreases and the damping factor increases with increasing prestrain in the range of prestrains used. The change in the phase velocity with prestrain is relatively uniform over the audio-frequency range. Good correlation of the leading edges of the experimentally measured and numerically synthesized strain pulses supports the high-frequency phase-velocity data of the first part.     

YIELD SURFACES AND PLASTIC FLOW OF 45 STEEL UNDER TENSION-TORSION LOADING PATHS

An experimental analysis on the subsequent yield-surfaces evolution using multiple specimens is presented for a 45 steel after a prescribed pre-strain loading in three different directions respectively, and the yielding is defined by a designated offsetting strain. The size of the subsequent yield surface is found smaller than the initial yield surface; the negative cross effects are observed in the normal loading direction, its shape is not a Mises circle but has a rather blunt nose in loading direction and flat in the opposite. These results strongly depend on the loading path and the prescribed offset plastic strain. The plastic flow direction to the subsequent yield surface is investigated, and it is found that the plastic flow direction deviates from the normal flow rule. The deviation differs from preloading case to preloading case. And the plastic flow direction would have a larger deviation from the normal of the yield surface, if the subsequent yield was defined by a smaller offset strain. Furthermore, the experiments are simulated using the Chaboche model, and the results show that it can rationally predict yield-surface only when yield is defined by a fairly large offset strain.     

Anisotropic work hardening of steel sheets under plane stress

This work is a follow-up of the previous report by Kim and Yin [Kim, K.H., Yin, J.J., 1997. Evolution of anisotropy under plane stress. J. Mech. Phys. Solids 45, 841–851] regarding the anisotropic work hardening of cold rolled steel sheets. Tensile prestrain has been applied at angles to the rolling direction and then tensile uniaxial yield stress and R-value distributions are measured. As reported earlier, the orientations of local maxima and minima in the yield stress are altered when the prestrain axis is not in the rolling direction. This led Kim and Yin [Kim and Yin (1997)] to suggest that the orientations of orthotropy axes are altered by the tensile prestrain at angles to the rolling direction. However, R-value distribution is found to be hardly affected by the prestrain. The unchanging R-value distribution shows that the material remembers the rolling direction even after the prestrain. An attempt is made to approximate the observed yield and flow behavior based upon isotropic-kinematic hardening with the quadratic yield function (Hill, 1948). The degree of approximation raises the issues of yield point definition, flexibility of yield function, non-associated flow rules, distortional hardening and others.     

Wedge indentation of thin films modelled by strain gradient plasticity

A plane strain study of wedge indentation of a thin film on a substrate is performed. The film is modelled with the strain gradient plasticity theory by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379–1406] and analysed using finite element simulations. Several trends that have been experimentally observed elsewhere are captured in the predictions of the mechanical behaviour of the thin film. Such trends include increased hardness at shallow depths due to gradient effects as well as increased hardness at larger depths due to the influence of the substrate. In between, a plateau is found which is observed to scale linearly with the material length scale parameter. It is shown that the degree of hardening of the material has a strong influence on the substrate effect, where a high hardening modulus gives a larger impact on this effect. Furthermore, pile-up deformation dominated by plasticity at small values of the internal length scale parameter is turned into sink-in deformation where plasticity is suppressed for larger values of the length scale parameter. Finally, it is demonstrated that the effect of substrate compliance has a significant effect on the hardness predictions if the effective stiffness of the substrate is of the same order as the stiffness of the film.     

Predicting the strain hardening characteristics of ageing alloys under combined loading

The paper examines the effect of the initial structure and prestrain on the yield stress of a number of ageing steels and alloys under combined loading in the cases of like and opposite directions of preloading and reloading. The parameters of yield loci are calculated for the case of combined two-axial tension. Their predicted dependence on temperature, ageing time, and prestrain is experimentally checked. As they increase, strain hardening changes from isotropic to kinematic and then to mixed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 116–125, June 2007.     

Mechanics of stretchable electronics on balloon catheter under extreme deformation

Stretchable electronics has been applied to balloon catheters for high-efficacy ablation, with tactile sensing integrated on the surface, to establish full and conformal contact with the endocardial surface for elimination of the heart sink caused by blood flow around their surfaces. The balloon of the catheter folds into uniform ‘clover’ patterns driven by the pressure mismatch inside (∼vacuum) and outside of the balloon (pressure ∼1 atm). The balloon catheter, on which microelectrodes and interconnects are printed, undergoes extreme mechanical deformation during its inflation and deflation. An analytic solution is obtained for balloon catheter inflation and deflation, which gives analytically the distribution of curvatures and the maximum strain in the microelectrodes and interconnects. The analytic solution is validated by the finite element analysis. It also accounts for the effect of inflated radius, and is very useful to the optimal design of balloon catheter.     

Controlled buckling of thin film on elastomeric substrate in large deformation

Electronic systems with large stretchability have many applications. A precisely controlled buckling strategy to increase the stretchability has been demonstrated by combining lithographically patterned surface bonding chemistry and a buckling process. The buckled geometry was assumed to have a sinusoidal form, which may result in errors to determine the strains in the film. A theoretical model is presented in this letter to study the mechanics of this type of thin film/substrate system by discarding the assumption of sinusoidal buckling geometry. It is shown that the previous model overestimates the deflection and curvature in the thin film. The results from the model agree well with finite element simulations and therefore provide design guidelines in many applications ranging from stretchable electronics to micro/nano scale surface patterning and precision metrology.     

Laser-induced porous graphene on Polyimide/PDMS composites and its kirigami-inspired strain sensor

The laser-induced porous graphene(LIG) prepared in a straightforward fabrication method is presented,and its applications in stretchable strain sensors to detect the applied strain are also explored. The LIG formed on the polyimide/polydimethylsiloxane(PI/PDMS) composite exhibits a naturally high stretchability(over 30%), bypassing the transfer printing process compared to the one prepared by laser scribing on PI films. The PI/PDMS composite with LIG shows tunable mechanical and electronic performances with different PI particle concentrations in PDMS. The good cyclic stability and almost linear response of the prepared LIG's resistance with respect to tensile strain provide its access to wearable electronics. To improve the PDMS/PI composite stretchability, we designed and optimized a kirigami-inspired strain sensor with LIG on the top surface, dramatically increasing the maximum strain value that in linear response to applied strain from 3% to 79%.     

Mechanics of stretchable electronics with high fill factors

Mechanics models are developed for an imbricate scale design for stretchable and flexible electronics to achieve both mechanical stretchability and high fill factors (e.g., full, 100% areal coverage). The critical conditions for self collapse of scales and scale contact give analytically the maximum and minimum widths of scales, which are important to the scale design. The maximum strain in scales is obtained analytically, and has a simple upper bound of 3t_scale/(4ρ) in terms of the scale thickness t_scale and bending radius ρ.     

Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes

Bilayer electrode, composed of a current collector layer and an active material layer, has great potential in applications of in-situ electrochemical experiments due to the bending upon lithiation. This paper establishes an elastoplastic theory for the lithiation induced deformation of bilayer electrode with consideration of the plastic yield of current collector. It is found that the plastic yield of current collector reduces the restriction of current collector to an active layer, and therefore, enhances in-plane stretching while lowers down the rate of electrode bending. Key parameters that influence the elastoplastic deformation are identified. It is found that the smaller thickness ratio and lower elastic modulus ratio of current collector to an active layer would lead to an earlier plastic yield of the current collector, the larger in-plane strain, and the smaller bending curvature, due to balance between the current collector and the active layer. The smaller yield stress and plastic modulus of current collector have similar impacts on the electrode deformation.     

基于气压鼓泡法研究石墨烯力学性能

通常假设二维材料为连续介质薄膜,然后采用连续介质薄膜的研究方法进行二维材料力学性能研究,其中气压鼓泡法是一种主要测试方法．但实验观测发现,悬空石墨烯并非处于气压鼓泡测试分析模型中假设的固支边界条件,而是处于一种粘附边界条件：靠近孔壁边界处,有小部分材料通过范德华吸引粘附在基底柱形孔的侧壁上,而且粘附部分可以在极小载荷作用下剥离．这导致石墨烯悬空部分的实际半径大于基底孔半径,即鼓泡实验中的石墨烯是一种松弛薄膜,而非通常认为的预拉伸薄膜．通过有限元数值模拟研究发现,可基于含有名义松弛应变的鼓泡分析模型获得处于粘附边界条件下的石墨烯弹性模量．     

Experimental determination of strain-induced anisotropy during nonproportional straining of an A1/Mg alloy at room temperature

A servohydraulic, computer controlled MTSn axial-torsion testing machine with a bi-axial clip-on extensometer is used to test thin-walled tubes of an A1/Mg alloy under strain control. A plastic offset strain of 10⁻⁴ determines the yield surfaces. Straining and yield surface probing is governed by a computer program which also controls digital data acquisition. Yield surfaces in stress and in strain space as well as the axial and shear stress-strain diagrams can be reconstructed from the digitally recorded data. The specimens were subjected to a strain path in the form of a regular 16-sided polygon which was followed on some specimens by a square path. The total inelastic strain path length can exceed 15% while the equivalent strain excursion is less than 2%. It is shown that yield surfaces measured on specimens withclose initial stress-strain diagrams are very consistent and that yield surface probing has an insignificant effect on subsequent yield surfaces. Yield surfaces are shown to translate, changein shape and size and to exhibit a cross effect. A post processor which includes a least square smoothing routine calculates the area and the centroid of each yield surface. The size increase is initially rapid but the rate of increase decreases as a saturation is approached. After strining for less than 1% in a fixed direction a characteristic yield surface shape is established. Yield surfaces obtained at the same point in strain space with identical prestrain direction of at least 1% but with increased amounts of accumulated plastic strain have the same shape but show an increase in size. The yield surfaces differ in shape and size when the same strain point is reached from different directions. The centroid of the yield surface in stress space moves almost in a circular path for a polygonal strain path. All stress space yield surfaces contain the origin but this is not the case for the surfaces in strain space.