Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

Dynamic stress chain formation in a two-dimensional particle bed

Cure cast plastic bonded explosives (PBXs) consist of relatively hard particles in a soft binder. Under compressive loading, the explosive cyrstals come into contact that causes high stress concentrations. The lines along which the crystals are loaded are called stress chains. Damage done to these particle beds during compressive loading can lead to reaction. The photoelastic effect of PMMA is exploited to examine the stress state within a two-dimensional particle bed. Stress chain development within the bed is recorded and is shown to increase the stress state within some particles while leaving others unloaded. These concentrations form early in the loading process, leading to fracture along the stress bridges and generating likely reaction initiation sites. Through material point method simulations, contact friction is shown to have a large effect on the stress distribution within the particle bed.     

High temperature creep behaviour of an FeAl intermetallic strengthened by nanoscale oxide particles

The creep behaviour of an FeAl intermetallic strengthened by nanosized oxide particles has been examined at temperatures of 700–825 °C. For all temperatures the strain rate shows a power law dependence on the applied stress. At the lowest temperature and with the highest stresses there is evidence of a threshold stress produced by the difficulty of overcoming the particle barriers, while for higher temperatures as well as at low stresses there is no threshold stress and creep appears to be controlled by general climb. The fine oxide particles produce good strengthening at low temperatures but are more readily overcome at high temperatures due to their very small size and limited attractive relaxation force. Despite such fall in creep strength, this material remains one of the strongest iron aluminides to the temperature range evaluated.     

Micromechanical modelling of the static and cyclic loading of an Al 2124-SiC MMC

The objective of this study was to use micromechanical finite element models to simulate both the static and cyclic mechanical behaviour of a metal matrix composite: a forged Al 2124 alloy reinforced with 17% SiC particles, at two different temperatures: room temperature and 150°C. In the simulations, periodic unit cell models incorporating the explicit representation of the matrix and the reinforcing particles in both 2D and 3D, were used. Micromechanical models with both idealised and realistic reinforcing particle shapes and distributions were generated. The realistic particle shapes and distributions were inferred from experimental SEM micrographs. The pattern and intensity of the plastic deformation within the matrix was studied and the macroscale behaviour of the composite was inferred from average stress and strain values. In order to include the effects of residual stresses due to the processing of the material, a quenching simulation was performed, prior to the mechanical loading, and its effects on the macroscopic tensile behaviour of the MMC was assessed. The effects of removing the periodicity constraint on the models by using a cell embedding technique was investigated. In order to try and model the deformation behaviour of the matrix more accurately, crystal plasticity models, which included the explicit representation of individual grains were examined for different matrix grain morphologies. The results of the simulations were compared with experimental results for the MMC in terms of macroscopic tensile stress–strain curves. Finally, the effects of different matrix strain hardening models were examined in order to investigate the cyclic behaviour of the MMC.     

A novel Volume-Compensated Particle method for 2D elasticity and plasticity analysis

A novel Volume-Compensated Particle model (VCPM) is proposed for the modeling of deformation and fracture in solids. In this proposed method, two potentials are introduced to model the interactions between material particles, i.e., a local pair-wise potential and a non-local multi-body potential. The local pair-wise potential is utilized to account for the constitutive relationship within the connecting bonds between particles while the non-local multi-body potential is employed for considering the volumetric effects under general mechanical loadings. The potential coefficients are determined by matching the potential energy stored in a discrete unit cell to the strain energy at the classical continuum level. A volume conservation scheme is proposed to model the plastic deformation. The validity of the proposed model is tested against the classical elasticity and elasto-plasticity benchmarks before its application to fracture problems. Several conclusions are drawn based on the proposed study.     

漂珠颗粒材料静动态力学性能与破碎机理研究

为考察脆性空心颗粒材料冲击载荷下的力学特性，以具有不同粒径分布的粉煤灰漂珠为研究对象，对其静动态力学性能进行实验研究。通过限制颗粒材料压缩应变为50%，分析颗粒破碎率和破碎机理与材料宏观应变率效应的关系。结果表明:（1）不同粒径的漂珠颗粒材料在动态压缩下较准静态压缩下颗粒材料的强度均有明显的增强，在0.001和150 s?1大小颗粒的强度分别提高200%和195%，在150和300 s?1大小颗粒的强度分别提高39%和51.5%，在300和800 s?1大小颗粒的强度并未发生明显的变化；（2）在相同加载速度下粒径较小的颗粒比大粒径颗粒的强度和吸能效果分别提高35%～40%和35%～48%；（3）对破碎后颗粒粒径分布曲线分析可知，随着加载速度的增加，大小颗粒的破碎率和破碎程度都会增大，且在相同加载速度下大颗粒的破碎率较小颗粒的破碎率高；（4）Hardin破碎势分析表明，单位输入能量下颗粒的相对破碎势随冲击速度增大而减小，动态冲击下用于颗粒破碎的能量利用率降低，从而导致材料在相同压缩量下产生更高的能量耗散和应力水平，即表现为宏观的应变率效应。     

The structural performance of the periodic truss

Matrix methods of linear algebra are used to analyse the structural mechanics of the periodic pin-jointed truss by application of Bloch's theorem. Periodic collapse mechanisms and periodic states of self-stress are deduced from the four fundamental subspaces of the kinematic and equilibrium matrix for the periodic structure. The methodology developed is then applied to the Kagome lattice and the triangular-triangular (T-T) lattice. Both periodic collapse mechanisms and collapse mechanisms associated with uniform macroscopic straining are determined. It is found that the T-T lattice possesses only macroscopic strain-producing mechanisms, while the Kagome lattice possesses only periodic mechanisms which do not generate macroscopic strain. Consequently, the Kagome lattice can support all macroscopic stress states. The macroscopic stiffness of the Kagome and T-T trusses is obtained from energy considerations. The paper concludes with a classification of collapse mechanisms for periodic lattices.     

冲击载荷下脆性空心颗粒破碎机理

为考察脆性空心颗粒在冲击载荷作用下的应变率效应和破碎行为的细观机理,以粉煤灰漂珠为研究对象,基于低速冲击实验和有限元数值模拟,对比了典型空心颗粒材料在不同加载速率下的力学响应特性和细观压溃行为,阐释了材料宏观应变率效应产生的细观机理,获得以下结果。（1）在0.001～300 s?1应变率范围,漂珠颗粒的破碎率和Hardin破碎势平均提升了约21%和10%～30%,材料比吸能提升了50%～125%,比吸能的额外增加主要与动态颗粒滑移产生的摩擦耗能相关。颗粒平均尺寸较大的试样体现出更强的应变率效应。（2）初始压溃阶段的应力应变响应特征的数值模拟结果与实验结果较吻合,低速冲击下动态二次压溃现象产生的细观机理为动态颗粒滑移和压紧行为对加载速率的依赖性。(3) 数值模拟表明,冲击加载下产生相同应变时颗粒的损伤程度和范围大于准静态加载,这与实验所得破碎势随应变率增加的结果一致。对比低速冲击实验的相对破碎势分析和细观数值模拟结果可知,脆性颗粒堆积材料在动态冲击下表现出的宏观应变率效应主要归因于颗粒压溃行为的率敏感性和动态加载下颗粒破碎能量利用率的降低。     

Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

Thermoelastic behavior of functionally graded particulate materials is investigated with a micromechanical approach. Based on a special representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived with pair-wise particle interactions, and a set of governing equations for the thermoelastic behavior of functionally graded materials is presented. The effective coefficient of thermal expansion at a material point is solved through the overall averaged strain of two phases induced by temperature change under the stress-free condition, and is shown to exhibit a weak anisotropy due to the particle interactions within the graded microstructure. When the material gradient is eliminated, the proposed model predicts the effective coefficient of thermal expansion for uniform composites as expected. If the particle interactions are disregarded, the proposed model recovers the Kerner model. The proposed semi-analytical scheme is consistent and general, and can handle any thermal loading variation. As examples, the thermal stress distributions of graded thermal barrier coatings are solved for two types of thermal loading: uniform temperature change and steady-state heat conduction in the gradation direction.     

Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.     

A numerical analysis of the shear behavior of granular soil with fines

Shear behavior of granular soil with fines is investigated using the discrete element method(DEM) and particle arrangements and inter-particle contacts during shear are examined.The DEM simulation reveals that fine particles play a vital role in the overall response of granular soil to shearing.The occurrence of liquefaction and temporary reduction of strength is ascribed mainly to the loss of support from the fine particle contacts(S-S) and fine particle-to-large particle contacts(S-L) as a consequence of the removal of fine particles from the load-carrying skeleton.The dilative strain-hardening response following the strain-softening response is associated with the migration of fine particles back into the load-carrying skeleton,which is thought to enhance the stiffness of the soil skeleton.During shear,the unit normal vector of the large particle-to-large particle(L-L) contact has the strongest fabric anisotropy,and the S-S contact unit normal vector possesses the weakest anisotropy,suggesting that the large particles play a dominant role in carrying the shear load.It is also found that,during shear,fine particles are prone to rolling at contacts while the large particles are prone to sliding,mainly at the S-L and L-L contacts.     

钟摆状态下湿颗粒坍塌流动行为及其动力相似性

基于建立的湿颗粒离散动力学模型,本文系统研究了钟摆状态下湿颗粒柱在重力驱动下的坍塌流动过程,主要考虑了颗粒粒径、液体表面张力系数和液体含量等参数对系统坍塌流动模式和动力学行为的影响。研究发现,在湿颗粒系统中,颗粒粒径和液体表面张力系数会改变颗粒间的毛细力大小,引起系统发生不同的坍塌流动模式,而液体含量仅定量影响颗粒坍塌后的堆积形态。在此基础上,进一步探讨了不同模式下系统坍塌流动行为与模型参数的相关性,发现无量纲Bond数是决定钟摆状态下湿颗粒物质坍塌流动动力学行为的本质因素。     

激波驱动的气固两相流的动态压力测量

利用水平圆柱形激波管对激波驱动的可压缩性气固两相流进行了试验研究.利用压电式压力传感器、电荷放大器、示波器及计算机组成的压力信号测试系统, 对激波与颗粒作用前后的气相参数进行测量及分析. 试验中测得了激波在管中的传播速度, 波后气流的压力, 反射激波、透射激波的压力和速度等. 分别考察颗粒、装载比、驱动气源以及入射激波马赫数等因素的差异对气相参数的影响.试验结果表明: 激波与颗粒群相互作用时, 会产生反射激波和透射激波,其强度与驱动气源、颗粒大小、颗粒装载比等参数有关;激波衰减率随着装载比、马赫数的增大而减小. 研究指出,在颗粒群被激波加速的初始阶段, 颗粒间的弹性碰撞起着重要的作用.      

Modeling the dynamic response of visco-elastic open-cell foams

This article introduces a mesoscopic formulation for modeling the dynamic response of visco-elastic, open-cell solid foams. The effective material response is obtained by enforcing on a representative 3D unit cell the principle of minimum action for dissipative systems. The resulting model accounts explicitly for the foam topology, the elastic and viscous properties of the cell wall, and the inertial effects arising from non-affine motion within the cells. The microinertial effects become significant in retarding the foam collapse during exceedingly high strain-rate loading. As an application example, a heterogenous case of compressive deformation at high strain rate is simulated utilizing the present model as a constitutive update in a non-linear finite element analysis code. This FEM simulation shows the ability of the model to capture the progressive foam collapse during the dynamic compression as observed in experimental studies. Using the microscopic model, the inertial and viscous strain-rate effects are investigated through the foam density, viscosity, and relative density. Based on the physics incorporated into the local cell model, we provide insight into the physical mechanisms responsible for the experimentally observed strain-rate effects on the behavior of dynamically loaded foam materials.     

Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation

The determination of an effective property in composite materials necessitates the knowledge of some averaged field quantities in the constituents (like the average heat intensity or average strain) of a composite sample, which is subjected to homogeneous boundary conditions. In the generalized self-consistent scheme (GSCS) which is today a classical micromechanics model suited for the determination of the effective properties of matrix-based composites, those average quantities are estimated by using an auxiliary configuration in which a particulate phase is first surrounded by some matrix material and then embedded in the effective medium. In the present study, we revisit the GSCS both for two- and multi-phase matrix-based composites containing spherical particles, and clarify aspects related to the volume fractions of the particle core and matrix shell within the composite element which is embedded in the effective medium. The contribution of this study is believed to be mainly on the conceptual side and resides in a new formulation of the method in which the embedding volume fractions are determined in the course of the analysis by means of some fundamental relations on the averaged fields. The study is carried out in thermal conduction and elasticity and contains new results on the effective shear modulus of multi-phase composites.     

The role of a realistic volume constraint in modelling a two dimensional granular assembly

This paper presents a deceptively simple mathematical model for the deformation of granular materials composed of rigid particles. The model captures many of the diverse features of the behaviour of such a material and emphasises the importance of volume constraints in situations where the deformation is mainly by particle rearrangement. It is constructed using a simple dissipation function and a rather more complicated dilatancy rule containing an updateable reference strain. This allows the solid-like and fluid-like properties of granular materials to be reconciled in a single model.The model has been used to simulate experiments that use an analogue of an ideal granular material [Joer, H.A., Lanier, J., Fahey, M., 1998. Deformation of granular materials due to rotation of principal axes. Geotechnique 48 (5), 605-619] consisting of a two dimensional assembly of thin PVC rods. These experiments clearly illustrate: partially reversible dilatancy in direct shear tests; cyclic shearing leading to liquefaction in constant volume shear tests; and non-coaxiality of the principal axes of stress and strain increment in circular loading tests. These radically different modes of deformation provide a challenging data set that allows the model's potential to be clearly demonstrated.The authors believe that the comparison of these experimental results and our simulations give strong support to the assertion that volume changes associated with shear deformation are responsible for the rotational kinematic hardening seen in granular materials, and hence, the non-coaxiality of the stress and strain-rate tensors.     

Statistics of particle interactions in dense granular material under uniaxial compression

Stress evolution in a dense granular material is closely related to interactions of contacting particles. We investigate statistics related to particle interactions and the relationship between the averaged local relative motion and the macroscopic motion. The validity of the Voigt and Reuss assumptions is examined, and extensions to these assumptions are proposed. Effects of history in the dense granular material are investigated. Statistical samples used in this paper are obtained using three-dimensional numerical simulations of dense granular media under uniaxial cyclical compression. The results show that stresses arise mostly from normal forces between particles, and direct contributions from frictional tangential forces between particles are small. Tangential friction, however, significantly increases the particle contact time, and thus reduces the rate of contact breakage. The contact breakage rate is demonstrated to be a stress relaxation rate. Therefore, stress increases significantly with friction between particles as a result of prolonged relaxation time.     

力-热载荷下双金属复合管的屈曲失效研究

采用有限元方法研究了力-热载荷下双金属复合管的屈曲失效行为,通过三维有限元建模考虑了双金属复合管的准静态复合成型制造过程中产生的残余应力,分析了温度及内压两个主要参数对双金属复合管屈曲失效的影响。结果表明,高温导致材料发生软化,抑制了双金属复合管的屈曲;弯矩、内压及热载荷联合作用下,复合管内介质温度降低,复合管弯矩达到最大值对应的曲率减小,而弯曲承载能力增大,外基管的椭圆率也增大;内压变化对复合管的弯曲承载能力和外基管的椭圆率影响较小。     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.