﻿ 宣纸流变模型的研究
 林业科学  2008, Vol. 44 Issue (10): 113-119 PDF
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#### 文章信息

Gao Hui, Shao Zhuoping

Study on Rheological Model of Xuan Paper

Scientia Silvae Sinicae, 2008, 44(10): 113-119.

### 作者相关文章

Study on Rheological Model of Xuan Paper
Gao Hui, Shao Zhuoping
College of Forestry and Gardening, Anhui Agricultural University Hefei 230036
Abstract: In this paper, the creep and relaxation of Xuan paper during the stretching process were studied. The results indicated that Burgers model could perfectly describe the creep of Xuan paper. Elastic, viscoelastic and plastic strain in the total creep respectively accounted for 62%~78%, 17%~25%, and 4%~13%.At certain temperature and moisture, increased stress increases elastic, viscoelastic and plastic strain in the range of 0.2~0.8σmax. Furthermore, the proportion of viscoelastic and plastic strain increased, while the proportion of elastic strain decreased. Theeffects of stress on the final proportion of strain decreased. Under the same tensile stress, creep of cross direction was less than that of longitudinal direction in the same paper. A five_element Maxwell model was effective to describe relaxation of Xuan paper. The parameters of five_element Maxwell model were slightly affacted by strain levels. So, these parameters could be regarded as constants.
Key words: Xuan paper    creep    relaxation    rheological model

1 材料与方法 1.1 原料与试样制备

1.2 试验方法 1.2.1 试验设备

1.2.2 试验原理

1) 宣纸的蠕变  采用伯格斯(Burgers)四元件模型描述纸张的蠕变行为。伯格斯模型实质上是一个麦克斯韦模型和一个开尔文模型串联，如图 1。设麦克斯韦模型和开尔文模型的伸长分别为ε1ε2，它们的和就是伯格斯模型的伸长ε。由于串联，三者的总拉力都是σ。解为：

 图 1 Burgers模型 Figure 1 Burgers model
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 图 2 蠕变-回复曲线 Figure 2 Curve of creep and reverting
 图 3 蠕变-回复曲线中应力和应变的关系 Figure 3 Relation of stress and strain in creep and reverting curve
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 (3)

 (4)
 (5)
 (6)

2) 宣纸的松弛  用带平衡常数的2阶5参数Maxwell流变模型进行拟合(图 4)。其数学模型为：

 图 4 五元件Maxwell流变模型 Figure 4 Five-element Maxwell model
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2 结果与分析 2.1 宣纸蠕变数学模型

 图 5 不同应力水平实测蠕变曲线和计算拟合曲线的比较 Figure 5 Comparison of experimental creep curves with calculation fitting curves under different stress levels 1.σ0＝2.7464 MPa；2.σ0＝4.100 8 MPa；3.σ0＝5.492 9MPa；4.σ0＝6.847 3 MPa；5.σ0＝8.201 7 MPa；6.σ0＝9.593 7 MPa；7.σ0＝10.948 1 MPa.

σ＝0.2σmax=2.746 4 MPa时，ε%=0.269 5+8.392 0×10-6t+0.062 1(1-e-5.542 3×10-3t)，R2=0.991 0；

σ＝0.3σmax=4.100 8 MPa时，ε%=0.350 0+1.894 5×10-5t+0.088 7(1-e-5.303 6×10-3t)，R2=0.964 8；

σ＝0.4σmax=5.492 9 MPa时，ε%=0.411 2+2.867 6×10-5t+0.104 7(1-e-3.598 9×10-3t)，R2=0.990 5；

σ＝0.5σmax=6.847 3 MPa时，ε%=0.498 5+4.654 8×10-5t+0.150 7(1-e-3.566 3×10-3t)，R2=0.9917；

σ＝0.6σmax=8.201 7 MPa时，ε%=0.566 1+6.204 2×10-5t+0.220 0(1-e-2.938 5×10-3t)，R2=0.965 2；

σ＝0.7σmax=9.593 7 MPa时，ε%=0.641 5+6.517 6×10-5t+0.248 7(1-e-3.146 7×10-3t)，R2=0.991 0；

σ＝0.8σmax=10.948 1 MPa时，ε%=0.696 3+7.421 8×10-5t+0.275 9(1-e-2.546 2×10-3t)，R2=0.981 1。

 图 6 弹性应变与应力水平的关系 Figure 6 Relationship between elastic strain and stress level

 图 7 黏弹性应变与应力水平的关系 Figure 7 Relationship between viscoelastic strain and stress level

 图 8 塑性应变与应力水平的关系 Figure 8 Relationship between plastic strain and stress level
 图 9 应变分量与应力水平的关系 Figure 9 Relationship between strain ratio and stress level

2.2 宣纸纵向和横向蠕变比较

 图 10 宣纸纵向和横向蠕变比较 Figure 10 Creep comparison between long direction and cross direction of Xuan paper
2.3 宣纸松弛数学模型

 图 11 应变水平对应力松弛的影响 Figure 11 Effect of strain levels on stress relaxation curves

ε＝1.0%时，σ＝3.474 9+1.297 8e-0.046 t+ 0.718 4e-0.001 18tR2=0.986 2；

ε＝1.5%时，σ＝4.690 6+1.728 4e-0.04 t+ 1.063 0e-0.001 13 tR2=0.993 1；

ε＝2.0%时，σ＝5.673 3+2.471 4e-0.033 6 t+ 1.200 5e-0.001 07 tR2=0.989 3；

ε＝2.5%时，σ＝5.993 6+2.529 6e-0.037 7 t+1.198 1 e-0.001 42 tR2=0.991 1。

3 结论

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