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無紡布的粘彈性泊松比

2023-06-20 13:44夏騰騰葛陳勇李健李紅光李勇
現(xiàn)代紡織技術(shù) 2023年2期
關(guān)鍵詞:粘彈性泊松比無紡布

夏騰騰 葛陳勇 李健 李紅光 李勇

摘要:為了研究無紡布的粘彈性力學(xué)行為,精確計算其粘彈性泊松比。以粘彈性力學(xué)理論為基礎(chǔ),結(jié)合Laplace變換和蠕變應(yīng)力條件,推導(dǎo)了由橫向應(yīng)變和松弛模量計算粘彈性泊松比的精確表達式。由蠕變實驗和松弛實驗數(shù)據(jù),獲得了無紡布橫向應(yīng)變和松弛模量隨時間變化的Prony級數(shù),并利用1stOpt軟件模擬了無紡布的粘彈性泊松比時變曲線。結(jié)果表明:在蠕變條件下,隨著載荷作用時間增加,無紡布泊松比逐漸增大并趨近于0.25。該方法可有效獲得無紡布的粘彈性泊松比,為其后續(xù)生產(chǎn)加工所涉及的力學(xué)指標(biāo)計算提供參考值。

關(guān)鍵詞:無紡布;泊松比;粘彈性;蠕變;松弛

中圖分類號:TS171

文獻標(biāo)志碼:A

文章編號:1009-265X(2023)02-0107-05

泊松比是衡量材料力學(xué)性能的重要指標(biāo)之一,其精確表達和測定對相關(guān)研究工作極為重要[1-2]。部分學(xué)者對針織物、機織物、無紡布等的泊松比做了研究[3-5],但多將織物作為彈性材料考慮,即認(rèn)為泊松比為常數(shù)。粘彈性材料的泊松比一般表現(xiàn)出與溫度和時間的相關(guān)性,若假定為常數(shù),會使得其相關(guān)應(yīng)力分析和強度計算產(chǎn)生較大誤差[6]。隨著紡織產(chǎn)業(yè)發(fā)展,無紡布產(chǎn)量和使用量逐年增加,對于無紡布力學(xué)性能的研究也逐漸被重視。通過拉伸測試發(fā)現(xiàn),無紡布具有典型的粘彈性屬性。作為材料的基本力學(xué)參數(shù)之一,無紡布粘彈性泊松比的精確測定必不可少。

目前,關(guān)于材料粘彈性泊松比的研究較多,但針對紡織材料的研究尚未見到。Lakes等[7]對線性粘彈性固體中的泊松比進行了理論分析,發(fā)現(xiàn)粘彈性泊松比與加載時間呈函數(shù)關(guān)系,但并不一定隨時間單調(diào)增大。鄭健等[8]采用遺傳積分形式表達粘彈性泊松比,結(jié)合蠕變實驗條件,推導(dǎo)并計算了固體推進劑的粘彈性泊松比。申志彬等[9]提出了一種基于數(shù)字圖像法的固體推進劑泊松比高精度測量方法,研制相應(yīng)的測試系統(tǒng)并測定了HTPB推進劑的粘彈性泊松比。Hoshino 等[6]提出利用二維數(shù)字圖像法直接測量動態(tài)粘彈性實驗中的泊松比的方法,并通過測試環(huán)氧樹脂的材料特性進行了驗證。

基于粘彈性力學(xué)理論,本文建立了粘彈性泊松比表達式,結(jié)合蠕變實驗和松弛實驗測定材料拉伸指標(biāo),精確計算了無紡布粘彈性泊松比,以期為紡織材料的泊松比測定提供參考。

1粘彈性泊松比計算

常規(guī)彈性泊松比v定義為:

v=-εx/εy(1)

式中:εx為材料橫向應(yīng)變;εy為材料縱向應(yīng)變。

無紡布具有典型的粘彈性屬性,在載荷作用下會產(chǎn)生松弛或蠕變,且橫向應(yīng)變響應(yīng)εx(t)滯后于縱向變形歷史εy(t) [10-11]。因此,直接由拉伸過程實測值εx(t)、εy(t)計算,無法得到精確泊松比v(t)。

基于彈性-粘彈性對應(yīng)原理,在恒定載荷拉伸作用下,粘彈性時域泊松比v(t)為:

v(t)=-εx(t)/εy(t)(2)

粘彈性泊松比v(t),表征在拉伸靜載作用下橫向應(yīng)變εx(t)對縱向應(yīng)變εy(t)的響應(yīng),是橫向變形的一個記憶函數(shù)[12]。

對于線性粘彈性材料,定義Laplace變換域內(nèi)的泊松比v(s)為:

v(s)=-εx(s)/εy(s)(3)

式中:縱向應(yīng)變εy(s)=σy(s)/E(s);蠕變實驗中,縱向拉伸應(yīng)力σy(s)=σ0/s;符號上的“-”表示Laplace變換算符。

則式(3)可寫為:

v(s)=-εx(s)sE(s)/σ0(4)

式中:σ0為蠕變拉伸應(yīng)力;E為拉伸松弛模量。

利用卷積定理,對式(4)求Laplace逆變換,得:

v(t)=-1σ0∫t0E(t-τ)εx(τ)dτ(5)

利用式(5),可由εx(t)和E(t)的實驗值求得粘彈性泊松比v(t)的精確值,是間接測試粘彈性泊松比的理論基礎(chǔ)。

令εx(t)、E(t)為Prony級數(shù)形式,如下:

εx(t)=εxe+∑mi=1εxiexp(-t/τi)

E(t)=Ee+∑nj=1Ejexp(-t/τj)(6)

式中:m、n為Prony級數(shù)的階數(shù);εxe為最終應(yīng)變;εxi為各階應(yīng)變量;τi為各階蠕變時間;Ee為平衡模量;Ej為各階松弛模量;τj為各階松弛時間。

將式(6)代入式(5)并整理,即得材料蠕變的粘彈性泊松比精確表達式:

v(t)=-1σ0[Ee∑mi=1εxi(exp(-t/τi)-1)+

∑mi=1∑nj=1εxiEjτjτj-τi(exp(-t/τi))-exp(-t/τj))](7)

2實驗

2.1實驗材料

本研究選用佳聯(lián)達無紡布有限公司生產(chǎn)的聚丙烯(PP)熔噴無紡布(以下簡稱無紡布),纖維間接觸形式為點粘合,幅寬143 mm、厚度0.305 mm、平方米質(zhì)量30 g/m2。

考慮試樣厚度較小,忽略無紡布厚度方向應(yīng)力及應(yīng)變分量,僅討論無紡布的二維平面泊松比[4]。因所選無紡布內(nèi)部纖維不存在經(jīng)緯取向,本文認(rèn)定其為平面各向同性材料。

參考標(biāo)準(zhǔn)GB/T 24218.3—2010《紡織品 非織造布試驗方法 第3部分:斷裂強力和斷裂伸長率的測定(條樣法)》,并根據(jù)實際情況進行相關(guān)實驗設(shè)置。

2.2蠕變實驗

試樣上下端用夾具夾持,懸掛并施加縱向載荷。試樣尺寸為300 mm×70 mm,夾持距離200 mm。為避免卷邊影響,測量位置距邊緣10 mm,即測量寬度為50 mm。為使無紡布不發(fā)生結(jié)構(gòu)破壞且橫向應(yīng)變可測量,確定縱向載荷為0.239 MPa(由下端夾具和砝碼共同施加,夾具20.7 g,砝碼500 g),載荷瞬時施加并持續(xù)12 h。實驗示意如圖1(a)所示。測量并記錄試樣中部最窄處的寬度隨蠕變時間變化情況,進行5次實驗并取平均值,計算得到布料中部橫向應(yīng)變εx′。考慮布料在較小載荷作用下存在輕微頸縮現(xiàn)象,以0.5εx′作為等效橫向應(yīng)變εx,得到εx-t曲線。

2.3松弛實驗

儀器設(shè)備采用YT010-1000型土工布綜合強力試驗機,試樣尺寸為300 mm×50 mm,夾持距離200 mm。本實驗數(shù)據(jù)處理采用基于Prony級數(shù)的數(shù)據(jù)擬合法[13],該方法綜合考慮了松弛實驗加載階段和松弛階段,初始應(yīng)變和加載速度對計算結(jié)果無影響,考慮實驗效率且避免沖擊載荷,確定拉伸速度20 mm/min。考慮無紡布不發(fā)生結(jié)構(gòu)破壞且應(yīng)力可測量,拉伸試樣至0.05縱向應(yīng)變后停止,保持拉伸狀態(tài)12 h。實驗示意如圖1(b)所示。記錄拉力值隨松弛時間變化情況,進行5次實驗并取平均值,計算拉伸應(yīng)力σ,得到σ-t曲線。

3結(jié)果與分析

3.1蠕變實驗結(jié)果

通過蠕變實驗,得到無紡布蠕變過程等效橫向應(yīng)變隨時間變化關(guān)系,如圖2所示。

由圖2可知,載荷施加瞬間,試樣產(chǎn)生約0.023的等效橫向應(yīng)變,該階段應(yīng)變主要由纖維及纖維網(wǎng)的彈性變形引起。其后,隨著蠕變時間的增加,橫向應(yīng)變逐漸增大并趨近于定值,該階段應(yīng)變歸因于無紡布內(nèi)部纖維間的粘結(jié)點逐步剝離和滑移。

采用Levenberg-Marquardt優(yōu)化算法[14],擬合蠕變階段(瞬時應(yīng)變之后)實驗曲線,得到無紡布等效橫向應(yīng)變εx(t)的6階Prony級數(shù)表達式:

εx(t)=εxe+∑m=6i=1εxiexp(-t/τi)=-0.03491+

0.00202e-t/11759.96575+0.007e-t/11031.19268+

0.00183e-t/204.64279+0.00012e-t/444.43763+

0.00077e-t/30.03434+0.00013e-t/0.10405

(8)

3.2松弛實驗結(jié)果

通過松弛實驗,得到無紡布應(yīng)力松弛過程縱向應(yīng)力隨時間變化關(guān)系,如圖3所示。

由圖3可知,初始松弛階段,試樣應(yīng)力下降較為劇烈,說明該無紡布具有較強的松弛特性,該階段應(yīng)力變化主要由纖維伸直及滑移引起。隨后,應(yīng)力下降趨勢逐漸放緩,并趨近于定值,該階段應(yīng)力變化歸因于伸直后纖維的應(yīng)力松弛。

采用基于Prony級數(shù)的數(shù)據(jù)擬合法和Levenberg-Marquardt優(yōu)化算法,擬合松弛階段實驗曲線,得到無紡布松弛模量E(t)的6階Prony級數(shù)表達式:

E(t)=Ee+∑n=6j=1Ejexp(-t/τj)=4.42628+

1.09253e-t/32028.50978+0.73885e-t/282.31417+

0.58798e-t/3771.29624+1.60838e-t/57.29553+

0.52102e-t/1346.1015+7.18362e-t/7.14774

(9)

3.3粘彈性泊松比計算結(jié)果與分析

在已知無紡布橫向應(yīng)變εx(t)和松弛模量E(t)的6階Prony級數(shù)(相關(guān)系數(shù)R均大于0.999)后,將其擬合參數(shù)代入式(7),使用1stOpt軟件編制計算程序,計算步長為t=1 s。依據(jù)計算結(jié)果,使用Origin軟件繪制式(7)曲線,得到無紡布在蠕變條件下的泊松比隨時間變化關(guān)系,如圖4所示。

由圖4可知,無紡布的粘彈性泊松比具有明顯的時間效應(yīng)。在蠕變過程中,隨著載荷作用時間的增加,無紡布泊松比逐漸增大并趨近于定值。在初始時段,泊松比由0迅速增大至0.08左右,呈“階躍”性變化;之后變化趨勢逐漸放緩,直至趨近于0.25。由此,可將0.08作為無紡布初始粘彈性泊松比,則泊松比為隨時間從0.08逐漸趨近于0.25的值。本文所得無紡布粘彈性泊松比在正常泊松比范圍(0~0.5)內(nèi),且符合絕大部分材料泊松比約為1/3的情況[15]。泊松比趨近值(v=0.25),與高曉平[3]所得聚丙烯熱粘合無紡布(點粘合)彈性泊松比結(jié)果相近,存在差異可能是由于布料規(guī)格、生產(chǎn)工藝等不同,但仍具有一定參考價值。

4結(jié)論

粘彈性材料泊松比不能簡單假定為常數(shù),而是一個與時間相關(guān)的函數(shù)?;跓o紡布的粘彈性屬性,本文推導(dǎo)了橫向應(yīng)變εx(t)和松弛模量E(t)等效計算泊松比的方法。以Prony級數(shù)擬合蠕變實驗和松弛實驗數(shù)據(jù)得到εx(t)、E(t),再經(jīng)1stOpt軟件計算得到了無紡布泊松比與時間的關(guān)系,發(fā)現(xiàn)無紡布泊松比逐漸增大并趨近于0.25。所得結(jié)果符合常規(guī)泊松比范圍,且與相關(guān)研究吻合較好。本文所述方法,可較為簡便地計算無紡布等紡織材料的粘彈性泊松比,為其后續(xù)生產(chǎn)加工所涉及的力學(xué)指標(biāo)計算提供參考值。

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Viscoelastic Poisson's ratio of nonwovens

XIA Tengteng1,2, GE Chenyong3, LI Jian1,2, LI Hongguang4, LI Yong1,2

(1.The Mechanical Engineering College, Tarim University, Alaer 843300, China;

2.The Key Laboratory of Colleges & Universities under the Department of Education of Xinjiang Uygur Autonomous Region, Alaer 843300, China;

3.Alaer Fiber Inspection Institute, Alaer 843300, China;

4.Alar City Zhongtai Textile Technology Co., Ltd., Alaer 843300, China)

Abstract: The nonwoven is widely used in many industries and occupies a large proportion in the textile industry for its excellent performance, low cost and diversified types,. With the utilization of nonwovens in various industries, the output and usage have increased year by year. Therefore, in order to promote the use of nonwovens, it is necessary to study the mechanical properties of nonwovens. It can be found from the tensile test curve that all kinds of nonwovens have typical viscoelastic properties. Poisson's ratio, as one of the important indexes to measure the mechanical properties of materials, has been concerned and studied by many scholars, and some of them have studied the viscoelastic Poisson's ratio of materials. However, most studies focus on the viscoelastic Poisson's ratio of solid propellants, epoxy resins, and other materials. The research on textile materials has not been reported, but it has great research value.

The conventional polypropylene (PP) melt-blown nonwoven was selected as the object, the viscoelastic mechanical behavior of the nonwoven was tested, and its viscoelastic Poisson's ratio was accurately calculated. Based on the theory of viscoelastic mechanics, combined with Laplace transform and creep stress conditions, the exact expression of viscoelastic Poisson's ratio was calculated by transverse strain (under creep conditions) and relaxation modulus. The internal fibers of nonwovens are disordered and thin, so they can be regarded as isotropic materials (ignoring the stress and strain in the thickness direction), and only the two-dimensional planar Poisson's ratio is studied. The creep and relaxation experiments of nonwovens were carried out according to the standard GB/T 23218.3—2010, and the curves of transverse strain and relaxation modulus were obtained and fitted into the 6th-order Prony series. The Prony series of transverse strain and relaxation modulus were substituted into the expression of viscoelastic Poisson's ratio, and the time-varying curve of viscoelastic Poisson's ratio of nonwovens under creep condition was calculated by using 1stOpt software. In this study, the calculation method of viscoelastic Poisson's ratio was introduced into textile materials, and the viscoelastic Poisson's ratio of the selected nonwoven was analyzed and measured. It is found that as the loading time increases, the viscoelastic Poisson's ratio of the material gradually increases and tends to be constant. The viscoelastic Poisson's ratio approach value of the nonwoven selected in this paper is close to 0.25, which is in line with the Poisson's ratio range of conventional materials and is close to the value of conventional elastic Poisson's ratio in related research.

The method can effectively determine the viscoelastic Poisson's ratio of nonwovens, with simple operation and reliable results, which can provide reference for the determination of Poisson's ratio of other textile materials.. The accurate determination of viscoelastic Poisson's ratio also provides a reference value for the calculation of mechanical indexes involved in the subsequent production and processing of textile materials.

Keywords: nonwoven; Poisson's ratio; viscoelasticity; creep; relaxation; time-varying curve

收稿日期:20220630

網(wǎng)絡(luò)出版日期:20220914

基金項目:兵團財政科技計劃項目(2021BB022)

作者簡介:夏騰騰(1998—),男,甘肅天水人,碩士研究生,主要從事材料性能研究與應(yīng)用方面的研究。

通信作者:葛陳勇,E-mail:329439500@qq.com

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