Study on mechanical properties and damage characteristics of booster explosives under static compression
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摘要: 为研究聚黑-14C（JH-14C）传爆药静态压缩力学性能及损伤特性，开展准静态压缩实验，获得了不同应变率下的应力-应变曲线，建立了描述不同应变率下JH-14C力学行为的非线性本构模型；利用扫描电镜（SEM）对回收试样进行细微形貌观测，获得了准静态压缩JH-14C损伤特性的表征。结果表明：JH-14C压缩强度随应变率的升高而提高；实验与计算结果对照验证了本构模型的有效性；准静态压缩实验中，JH-14C主要损伤模式为脱湿和穿晶断裂。Abstract: In order to study the static compression mechanical properties and damage characteristics of the JH-14C booster explosive, quasi-static compressive experiments were performed on a testing machine equipped with an environmental chamber (INSTRON). According to the GJB 770B–2005 powder test method, dimensions of the cylindrical specimen were set as
∅ 12.5 mm×12.5 mm in the static compressive experiments. During compression, only one extensometer was used. All experiments were performed at a crosshead speed of 0.012 5, 0.062 5, 0.125, 0.625 and 1.25 mm/s at room temperature (25 °C), which led to a nominal strain rate of 0.001, 0.005, 0.01, 0.05 and 0.1 s−1, respectively. The average stress-strain values and standard deviations were calculated using five replicable experiments for each condition. The experimental results were compared with X0242 and PBX-9501, and the mechanical properties of JH-14C were analyzed. According to the mechanical properties of JH-14C at low strain rates, the original Ramberg-Osgood constitutive relationship was modified, and a nonlinear constitutive model including the strain rate term was established to describe the mechanical behavior of JH-14C at low strain rates. The micro morphologies of the recovered samples was observed by a scanning electron microscope (SEM) and compared with that of PBX-9501. The damage mode was analyzed to characterize the damage characteristics of JH-14C under quasi-static compression. The results show that the compressive strength of JH-14C increases with the increase of strain rate. The validity of the constitutive model was verified by comparing the experimental and calculated results. In the quasi-static compression experiments, the energetic particles and the binder were debonded. With the increase of the pressure, the original crack and the micro-crack formed by debonding on the energetic particles were converged and coalesced to form a macro crack, which led to the rupture and failure of the explosive.-
Key words:
- JH-14C /
- booster explosive /
- quasi-static /
- strain rate /
- constitutive model /
- damage mode
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开孔泡沫铝具有三维连通的孔结构, 通过向其孔洞中填入泡沫聚氨酯等黏弹性高分子材料, 能够起到良好的缓冲、吸能和减震作用。利用聚氨酯泡沫铝复合材料的抗冲击性能和吸能特性, 可以有效地提高抵抗爆炸等冲击作用所产生的危害, 对制造抗冲击防护材料具有重要意义。然而, 要成为性能优异的冲击吸能材料[1-7], 需要知道泡沫聚氨酯材料在填充到泡沫铝孔隙中后其压缩变形行为和吸能性。
在泡沫铝材料和聚氨酯材料的实验研究方面, V.S.Deshpande等[8]通过实验得出泡沫铝的力学性能与应变率无关的结论; K.A.Dannemann等[9]采用常规分离式霍普金森压杆技术实验, 发现闭孔Alporas泡沫铝具有明显的应变率效应; 王永刚等[10]利用改进了的SHPB技术对泡沫铝进行了高应变率下的动态压缩实验, 王志华等[11]利用SHPB实验技术和MTS材料试验机对开孔泡沫铝进行了准静态和动态压缩实验研究, 卢子兴等[12]对高密度硬质聚氨酯泡沫塑料的拉伸力学性能进行了研究。在本构模型的研究中, 主要成果有可用于金属大变形、高应变率和高温情况下的本构模型----Johnson-Cook模型[13], J.A.Sherwood等[14]提出了考虑环境温度和相对密度及应变率等因素的经验型本构关系等, A.G.Hanssen等[15]提出了泡沫铝在单轴受压或静水压力下的应变强化模型, 胡玲玲等[16]提出了泡沫铝材料的一维黏塑性本构模型。以上研究成果主要是对泡沫金属和聚氨酯材料单独进行的。本文中对聚氨酯泡沫铝复合材料的动态力学性能进行较系统的实验研究, 并通过考虑聚氨酯填充量对复合材料动力学性能的影响, 提出适用于该复合材料的本构模型。
1. 聚氨酯泡沫铝复合材料制备
采用高压渗流法制造开孔泡沫铝板材, 并通过线切割将板材加工成直径74.00 mm的48个圆柱形薄试件待用; 聚氨酯由白料(包括聚醚三元醇、发泡剂、催化剂、泡沫稳定剂等)和黑料(甲苯二异氰酸酯:PM200)按其先后顺序进行1:1的质量比例混合(所得泡沫聚氨酯的密度约为0.3 g/cm3)以后, 迅速将其倒入装有泡沫铝试件的密闭容器(将废旧塑料瓶进行改装后作为反应容器)中加压发泡(加压方法采用活塞手动加压), 使发泡产生的聚氨酯泡沫能尽可能多地填充到泡沫铝试件的孔隙之中。
经过打磨以后就得到聚氨酯泡沫铝的48个复合试件。经过40 ℃恒温固化和自然风干后, 再称其质量, 通过泡沫铝的质量增量来确定聚氨酯的填充量。为便于分析, 将所有试件按相对密度的升序变化排列。制备的48个试件分成4组, 每组12个试件。
2. 动态冲击实验
动态荷载利用直径74 mm的直锥变截面大直径SHPB装置施加冲击荷载, 由于应变率只与子弹速度相关, 而弹速取决于气压, 因此设计了由0.3、0.4、0.6 MPa 3种气压大致得到的1 000、1 600、1 900 s-1等3种应变率。图 1是聚氨酯泡沫铝试件在应变率为1 900 s-1下冲击前后的形状对比。
图 1 聚氨酯泡沫铝试件在应变率1 900 s-1下冲击前后的形状对比Figure 1. Shape contrast of polyurethane foam aluminum test-pieces before and after impact at strain rate of 1 900 s-1图 2给出了聚氨酯泡沫铝在应变率为1 000、1 600、1 900 s-1等3种应变率下动态压缩时的应力应变曲线。从图 2(a)中可以看到, 低应变率的聚氨酯泡沫铝基本上只表现出了2个变形阶段的特征, 即弹性段和应力上升的塑性段, 没有出现明显的密实段, 这是由于撞击杆的速度较低, 撞击能量不足以将聚氨酯泡沫铝压实, 所以压缩曲线不完整。
图 2 不同应变率下聚氨酯泡沫铝试件的应力应变曲线Figure 2. Stress-strain curves of polyurethane foam aluminum test-pieces at different strain rate应变率相对较高的图 2(b)~(c)中的应力应变曲线却表现出了线弹性段、应力上升的塑性段和密实段3个变形阶段的特征, 同种应变率下线弹性阶段基本都是重合的, 说明复合材料的动态弹性模量与相对密度无关; 聚氨酯泡沫铝的塑性段曲线有所抖动, 而且随着相对密度和应变率的上升波动减弱, 这说明抖动除了泡沫铝的非线性行为以外, 还有聚氨酯的影响因素; 另外由图 2可以看出, 聚氨酯泡沫铝的屈服强度和流变应力随应变率的增加而提高。
由图 3可知, 泡沫聚氨酯质量的增加量与屈服强度的提高呈近似线性关系。
3. 聚氨酯泡沫铝动态本构模型的建立
文献[14]在建立聚氨酯泡沫本构关系时将环境温度和相对密度及应变率等因素考虑进去, 提出了经验型本构关系:
σ=H(T)G(ρ)M(ε,˙ε)f(ε) (1) 式(1)中环境温度T与相对密度ρ对应力的影响是单一的, 与应变ε、应变率
基本上无关; 而M(ε, ˙ε)则主要反映了应变率对应力的影响, 形状函数f(ε)定义为在某一参考相对密度、参考温度、准静态加载下的应力、应变的曲线函数。
胡时胜等[17]对本构关系(1)进行了修正, 在修正的本构关系中不包含温度, 关于应变率对应力的影响则采用基于热激活机制的Seeger模型, 得到拟合的本构关系:
σ=[ρρ0]AεB(ρρ0−1)[1+Clg˙ε˙ε0]6∑i=1Aiεi (2) 式中:
为选定的一种参考应变率, C为拟合参数。
图 4是聚氨酯质量分数与屈服强度的关系曲线图。根据图 4, 本构关系的影响可近似取线性关系表示为:
图 4 屈服强度与聚氨酯质量分数的数据拟合Figure 4. Data fitting of yield intensity vs mass of polyurethaneP(m)=Hm+k 式中:m为聚氨酯含量, H、k为常数。
由本文实验数据进行分析可知, 相对密度对应力的影响近似为线性关系, 与本构关系(1)结论一致, 可表示为:
G(ρ)=J(ρ−ρ0)+1 式中:J为常数。
关于应变率对应力的影响仍采用本构关系(2)中的关系。最终可得拟合的本构方程为:
σ=P(m)G(ρ)M(ε,˙ε)f(ε)=(Hm+k)[J(ρ−ρ0)+1](1+Clg˙ε˙ε0)n∑i=1Eiεi (3) 由图 4拟合直线可得:P(m)=63.2m+13.723。相关系数R1=0.929 96, 拟合效果很好。
当
时, 动态应力应变曲线便可确定形状函数
的形式。显然, 函数表达式中的参数越多, 拟合效果会越好, 但相应地也增加了计算的难度和复杂性, 本文中选取n=4时的函数。
利用形状函数
令
利用试件7、25、39、48的应力应变曲线进行二次拟合曲线得:
y=−18860x4+21117x3−6818.4x2+913.79x 由相关系数R2=0.962 9可知, 其拟合性比较好。
当
时, 由实验数据拟合得到C=1.05;
当
时, 可拟合得到J=22.34;
则得聚氨酯泡沫铝的本构方程为:
σ=P(m)G(ρ)M(ε,˙ε)f(ε)=(63.2m+13.723)[22.34×(ρ−0.293)+1](1+1.05lg˙ε1900)×(−18860ε4+21117ε3−6818.4ε2+913.79ε) (4) 下面分析聚氨酯含量、应变率和相对密度不同时对拟合的本构模型应力应变曲线的影响并与实验数据对比。
由图 5可知, 聚氨酯泡沫铝的本构模型(4)在相对密度为0.274~0.293之间, 应变率在1 000~1 900 s-1之间, 其拟合结果与实际应力应变曲线吻合较好, 特别是相对密度越接近0.293, 应变率越接近1 900 s-1, 其拟合效果越好。
由图 5(e)可知, 试件36的实验条件都处于相对密度和应变率适用范围的下限, 所以拟合效果就比较差, 但是在线弹性阶段和进入塑性阶段初期, 其拟合效果比较好, 塑性阶段进入密实阶段, 拟合效果开始变差。
4. 结论
通过对聚氨酯泡沫铝冲击实验和动态本构模型的分析, 可以得到以下结论:
(1) 聚氨酯泡沫铝的动态弹性模量与相对密度无关。
(2) 屈服强度和流变应力与应变率和泡沫铝的相对密度成正比。
(3) 拟合的本构模型在相对密度为0.274~0.293之间, 应变率在1 000~1 900 s-1之间, 拟合结果与实际应力应变曲线吻合较好, 特别是相对密度越接近0.293, 应变率越接近1 900 s-1, 拟合效果越好; 实验条件都处于相对密度和应变率适用范围的下限时, 拟合效果开始变差, 说明本构方程的使用有一定的局限性。
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图 2 应力-应变关系和试件变形过程
Figure 2. Stress-strain relationship and the corresponding specimen deformation process
图 4 理论与实验的准静态压缩应力-应变曲线比较
Figure 4. Comparisons between theory and experiment quasi-static stress-strain curves
图 8 JH-14C试样的径向截面细观形貌
Figure 8. Micrographs of the radial cross-section of the JH-14C specimen
表 1 模型拟合结果的相关系数
Table 1. Correlation coefficients of the model fitting results
˙ε/s−1 R2 0.1 0.990 5 0.05 0.997 5 0.01 0.998 7 0.005 0.992 5 0.001 0.984 2 
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