1. Definitions
Tensile index is the core mechanical index used in the paper industry to evaluate the bonding strength and material properties of paper and cardboard intrinsic fibers. It is a physical quantity obtained after normalization by introducing paper quantitative factors on the basis of tensile strength, which is defined as: the maximum tensile strength that can be withstood per unit width and per unit quantitative paper. The tensile index eliminates the influence of quantitative differences in paper on strength comparison, allowing horizontal comparison of mechanical properties between different quantitative papers. Its mathematical expression is:
X = (F / (b × w)) × 103
Among them, X represents the tensile index, which is measured in Newton-milligrams; F represents the maximum tension of the specimen, in Newton; b represents the width of the specimen in millimeters; w represents the quantity of the specimen in grams per square meter. The higher the tensile index, the stronger the paper's ability to resist tensile failure under the same quantitative conditions, i.e., the higher structural strength per unit mass.
2. Principle
The tensile index is determined based on the basic principles of tensile testing in material mechanics, while combining the peculiarities of the paper structure. When the rectangular strip is subjected to a gradually increasing longitudinal load in the direction of tension, the inside of the paper begins to be stressed. This stress is mainly borne by the fiber itself, the bonding surface transfer between the fibers, and the intertwined network between the fibers.
From the analysis of microscopic mechanisms, the tensile resistance of paper mainly depends on three factors: the strength of the fiber itself, the bonding strength between the fibers and the distribution of the fiber network. In the initial stage of tensile, the stress is mainly transmitted by the bonding surface between the fibers. With the increase of load, part of the bonding point begins to fail, and the stress is gradually transferred to the fiber individual. When the ultimate load is reached, it is mainly manifested as the breakage of the fiber or the simultaneous failure of a large number of binding points. Tensile strength is the macroscopic manifestation of this complex process.
However, tensile strength alone cannot be fairly compared between different quantities of paper. Paper with high quantitation usually has a large thickness, a large number of fibers participating in the stress, and naturally higher tensile strength. The introduction of the tensile index is to solve this problem, by dividing the tensile strength by the quantitative to obtain the strength value contributed by the unit mass, so as to strip away the quantitative factors, so that the comparison focuses on the characteristics of fiber raw materials, fiber bonding quality and the formed structure itself. This treatment makes the tensile index an indicator of the "efficiency" of the paper, reflecting the ability of the material to maintain strength under the premise of lightweight.
The relationship between tensile index and tensile strength and quantification can be further expressed as follows:
X = (σ × L) / w
Among them, σ is the tensile strength and L is the effective length of the specimen. This relationship reveals that the tensile index is a function of the ratio of tensile strength to quantification, essentially reflecting the specific strength characteristics of the material.
3. Measurement method
The measurement of tensile index needs to follow strict standardized operating procedures, from sample preparation, environmental conditioning to test implementation, each link directly affects the accuracy and comparability of the final result.
Specimen preparation and pretreatment:Cutting the specimen is the first step in measurement. According to the standard, rectangular strips of paper with a width of 15 mm or 25 mm and long enough to meet the clamping requirements are usually cut, with flat edges, no breakage, and no wrinkles. The specimen should be representative, cut along the longitudinal and horizontal directions of the paper to evaluate the directional differences of the paper. The cut specimen must be pretreated under standard temperature and humidity conditions, usually in an environment with a temperature of 23 degrees Celsius and a relative humidity of 50%, and the adjustment time is not less than 4 hours to make the specimen moisture reach a balanced state. This step is crucial because the mechanical properties of the paper are extremely sensitive to ambient humidity.
Quantitative assays:The calculation of the tensile index requires accurate quantitative data of the specimen. The quantity can be calculated by cutting the paper of the specified area and weighing the mass. Quantitative measurements should be performed on the same batch of specimens as the tensile strength test, or parallel specimens under the same conditions to ensure the accuracy of data matching.
Tensile determination:The pretreated specimen is installed between the upper and lower grippers of the tensile testing machine. The gripper should have sufficient clamping force to prevent the specimen from slipping during the stretching process, and at the same time avoid damage to the edge of the specimen caused by over-clamping. The upper and lower gripper spacing is set as a standard span, usually 180 mm or 100 mm. Start the testing machine and apply a tensile load at a constant rate until the specimen breaks. The maximum force value is recorded, which is the tension F. During the test, the fracture position should be observed, if the fracture occurs within 5 mm from the edge of the gripper, the result may be affected by the clamping effect, and should be discarded and retested. At least 5 to 10 strands are tested in each specimen direction, and the average value is taken as the representative value of the tension in that direction.
Tensile index calculation:According to the measured tensile F, sample width b and quantitative w, the tensile index is calculated by substituting the formula. When calculating, pay attention to unit conversion to ensure that all physical quantity units are consistent. For those who need to report the results of vertical and horizontal respectively, they should be calculated separately; For those who are required to report averages or geometric averages, data processing is carried out in accordance with the standards.
Result Record:In addition to recording the tensile index value, it is also necessary to record the elongation or length of the fracture, as well as the fracture morphology and failure mode. The fracture flush or whisker-shaped reflects the difference in fiber bonding strength and fiber length, which can be used as auxiliary information to analyze the internal structure of the paper.
4. Influencing factors
As a comprehensive index to characterize the intrinsic strength of paper, the tensile index is inextricably linked by many factors throughout the entire process from raw materials to paper. Understanding these factors is crucial for optimizing production processes and controlling product quality.
Fiber raw material characteristics:The type, morphology and chemical composition of fibers are the basic factors that determine the tensile index. The longer length of softwood fibers is conducive to interweaving and stress transfer between fibers, and usually gives paper a higher tensile index. Hardwood fibers are shorter and have a relatively low tensile index. Non-wood fibers such as bamboo pulp and grass pulp have fiber characteristics in between. The cell wall thickness and cavity diameter ratio of fibers affect the flexibility and binding area of fibers. The chemical composition of fibers, especially the cellulose content, hemicellulose content and lignin residues, directly affects the strength of the fibers and the ability to bind between fibers. Due to its amorphous structure and hydrophilicity, hemicellulose can promote the formation of hydrogen bonds between fibers after swelling, which makes a positive contribution to the anti-tension index.
Pulping process:The pulping method significantly changes the fiber morphology and surface properties, which in turn affects the tensile index. The chemical pulp is soft and malleable due to the removal of a large amount of lignin, and it is easy to separate and broom during pulping, which is conducive to the formation of a dense structure and strong bond, and the tensile index is high. The mechanical pulp retains more lignin, the fibers are harder, the binding capacity is limited, and the tensile index is low. The strength of the cooking process affects the degree of damage to the fibers, and excessive cooking will reduce the strength of the fibers themselves. Chemical treatments in the bleaching process may cause cellulose degradation, adversely affecting the anti-tensile index.
Pulping and grinding:Pulping is the core process of regulating the tensile index. Through mechanical action, the fibers are cut off, crushed, and split, which increases the specific surface area and free hydroxyl groups of the fibers, promotes the swelling and fine fibrosis of the fibers during the pulping process, and thus enhances the hydrogen bonding between the fibers. Moderate beating can significantly improve the tensile index; However, excessive pulping will lead to excessive cutting of fibers, reducing the average length and reducing the tensile index. The selection of beating methods, such as the use of disc mills, cone grinders, as well as parameters such as pulping concentration, temperature, and number of passes, should be optimized according to the characteristics of raw materials and product requirements.
Wet Chemistry & Additives:The chemical additives added to the slurry had a significant effect on the tensile index. Reinforcing agents such as cationic starch, polyacrylamide, etc., can form additional bond bridges between fibers and improve bond strength. Sizing agents such as rosin gum and AKD, although mainly endowed paper with water resistance, may form a hydrophobic film on the surface of the fiber, inhibiting the formation of hydrogen bonds to a certain extent, and may have a slight negative impact on the tensile index. The addition of fillers such as calcium carbonate and kaolin will occupy the bonding space between the fibers, hinder the direct contact of the fibers, and usually lead to a decrease in the tensile index, so it is necessary to balance the contradiction between optical performance and strength performance.
Papermaking process:Processes such as paper machine flow system, forming dehydration, pressing and drying all affect the tensile index of the final product. The flocculation of the slurry in the flow process affects the uniformity of the paper page, and the stress distribution of paper with poor uniformity is uneven, easy to break at weak points, and the tensile index is low. The dehydration rate and vacuum degree during molding dehydration affect the directional arrangement and Z-directional distribution of the fibers. Pressing increases the fiber contact area through mechanical pressure, promotes bond formation, and has a positive effect on the tensile index. The temperature curve and drying rate during the drying process affect the shrinkage of the fibers and the generation of internal stress, and too fast drying may cause the paper to become brittle and the tensile index to decrease.
Ambient Humidity:Paper is a hygroscopic material, and ambient humidity has a significant impact on mechanical properties. When the humidity increases, the fibers absorb water and swell, and the hydrogen bonds between the fibers are replaced by water molecules, and the bonding strength decreases, resulting in a decrease in the tensile index. On the contrary, in dry environments, the tensile index is relatively high. This characteristic requires strict control of ambient temperature and humidity when measuring the tensile index, and the test conditions must be noted in the report.
Directionality:Due to the priority arrangement of fibers along the direction of the paper machine during the papermaking process, the paper exhibits obvious anisotropy. The longitudinal tensile index is usually higher than the transverse, and the ratio of longitudinal to transverse can reach 1.5 to 3.0. This difference in directionality is an important factor that must be considered in the use and processing of paper.
5. Application
As the core index for evaluating the structural strength of paper in the paper industry, the tensile index has extensive and in-depth application value in product development, quality control and process optimization.
Paper product research and development:In the process of new product development, the tensile index is the key basis for evaluating the effects of different fiber raw material ratios and different process routes. For example, when developing low-quantitation, high-strength packaging paper, R&D personnel compare the tensile index of different softwood pulp ratios to determine the best formulation that meets both strength requirements and controls costs. For special papers such as decorative base paper, electrolytic capacitor paper, etc., the tensile index is the basic index to ensure the subsequent processing and use performance.
Production process control:In the daily quality control of paper production, the tensile index is an important parameter to monitor the pulping effect, the chemical state of the wet part and the operation stability of the paper machine. By continuously detecting the tensile index and its coefficient of variation, operators can promptly detect problems such as fluctuations in beating degree, abnormal addition of additives, or changes in pressing pressure, and make process adjustments. The longitudinal and transverse differences in tensile index are also the basis for monitoring the degree of orientation of the fibers.
Raw material evaluation and procurement:In the pulp procurement process, the tensile index is an important indicator to evaluate the quality consistency of different suppliers and different batches of slurry. By measuring the tensile index of laboratory sheets, the potential strength of different slurries can be compared, providing a scientific basis for purchasing decisions. For paper enterprises using secondary fibers, the tensile index can also be used to evaluate the quality deterioration of recycled fibers and guide the control of the number of reuses.
Product Standards & Trade:In many national standards, industry standards or trade contracts for paper products, the tensile index is listed as an important quality indicator. For example, in product standards such as printing paper, packaging paper, and kraft paper, there are clear grade requirements and test methods for the anti-tension index. In quality disputes and arbitration inspections, the tensile index is the objective basis for determining whether a product meets the requirements.
Material Selection and Performance Prediction:For downstream processing enterprises, the tensile index is an important reference for choosing the right paper material. The printing enterprise evaluates the ability of the paper to withstand tension on the rotary printing machine according to the tensile index to avoid paper breakage during the printing process; paper bag processing enterprises design the bearing capacity and safety factor of paper bags according to the tensile index; Composite processing enterprises evaluate the strength reserve of paper as a substrate through the tensile index. In finite element analysis and numerical simulation, the tensile index can be used as an input parameter to predict the behavior of paper under complex stress.
Research and teaching:In the scientific research of papermaking science and engineering, the tensile index is a common index for evaluating new theories, new methods and new materials. To study the effect of fiber modification, the mechanism of action of new reinforcements, and the effects of different drying methods, the tensile index needs to be used as an important characterization method. In the experimental teaching of related majors in colleges and universities, the determination of tensile index is the basic practical content for students to understand the relationship between paper structure and performance.
6. Summary
As a basic and core mechanical index in the paper industry, the tensile index profoundly reveals the internal connection between paper strength and quantification. Through the normalization process in the definition, it successfully converts the absolute tensile resistance of paper into the relative strength under unit quantification, so that different quantitative papers can be compared at the same scale, providing a scientific basis for material selection and process optimization. The principle is rooted in the structural characteristics of the fiber network of paper, which reflects the comprehensive effect of fiber strength, fiber-to-fiber bonding force and fiber morphology distribution. In terms of measurement methods, every step from specimen preparation and environmental conditioning to tensile testing and quantitative measurement needs to follow standardized procedures to ensure the accuracy, repeatability and comparability of results. The factors affecting the tensile index cover multiple dimensions such as fiber raw material characteristics, pulping process, pulping process, wet chemistry, paper machine operating parameters and environmental conditions, which requires paper engineers to have a system concept to understand and control paper quality from the perspective of the whole process. In the application field, the tensile index has widely penetrated into all aspects of the paper industry, such as product research and development, production control, raw material evaluation, quality standards and scientific research, and has become an important bridge connecting fiber raw material selection, process condition optimization and final product performance. With the development of the paper industry in the direction of low quantitation, high strength and functionalization, the tensile index will become more and more important as a key index for evaluating material efficiency and structural rationality. In the future, with the advancement of multi-scale characterization technology and numerical simulation methods, the understanding and application of the anti-tension index will continue to deepen, providing continuous support for technological progress and product upgrading in the paper industry.