Research progress on inter-ply slipping in prepreg stacking preforming
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摘要: 层间滑移是预浸料叠层预成型中重要成型机制之一，层间滑移机制的研究可以对起皱和撕裂等缺陷进行有效预测和控制，对提高复合材料的力学性能和使用寿命具有重要的理论意义。目前，层间滑移机制的研究主要通过层间滑移测试和层间滑移模型构建的方式进行，其中最常用的测试方法是通过自主搭建层间滑移装置进行不同预浸料铺层和工艺条件下的性能测试；在模型构建方面，根据层间滑移模型的构成特点，可将模型分为三类：早期混合模型、基于Stribeck理论的唯象模型和经验模型。本文首先对层间滑移装置进行分类综述，剖析了每种类型装置的优缺点，然后详细介绍了层间滑移性能的表征及模型的构建等研究成果，最后对树脂基复合材料成型中的层间滑移发展方向进行了展望。Abstract: Inter-ply slipping is one of the important mechanisms in prepreg stacking preforming, and the research of inter-ply slipping mechanism can effectively predict and control the defects such as wrinkling and tearing, which is of great theoretical significance to improve the mechanical properties and service life of composites. At present, the research on inter-ply slipping mechanism mainly involves inter-ply slipping tests and the construction of inter-ply slipping models. The most commonly used test method is to conduct inter-ply slipping test using the homemade measuring device under different prepreg layups and process conditions. In terms of model construction, according to the characteristics of the inter-ply slipping model, the model can be classified into three categories: early mixed models, phenomenological models based on Stribeck theory and empirical models. In this paper, firstly, the classification of inter-ply slipping devices is reviewed, and the advantages and disadvantages of each type of device are dissected. And then the research results such as the characterization of inter-ply slipping performance and the construction of models are introduced in detail. Finally, the development direction of inter-ply slipping in the resin-matrix composite forming is looked forward to.
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图 2 两种类型pull-through法原理示意图
Figure 2. Schematic diagram of two types of pull-through principle
表 1 不同学者建立的层间滑移装置简介
Table 1. Introduction to inter-ply slipping device established by different scholars
Sholar Experimental principle Heating method Loading method Specificities Murtagh et al.[45](1995) pull-out Heating plate Hydraulic press/Weight Two test methods were used and were among the earlier scholars to conduct pull-out tests. Martin et al.[44](1996) pull-out Heating plate Pneumatic cylinder Use locating pins to lock the platens together to prevent misalignment. Lebrun et al.[47](2004) pull-out Cartridge heaters Springs It is possible to perform prepreg-prepreg and tool-prepreg slip experiments. Ersoy et al.[46](2005) pull-out Heating plate Springs A rubber mat is used under the prepreg to ensure even pressure distribution. Kaushik and Raghavan[65](2010) pull-through Heating plate Pneumatic cylinder Inter-ply slip test system for autoclave environments. Larberg and Åkermo[53](2011) pull-through Temperature chamber Pneumatic cylinder The stability of this part must be ensured when pulling the hinge mechanism consisting of cylinders. Joven[48](2013) pull-out Heating plate Pneumatic cylinder Flexible bushings are fitted to the test stand base to increase the sensitivity of the system, but only for temperature testing. Sun et al.[49](2014) pull-out Heating film Springs Aluminum plates and rubber pads were used between the heating films and the specimen to ensure that the temperature and pressure were uniformly distributed over the testing areas. Erland et al.[41](2015) pull-through Temperature chamber Pneumatic cylinder Similar to the device designed by Larberg[40]. Yu et al.[66,67](2021) pull-through Non-heating device Weight Simple structure, but lacks a heating device. Kim et al.[62](2021) pull-through Resistance wire Pneumatic cylinder The pressure between the pressure plate and the mounting surface should not be excessive. Rashidi et al.[54,68](2021) pull-through Heating plate Hydraulic cylinder Uniform normal pressure distribution must be ensured, and the device can also achieve the same parameters as in a hot press tank. Liu et al.[69](2021) pull-through Temperature chamber Rotating shaft Pressure is adjusted by rotating the Rotating shaft. Li et al.[61](2023) pull-through Heating plate Pneumatic cylinder The cylinder applying pressure part is similar to the device of Zhao[47]. Dutta et al.[70](2023) pull-through Cartridge heaters Pneumatic cylinder Similar to the device designed by Larberg[40]. Liu et al.[64](2023) pull-through Temperature chamber Springs The structure is simple and can only be used for inter-ply slipping experiments between the tool and the prepreg. Aveiga et al.[52](2023) pull-out Cartridge heaters Pneumatic cylinder It can be tested between prepregs and prepregs, as well as between prepregs and tools. 
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表 2 Stribeck理论相关模型
Table 2. Related model of Stribeck theory
Model contributor Time Model expression Parameter meaning Chow[93] 2002 $ {\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}=\dfrac{{\mu }_{c}\cdot \left(a\cdot {N}_{\mathrm{T}}\right)+\left(m\cdot {\dot{\gamma }}^{n-1}\right)\cdot \dot{\gamma }\cdot {A}_{\mathrm{r}}}{{N}_{\mathrm{T}}} $ Where $ {\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}} $ is the effective coefficient of friction; $ {\mu }_{c} $ the Coulomb friction coefficient; $ {N}_{\mathrm{T}} $ the normal load; $ {A}_{\mathrm{r}} $ the contact area of the fluid film;
$ a $ portion of Coulomb friction; $ m $ the consistency, $ n $ the Power-Law index; and $ \dot{\gamma } $ the shear rate.Gorczyca-Cole et al.[89] 2007 $ {\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}={C}_{1}\cdot {H}+{C}_{2}-{S}_{\mathrm{t}\mathrm{t}} $ Where $ {C}_{1} $ and $ {C}_{2} $ is the model coefficient; $ {S}_{\mathrm{t}\mathrm{t}} $ the linear shift term; and H the Hersey number. Liu et al.[69] 2021 $ {\mu }_{\mathrm{k}}=0.22\cdot {{\mathrm{e}}}^{27.25\tfrac{\eta \nu }{N}}-7.42\times {10}^{-4}\cdot \mathrm{\Delta }T-0.03 $ Where $ {\mu }_{\mathrm{s}} $ is the static friction coefficient; $ v $ the sliding velocity; $ N $ the normal force; and $ \mathrm{\Delta }T $ the temperature difference. $ {\mu }_{\mathrm{s}}=5.02\cdot \left({\dfrac{v}{N}}\right)^{0.12}-6.35\times {10}^{-3}\cdot \mathrm{\Delta }T $
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表 3 经验模型
Table 3. Empirical Model
Model contributor Time Model expression Parameter meaning Lin et al.[42] 2006 $ \tau =\text{565}\cdot {10}^{-6}\sqrt[3]{\dfrac{{U}^{1.37}\cdot P}{4.0\cdot {10}^{-6}{a}_{\mathrm{T}}}} $
$ {a}_{\mathrm{T}}={10}^{-282.85\left(\tfrac{1}{T}-\tfrac{1}{180}\right)} $where $ \tau $ is the shear stress in MPa, U the velocity in mm/s, P the normal pressure in MPa and T the temperature in℃. Wang et al.[21] 2019 $ \tau ={k}_{1}d\left(d < dy\right) $
$ \tau ={p}_{1}+{p}_{2}/d\left({d}_{y}\leqslant d\leqslant {d}_{h}\right) $
$ \tau ={\tau }_{\mathrm{h}}+{k}_{3}\left(d-{d}_{h}\right)\left(d > {d}_{h}\right) $where $ \tau $ is the tangential stress; $ d $ the relative slipping displacement; $ {d}_{y} $ the displacement at yield point; $ {d}_{h} $ the displacement at harding point; and $ {k}_{1} $, $ {p}_{1} $, $ {p}_{2} $, $ {k}_{3} $ the model parameters. Sourki et al.[94] 2021 $ {\widehat{\mu }}_{{m}_{i}}\left(\alpha \right)={a}_{0}+\displaystyle\sum\nolimits _{n=1}^{N}\left[{a}_{n}\cos\alpha \omega +{b}_{n}\sin\alpha \omega \right] $
$ {P}^{\text{'}}=P\left[H\left(P-{P}_{p}\right)-H\left(P-{P}_{p+1}\right)\right] $
$ {\mu }_{\mathrm{i}}={\widehat{\mu }}_{\mathrm{p}\mathrm{i}}\left(\alpha \right)+\dfrac{{\widehat{\mu }}_{\mathrm{p}\mathrm{i}}\left(\alpha \right)-{\widehat{\mu }}_{\mathrm{p}\mathrm{i}}\left(\alpha \right)}{{P}_{\mathrm{p}+1}-{P}_{\mathrm{p}}}\left({P}^{\text{'}}-{P}_{\mathrm{p}+1}\right) $Where $ {\widehat{\mu }}_{{\mathrm{m}}_{\mathrm{i}}}\left(\alpha \right) $ is the static (when $ i=s $), or dynamic (when $ i=k $) coefficient of friction at the given pressure level m, as a function of the ply orientation $ \alpha $; $ H $(.) the Heaviside step function; $ {a}_{0} $, $ {a}_{\mathrm{n}} $, $ {b}_{\mathrm{n}} $ and $ \omega $ are the coefficients and period of the Fourier series. Here $ M=\text{3} $ for the given three pressure levels, and $ N=\text{8} $ for the number of Fourier terms used for the fit. Li et al.[61] 2023 $ {\tau }_{\mathrm{l}}=Es $
$ {\tau }_{\mathrm{y}}=A+B*{s}^{C} $
$ {\tau }_{\mathrm{H}}={H}_{\mathrm{s}}+{\tau }_{0} $where $ \tau $ is the tangential stress; $ s $ the sliding distance; $ E $ the elastic parameters; $ A $, $ B $ and $ C $ yield model parameters; and $ {\tau }_{0} $ the Y-axis intercept of the hardening curve.
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