弹道明胶老化初级阶段的模型

用流变震荡模式研究了10 wt%浓度的弹道明胶在冷却和等温下的老化行为.对明胶从sol-gel点冷却到某个目标温度的过程,通过不同冷却速率的实验,建了一个弹性模量与温度的线性关系.不同温度下明胶的等温老化实验表明,弹性模量-时间曲线具有相似的形状.依据Normand提出的二级反应动力学模型,引入一个表征明胶老化行为的速率常数,构建了一个预测弹道明胶在老化初级阶段的弹性模量演化的模型.该模型中模量-温度关系在初始和无穷大时是直线,其他模量-温度线是近似直线,并交于sol-gel点.老化速率常数和过冷度之间符合Flory-Weaver方程.对弹性模量和老化时间进行归一化处理,可将不同温度下的老化曲线叠加成一条主曲线.

Modeling the Early-stage Aging Behavior of Ballistic Gelatin

Ballistic gelatin has been adopted as a standard target block for experimental studies on the end effect of bullets and fragments.Therefore,its structural stability,that is,the aging behavior will affect the evaluation results considerably.In this work,the aging behavior of 10 wt％ ballistic gelatin is studied by using the rheological small-strain-oscillatory experiment.For the cooling stage from the melting temperature (the sol-gel point) to a target temperature,the aging mechanism is generally complicated by uneven and unstable temperature field.Since the gelatin specimen is thin,we can neglect the uneven and unstable temperature field and have established a linear dependence of the elastic modulus on the cooling rate via various experimental cooling rates.This is to provide estimations for the initial elastic modulus needed in the later isothermal-aging model.The isothermal-aging behavior shows that the elastic-modulus-time curves of the ballistic gelatin are self-similar in shape for different temperatures.For fixed aging time,it is found that the elastic modulus decreases linearly with the aging temperature and intersects near the sol-gel point of the ballistic gelatin,301 K.Inspired by the second-order reaction kinetics model,proposed by Normand et al.,an aging rate constant,k,is introduced and a model to predict the elastic modulus for the early stage (less than 20 h) of isothermal aging is constructed:G'(t,T) =G'0(T) + G'a(T)kt/(1 + kt).In this model,the modulus-temperature lines are linear at the initial,G'0(T),and the (assumed) infinite aging time,G'∞(T).And these lines intersect around the sol-gel point.The relationship between the aging-rate constant and the degree of undercooling,△T,can be well described by the Flory-Weaver equation.The relative error between the prediction of the second-order reaction kinetics model and the experimental values are less than 10％.In addition,the modulus-temperature curves for various fixed aging time,calculated by the model,indeed show approximately linear behavior.A dimensionless master curve is constructed by normalizing the elastic modulus and the aging time for different aging temperatures.This result indicates that the variation of temperature just changes the time scale factor,that is,it alters the aging-rate constant.The second-order kinetics model developed in this paper provides a pragmatic tool to predict the aging moduli of 10 wt％ gelatin in ballistic experiments.