Three-dimensional Full-field Measurements of Large Deformations in Soft Materials Using Confocal Microscopy and Digital Volume Correlation

A three-dimensional (3-D) full-field measurement technique was developed for measuring large deformations in optically transparent soft materials. The technique utilizes a digital volume correlation (DVC) algorithm to track motions of subvolumes within 3-D images obtained using fluorescence confocal microscopy. In order to extend the strain measurement capability to the large deformation regime (>5%), a stretch-correlation algorithm was developed and implemented into the Fast Fourier Transform (FFT)-based DVC algorithm. The stretch-correlation algorithm uses a logarithmic coordinate transformation to convert the stretch-correlation problem into a translational correlation problem under the assumption of small rotation and shear. Estimates of the measurement precision are provided by stationary and translation tests. The proposed measurement technique was used to measure large deformations in a transparent agarose gel sample embedded with fluorescent particles under uniaxial compression. The technique was also employed to measure non-uniform deformation fields near a hard spherical inclusion under far-field uniaxial compression. Introduction of the stretch-correlation algorithm greatly improved the strain measurement accuracy by providing better precision especially under large deformation. Also, the deconvolution of confocal images improved the accuracy of the measurement in the direction of the optical axis. These results shows that the proposed technique is well-suited for investigating cell-matrix mechanical interactions as well as for obtaining local constitutive properties of soft biological materials including tissues in 3-D.     

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress-strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading-reloading cycles are presented.     

Deformation and fracture of surface-hardened materials at meso- and macroscale levels

Investigated in this work is the plastic deformation of representative mesovolumes of the steel 65Cr13 samples. They were surface-hardened by ion nitriding. An evolution of inner structure and stress–strain state in the mesovolumes with different thickness of surface-hardened layer was analyzed under tension and compression. A site of the working part of a cross-section of the sample was examined in the area of neck formation. To simulate the two-dimensional behavior of the deformed steel samples, two formulations are given. They include the strain hardening effects and crack formation. The results are presented and discussed.     

Theoretical and experimental study of the isothermal mechanical behaviour of alloys in the semi-solid state

An isothermal constitutive model for semi-solid alloys based on the concepts of mechanics of continuous media and the theory of mixtures is presented. The model is applicable to semi-solid states obtained either by solidification from liquid state or partial remelting from solid state in which each of the solid and the liquid phases is contiguous. During deformation their behaviours are coupled: the densification of the solid matrix considered as a porous viscoplastic medium saturated with a liquid drives the fluid flow behaviour, and the resulting pressure distribution in the liquid affects in turn the stresses and the densification of the solid. The identification procedure of the model uses two types of mechanical tests: uniaxial compression and drained die pressing (filtration) carried out with A356 alloy. The identification results are then validated using drained triaxial compression.     

An efficient constitutive model for room-temperature,low-rate plasticity of annealed Mg AZ31B sheet

Metals and alloys with hexagonal close packed (HCP) crystal structures can undergo twinning in addition to dislocation slip when loaded mechanically. The complexity of the plastic response and the limited extent of twinning are impediments to their room-temperature formability and thus their widespread adoption. In order to exploit the unusual deformation characteristics of twinning sheet materials in designing novel forming operations, a practical plane stress material model for finite element implementation was sought. Such a model, TWINLAW, has been constructed based on three phenomenological deformation modes for Mg AZ31B: S (slip), T (twinning), and U (untwinning). The modes correspond to three testing regimes: initial in-plane tension (from the annealed state), initial in-plane compression, and in-plane tension following compression, respectively. A von Mises yield surface with initial non-zero back stress was employed to account for plastic yielding asymmetry, with evolution according to a novel isotropic and nonlinear kinematic hardening model. Texture and its evolution were represented throughout deformation using a weighted discrete probability density function of c-axis orientations. The orientation of c-axes evolves with twinning or untwinning using explicit rules incorporated in the model.     

有限弹塑性变形的几何模型

以连续介质力学内变量理论为基础,建立了一个以材料内部微结构变量为底流形。材料外部变形状态为对应纤维的材料状态纤维丛模型,使材料的力学特性与模型的几何性质自然对应起来．在模型上讨论和分析了有限弹塑性变形中变形梯度的Ｌｅｅ和Ｃｌｉｆｔｏｎ的分解和联系,并证明了塑性变形为沿内变量演化在纤维丛的水平空间的运动由此获得了塑性变形随内变量演化的变化方程和塑性速率梯度与内变演化的协调关系．     

Crystallographic orientation and size dependence of tension-compression asymmetry in molybdenum nano-pillars

Uniaxial tension and compression experiments on [0 0 1] and [0 1 1] oriented molybdenum nano-pillars exhibit tension-compression asymmetry, a difference in attained stresses in compression vs. tension, which is found to depend on crystallographic orientation and sample size. We find that (1) flow stresses become higher at smaller diameters in both orientations and both loading directions, (2) compressive flow stresses are higher than tensile ones in [0 0 1] orientation, and visa versa in [0 1 1] orientation, and (3) this tension-compression asymmetry is in itself size dependent. We attribute these phenomena to the dependence of twinning vs. antitwinning deformation on loading direction, to the non-planarity of screw dislocation cores in Mo crystals, and to the possibly lesser role of screw dislocations in governing nano-scale plasticity compared with bulk Mo.     

2D编织陶瓷基复合材料应力-应变行为的试验研究和模拟

本文对2D编织陶瓷基复合材料拉伸应力-应变行为进行了试验研究和理论模拟。将2D编织结构简化为：正交铺层结构和纤维束波动结构。基于基体随机开裂、纤维随机断裂的统计分布理论,得到正交铺层结构的应力-应变关系;基于体积平均方法,将纤维束波动部分分割为若干子单元;由于纤维束的波动使各子单元材料方向与加载方向不一致,因此考虑了各子单元的线性行为和非线性行为对材料响应的影响,同时引入强度分析模型,得到纤维束波动部分的应力-应变关系。结合正交铺层部分和纤维束波动部分的应力-应变关系,得到2D编织结构的应力-应变行为,理论与试验吻合较好。     

Analysis of the influence of polymer viscosity on the dispersion of magnesium hydroxide in a polyolefin matrix

The dispersion of Mg(OH)₂ agglomerates at low concentration in a polymer melt was investigated in a transparent counter-rotating shear cell. The influence of the viscosity of the matrix, the initial agglomerate size and the infiltration of the matrix was evaluated. Mg(OH)₂ agglomerates have a low cohesion and a fractal structure. Two dispersive mechanisms already mentioned in the literature were identified: erosion and rupture. Critical conditions for rupture were measured and particle size analysis was performed in order to determine the kinetics of erosion. The infiltration of the matrix, which depends on the viscosity, was found to play a key role on dispersion mechanisms. In contrast to previous works, infiltration is more important with the high viscosity matrix. In infiltrated matrix, rupture was found to occur firstly through plastic deformation of the infiltrated agglomerate, and then the agglomerates split into small fragments. In the low viscosity matrix, fragments produced either by rupture or erosion are small aggregates.     

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题．针对金属－陶瓷功能梯度圆板,考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况,应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性振动微分方程．考虑周边夹支边界条件,利用伽辽金法得到了横向非线性固有振动方程,并确定了静载荷引起的静挠度．用改进的多尺度法求解强非线性方程,得出非线性固有频率表达式．通过算例,分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况．结果表明,非线性固有频率随金属含量的增加而降低;随转速和圆板厚度的增大而升高;随功能梯度圆板表面温度的升高而降低．     

CuAlNi单晶形状记忆合金压缩特性的实验研究

具有相变伪弹性特性的CuAlNi单晶是目前应用最广泛的形状记忆合金之一。这种材料被广泛应用在工程、生物和医学科学等领域。由于单晶是各向异性，没有多晶中晶粒之间的相互作用，因而在特定晶向上的力学性能稳定。但是这种材料的一些基本性质，如压缩状态下马氏体的发生、生长和传播等还没有人详细研究。本文主要研究CuAlNi单晶在特定晶向上的变形过程，它的应力—应变特性，并利用特殊的显微成像系统首次获得了沿[110]方向压缩时二维马氏体的发生、生长和传播过程。     

Experimental Observations on Dynamic Response of Selected Transparent Armor Materials

Structural transparent material systems are critical for many military and civilian applications. Transparent armor systems can consist of a wide variety of glass laminate assemblies with polymeric bonding interfaces and backing as well as the inclusion of polycrystalline ceramic (AlON, spinel) and single crystals (sapphire) as front facing materials. Over the last 20 years as the threats have escalated and become more varied, the challenges for rapidly developing optimized threat specific transparent armor packages have become extremely complex. Ultimate failure of structural ceramics in impact events is a function of the temporal and spatial interaction of the macro-stresses at the macro-, micro- and nano-structural scale, including elastic and inelastic (plastic) deformation, crack nucleation, damage evolution and resulting failure from the macro-scale (top down) and/or from the nano-scale (bottom up). In order to accelerate the development of validated design and predictive performance models, a systematic series of experimental investigations have been carried out on various non-crystalline ceramics (glass), single crystal (sapphire) and polycrystalline ceramics (AlON). The Edge-on Impact (EOI) test coupled with a high-speed Cranz-Schardin film camera has been extensively used on a variety of monolithic and laminated glasses, AlON and crystallographically controlled sapphire single crystals to visualize and quantify stress wave, crack and damage propagation. A modified Kolsky bar technique instrumented with a high speed digital camera has been utilized in an unconfined and confined test sample mode to examine the dynamic deformation and failure of AlON undergoing uniaxial, high strain rate compression. Real time photography has clearly demonstrated the critical influence of defects and post mortem characterization of fragments resulting from these tests have revealed the influence of micro-deformational twining and cleavage down to the nano-scale. Finally, a brief summary of work using ultra-high-speed photography of the impact of conventional projectiles on glass and AlON will be presented. These experimental results will be absolutely critical to help evolve and validate existing models used in computer codes to simulate the impact performance of brittle materials.     

Deformation processes below a plate sinkage test on sandy loam soil: theoretical approach

Mathematical models to predict the mode and extent of deformation occurring below sinkage plates are presented in the first part of this paper which encompasses the theoretical approach to the subject. These models are based on previous work by Earl (Earl R. Assessment of the behaviour of field soils during compression. Journal of Agricultural Engineering Research 1997;68:147–57)who developed a procedure to predict the likely mode of deformation using confined compression tests carried out alongside plate sinkage tests. This work suggested that soil behaviour, during increasing compression under a sinkage plate, is governed by three processes; (i) compaction below the plate with constant lateral stress, (ii) compaction with increasing lateral stress, and (iii) displacement and compaction of soil laterally. The aim of this second part to the paper is to observe soil deformation processes occurring below a circular sinkage plate to examine (i) whether the three phases of deformation referred to above occur in practice, and (ii) the accuracy of the models for predicting the soil deformation processes that occur. Tests were carried out on sandy loam soil under controlled conditions in a soil bin. Observations of deformation processes, recorded using long-exposure photography, revealed that during the initial stages of sinkage (a few millimetres), the corresponding disturbance of soil below the plate extended disproportionately further and was cylindrical in form. As sinkage progressed, the deformation process went through a transitional stage before reaching the more widely recognised form of the development of an inverted cone of compacted soil directly below the plate which moved with the plate causing lateral soil movement and compaction. Predictions for a medium density sandy loam were found to be in broad agreement with soil behaviour under a semi-circular sinkage plate observed behind a sheet of tempered glass under controlled conditions in a soil tank.     

Incremental versus total-strain theories for proportionate and nonproportionate loading of torsion-tension members

Incremental and total-strain theories have been presented in the literature for hollow and solid circular torsion-tension members. The differential equations obtained for the incremental theory have been solved only for the conditions that the torsion-tension member is made of a nonstrain-hardening material and is subjected to restricted deformation histories. Computer programs were written to obtain numerical incremental solutions for hollow and solid circular torsion-tension members made of strain-hardening materials and subjected to any deformation or loading path. Test data were obtained for three different materials: (a) a nonstrain-hardening steel, annealed SAE 1035 steel, with identical properties in tension and compression; (b) a strain-hardening steel, annealed rail steel, with identical properties in tension and compression; (c) a strainhardening alumimum alloy, 2024-T4, with different properties in tension and compression. In all cases, the average of the tension and compression stress-strain diagram was approximated by two straight lines to obtain material properties. Test data for proportionate loading were in excellent agreement with either the total-strain theory or the incremental-strain theory. Data for nonproportionate loading, in which one deformation was kept constant as the other was increased, fell between the two theories and were in closer agreement with the predictions of the incremental theory.     

Spherical indentation of composite laminates with controlled gradients in elastic anisotropy

Three-dimensional elastic analyses and experiments of indentation of thick laminated plates of carbon fiber reinforced epoxy are presented. Pointwise, the material is characterized as a linear elastic orthotropic material. The in-plane orientation of the carbon fibers is systematically varied as a function of depth. The influence of fiber orientation as a function of depth on the indentation response is considered along with the relationship between the indenter force vs depth. The fiber orientation profiles considered are those of a continuous linear variation between 90° at the outer surfaces and 0° at the center plane of the laminate, and a cross ply laminate involving alternating 90° and 0° layers through thickness. Experimentally, it is found that for the case of a cross-ply laminate, the indentation produces delaminations localized at the interfaces that separate planes of dissimilar orientation. For this case, stress concentrations at interfaces between plies of dissimilar orientation coincide with the observed sites of delamination. For the graded case, evidence of enhanced nonlinear deformation is found, without the nucleation of cracks. Computations show that for the graded material, tensile stresses perpendicular to fibers are suppressed significantly, possibly explaining the absence of matrix cracks in this material. Measured and computed indenter force-depth variations were found to be in good agreement. Experiments and computations also reveal that the orientation-graded material is more compliant when subjected to indentation than the conventional cross-ply laminate.     

The influence of crystallographic orientation on the deformation behaviour of single crystals containing microvoids

This study deals with the influence of microvoids on the deformation and damage behaviour of ductile materials. Fully three dimensional simulations were performed for different void configurations. The crystallographic orientation of the void surrounding matrix was varied to accurately investigate its impact on void growth. The results of the simulations have shown that the void growth and deformation behaviour on a microscopic scale significantly depend on the crystallographic orientation of an anisotropic matrix material.     

Short-Term Microdamageability of Fibrous Composites with Transversally Isotropic Fibers and a Microdamaged Binder

The theory of microdamageability of fibrous composites with transversally isotropic fibers and a microdamaged isotropic porous matrix is proposed. Microdamages in the matrix are simulated by pores filled with particles of the destroyed material that resist compression. The criterion of damage in the matrix microvolume is taken in the Schleicher–Nadai form. It accounts for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with Weibull distribution. The stress–strain state and effective properties of the material are determined from the stochastic equations of the elastic theory for a fibrous composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the matrix. Nonlinear diagrams of the concurrent processes of deformation of fibrous materials and microdamage of the matrix are plotted. The effect of the physical and geometrical parameters on them is studied