Breaking length

Definition and basic concept of fracture length

Breaking length is a common index to characterize the tensile strength of thin materials such as paper, cardboard, textile film, etc., which is defined as the calculated length when a material breaks due to stretching under its own weight. In a physical sense, the fracture length reflects the theoretical length of the material due to its own mass in the vertical suspension state. This concept was first applied to the paper industry because it is independent of specimen width and quantitation, allowing for an intuitive comparison of the strength properties of different quantitative papers. The fracture length is measured in kilometers, and the higher the value, the higher the tensile strength of the material. For paper, the breaking length is usually between 2 km and 8 km, and specialty or high-strength paper can reach more than 10 km. Break length is not only a strength index, but also a comprehensive parameter used in materials science to evaluate fiber bonding strength and fiber strength.

Physical principle of fracture length

The physical nature of fracture length is based on the relationship between tensile strength and mass per unit length in material mechanics. When the material specimen is subjected to axial tensile load, the internal tensile stress is balanced with the external force. When the tensile stress exceeds the tensile strength of the material, the specimen will fracture. The concept of fracture length translates this ultimate stress into an intuitive length scale that is independent of the specimen geometry and facilitates comparison between different materials.

From a mechanical point of view, there is a definite mathematical relationship between the fracture length and the tensile strength and quantification of the material. Considering a strip material with a width of b and a length of L, with a cross-sectional area of A and a density of ρ, the mass of the material is m = ρ· A· L。 If the material is suspended vertically, the maximum tensile stress generated by its own weight appears at the suspension point, and the stress value is σ = ρ·g· L。 When this stress reaches the tensile strength σ of the material_bThe material breaks, and the length L at this time is the fracture length L_B。 From this:

σ_b = ρ·g· L_B

In the formula, σ_bIt represents the tensile strength of the material, ρ represents the density of the material, g represents the acceleration of gravity, and L_BRepresents the length of the fracture. This relationship reveals an intrinsic link between fracture length and material tensile strength and density.

In practical applications, the density of materials such as paper is not easy to determine directly, while quantification is a more commonly used indicator. Quantitative g is defined as the mass per square meter of material, and its relationship to density ρ and thickness t is g = ρ·t. At the same time, the tensile strength is σ_bThe relationship with the tension F is σ_b = F / (b·t)。 Substituting these two relationships into the above equation gives a practical formula for calculating the fracture length:

L_B = F / (g·b·g)

Simplified to get:

L_B = F / (g·b) × 10³

In the formula, L_Brepresents the length of the fracture, the unit is kilometers; F represents the tensile strength of the specimen, and the unit is Newton; g represents the quantity of the specimen, in grams per square meter; b represents the width of the specimen in millimeters. The factor 10³ is used for unit conversion. This formula is the basic basis for determining the fracture length in the laboratory, which shows that the fracture length can be calculated by measuring the tensile resistance and quantitatively calculating it, without the need to conduct the suspension fracture experiment directly.

From the perspective of fiber material science, the fracture length reflects the combined effect of the bonding strength between fibers and the strength of the fibers themselves. When materials such as paper are stretched, stress is transferred through the bonding points between the fibers. If the fiber bonding strength is high enough, the fracture will occur in the fiber itself, manifesting as fiber fracture; If the bond strength is insufficient, the fracture will occur at the bonding point between the fibers, manifesting as the fiber being pulled out without fracture. Therefore, the length of the fracture depends not only on the strength of the fiber itself, but also on the bonding between the fibers. Processes such as beating, adding reinforcements, and calendering improve the fracture length by improving fiber bonding.

The fracture length has unique advantages as a strength index. Traditional tensile strength is expressed as force per unit cross-sectional area, but the thickness of paper is difficult to measure accurately, and the thickness varies greatly, making the tensile strength not comparable between different papers. Break length eliminates the effects of thickness and width by introducing quantitation, allowing different quantitations of paper to compare strength performance on the same scale. This normalization makes fracture growth a universal language for paper strength comparison.

Measurement method of fracture length

The laboratory measurement of the fracture length is an indirect measurement method, that is, the tensile and quantification of the specimen are measured separately, and then the fracture length is calculated according to the formula. The measurement process includes steps such as sample preparation, state adjustment, tension test, quantitative determination, and result calculation.

Sample preparation is the basis for reliable results. Cut the specified size of the specimen strip from the sample to be tested, the standard specimen width is usually 15 mm or 25 mm, and the length should be sufficient for clamping and testing, generally not less than 250 mm. When sampling, attention should be paid to directionality, paper and other materials usually have longitudinal and horizontal strength differences, longitudinal and horizontal specimens should be cut separately, and the direction should be marked on the specimen. At least 10 valid samples were taken from each test direction to ensure statistical reliability. When cutting the spline, the edges should be flat, no burrs, and no damage to avoid human defects affecting the test results.

State adjustment is a necessary step to ensure the comparability of test results. The standard conditions for paper testing are usually 23±1 degrees Celsius, 50% relative humidity ±2%, and the adjustment time is at least 4 hours, which needs to be extended to 24 hours for moisture-sensitive materials. State regulation allows the specimen to achieve moisture balance, eliminating the effect of ambient humidity on paper strength and quantification.

The tensile test is carried out on a tensile testing machine. The testing machine should have an appropriate range and accuracy, and the accuracy of the force value sensor should not be less than 0.5%. The gripper should be able to hold the specimen firmly without slippage and damage, and the clamping surface should be notched or padded with appropriate material to increase friction. The initial distance between the two fixtures is called the clamping distance, and the standard clamping distance is usually 180 mm or 100 mm. During the test, the two ends of the specimen are clamped flat into the upper and lower fixtures to make the specimen axis coincide with the tensile direction to avoid deflection. A tensile load is applied at a constant speed, typically 20 mm per minute or 100 mm per minute until the specimen breaks. The maximum force value at the time of fracture is recorded, which is the tension resistance. For specimens in each direction, no less than 10 tests are conducted, and the arithmetic average of the tension resistance is calculated.

Quantitative determination is another key parameter in the calculation of fracture length. A specimen of a specified area, usually 100 square centimeters or more, is cut from the same sample and weighed with an analytical balance. The quantitative calculation is as follows:

g = m / A × 10⁴

where g represents quantitative, the unit is grams per square meter; m represents the mass of the specimen in grams; A represents the area of the specimen in square centimeters. For paper, quantification of at least 5 specimens is usually measured, taking the arithmetic average as the final result. When determining and quantifying, it is necessary to ensure that the specimen has been adjusted for state adjustment, and the weighing environment should be kept stable to avoid air flow and static interference.

The calculation of fracture length is based on tensile and quantitative measurements, and the calculation formula is:

L_B = F / (g·b) × 10³

In the formula, L_Brepresents the length of the fracture, the unit is kilometers; F represents the average tension in Newton; g stands for average quantitative in grams per square meter; b represents the width of the specimen in millimeters. The longitudinal and transverse fracture lengths are calculated respectively, and the results are revised to two decimal places. For materials with obvious anisotropy, the longitudinal and horizontal average or ratio should also be calculated as a comprehensive evaluation index.

In addition to conventional methods, the fracture length can also be determined by pendulum tensile strength meter. This type of instrument correlates the pendulum energy with the tension and reads the tension value directly. The modern electronic tensile testing machine is equipped with a computer data acquisition system, which can automatically record the force-elongation curve, calculate the tensile, elongation and breaking length, and improve the testing efficiency and accuracy. For extremely thin or weak materials, small-range sensors and special fixtures should be selected to avoid premature breakage of the specimen at the clamping site.

Key factors that affect the measurement of fracture length

Breaking length measurements are influenced by a combination of factors, from the material itself to the control of test conditions, each of which can have a significant impact on the final result.

The characteristics of fiber raw materials are the fundamental factors affecting the fracture length. Different types of fibers have different intrinsic strengths, cotton fiber and hemp fiber have higher strength, followed by wood fiber, and grass fiber is lower. The length of the fiber affects the degree of interweaving between the fibers, and the network structure formed by long fibers is more developed, the stress transfer is more effective, and the fracture length is higher. The thickness of the fiber affects the number of fiber roots per unit mass, and the fine fibers form more binding points, which is conducive to the improvement of strength. The chemical composition of fibers is equally important, and fibers with high cellulose content and moderate content of hemicellulose and lignin are more likely to form good bonds. Pulping methods such as chemical pulp, mechanical pulp, semi-chemical pulp, etc., change the shape and surface properties of the fiber, which in turn affects the strength of the paper.

The beating process is a key link in regulating the fracture length. Pulping causes fibers to be cut, swollen and finely fibrosized, increasing the specific surface area and flexibility of fibers, and promoting inter-fiber bonding. Proper beating can significantly increase the breaking length, but excessive beating will cause the fibers to break excessively, reducing the strength. Pulping methods such as free pulping and viscous pulping produce different fiber shapes, which affect the strength characteristics of the paper. As an index to measure the degree of beating, there is a certain correlation with the length of the break, but it is not a simple linear relationship due to the influence of fiber type and beating method.

The process parameters have an important impact on the fracture length. The wet pressing process improves the tightness of the paper sheet and the fiber contact area through mechanical pressure, strengthens the fiber bonding, and improves the fracture length. Calendering smooths the surface of the page, but over-calendering can damage fiber bonding, leading to a decrease in strength. The temperature and tension control during drying affect the shrinkage and internal stress distribution of the fibers, which in turn affects the fracture length. The addition of papermaking chemical additives such as reinforcers and retention agents can improve the breaking length by improving fiber bonding or increasing cross-linking between fibers.

The structural properties of paper directly affect the breaking length. The uniformity of the paper reflects the uniformity of the fiber distribution, and the paper with poor uniformity has local weak areas, and the stress is concentrated during stretching, resulting in low fracture length. The directionality of paper, that is, the difference in strength between the longitudinal and transverse directions, comes from the directional arrangement of fibers during the copying process, and the longitudinal fracture length is usually higher than that of the transverse direction. The tightness and porosity of the paper affect the bonding area between the fibers, and the denser the paper fibers are more closely bonded and the fracture length is higher. The moisture content of paper has a significant impact on the tensile strength, and the increase of moisture makes the fibers swell, the bonding between fibers weakens, and the fracture length decreases, which is the reason why state regulation is crucial.

The choice of test conditions directly affects the accuracy of the measurement results. The measurement accuracy of the specimen width affects the fracture length calculation, and small deviations can cause the results to vary proportionally. The control of the clamping force of the fixture is very important, and insufficient clamping force will cause the specimen to slip, so that the measured tension is low; Excessive clamping force may damage the specimen and break in advance at the clamping point. The selection of tensile speed must comply with the standard regulations, too fast will make the material brittle and high strength; If the speed is too slow, the strength may be low due to creep. The accuracy of the clip distance affects the elongation determination, but has little effect on the maximum tension, provided that the clip distance is within the standard range.

The role of environmental factors cannot be ignored. Changes in temperature and humidity directly affect the balanced moisture of paper, which in turn changes its mechanical behavior. Rising temperatures usually cause a slight decrease in paper strength; The increase of humidity makes the paper absorb moisture and expand, weaken the bond between fibers, and significantly decrease the fracture length. Therefore, the regulation and control of the standard test environment is the basis for guaranteeing comparability of results. Temperature fluctuations and airflow disturbances during testing can also affect the results and should be tested under stable environmental conditions.

The standardization of the operator is also a factor affecting the outcome. Whether the specimen remains vertical and without torsion during installation, whether the clamping is uniform, whether the data reading is accurate, and the identification and treatment of abnormal conditions such as slippage and jaw fracture all require standardized operation and rich experience. For samples with poor uniformity or uneven strength, the test results may be more discrete, and the number of tests needs to be increased and statistical analysis should be performed correctly.

Applications of fracture length in the industrial field

As the core index for evaluating the strength performance of paper, the breaking length has a wide range of application value in the paper industry, printing and packaging, quality supervision and material research and development.

In paper industry production, break length is an important parameter for quality control. Paper companies monitor the stability of the production process by detecting the length of the break online and offline. When the fracture length fluctuates abnormally, the process personnel can find the cause from the aspects of fiber raw material ratio, pulping degree control, wet pressure pressure, drying conditions, etc., and adjust the process parameters in time. For the production of high-strength paper such as kraft paper, cable paper, industrial paper, etc., the breaking length is the main basis for determining the product grade. According to user needs and product standards, papermaking enterprises set internal control indicators for breaking length to ensure that the products from the factory meet the quality requirements. During the development of new grades, the fiber ratio, pulping process and chemical additive formulation are optimized by comparing the breaking length under different process conditions.

In the printing industry, breaking length is closely related to the operating performance of the press. In rotary printing machines, paper ribbons are subjected to large tensile tension during high-speed operation, and paper with insufficient breakage length is prone to paper breakage, resulting in printing downtime and quality accidents. Printing companies choose paper with appropriate breakage length according to printing speed and tension requirements to ensure a smooth printing process. During the offset printing process, the paper needs to withstand the action of printing pressure and dampening fluid, and the breaking length reflects the ability of the paper to resist these effects without breaking. For delicate products that need to be printed multiple times, the breaking length is a reference index for evaluating the reprintability of paper. Publishing paper, book paper and other product standards usually stipulate the minimum requirements for breaking length to ensure printing and processing performance.

In the field of packaging, the length of the break is related to the strength and processing adaptability of the packaging material. Paper bag paper, cement bag paper, etc. need to withstand impact and tensile loads during filling and handling, and the length of the break is an important indicator to evaluate its applicability. The fracture length of the face paper and core paper of corrugated cardboard affects the edge compressive strength and bending performance of the cardboard, which in turn affects the stacking strength of the carton. Packaging paper and cardboard need to be folded, credged, grooved and other processes in the process of bag and box making, and the length of the break reflects the ability of the material to resist these processes without rupture. Food packaging paper, such as tea bag paper, filter paper, etc., the breaking length affects its running performance on automatic packaging machines.

In the field of quality supervision and product inspection, breakage length testing is an important means to ensure that paper products meet standards and specifications. Paper product standards such as GB/T 451.3 and GB/T 453 clearly stipulate the breaking length indicators of different types and grades of paper, and the third-party testing agency will inspect according to the standard method and issue a credible test report. In the inspection of import and export paper, the length of the break is a routine test item to verify whether the product meets the requirements of the trade contract. In the quality control of government procurement and major event paper, strength indicators such as fracture length are important bases for judging paper quality. In consumer rights protection and product quality dispute resolution, the fracture length test results can be used as a reference for technical evaluation.

In the field of material research and development, break length is the basic parameter for evaluating the properties of new fiber materials and papers. In the study of plant fiber modification, the effect of fiber modification was evaluated by measuring the fracture length of paper under different treatment conditions. In the development process of chemical additives such as dry strength agents, wet strength agents, cross-linking agents, etc., fracture length is the core index to evaluate the enhancement effect of additives. In the study of waste paper recycling, the decay degree of fiber quality and the application potential of recycled paper were evaluated by comparing the breaking length of paper under different recycling times and deinking processes. In the research and development of special papers such as insulating paper, battery separator paper, filter materials, etc., the breaking length is the basic parameter of mechanical properties, and together with other functional properties, it constitutes a comprehensive evaluation system.

In the field of education and scientific research, the rupture length test is the basic project of paper performance experimental teaching. Through the fracture length measurement experiment, the students majoring in light chemical engineering mastered the tensile strength test method and data processing skills, and understood the relationship between fiber bonding and paper strength. In the study of papermaking technology, the fracture length and other strength indicators such as fracture resistance, tear degree, and ring compression strength constitute a comprehensive evaluation system for the mechanical properties of paper. The correlation analysis between fracture length and fiber morphological parameters such as fiber length, roughness, cell wall thickness, etc. provided data support for revealing the mechanism of paper strength. In the study of new fiber resources and pulping methods, the breaking length is the primary index for evaluating the potential of papermaking.

In the field of standard formulation and technical specifications, the fault length detection method has been included in a number of national and industry standards. GB/T 12914 specifies the method for determining tensile strength, which provides a basis for the calculation of fracture length. Product standards for different paper types, such as newsprint, offset printing paper, kraft paper, cigarette paper, etc., all stipulate the specific index requirements for breaking length. The ISO 1924 series of international standards also adopts the principles of tensile resistance and quantitative calculation of fracture length. The formulation and revision of these standards require a large amount of experimental data support, and the rupture length test plays a fundamental role in it.

Summary and outlook

As a characteristic index to characterize the tensile strength of thin materials such as paper, the fracture length is used to calculate the strength properties of different quantitative materials by calculating the ratio of tensile strength to quantitative from the physical model of material self-weight fracture. This index not only avoids the difficulty of thickness measurement, but also directly reflects the comprehensive effect of fiber bonding strength and fiber strength. Through standardized sample preparation, state adjustment, tensile testing and quantitative determination, the fracture length can be quantified as the basic data for engineering control and scientific research. From fiber raw material properties to pulp and paper processes, from specimen geometry to test environmental conditions, the combination of factors requires solid expertise and rigorous operating practices. In a wide range of fields such as paper production, printing processing, packaging applications, quality supervision and material research and development, breaking length detection has become an important technical means to evaluate paper strength, optimize process formulas, and ensure product quality.

Looking ahead, fracture length detection technology is developing in the direction of automation, online and diversification. The automatic sampling and testing system integrates tensile strength meters, quantitative testers, and data management systems to automate the entire process from specimen delivery, parameter measurement, and result calculation, greatly improving testing efficiency and data reliability. Online tensile strength testing technology monitors the strength changes of the web in real time by installing special sensors on the machine, providing real-time information for process control and product quality prediction. Multi-parameter synchronous testing techniques such as simultaneous measurement of tensile strength, elongation and tensile energy absorption can more comprehensively evaluate the toughness and fracture resistance of materials.

With the continuous emergence of new paper-based materials, the application range of the concept of breaking length is expanding. Nanocellulose-reinforced paper-based materials exhibit extremely high breaking length potential, which provides the possibility for the development of high-performance paper-based structural materials. In biodegradable packaging materials, the fracture length is the basic index of mechanical properties, and together with the degradation performance and barrier performance, it constitutes a comprehensive evaluation system. Functional paper-based materials such as conductive paper, filter materials, biosensor substrates, etc., put forward new requirements for mechanical properties, and the fracture length test needs to adapt to small size, special environment and other conditions. In the study of interface modification of composite materials, the fracture length can be used to evaluate the interfacial bonding effect between fibers and the matrix, which provides a reference for the optimal design of composite materials.

In the context of digitalization and smart manufacturing, long data is becoming more closely linked to production process parameters. Based on a large amount of historical test data and machine learning algorithms, the correlation model between fracture length and process parameters such as pulping degree, wet pressure pressure, and drying curve can be established to achieve predictive control of product quality. The combination of fracture length data with fiber morphology analysis and paper structure characterization provides richer information for in-depth understanding of paper strength mechanism. As the basic index for paper strength evaluation, the fracture length will continue to play an irreplaceable role in the development of pulp and paper science and technology and the application innovation of paper-based materials.