针叶木浆和蔗渣浆的纤维形变及其纸张的应力—应变特性
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摘要
应力-应变特性是纸张的重要性能之一，纸张的抗张强度和伸长率可定义为纸张应力-应变曲线的断裂坐标终点。与抗张强度相比，某种程度上纸张断裂伸长率的重要性一直都被低估了。纤维性能，包括纤维长度、宽度、粗度、细小纤维含量等，是决定纸张的应力-应变特性的重要因素。然而，作为纤维性能组成要素之一，纤维形变对纸张性能的影响常常被忽视。纤维形变是指纤维细胞壁上的纤维素结晶区相对于整个纤维轴向发生了偏移，包括卷曲、扭结、微压缩、位错点等不同类型，其中，纤维卷曲和扭结是可以定量检测的。纤维形变会影响纸张中纤维承受载荷的能力，从而影响纸张的应力-应变特性。本研究以漂白硫酸盐针叶木浆和蔗渣浆为对象，考察不同机械作用方式和条件下纤维形变的变化规律，研究纤维形变对纤维强度和其纸张的应力-应变特性的影响，尤其是对纸张抗张强度和伸长率的影响，旨在为制浆造纸过程提供理论指导。
不同机械处理作用下漂白硫酸盐松木浆产生纤维形变的数量和程度不同，特别是高浓和低浓条件下差异很大。高浓翼式离解机处理会产生大量的纤维形变，包括纤维卷曲和扭结。高浓E氏压紧机处理除了切断纤维外，主要产生纤维扭结。低浓打浆(即瓦利打浆)则会减少纤维形变，使纤维伸直。纤维形变程度发生显著变化主要是在高浓机械处理的初始阶段。此外，单独的高温加热处理可以明显地引起纤维形变。纤维强度与纤维的扭结指数具有良好的相关性，优于其与纤维形态因子(即纤维卷曲指数)的相关性。
对表征浆料纤维位错点或缺陷点数量的“盐酸法”纤维断裂数量进行了改进，采用数均纤维长度代替原方法中质均纤维长度，用断裂指数(cleavage index)代替断裂数量(cleavage)，得到断裂指数的计算公式为Cleavage index=l/L-1/L_o，其中L为盐酸处理后的纤维的数均长度，L_o为未经盐酸处理的纤维的数均长度，便于不同纤维长度浆料样品的比较。考察不同机械作用下纤维断裂指数的变化规律，发现针叶木浆纤维断裂指数随着高浓翼式离解机作用而增加，但随着低浓打浆的进行而降低。采用纸张的干、湿零距抗张强度指数的差值，作为评价纤维损伤程度的指标。在高浓翼式离解机作用下，干、湿零距抗张强度的差值随着纤维断裂指数的减小而减小；对于低浓打浆，干、湿零距抗张强度的差值则随着纤维断裂指数的减小而增大，这表明盐酸对纤维的可及度不一定与纤维的机械强度相关。断裂指数可能不与纤维上的机械损伤直接相关，但是有可能与纤维的表面化学和纤维细胞壁结构有关。
高浓机械处理后纤维并不能直接用于造纸，往往需要有后续的低浓打浆处理。对于漂白蔗渣浆，高浓磨浆主要是引起纤维卷曲，这种卷曲的纤维形态十分稳定，难以在后续PFI磨浆中去除。对于漂白硫酸盐针叶木浆，虽然高浓磨浆下产生了大量纤维卷曲和扭结，但是部分的纤维形变是可逆的，可以通过后续PFI打浆或低浓打浆去除。通过偏光显微镜下观察发现，针叶木浆经高浓机械处理后产生了纤维卷曲、扭结、位错点、微压缩等不同类型的纤维形变。其中，纤维上的微压缩是不可逆的，能够在后续低浓打浆中保留下来，其有利于提高纸张伸长率。纤维卷曲程度的增加并不必然带来纸张伸长率的提高。研究中提出了一种工艺“高浓机械处理接着低浓打浆”，采用该工艺能够在较低的打浆度时（即浆料具有较好的滤水性能），同时获得较好的纸张抗张强度和伸长率，对实际生产具有指导意义。
标准干燥和自由收缩干燥下纸张的伸长率性能取决于不同的因素。当纸张经自由收缩干燥得到，干燥时的纸张收缩率起主导作用，纸张的伸长率与干燥收缩率具有良好的线性关系。当纸张通过标准干燥制备时，纤维形变和纤维细胞壁的形貌对纸张伸长率的影响更加重要。
基于纸张抗张强度Page方程计算得到的针叶木浆和蔗渣浆的剪切结合强度随着打浆的进行而提高，其变化范围分别为4.0~11.1MPa和6.8~16.7MPa；基于Shallhorn-Karnis抗张强度模型得到的剪切结合强度则不随打浆而变化，针叶木浆和蔗渣浆的剪切结合强度分别约为1.7MPa和2.2MPa。蔗渣浆的剪切结合强度大于针叶木浆的剪切结合强度，这可能与蔗渣浆和针叶木浆纤维的表面化学性质不同有关。不同打浆工艺下，相对结合面积（RBA）的增加是纸张抗张强度提高的主要原因。高浓磨浆对纸张相对结合面积和层间结合强度的积极作用将在后续低浓打浆过程中呈现出来。
以不同打浆方式下得到的一系列漂白硫酸盐针叶木浆为样本，基于“纸张断裂伸长率是单根纤维的伸长率潜能和引起纸张发生断裂的所有因素共同作用的结果”这一假设，建立了基于纤维形变的纸张伸长率变化的半经验数学模型s=φ(K, T)，其数学表达式为s=0.149K~(0.2104)T~(0.4279)，其预测值与测量值的相关系数R~2为0.72，模型中，参数K（扭结指数）主要反映纤维本身的伸长率潜能，参数T（抗张强度）则反映了引起纸张发生断裂的所有因素的影响。考虑到抗张强度和伸长率均是纸张应力-应变曲线断裂终点的坐标，抗张强度和伸长率将受到相同因素的影响，这是合理的。此外，参数T可用已有的纸张抗张强度模型公式来代替。
对于不同打浆方式下得到的针叶木浆，相对结合面积（RBA）是纸张抗张强度的变化的主要原因。因此，采用参数RBA代替模型s=φ(K, T)中的参数T，得到纸张伸长率的数学模型s=φ(K, RBA)，其表示式为s=0.0529K~(0.3646)RBA~(0.4754)，模型预测值与测量值的相关系数R~2为0.75，该模型的优点在于其形式简单、物理意义较明确，有利于模型在实际中的应用。需要指出的是，我们所建立的纸张伸长率模型并不是十分理想的，其主要原因在于：纤维扭结指数K或者卷曲指数Cw并不能完全地反映纤维本身的伸长性能。因此，建立更好的纸张伸长率模型的前提是，开发定量测定纤维上微压缩数量的方法，因为微压缩的数量将更直接地反映纤维伸长率潜能。
Stress-strain properties (or load-elongation properties) are one of the important paperproperties. Tensile strength and elongation of paper are defined by the end-point of the sheet’sload-elongation curve. Compared with the tensile strength of paper, the elongation is animportant but underrated functional property of paper. Fibre properties, including fibre length,width, coarseness, fines content and so on, play an important role in the load-elongationproperties of paper. However, the deformations of fibre are of high significance but easilyignored properties among them. In general, fibre deformations are the misalignment of thecellulose crystals in fibre wall relative to the overall fibril direction, which include fibre curl,kinks, dislocations, microcompresssion and so on. Fibre curl and kinks could be easilymeasured by commercial fibre analyzers. Fibre deformations affect the load-bearing ability offibres in the paper and further affect the load-elongation properties of the fibre network. Inpresent study, fibre deformations of bleached kraft softwood and bagasse pulps caused bydifferent kinds of mechanical treatments were inverstigated. The effects of fibre deformationson the fibre strength and load-elongation properties of paper, especially on the tensile strengthand elongation, were also studied.
The wing defibrator, E-compactor and conventional Valley beater were applied to treatbleached kraft pine pulp from the first thinning. Each mechanical treatment induced fibredeformations in its own characteristic way. The high consistency (HC) wing defibratorinduced fibre kinks and curl whereas the E-compactor, in addition to fibre cutting, favouredkinks. Low consistency (LC) Valley beating straightened the fibres and released fibredeformations. The biggest changes occurred at the beginning of the treatments. However, ahigh temperature treatment on its own seemed to increase the extent of fibre deformationsconsiderably. The zero-span tensile strength correlated better with the number of kinks thanwith the shape factor (fibre curl).
Some modifications were made on the hydrochloride acid (HCl) method developed byAnder et al, which was used to estimate the degree of fibre defects. Firstly, the arithmetic fibrelength parameter, including the contribution of fines fractions, was used instead of thelength-weighted fibre length in the original method. Secondly, the cleavage index was usedinstead of the cleavage in order to better compare fibres with different lengths. The cleavageindex was calculated by the equation Cleavage index=1/L-1/Lo, where Lois the arithmeticfibre length in mm for the control in water (or for untreated reference fibres), and L is thearithmetic fibre length in mm for HCl-treated fibres. The hydrochloride acid (HCl) treatment-induced cleavage index increased with the HC wing defibrator treatment butdecreased with the LC beating. The difference between the dry and wet zero-span tensilestrengths, which can be used for estimating the changes in fibre defects, increased with thecleavage index for LC beating but decreased for the HC wing defibrator treatment. Thisimplies that the chemical accessibility of HCl to the fibres and the HCl-induced fibre cuttingdo not necessarily correlate with the mechanical strength of the fibres. The cleavage indexmay not be directly related to the mechanical defects of the fibres but may be more dependenton the chemical conditions on the fibre surface and in the fibre wall.
The fibres treated by HC mechanical treatment are usually not appropriate forpaperpaking process and need a further LC beating to improve their properties. For bagassepulp fibres, HC refining caused fibre curl considerably, which were stable in the subsequentPFI refining. For pine pulp fibres, most of fibre deformations induced by HC refining werereversible and could be removed by a subsequent PFI refining or valley beating. Based onthe observation by polarized light microscope, HC wing defibrator treatment caused curl,kinks, dislocations, and microcompressions in the fibres. Among them, the small scaledeformations, such as microcompressions have an important role in the elongation potentialof sheets and they can be preserved in subsequent Valley beating, which tends to straightenthe fibres and release kinks and dislocated zones. Increasing fibre curl does not necessarilylead to improved paper elongation due to the reduced load-bearing ability of curly fibres inthe fibre network.The combined HC wing defibrator treatment and subsequent LC Valleybeating was found to be the best strategy to produce paper with a high level of elongation,maintaining high tensile strength, and good dewatering properties.
The elongation of the freely dried and restrained dried paper depends on different factors.In the case of freely dried paper, the shrinkage potential is the dominant factor and there is alinear correlation between the elongation and shrinkage potential of paper. While in the caseof restrained dried paper, the fibre wall morphology and microcompressions have a crucialrole.
Shear bond strength of softwood pulp and bagasse pulp fibres was estimated using Pageequation for tensile strength. The value increased in LC beating for softwood pulp from4.0MP to11.1MPa and for bagasse pulp from6.8MPa to16.7MPa. However, shear bondstrength of softwood pulp and bagasse pulp fibres estimated from Shallhorn-Karnis tensilestrength model almost stayed constant during different beating processes. Shear bond strengthwas approximately1.7Mpa for softwood pulp and2.2MPa for bagasse pulp. Nevertheless, theshear bond strength of bagasse pulp was better than that of softwood pulp fibres, which propably due to their charcteristic surface chemistry of the fibres. During different beatingprocesses, the increase of the relative bonded area (RBA) in paper resulted in theimprovement of the tensile strength of paper. The positive effects of HC refining on the RBAand internal bond strength of paper were realized during the sequent LC beating.
In this study, a semi-empirical model for paper elongation s=φ(K, T) was developed. Itwas constructed using data from different beating series of bleached softwood kraft pulps. Thehypothesis was that the elongation of paper depends on the extensibility potential of the singlefibres and on the factors related to fibre network structure that initiates the final fracture. Themodeling for the elongation of paper is as follows: s=0.149K~(0.2104)T~(0.4279). Its coeffeicent ofdetermination R~2is approximately0.72. The parameter of K (kink index) indicates theextensibility of the fibre and the parameter of T (tensile index) includes all the factors thataffect the initiation of paper fracture, which is reasonable considering tensile index andelongation both as the end-point coordinates of stress-strain curve of paper. Additionally, Tcan be estimated from fibre properties and RBA using Page equation or Shallhorn modeling.
The modeling of the elongation of paper was improved when the tensile index wasreplaced by relative bonded area (RBA) since the differences among the specimen mainlyfrom the RBA of paper. The expression is s=0.0529K~(0.3646)RBA~(0.4754). Its coefficient ofdetermination R~2is0.75. Preferable model is s=φ(K, RBA) since it is simple and explicit,which is beneficial in practical applications. However, it is worth to note that, this model ofthe elongation of paper is not perfect yet. The possible reason is that kink index or curl indexare not the best parameters for indicating the extensibility potential of fibres. Therefore, thepremise of a better elongation model of paper would be to develop a quantitative method forthe number of microcompressions of fibres, which more directly affect the elongationpotential of single fibres.
不同机械处理作用下漂白硫酸盐松木浆产生纤维形变的数量和程度不同，特别是高浓和低浓条件下差异很大。高浓翼式离解机处理会产生大量的纤维形变，包括纤维卷曲和扭结。高浓E氏压紧机处理除了切断纤维外，主要产生纤维扭结。低浓打浆(即瓦利打浆)则会减少纤维形变，使纤维伸直。纤维形变程度发生显著变化主要是在高浓机械处理的初始阶段。此外，单独的高温加热处理可以明显地引起纤维形变。纤维强度与纤维的扭结指数具有良好的相关性，优于其与纤维形态因子(即纤维卷曲指数)的相关性。
对表征浆料纤维位错点或缺陷点数量的“盐酸法”纤维断裂数量进行了改进，采用数均纤维长度代替原方法中质均纤维长度，用断裂指数(cleavage index)代替断裂数量(cleavage)，得到断裂指数的计算公式为Cleavage index=l/L-1/L_o，其中L为盐酸处理后的纤维的数均长度，L_o为未经盐酸处理的纤维的数均长度，便于不同纤维长度浆料样品的比较。考察不同机械作用下纤维断裂指数的变化规律，发现针叶木浆纤维断裂指数随着高浓翼式离解机作用而增加，但随着低浓打浆的进行而降低。采用纸张的干、湿零距抗张强度指数的差值，作为评价纤维损伤程度的指标。在高浓翼式离解机作用下，干、湿零距抗张强度的差值随着纤维断裂指数的减小而减小；对于低浓打浆，干、湿零距抗张强度的差值则随着纤维断裂指数的减小而增大，这表明盐酸对纤维的可及度不一定与纤维的机械强度相关。断裂指数可能不与纤维上的机械损伤直接相关，但是有可能与纤维的表面化学和纤维细胞壁结构有关。
高浓机械处理后纤维并不能直接用于造纸，往往需要有后续的低浓打浆处理。对于漂白蔗渣浆，高浓磨浆主要是引起纤维卷曲，这种卷曲的纤维形态十分稳定，难以在后续PFI磨浆中去除。对于漂白硫酸盐针叶木浆，虽然高浓磨浆下产生了大量纤维卷曲和扭结，但是部分的纤维形变是可逆的，可以通过后续PFI打浆或低浓打浆去除。通过偏光显微镜下观察发现，针叶木浆经高浓机械处理后产生了纤维卷曲、扭结、位错点、微压缩等不同类型的纤维形变。其中，纤维上的微压缩是不可逆的，能够在后续低浓打浆中保留下来，其有利于提高纸张伸长率。纤维卷曲程度的增加并不必然带来纸张伸长率的提高。研究中提出了一种工艺“高浓机械处理接着低浓打浆”，采用该工艺能够在较低的打浆度时（即浆料具有较好的滤水性能），同时获得较好的纸张抗张强度和伸长率，对实际生产具有指导意义。
标准干燥和自由收缩干燥下纸张的伸长率性能取决于不同的因素。当纸张经自由收缩干燥得到，干燥时的纸张收缩率起主导作用，纸张的伸长率与干燥收缩率具有良好的线性关系。当纸张通过标准干燥制备时，纤维形变和纤维细胞壁的形貌对纸张伸长率的影响更加重要。
基于纸张抗张强度Page方程计算得到的针叶木浆和蔗渣浆的剪切结合强度随着打浆的进行而提高，其变化范围分别为4.0~11.1MPa和6.8~16.7MPa；基于Shallhorn-Karnis抗张强度模型得到的剪切结合强度则不随打浆而变化，针叶木浆和蔗渣浆的剪切结合强度分别约为1.7MPa和2.2MPa。蔗渣浆的剪切结合强度大于针叶木浆的剪切结合强度，这可能与蔗渣浆和针叶木浆纤维的表面化学性质不同有关。不同打浆工艺下，相对结合面积（RBA）的增加是纸张抗张强度提高的主要原因。高浓磨浆对纸张相对结合面积和层间结合强度的积极作用将在后续低浓打浆过程中呈现出来。
以不同打浆方式下得到的一系列漂白硫酸盐针叶木浆为样本，基于“纸张断裂伸长率是单根纤维的伸长率潜能和引起纸张发生断裂的所有因素共同作用的结果”这一假设，建立了基于纤维形变的纸张伸长率变化的半经验数学模型s=φ(K, T)，其数学表达式为s=0.149K~(0.2104)T~(0.4279)，其预测值与测量值的相关系数R~2为0.72，模型中，参数K（扭结指数）主要反映纤维本身的伸长率潜能，参数T（抗张强度）则反映了引起纸张发生断裂的所有因素的影响。考虑到抗张强度和伸长率均是纸张应力-应变曲线断裂终点的坐标，抗张强度和伸长率将受到相同因素的影响，这是合理的。此外，参数T可用已有的纸张抗张强度模型公式来代替。
对于不同打浆方式下得到的针叶木浆，相对结合面积（RBA）是纸张抗张强度的变化的主要原因。因此，采用参数RBA代替模型s=φ(K, T)中的参数T，得到纸张伸长率的数学模型s=φ(K, RBA)，其表示式为s=0.0529K~(0.3646)RBA~(0.4754)，模型预测值与测量值的相关系数R~2为0.75，该模型的优点在于其形式简单、物理意义较明确，有利于模型在实际中的应用。需要指出的是，我们所建立的纸张伸长率模型并不是十分理想的，其主要原因在于：纤维扭结指数K或者卷曲指数Cw并不能完全地反映纤维本身的伸长性能。因此，建立更好的纸张伸长率模型的前提是，开发定量测定纤维上微压缩数量的方法，因为微压缩的数量将更直接地反映纤维伸长率潜能。
Stress-strain properties (or load-elongation properties) are one of the important paperproperties. Tensile strength and elongation of paper are defined by the end-point of the sheet’sload-elongation curve. Compared with the tensile strength of paper, the elongation is animportant but underrated functional property of paper. Fibre properties, including fibre length,width, coarseness, fines content and so on, play an important role in the load-elongationproperties of paper. However, the deformations of fibre are of high significance but easilyignored properties among them. In general, fibre deformations are the misalignment of thecellulose crystals in fibre wall relative to the overall fibril direction, which include fibre curl,kinks, dislocations, microcompresssion and so on. Fibre curl and kinks could be easilymeasured by commercial fibre analyzers. Fibre deformations affect the load-bearing ability offibres in the paper and further affect the load-elongation properties of the fibre network. Inpresent study, fibre deformations of bleached kraft softwood and bagasse pulps caused bydifferent kinds of mechanical treatments were inverstigated. The effects of fibre deformationson the fibre strength and load-elongation properties of paper, especially on the tensile strengthand elongation, were also studied.
The wing defibrator, E-compactor and conventional Valley beater were applied to treatbleached kraft pine pulp from the first thinning. Each mechanical treatment induced fibredeformations in its own characteristic way. The high consistency (HC) wing defibratorinduced fibre kinks and curl whereas the E-compactor, in addition to fibre cutting, favouredkinks. Low consistency (LC) Valley beating straightened the fibres and released fibredeformations. The biggest changes occurred at the beginning of the treatments. However, ahigh temperature treatment on its own seemed to increase the extent of fibre deformationsconsiderably. The zero-span tensile strength correlated better with the number of kinks thanwith the shape factor (fibre curl).
Some modifications were made on the hydrochloride acid (HCl) method developed byAnder et al, which was used to estimate the degree of fibre defects. Firstly, the arithmetic fibrelength parameter, including the contribution of fines fractions, was used instead of thelength-weighted fibre length in the original method. Secondly, the cleavage index was usedinstead of the cleavage in order to better compare fibres with different lengths. The cleavageindex was calculated by the equation Cleavage index=1/L-1/Lo, where Lois the arithmeticfibre length in mm for the control in water (or for untreated reference fibres), and L is thearithmetic fibre length in mm for HCl-treated fibres. The hydrochloride acid (HCl) treatment-induced cleavage index increased with the HC wing defibrator treatment butdecreased with the LC beating. The difference between the dry and wet zero-span tensilestrengths, which can be used for estimating the changes in fibre defects, increased with thecleavage index for LC beating but decreased for the HC wing defibrator treatment. Thisimplies that the chemical accessibility of HCl to the fibres and the HCl-induced fibre cuttingdo not necessarily correlate with the mechanical strength of the fibres. The cleavage indexmay not be directly related to the mechanical defects of the fibres but may be more dependenton the chemical conditions on the fibre surface and in the fibre wall.
The fibres treated by HC mechanical treatment are usually not appropriate forpaperpaking process and need a further LC beating to improve their properties. For bagassepulp fibres, HC refining caused fibre curl considerably, which were stable in the subsequentPFI refining. For pine pulp fibres, most of fibre deformations induced by HC refining werereversible and could be removed by a subsequent PFI refining or valley beating. Based onthe observation by polarized light microscope, HC wing defibrator treatment caused curl,kinks, dislocations, and microcompressions in the fibres. Among them, the small scaledeformations, such as microcompressions have an important role in the elongation potentialof sheets and they can be preserved in subsequent Valley beating, which tends to straightenthe fibres and release kinks and dislocated zones. Increasing fibre curl does not necessarilylead to improved paper elongation due to the reduced load-bearing ability of curly fibres inthe fibre network.The combined HC wing defibrator treatment and subsequent LC Valleybeating was found to be the best strategy to produce paper with a high level of elongation,maintaining high tensile strength, and good dewatering properties.
The elongation of the freely dried and restrained dried paper depends on different factors.In the case of freely dried paper, the shrinkage potential is the dominant factor and there is alinear correlation between the elongation and shrinkage potential of paper. While in the caseof restrained dried paper, the fibre wall morphology and microcompressions have a crucialrole.
Shear bond strength of softwood pulp and bagasse pulp fibres was estimated using Pageequation for tensile strength. The value increased in LC beating for softwood pulp from4.0MP to11.1MPa and for bagasse pulp from6.8MPa to16.7MPa. However, shear bondstrength of softwood pulp and bagasse pulp fibres estimated from Shallhorn-Karnis tensilestrength model almost stayed constant during different beating processes. Shear bond strengthwas approximately1.7Mpa for softwood pulp and2.2MPa for bagasse pulp. Nevertheless, theshear bond strength of bagasse pulp was better than that of softwood pulp fibres, which propably due to their charcteristic surface chemistry of the fibres. During different beatingprocesses, the increase of the relative bonded area (RBA) in paper resulted in theimprovement of the tensile strength of paper. The positive effects of HC refining on the RBAand internal bond strength of paper were realized during the sequent LC beating.
In this study, a semi-empirical model for paper elongation s=φ(K, T) was developed. Itwas constructed using data from different beating series of bleached softwood kraft pulps. Thehypothesis was that the elongation of paper depends on the extensibility potential of the singlefibres and on the factors related to fibre network structure that initiates the final fracture. Themodeling for the elongation of paper is as follows: s=0.149K~(0.2104)T~(0.4279). Its coeffeicent ofdetermination R~2is approximately0.72. The parameter of K (kink index) indicates theextensibility of the fibre and the parameter of T (tensile index) includes all the factors thataffect the initiation of paper fracture, which is reasonable considering tensile index andelongation both as the end-point coordinates of stress-strain curve of paper. Additionally, Tcan be estimated from fibre properties and RBA using Page equation or Shallhorn modeling.
The modeling of the elongation of paper was improved when the tensile index wasreplaced by relative bonded area (RBA) since the differences among the specimen mainlyfrom the RBA of paper. The expression is s=0.0529K~(0.3646)RBA~(0.4754). Its coefficient ofdetermination R~2is0.75. Preferable model is s=φ(K, RBA) since it is simple and explicit,which is beneficial in practical applications. However, it is worth to note that, this model ofthe elongation of paper is not perfect yet. The possible reason is that kink index or curl indexare not the best parameters for indicating the extensibility potential of fibres. Therefore, thepremise of a better elongation model of paper would be to develop a quantitative method forthe number of microcompressions of fibres, which more directly affect the elongationpotential of single fibres.
引文
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