Morphology-tensile behavior relationship in injection molded poly(ethylene terephthalate)/polyethylene and polycarbonate/polyethylene blends (II) Part II Tensile behavior

The tensile behavior of injection molded poly(ethylene terephthalate) (PET)/polyethylene (PE) and polycarbonate (PC)/PE blends was investigated. For the same blend, due to the difference in the elongated dispersed particle concentration, the specimens molded at higher injection speed had slightly higher tensile strength and modulus than those molded at lower speed. Moreover, the reinforcement effect of PC to PE matrix was more noticeable than PET to PE. For the stress-strain behavior, while the PET/PE blend behaved like a common injection-molded immiscible blend the PC/PE blend unusually underwent twice yielding regardless of the cross head speed. For the PET/PE blend, obvious debonding between the dispersed PET particles and the matrix PE occurred upon elongation, resulting in large grooves and voids behind the particles. The PET particles experienced slight plastic deformation from spheres to ellipsoids. The stress whitening first appeared in the necking zone then extended along cold drawing zone. For the PC/PE blend, the PC particles in the core layer experienced considerable plastic deformation throughout the tensile test. Consequently, most of PC particles in the fractured specimen were deformed into fibers. Owing to comparatively high amount of injection-induced fibers that distributed or transferred the external stress, the specimen of PC/PE blend first deformed evenly in the entire tested zone, characterized by stress whitening in the entire specimen. Then after the first yielding, the stress decreased slowly while the elongation continued. When the elongation reached a certain point, the fibers in the sub-skin layer could no longer endure the external stress, and accordingly the second yield took place. Additionally, the fibrillation of the spherical PC particles in the core layer appeared right after the second yielding point.     

Determining the stress-strain behaviour at large strains from high strain rate tensile and shear experiments

To characterise the high strain rate mechanical behaviour of metals, split Hopkinson bar experiments are frequently used. These experiments basically yield the force and elongation history of the specimen, reflecting not only the specimen material behaviour but also the specimen structural behaviour. Calculation of the real material behaviour from this global response is not straightforward, certainly for materials such as Ti6Al4V where due to low strain hardening, the specimen deformation is very inhomogeneous. However, for fundamental material research and constitutive material modelling, knowledge of the true effective stress versus plastic strain, strain rate and temperature is essential.In this contribution, a combined experimental-numerical approach for extraction of the strain rate and temperature dependent mechanical behaviour from high strain rate experiments is presented. The method involves the identification of the material model parameters used for the finite element simulations. The technique is applied to determine the stress-strain behaviour of Ti6Al4V using both high strain rate in-plane shear and tensile test results. For the tensile tests, even stress-strain data beyond diffuse necking are retrieved. A comparison is made between the material behaviour extracted from the tensile and the shear experiments. The material behaviour is modelled with the Johnson-Cook constitutive relation. It is found that the simultaneous use of tensile and shear tests to identify the model parameters gives a more generally applicable model. Validation of the material model and the finite element simulations is done by local strain measurements in the shear and tensile test by means of digital image correlation.     

未硫化橡胶非线性粘弹性本构模型研究

建立一种新的未硫化橡胶力学行为的描述方法。为了充分研究未硫化橡胶在不同变形模式下复杂的应力-应变行为,设计了3种不同的力学特性实验:单轴拉伸、压缩与剪切试验。发现未硫化橡胶的应力-应变关系表现出很强的非线性和率相关性。提出结合Yeoh应变能函数的广义Maxwell粘超弹性模型,拟合分析表明试验结果与模拟结果一致性较好。发现与硫化橡胶一样,必须采用多工况下的实验数据才能得到变形协调的粘弹性本构模型。实验结果和建立的本构模型有助于工程师更好的理解未硫化橡胶的力学行为,为橡胶的制造过程仿真提供理论基础。     

橡胶隔振器大变形有限元分析

以橡胶隔振器为研究对象,基于超弹性本构模型,对拉伸、压缩、剪切状态下分别进行有限元计算,探讨橡胶等不可压缩材料大变形有限元建模技术;重点研究橡胶结构不同受载方式下变形模式及有限元分析所需要的材料试验数据。经与试验结果对比分析,得到隔振器三种状态下,填充超弹本构模型最优的材料数据类型,为橡胶结构件的数值模拟提供有益参考。     

Three-dimensional elastoplastic finite element modelling of deformation and fracture behaviour of rubber-modified polycarbonates at different triaxiality

A periodic face-centred cuboidal cell model is provided to account for inter-particle interaction, and a particle-crack tip interaction model is developed to study the interaction between a blunting model I crack tip and the closest array of initially spherical rubber particles in an effective medium. Three-dimensional elastoplastic finite element analysis has been preformed to study the deformation and fracture behaviour of rubber-modified polycarbonates. The effective elastoplastic constitutive relation is derived by the method of homogenisation and local stress and strain distributions are obtained to explore the role of rubber cavitation in the toughening process at different stress triaxiality. 3D elastoplastic finite element results are compatible with experimental observations, that is, rubber particles can act as stress concentrators to initiate crazing or shear yielding in the matrix but they behave differently from voids at high triaxiality. Rubber cavitation plays an important role in the toughening process under high tensile triaxial stresses.     

Plastic deformation of EVA, EVOH and their multilayers

The high strain rate, plastic deformation of multilayer films is analyzed in relation to the tensile properties of the components. The multilayers combine ethylene-vinyl acetate (EVA) blend surface-layers with an ethylene-vinyl alcohol (EVOH) core-layer; the volume of the EVOH layer is varied from 1% to 20%. Individually, the components exhibit markedly different tensile behavior in terms of yielding and ductility in the temperature range from 55°C to 95°C. The EVA blend deforms homogeneously whereas EVOH forms a neck at an extension rate of 10,000%/min. It is shown that the true stress-strain relationship of the components in the plastic region can be described with two parameters, the true yield stress and the strain hardening parameter. Multilayers deform homogeneously, as does the EVA blend. A simple rule of mixtures approach is used to describe the plastic behavior of the multilayers as a function of temperature, composition and moisture, and to predict whether or not deformation will be uniform.     

316LN不锈钢高温拉伸颈缩区塑变行为

为准确测量颈缩发生后的应力-应变行为,本文综合物理实验、有限元模拟和MLR模型的方法确定颈缩区的塑变行为,建立316LN不锈钢高温本构模型.模型中,颈缩前的真应力-真应变呈幂函数关系,颈缩发生后,较低温度时应力随着应变的增加迅速下降,而当较高温度时应力随着应变的增加而缓慢下降,真应力-真应变呈非线性关系.基于MLR模型,修正了颈缩后不同温度、不同应变速率下的真应力-真应变曲线,并将有限元模拟的颈缩区长度与实测值相对比,相对偏差为4.73%.这说明修正后的应力-应变本构模型能够准确地描述316LN的高温塑性行为.     

2D-C/SiC复合材料开孔件拉伸强度有限元计算

对2D-C/SiC复合材料开孔试件最小净截面图像进行观测,获得试件材料内部宏观孔洞的分布形态及密度分布梯度。通过对2D-C/SiC复合材料拉伸应力-应变行为进行非线性拟合,并利用理论模型计算与实验验证相结合的方法得到了材料密度与其拉伸模量和强度的关系,描述了不同密度2D-C/SiC复合材料的拉伸应力-应变行为。在此基础上,将制备工艺造成的试件材料密度分布的非均匀性和材料拉伸应力-应变行为的非线性引入到有限元模型中,进行开孔试件拉伸剩余强度模拟计算,预测结果与实验结果吻合较好。     

金属芯压电纤维/聚合物复合材料压电-黏弹-塑性行为的细观力学模型

为了表征金属芯压电纤维增强聚合物基（MPF/PM）复合材料非线性、时变的压电-黏弹-塑性行为,基于变分渐近理论建立MPF/PM增量形式的细观力学模型。首先分别导出聚合物和MPF增量型本构方程,基于汉密尔顿扩展原理推导出MPF/PM压电-黏弹-塑性变分原理的能量泛函。考虑材料的时变和非线性特征,建立与求解瞬时有效机-电耦合矩阵有关的增量过程,并通过有限元技术实现模型的数值模拟。利用构建模型研究了不同铝芯体积分数、电场变化率和加载条件对MPF/PM有效全局应力-应变和单轴纵向拉伸性能的影响。结果表明,构建的模型能准确模拟MPF/PM多场耦合作用下的非线性、时变行为,为该新型智能材料的实际工程应用奠定理论基础。     

Predictive modelling of the properties and toughness of polymeric materials Part III Simultaneous prediction of micro- and macrostructural deformation of rubber-modified polymers

The deformation behaviour of heterogeneous tensile bars is investigated by using the recently developed multi-level finite element method (MLFEM) that allows for a numerical coupling between the microscopic and macroscopic stress-strain behaviour, combined with an accurate elasto-viscoplastic constitutive model (single-mode compressible Leonov model) and a detailed finite element model of the microstructure. The method is used to predict the influence of the microstructure on localisation phenomena in plane strain notched and hour-glass-shaped polycarbonate and polystyrene tensile specimen with different volume fractions of non-adhering or adhering rubbery particles. In Part I and II of this series it was already suggested that elimination of the unstable post-yield strain softening behaviour of a polymeric material by appropriate microstructural modifications may be essential for toughening. The results of the multi-level analyses presented in this paper confirm this statement. It is shown that a stable post-yield response, resulting from microstructural adaptations, is indeed a prerequisite for the distribution of plastic strains over the whole macro- and microstructure: massive shearing is promoted by the introduction of voids in the polycarbonate or load bearing pre-cavitated rubbery particles in the polystyrene. Furthermore, it is shown that the voids indeed reduce the macroscopic dilative stresses to safe values. The results suggest that localisations of strain and stress will always occur on a macro and/or micro level. Catastrophic failure, however, can be postponed by stabilisation of the post-yield behaviour of the material and reduction of the macroscopic dilative stresses through appropriate microstructural adjustments.     

Modelling the properties of rubber-modified epoxy polymers

A finite-element model for rubber particles in a polymeric matrix has recently been proposed which is based upon a collection of spheres, each consisting of a sphere of rubber surrounded by an annulus of matrix. We have used this model to investigate in detail the stress distributions in and around a rubber particle, or a void, in a matrix of epoxy polymer. We have deduced the bulk modulus of the rubber-toughened epoxy and considered the implications of the stress distributions on the observed toughening micromechanisms. Of particular concern has been the effects of the volume fraction and the properties of the rubber phase.     

2.5D C/SiC复合材料连续损伤本构模型

基于连续损伤力学建立了一种包含拉伸与剪切损伤变量的2.5D C/SiC复合材料连续损伤本构模型。分别开展了拉伸和剪切试验,获得应力-应变曲线,并通过拟合试验曲线获得各损伤变量的演化参数。采用子程序技术将本构模型嵌入商用有限元软件ANSYS,应用有限元法计算了材料的应力-应变曲线。考虑了拉剪损伤耦合效应,计算了偏轴拉伸情况下的应力-应变曲线。结果表明:沿经纱拉伸、沿纬纱拉伸以及面内剪切的应力-应变曲线与试验结果吻合,最大偏差依次为4.30%、3.09%及3.73%;偏轴拉伸计算与试验应力-应变曲线也吻合较好。      

Role of blend morphology in rubber-toughened polymers

The influence of blend morphology on mechanical behaviour of rubber-toughened polymers was investigated. Diglycidyl ether of bisphenol A epoxies toughnened by core-shell rubber particles were employed as the model systems. The blend morphology was varied by changing the composition of the shell of particles, the curing agent, and the extent of agitation prior to casting. It is shown that the most uniform dispersion of particles is obtained when the shell of the modifiers contains reactive groups. In the absence of the reactive groups and when a slow curing agent is employed, however, a highly connected microstructure is obtained. It was found that a blend with a connected microstructure provides significantly higher fracture toughness compared to a similar blend containing uniformly dispersed particles. The reason for this observation is that the connected morphology enables the shear bands to grow further from the crack tip and thus consume more energy before fracture occurs. Also, the yield strength in uniaxial tensile testing is significantly lower in the blend with the connected morphology. Therefore, it should contribute to a larger plastic zone size.     

材料模型对1Cr18Ni9Ti管材拉伸有限元仿真的影响

为研究材料模型对有限元模拟1Cr18Ni9Ti管拉伸的影响,将管材单向拉伸试验获取的真实应力应变曲线分别拟合成线性硬化和指数硬化材料模型,并用于有限元模拟。经对比分析认为,采用真实应力应变模型的分析结果与实验结果吻合良好,并能正确显示出颈缩发生时刻和颈缩形状;采用指数硬化模型的有限元模拟结果接近真实应力应变模型,颈缩区应力应变分布略显分散;采用线性硬化模型的有限元模拟结果未能显示实际管拉伸后期的局部颈缩形状。     

Effect of aspect ratio on large deformation and necking of polyethylene

Objective of the study is to examine influence of aspect ratio of rectangular cross-section on the tri-axial stress state developed by necking in tensile specimens of polyethylene. The first part of the paper presents an experimental study that used two types of high-density polyethylene (HDPE) as sample material to identify the thickness-dependent relationship between engineering stress and elongation from tensile tests. The experimental study also shows that thinner specimens, i.e. higher aspect ratio, have lower neck propagation speed and higher flow stress, thus higher rate of energy consumption for the neck propagation. The second part of the paper presents finite element simulation of large deformation and necking in HDPE when subjected to uni-axial tension. True stress–strain relationship and governing equation for visco-plastic deformation are determined from the finite element simulation based on experimental data for the two HDPEs, which reveals influence of aspect ratio of cross-section on the stress state during the necking process. Results from the study indicate that plane-stress condition prevails when the aspect ratio increases, i.e. by decreasing the specimen thickness. The finite element simulation also supports the observation that necking in specimens with higher aspect ratio, i.e. thinner specimens, generates higher percentage of reduction in the thickness direction but lower in the width direction. The overall capability for the deformation endurance was found to improve by reducing the specimen thickness. The paper concludes that finite element simulation has successfully demonstrated the influence of aspect ratio of the cross-section on the stress state in the necking process. The paper also concludes that by combining experimental testing and finite element simulation, time-dependent deformation behaviour can be separated from the time-independent deformation behaviour, which is almost impossible to achieve based on the experimental techniques that rely purely on measurement only.     

各向同性均质弹塑性材料圆棒试样单向拉伸试验变形特性与应力应变本构关系的相关性分析

针对各向同性均质弹塑性材料圆棒试样单向拉伸试验,分别从理论上以及采用有限元法分析了变形特性与应力应变本构关系的相关性,探讨了形成颈缩的必要条件及实际颈缩形貌的形成过程。结果表明,等效塑性应变ε_p达到一定临界值后,流变应力σ₀不再随等效塑性应变ε_p的增大而增大的材料的应力应变本构特性,以及试样为非理想圆柱体是产生颈缩的必要条件,颈缩后期内部形成断裂是导致颈缩区最小截面位置弧形轮廓线曲率半径较小的原因。      

Plane crack propagation in a hyperelastic incompressible material

We propose a crack propagation criterion for hyperelastic materials (rubber type material) within the framework of plane elasticity in finite deformation. The criterion is based on the examination of the asymptotic elastic field near the crack tip prior to propagation. According to this criterion, the propagation will take place for a critical value of the strain energy density intensity factor. The kink angle, obtained by applying the criterion of maximum opening stress, will depend on the fracture tensile stress of the actual material. We propose to use a local iterative finite element method to compute the asymptotic quantities involved in the criterion at a reasonable cost. Examples of computation for some hyperelastic laws simulating the behavior of vulcanized rubber are presented.     

Establishment and comparison of four constitutive relationships of PC/ABS from low to high uniaxial strain rates

The objective of this paper is to accurately predict the rate/temperature-dependent deformation of a polycarbonate (PC) and acrylonitrile-butadiene-styrene (ABS) blend at low, moderate, and high strain rates for various temperatures. Four constitutive models have been employed to predict stress–strain responses of PC/ABS under these conditions, including the DSGZ model, the original Mulliken–Boyce (M–B) model, the modified M–B model, and an adiabatic model named the Wang model. To more accurately capture the large deformation of PC/ABS under the high strain rate loading, the original M–B model is modified by allowing for the evolution of the internal shear strength. All of the four constitutive models above have been implemented in the finite element software ABAQUS/Explicit. A comparison of prediction accuracies of the four constitutive models over a wide range of strain rates and temperatures has been presented. The modified M–B model is observed to be more accurate in predicting the deformation of PC/ABS at high strain rates for various temperatures than the original M–B model, and the Wang model is demonstrated to be the most accurate in simulating the deformation of PC/ABS at low, moderate, and high strain rates for various temperatures.     

Modeling multiaxial impact behavior of a glassy polymer

In many applications of polymers, impact performance is a primary concern. Impact tests experimentally performed on molding prototypes yield useful data for a particular structural and impact loading case. But, it is generally not practical in terms of time and cost to experimentally characterize the effects of a wide range of design variables. A successful numerical model for impact deformation and failure of polymers can provide convenient and useful guidelines on product design and therefore decrease the disadvantages that arise from purely experimental trial and error. Since the specimen geometry and loading mode for multiaxial impact test provides a close correlation with practical impact conditions and can conveniently provide experimental data, the first step of validating a numerical model is to simulate this type of test. In this paper, we create a finite element analysis model using ABAQUS/Explicit to simulate the deformation and failure of a glassy ABS (acrylonitrile-butadiene-styrene) polymer in the standard ASTM D3763 multiaxial impact test. Since polymers often exhibit different behavior in uniaxial tensile and compression tests, the uniaxial compression or tensile tests are generally not representative of the three-dimensional deformation behavior under impact loading. A hydrostatic pressure effect (controlled by the parameter γ) is used to generalize a previously developed constitutive model ("DSGZ" model) so that it can describe the entire range of deformation behavior of polymers under any monotonic loading modes. The generalized DSGZ model and a failure criterion are incorporated in the FEA model as a user material subroutine. The phenomenon of thermomechanical coupling during plastic deformation is considered in the analysis. Impact load vs. displacement and impact energy vs. displacement curves from FEA simulation are compared with experimental data. The results show good agreement. Finally, equivalent stress, strain, strain rate and temperature distributions in the polymer disk are presented. Electronic Publication     

土与结构接触面土体软/硬化本构模型及数值实现

基于土与结构接触面变形特性分析,将接触面土体的剪切滑动面与单元体三维应力状态下的八面体面相对应,通过土的三维弹塑性本构模型在八面体面上的剪切应力-应变关系,建立了接触面土体剪切应力-应变关系;将接触面土体法向压缩变形与侧限压缩条件相对应,通过侧限压缩条件下的荷载变形关系,建立了接触面土体法向应力-应变关系;进一步将接触面土体切向与法向耦合,建立了接触面土体本构模型,模型只有4个材料参数,参数物理意义明确,可由等向压缩试验和常规三轴压缩试验确定。与接触面土体试验结果的对比分析表明,所建立的本构模型可较好地描述接触面土体切向软/硬化特性与法向变形规律。结合有限元软件ABAQUS,编制了FRIC模型子程序,通过模拟土与结构界面剪切滑移过程表明,编制的FRIC子程序可较好地模拟土与结构界面接触的非线性力学行为。