Rheology of Peeling
Rheology of Peeling
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剥离流变学
DOI：
10.2472/jsms.13.341
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
T. Hata
中科院分区：
文献类型：
--
作者：
T. Hata
本文从流变学的角度讨论了剥离强度与剥离速率的关系。首先从实验上证明了时间-温度叠加原理适用于不同增塑剂含量的无定形聚合物薄膜(乙烯基)在玻璃化转变温度(Tg)以上的剥离强度与速率的S曲线。Tg随温度的变化符合W.L.F.方程，其参考温度Ts远低于Tg+50°，其中Tg是用膨胀计量法测量的。这意味着在Tg的分数自由体积大于0.025，在我们的例子中显示为0.037。这一差异可用Ferry和Stratton关于泊松比小于1/2的聚合物伸展导致自由体积分数增加的理论来解释。由温度下的对数变化关系得到的表观活化能，对于增塑剂含量为0-40%的样品，表观活化能为46.5-33kcal/mol，这对于聚合物链段的粘性流动是合理的。根据这些实验结果，我们得出结论：剥离强度与剥离速率的关系本质上是流变性的，剥离过程不受Deryagin等人提出的静电机制的支配。其次，我们推导了胶带剥离强度与剥离速率的理论公式，假设胶粘层只在剥离端局部变形，其流变行为可用简单的Voigt模型描述。为简单起见，还假定剥离端的弯曲形状被视为半径为R的圆的一部分，剥离力P由剥离力P确定为R=√EoI/P，并且变形垂直于粘着表面。如果剥离以速度v稳定地进行，我们可以用两个圆心在(O，R)和(Vt，R)处的圆来表示剥离的初始阶段和随后的时间t。然后给出粘合层在原点的伸长率y是v、R和t的函数，以及它的时间导数dy/dt是v、R和y的函数。将它引入Voigt方程并积分方程dw=fdy from f=0到f=fB，其中fB表示临界表面力，我们得到了粘合断裂时的变形功Wd。在变形的工作中，我们必须保留弹性能量。设WD‘=WD-WE，则Wa、粘着功和Wd’之和等于作用力所做的功，即Wa+Wd‘=P(1-cosθ)，其中θ是剥离角度。经过必要的计算和一些合理的近似，我们得到了在L剥离(θ=π/2)的情况下，P-C1P1/4v+C2P1/2v2=Wa，C1=2√2h1/2/3(EoI)1/4·(Fb/E)3/2η，C2=2/(EoI)1/2(η/E)2Fb，其中Eo是决定剥离端曲率的聚合物膜的杨氏模数，i，其转动惯量，h，胶层厚度，η和E，粘滞系数和杨氏模数。该方程很好地描述了对数压力随时间变化的S曲线。
The dependence of the peeling strength on the peeling rate is treated in this paper rheologically. First we showed experimentally that the time-temperature superposition principle is applicable to the S-type curve of the peeling strength vs, the rate for the amorphous polymer films (Vinylite) of various plasticizer (DBP) contents above glass transition temperature (Tg). The dependence of the shift factor aT on the temperature obeyed the W. L. F. equation giving reference temperature Ts considerably lower than Tg+50°, where Tg is measured dilatometrically. This means that the fractional free volume at Tg is larger than 0.025, in our case showing 0.037. This discrepancy is explained by the theory of Ferry and Stratton on the increase of fractional free volume due to the extension of polymers of Poisson's ratio less than 1/2. The apparent activation energy at Ts evaluated from the dependence of log aT on temperature, are 46.5-33kcal/mol for samples of plasticizer contents 0-40%, which are reasonable values for the viscous flow of the polymer segments. From these experimental results we conclude that the dependence of the peeling strength on the rate is substantially rheological in character, and that the course of peeling is not governed by the electrostatic mechanism as proposed by Deryagin et al.Secondly, we derived a theoretical formula relating to the peeling strength to the rate of peeling in adhesive tapes, assuming that the adhesive layer is deformed locally only at the peeling end, and its rhelogical behavior is described by the simple Voigt model. It is also assumed for simplicity that the shape of the bend at the peeling end is regarded as a part of a circle of radius R, which is determined by the peeling force P as R=√EoI/P, and that the deformation is vertical to the adherend surface. If the peeling proceeds steadily with velocity v, we may represent the initial and proceeding stage after time t of peeling with two circles whose centers are at (O, R) and (vt, R). Then the elongation of the adhesive layer at the origin, y, is given as a function of v, R, and t, with its time derivative, dy/dt, as a function of v, R, and y. Introducing this into Voigt's equation and integrating the equation dW=fdy from f=0 to f=fb where fb means the critical surface force, we obtain work of deformation, Wd, at the adhesion break. In the work of deformation, elastic energy We must be reserved. Put Wd'=Wd-We, then the sum of Wa, work of adhesion, and Wd' equals to the work done by the applied force, that is Wa+Wd'=P(1-cosθ), where θ is peeling angle. Carrying necessary calculation with some reasonable approximations, we obtain the following equation in the case of L-peeling (θ=π/2), P-C1P1/4v+C2P1/2v2=Wa, C1=2√2h1/2/3(EoI)1/4·(fb/E)3/2η, C2=2/(EoI)1/2(η/E)2fb, where Eo is Young's modulus of polymer film which determines the curvature at the peeling end, I, its moment of inertia, h, the thickness of the adhesive layer, η and E, viscosity coefficient and Young's modulus of the adhesive. This equation represents well the S-type curve of logP vs.