反复低速冲击下短纤复材的损伤研究
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摘要
本文首先以随机分布短玻纤增强不饱和聚酯树脂为材料，利
用MTS试验机模拟低速冲击加载，研究了单调低速冲击和反复
低速冲击条件下、短纤维复合材料的力学行为和损伤特征。接着，
以实验数据为依据，借助于粘弹性力学、短纤复材细观力学和
Eshelby等效包容体理论，导出了E~m_0、／E~f>>(d_f/lf)~2时、随机分布短
纤维的增强系数表达式(见式(3.2-17、14、22))；建立了适用于小
应变、准静态和低速冲击加载的、随机分布短纤维复合材料一维
率相关本构方程(见式(3．3-3))。进一步，作者运用经典热力学、
连续介质热力学和Prigogine耗散结构理论，证明了适用于任何
耗能过程的最小耗能原理；导出了连续介质热力学系统在时间为
t的一个不可逆过程中，总耗散能的普遍表达式（见式 （4．2-11））；
分析了反复冲击载荷下，复材的热力学耗能过程。利用本文建立
的短纤复材一维率相关本构方程和最小耗能原理，作者又推导出
了单轴反复低速冲击条件下、随机分布短纤复材耗散能的计算公
式（式4．3-5））、损伤变量表达式（式（4．3-13））和损伤演变方程（式
4．3-14））。最后，根据实验得到的割线模量下降规律和本文导出
的损伤演变方程，作者给出了单轴反复低速冲击加载下、随机分
布短纤维复合材料的寿命预报公式（见式（5．2-4））；并结合实验数
据，介绍了具体寿命预报办法，讨论了寿命预报结果。
In the beginning of this papef, random short-glass-fibre
reinforced Unsaturated Polyester Resin was used to study the
mechanical behavior and damage character of short-fibre composites
under unidirectional low velocity impact and repeated low velocity
impact, by means of Material Test System (MTS) to simulate low
velocity impact loading. Next, according to experimenta1 data and
with the help of Mechanics of Viscoelasticity Micromechanics of
short-fibre composites and Theory of Eshelby Equivalent Inclusion,
the reinforcement coefficient formula (shown as formula (3.2-l7、
l4、22)) of random short-fibre was deduced when E~m0_0/E~f>>(d_f/l_f)~2;
one-dimensional rate-dependence constitutive equation (shown as
formula (3.3-3)) of random short-fibre composites adapting to small
strain, quasi-static and low velocity impact loading was built up.
Subsequently, Classical Thermodynamics, Continuum
Thermodynamics and Theory of Prigogine dissipation structure were
used to verify the principle of least energy consumption adaPting to
any course of energy consumption; to deduce the general formula of
tota1 dissipation energy (shown as formula (4.2-ll)) of continuum
thermodynamics system in a irreversible process with the time of t; to
analyze the thermodynamics energy consumption process of
composites under repeated impact loading. Using the one-
dimensional rate-dependence constitutive equation of short-fibre
composites and principle of least energy consumption built up in this
paper, calculation formula of dissipation energy (formula (4.3-5)),
fOrmula of damage variable (fOrmula (4.3--l3)) and evolutionary
' equation of damage (formula (4.3--l4)) of random short-fibre
composites were deduced under uniaxial repeated 1ow velocity impact.
Finally, according to secant-module declining law obtained from
experiment and the evolutionary equation of damage deduced in this
paper, life prediction fOrmula (shown as fOrmula (5.2--4)) of random
short-fibre comPosites under uniaxial repeated low velocity imPact
loading was given; using experimentaI data, detail life prediction
method was introduced and the life prediction result was discussed.
用MTS试验机模拟低速冲击加载，研究了单调低速冲击和反复
低速冲击条件下、短纤维复合材料的力学行为和损伤特征。接着，
以实验数据为依据，借助于粘弹性力学、短纤复材细观力学和
Eshelby等效包容体理论，导出了E~m_0、／E~f>>(d_f/lf)~2时、随机分布短
纤维的增强系数表达式(见式(3.2-17、14、22))；建立了适用于小
应变、准静态和低速冲击加载的、随机分布短纤维复合材料一维
率相关本构方程(见式(3．3-3))。进一步，作者运用经典热力学、
连续介质热力学和Prigogine耗散结构理论，证明了适用于任何
耗能过程的最小耗能原理；导出了连续介质热力学系统在时间为
t的一个不可逆过程中，总耗散能的普遍表达式（见式 （4．2-11））；
分析了反复冲击载荷下，复材的热力学耗能过程。利用本文建立
的短纤复材一维率相关本构方程和最小耗能原理，作者又推导出
了单轴反复低速冲击条件下、随机分布短纤复材耗散能的计算公
式（式4．3-5））、损伤变量表达式（式（4．3-13））和损伤演变方程（式
4．3-14））。最后，根据实验得到的割线模量下降规律和本文导出
的损伤演变方程，作者给出了单轴反复低速冲击加载下、随机分
布短纤维复合材料的寿命预报公式（见式（5．2-4））；并结合实验数
据，介绍了具体寿命预报办法，讨论了寿命预报结果。
In the beginning of this papef, random short-glass-fibre
reinforced Unsaturated Polyester Resin was used to study the
mechanical behavior and damage character of short-fibre composites
under unidirectional low velocity impact and repeated low velocity
impact, by means of Material Test System (MTS) to simulate low
velocity impact loading. Next, according to experimenta1 data and
with the help of Mechanics of Viscoelasticity Micromechanics of
short-fibre composites and Theory of Eshelby Equivalent Inclusion,
the reinforcement coefficient formula (shown as formula (3.2-l7、
l4、22)) of random short-fibre was deduced when E~m0_0/E~f>>(d_f/l_f)~2;
one-dimensional rate-dependence constitutive equation (shown as
formula (3.3-3)) of random short-fibre composites adapting to small
strain, quasi-static and low velocity impact loading was built up.
Subsequently, Classical Thermodynamics, Continuum
Thermodynamics and Theory of Prigogine dissipation structure were
used to verify the principle of least energy consumption adaPting to
any course of energy consumption; to deduce the general formula of
tota1 dissipation energy (shown as formula (4.2-ll)) of continuum
thermodynamics system in a irreversible process with the time of t; to
analyze the thermodynamics energy consumption process of
composites under repeated impact loading. Using the one-
dimensional rate-dependence constitutive equation of short-fibre
composites and principle of least energy consumption built up in this
paper, calculation formula of dissipation energy (formula (4.3-5)),
fOrmula of damage variable (fOrmula (4.3--l3)) and evolutionary
' equation of damage (formula (4.3--l4)) of random short-fibre
composites were deduced under uniaxial repeated 1ow velocity impact.
Finally, according to secant-module declining law obtained from
experiment and the evolutionary equation of damage deduced in this
paper, life prediction fOrmula (shown as fOrmula (5.2--4)) of random
short-fibre comPosites under uniaxial repeated low velocity imPact
loading was given; using experimentaI data, detail life prediction
method was introduced and the life prediction result was discussed.
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