含气固两相夹杂复合材料宏观本构关系的研究
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摘要
本文以物理发泡新型工艺成型微孔泡沫塑料为工程背景，对含气固两相夹杂复合材料宏观本构关系进行了研究，初步探讨了气泡内压及其在外载作用下内压的变化对单个气泡变形规律和对整个复合材料宏观拉伸性能的影响。
首先，从实验和理论两个方面研究了具有非线性粘弹性特征的聚丙烯材料的本构关系，提出了能够较好的拟合实验曲线的非线性粘弹性本构模型，并运用“对应材料”的概念，将非线性粘弹性问题进行了线性化处理。
其次，运用增量法，分析了无限大非线性粘弹性基体含单个微气泡复合材料的气泡长大规律，得到了显含内压的增量型气泡变形表达式。根据该式较为详细地探讨了气泡内压、内压变化、Poisson比、椭球度等在单向拉伸和一维应变两种加载方式下，对微气泡长大规律的影响。计算表明气泡内压的变化对其变形影响非常微小，以至可以忽略，而Poisson比、椭球度对气泡变形的影响都与加载方式有关。
运用Eshelby等效夹杂理论和Mori-Tanaka平均场概念，研究了含气固两相夹杂复合材料的宏观本构关系，得到了显含初始应力和内压变化的增量型表达式。通过数值计算，分析了初始应力、加载速率、体积份数、内压变化等在不同加载方式下对宏观本构的影响，计算结果表明：无论是单向拉伸条件下还是一维应变条件下，气泡内压都对复合材料的宏观拉伸性能有所削弱，内压越大，削弱的程度也就越高。气泡体积份数对复合材料的比强度的影响与加载方式有关，在单向拉伸时，其比强度基本不随孔洞体积份数变化；在一维应变时，其比强度随气泡体积份数的增加而单调地下降。
最后，本文还对粒子填充流变材料微孔洞成核进行了探讨，运用能量准则，分析了大气压力对界面脱粘局部临界应力的影响，得到了显含大气压力、粒径和界面粘结能等参量的局部临界应力表达式。文中还导出了基体为标准线性固体时的
摘要
临界开裂时刻表达式，在此基础上，讨论了当基体为Maxwell体时粒径、界面粘
结能、应变速率等参量对局部临界开裂时刻的影响。
本文总体上具有如下两个方面特点，一是所研究的复合材料的基体具非线性粘
弹性性质。在以往对复合材料有效性能的研究中，复合材料的基体较多具有线性、
弹塑性、非线性弹性或非线性弹塑性，而有关非线性粘弹性这方面的研究工作较
少见到相关报道。二是考虑了气泡内压对气泡变形和复合材料性能的影响。在以
往的研究中，气泡往往被看作无内压孔洞，因而没有考虑内压的影响。
本文的研究工作，在一定程度上可为低发泡塑料的强韧化设计提供了理论分
析依据。
Microcellular foam plastics made by the new physical foaming technics has developed very quickly and becomes one of the host study regions in recent years. This paper is concerned with the macroscopic constitutive relations of the microcellular foam plastics with considering the internal pressure of bled.
Firstly, a new nonlinear visoelastic constitutive model is proposed which can adequately describes observations in the Polypropylene-unaxial tensile tests. According to the concept of "elastic related material", the nonlinear visoelastic stress-strain relation is linearized.
Secondly, the strain of single air bleb in the infinite matrix is studied under the different loading conditions. With the increment method, a differential expression of the bled strain is derived, in the expression, the bled strain can be expressed by the void pressure and Poisson's ratio of matrix. The numerical results show that the influence of the pressure on the void strain is so small that it can be neglected, and the influences of Poisson's ratio and configuration of the bled are both related to the loading condition.
Thirdly, by means of the Eshelby-Mori-Tanaka method, the macroscopic constitutive relation is derived, and it can be expressed by the-void pressure, void
fraction, the initial stress of matrix and loading rate. Numerical results indicate that, the
strength per unit volume of the matrix doesn't change with the void fraction under the uniaxial loading, but declines with the void fraction under the uniaxial strain loading. The initial stress of the matrix caused by the void pressure reduces the effective tensile performance of composite. The influence of Poisson's ratio of matrix and the rate of loading on overall constitutive relations are also discussed under different loading conditions by the numerical method.
Finally, the effect of atmospheric pressure on the interfacial debonding in
particulate-reinforced rheological materials is studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived, and it can be expressed by interfacial adhesive energy, particle radius and atmospheric pressure. An equation describing critical time of interfacial debonding is formulated.
Compared with other researches, there are two main characteristics in this paper. One is that the matrix of the composite is a nonlinear visoelastic material, the other is the internal pressure of bled is considered when the strain of bled and the macroscopic constitutive relations of composite are analyzed.
The present work may be used to supply some guidelines for the design of Microcellular foam plastics.
首先，从实验和理论两个方面研究了具有非线性粘弹性特征的聚丙烯材料的本构关系，提出了能够较好的拟合实验曲线的非线性粘弹性本构模型，并运用“对应材料”的概念，将非线性粘弹性问题进行了线性化处理。
其次，运用增量法，分析了无限大非线性粘弹性基体含单个微气泡复合材料的气泡长大规律，得到了显含内压的增量型气泡变形表达式。根据该式较为详细地探讨了气泡内压、内压变化、Poisson比、椭球度等在单向拉伸和一维应变两种加载方式下，对微气泡长大规律的影响。计算表明气泡内压的变化对其变形影响非常微小，以至可以忽略，而Poisson比、椭球度对气泡变形的影响都与加载方式有关。
运用Eshelby等效夹杂理论和Mori-Tanaka平均场概念，研究了含气固两相夹杂复合材料的宏观本构关系，得到了显含初始应力和内压变化的增量型表达式。通过数值计算，分析了初始应力、加载速率、体积份数、内压变化等在不同加载方式下对宏观本构的影响，计算结果表明：无论是单向拉伸条件下还是一维应变条件下，气泡内压都对复合材料的宏观拉伸性能有所削弱，内压越大，削弱的程度也就越高。气泡体积份数对复合材料的比强度的影响与加载方式有关，在单向拉伸时，其比强度基本不随孔洞体积份数变化；在一维应变时，其比强度随气泡体积份数的增加而单调地下降。
最后，本文还对粒子填充流变材料微孔洞成核进行了探讨，运用能量准则，分析了大气压力对界面脱粘局部临界应力的影响，得到了显含大气压力、粒径和界面粘结能等参量的局部临界应力表达式。文中还导出了基体为标准线性固体时的
摘要
临界开裂时刻表达式，在此基础上，讨论了当基体为Maxwell体时粒径、界面粘
结能、应变速率等参量对局部临界开裂时刻的影响。
本文总体上具有如下两个方面特点，一是所研究的复合材料的基体具非线性粘
弹性性质。在以往对复合材料有效性能的研究中，复合材料的基体较多具有线性、
弹塑性、非线性弹性或非线性弹塑性，而有关非线性粘弹性这方面的研究工作较
少见到相关报道。二是考虑了气泡内压对气泡变形和复合材料性能的影响。在以
往的研究中，气泡往往被看作无内压孔洞，因而没有考虑内压的影响。
本文的研究工作，在一定程度上可为低发泡塑料的强韧化设计提供了理论分
析依据。
Microcellular foam plastics made by the new physical foaming technics has developed very quickly and becomes one of the host study regions in recent years. This paper is concerned with the macroscopic constitutive relations of the microcellular foam plastics with considering the internal pressure of bled.
Firstly, a new nonlinear visoelastic constitutive model is proposed which can adequately describes observations in the Polypropylene-unaxial tensile tests. According to the concept of "elastic related material", the nonlinear visoelastic stress-strain relation is linearized.
Secondly, the strain of single air bleb in the infinite matrix is studied under the different loading conditions. With the increment method, a differential expression of the bled strain is derived, in the expression, the bled strain can be expressed by the void pressure and Poisson's ratio of matrix. The numerical results show that the influence of the pressure on the void strain is so small that it can be neglected, and the influences of Poisson's ratio and configuration of the bled are both related to the loading condition.
Thirdly, by means of the Eshelby-Mori-Tanaka method, the macroscopic constitutive relation is derived, and it can be expressed by the-void pressure, void
fraction, the initial stress of matrix and loading rate. Numerical results indicate that, the
strength per unit volume of the matrix doesn't change with the void fraction under the uniaxial loading, but declines with the void fraction under the uniaxial strain loading. The initial stress of the matrix caused by the void pressure reduces the effective tensile performance of composite. The influence of Poisson's ratio of matrix and the rate of loading on overall constitutive relations are also discussed under different loading conditions by the numerical method.
Finally, the effect of atmospheric pressure on the interfacial debonding in
particulate-reinforced rheological materials is studied. Based on an energy criterion, a simple formula of local critical stress for interfacial debonding is derived, and it can be expressed by interfacial adhesive energy, particle radius and atmospheric pressure. An equation describing critical time of interfacial debonding is formulated.
Compared with other researches, there are two main characteristics in this paper. One is that the matrix of the composite is a nonlinear visoelastic material, the other is the internal pressure of bled is considered when the strain of bled and the macroscopic constitutive relations of composite are analyzed.
The present work may be used to supply some guidelines for the design of Microcellular foam plastics.
引文
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