预浸织物细观变形机理及本构关系研究
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摘要
空间充气展开结构作为一种新型的航天工程结构,由于其质量轻、折叠后体积小、展开可靠性高等优点,使空间充气展开结构成为未来航天工程构建大型空间结构的有效途径。预浸织物是空间充气展开结构的关键结构材料。由于预浸织物材料中包含未固化的树脂,因此其变形特性与机理既不同于纯织物材料,也不同于传统的复合材料——固化后的织物复合材料。用来描述纯织物材料和固化后的织物复合材料的本构方程不能适用于预浸织物材料,那么就需要根据本构原理来建立预浸织物的本构方程。预浸织物由织物和未固化的树脂组成,因此在研究中应同时考虑固体增强相与流体的作用,这是一个新的力学问题,对复合材料力学起到扩展的作用。对预浸织物本构方程的研究为空间充气展开结构的结构设计以及静力学、动力学和热分析等研究提供了理论基础。
本文研究预浸织物的剪切变形。通过像框剪切试验来测定预浸织物的剪切性能。由于预浸织物是粘弹性材料,变形与时间有关,因此本文进行了不同加载速率的试验。通过对试验曲线的分析进一步验证了预浸织物在发生剪切变形时具有明显的非线性和阶段性的规律。
通过对预浸织物各个组分材料之间的相互作用及变形机理的分析,本文将预浸织物的剪切变形分为剪切锁定前和剪切锁定后两个阶段,并且分别建立了不同阶段的各组分材料的细观分析模型。在剪切锁定前阶段,建立树脂的阻尼计算模型,经、纬向纤维束在交叉处的摩擦的计算模型。随着剪切的继续进行,树脂被不断的从纤维束的孔隙中挤压出去,直至纤维束之间相互接触。进入剪切锁定后阶段,建立纤维束的挤压力矩模型,通过这些计算模型建立了剪切锁定前和剪切锁定后的力矩平衡方程,通过对力矩平衡方程的计算得到了理论分析曲线,最后通过试验曲线对理论分析结果进行验证。结果表明,理论分析曲线与试验曲线吻合的较好。
从热力学第二定律出发,根据预浸织物的性质设定Helmholtz自由能函数由5个变量表示,根据不变量理论推导出由这5个变量组成的能够反映预浸织物的粘弹特性的不变量。依据本构方程的基本原理通过这些不变量建立了预浸织物材料的宏观本构方程。此本构方程既描述了经、纬向纤维束的单独作用,又描述了纤维束之间的耦合作用,较好地反映了预浸织物的非线性的粘弹性的性质。最后,通过不同加载速率的像框剪切试验结果对本构方程的理论计算结果进行验证,本构方程理论结果与试验结果符合较好。
The space inflatable structure is a novel structure applied in space engineering. Because of the light mass, small folded volume and high deployment reliability and so on, it becomes a valid path for building large space structure in future space engineering. Pre-impregnated fabric is the key material used in the space inflatable structure. However, because the resin of the pre-impregnated fabric is uncured, its deformation character and mechanism differ from the pure fabric material and the cured fabric composite. Consequently, the constitutive equations of pure fabric and the cured fabric composite can not be applicable to pre-impregnated fabric. Therefore, a constitutive equation is needed to be established according to the constitutive principle. The pre-impregnated fabric is made of fabric and uncured resin. As a result, the strengthened solid and fluid should be concerned in the research. This is a new mechanical problem. It extends composite material mechanics. Investigations on the constitutive equation of pre-impregnated fabric will provide the theories for designing and the statics, dynamics and thermal analysis research of the space inflatable structure.
Shear finite deformation is the sole concern of this paper. Picture frame experiment is adopted to test the shear properties of fabric materials. Because pre-impregnated fabric is the viscoelastic material, of which deformation is associated with time, the present paper carries on the different displacement rate experiments. Obviously, nonlinearity and phases when pre-impregnated fabric is deformed can be further verified through experiment curve, which provides the basis for the establishment of the mesoscopic analytical model and the constitutive equation of the pre-impregnated fabric.
Through analysis of every constituent mutual interacting and deformation mechanism of the pre-impregnated fabric, the shear deformation is divided by shear and compaction phases and some analytical models are built according to different phases. These models are the resin damping function and the crossover friction of the warp and weft tows in the shearing phase. Along with shearing, resin will be driven from the inter-tow region and the tows are interacted. In the compaction phase, a lateral compaction shear resistance moment is occurred. A balanced equation is built through these analytical models and a theoretical curve is obtained. The picture frame experiment curve is used to verify the theoretical curve and the two curves are well coincided.
According to the properties of pre-impregnated fabric, Helmholtz free energy function is indicated by 5 variables from the second law of thermodynamics. On the principle of invariables, several invariants have been deduced which can describe the viscoelastic properties of pre-impregnated fabric. In response to basic theory of constitutive equation, a constitutive equation is obtained. This constitutive equation can objectively describe the viscoelastic properties of pre-impregnated fabric. At last, different displacement rates of picture frame experiments are used to verify the constitutive equation and the two curves are well coincided.
本文研究预浸织物的剪切变形。通过像框剪切试验来测定预浸织物的剪切性能。由于预浸织物是粘弹性材料,变形与时间有关,因此本文进行了不同加载速率的试验。通过对试验曲线的分析进一步验证了预浸织物在发生剪切变形时具有明显的非线性和阶段性的规律。
通过对预浸织物各个组分材料之间的相互作用及变形机理的分析,本文将预浸织物的剪切变形分为剪切锁定前和剪切锁定后两个阶段,并且分别建立了不同阶段的各组分材料的细观分析模型。在剪切锁定前阶段,建立树脂的阻尼计算模型,经、纬向纤维束在交叉处的摩擦的计算模型。随着剪切的继续进行,树脂被不断的从纤维束的孔隙中挤压出去,直至纤维束之间相互接触。进入剪切锁定后阶段,建立纤维束的挤压力矩模型,通过这些计算模型建立了剪切锁定前和剪切锁定后的力矩平衡方程,通过对力矩平衡方程的计算得到了理论分析曲线,最后通过试验曲线对理论分析结果进行验证。结果表明,理论分析曲线与试验曲线吻合的较好。
从热力学第二定律出发,根据预浸织物的性质设定Helmholtz自由能函数由5个变量表示,根据不变量理论推导出由这5个变量组成的能够反映预浸织物的粘弹特性的不变量。依据本构方程的基本原理通过这些不变量建立了预浸织物材料的宏观本构方程。此本构方程既描述了经、纬向纤维束的单独作用,又描述了纤维束之间的耦合作用,较好地反映了预浸织物的非线性的粘弹性的性质。最后,通过不同加载速率的像框剪切试验结果对本构方程的理论计算结果进行验证,本构方程理论结果与试验结果符合较好。
The space inflatable structure is a novel structure applied in space engineering. Because of the light mass, small folded volume and high deployment reliability and so on, it becomes a valid path for building large space structure in future space engineering. Pre-impregnated fabric is the key material used in the space inflatable structure. However, because the resin of the pre-impregnated fabric is uncured, its deformation character and mechanism differ from the pure fabric material and the cured fabric composite. Consequently, the constitutive equations of pure fabric and the cured fabric composite can not be applicable to pre-impregnated fabric. Therefore, a constitutive equation is needed to be established according to the constitutive principle. The pre-impregnated fabric is made of fabric and uncured resin. As a result, the strengthened solid and fluid should be concerned in the research. This is a new mechanical problem. It extends composite material mechanics. Investigations on the constitutive equation of pre-impregnated fabric will provide the theories for designing and the statics, dynamics and thermal analysis research of the space inflatable structure.
Shear finite deformation is the sole concern of this paper. Picture frame experiment is adopted to test the shear properties of fabric materials. Because pre-impregnated fabric is the viscoelastic material, of which deformation is associated with time, the present paper carries on the different displacement rate experiments. Obviously, nonlinearity and phases when pre-impregnated fabric is deformed can be further verified through experiment curve, which provides the basis for the establishment of the mesoscopic analytical model and the constitutive equation of the pre-impregnated fabric.
Through analysis of every constituent mutual interacting and deformation mechanism of the pre-impregnated fabric, the shear deformation is divided by shear and compaction phases and some analytical models are built according to different phases. These models are the resin damping function and the crossover friction of the warp and weft tows in the shearing phase. Along with shearing, resin will be driven from the inter-tow region and the tows are interacted. In the compaction phase, a lateral compaction shear resistance moment is occurred. A balanced equation is built through these analytical models and a theoretical curve is obtained. The picture frame experiment curve is used to verify the theoretical curve and the two curves are well coincided.
According to the properties of pre-impregnated fabric, Helmholtz free energy function is indicated by 5 variables from the second law of thermodynamics. On the principle of invariables, several invariants have been deduced which can describe the viscoelastic properties of pre-impregnated fabric. In response to basic theory of constitutive equation, a constitutive equation is obtained. This constitutive equation can objectively describe the viscoelastic properties of pre-impregnated fabric. At last, different displacement rates of picture frame experiments are used to verify the constitutive equation and the two curves are well coincided.
引文
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