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A test method to measure fatigue crack growthrate of rubbery materialsAbstract Crack growth characteristics of rubbery materials are an important factor determining the strength and durability of thematerials. It is necessary to define the means of measuring the fatigue crack growth rate of rubbery materials. In this paper, a test method is introduced using a newly designed test machine. Measurements were made in order to characterize the fatigue crackgrowth behavior under repeatedloadexpressed as a crack growth rate, i.e. crack length per cycle, as a function of the tearing energy, determined by a broad range of the strain energy density in a test piece of pure shear geometry. Measurements were also made to observe the effects of test temperature and loading frequency. A high speed CCD camera is utilized to allow in situ measurements following the path of the crack growth simultaneously. The power law dependency between crack growth rate and tearing energy was confirmed by the new test methodology. Comparison of the fatigue crack growth behavior between NR and SBR rubber compounds was made, and the exponent a values of the NR compound were found to be, in general, lower than those of the SBR compound, indicating that the NR compound is more resistant to fatigue crack growth than the SBR compound.1. Introduction Certain rubbery products such as tires, an importantcomponent of vehicles not only in supporting their heavy loads but also in ensuring their braking andtraction, are subjected to dynamic bending while in use and may fail because of the appearance of cracks andtheir progressive growth. This phenomenon is known as fatigue, which has been defined as a failure resulting from the crack growth initiated by naturally occurring flaws in the rubber matrix under repeated loads accompanied by relatively small deformations 1. Recently, Ellul 2 made an excellent review for mechanical fatigue of rubber. Fatigue life is conventionally defined as the number of cycles to break a specimen into two pieces at a particular stress for stresscontrolled, or at a particular strain for strain-controlled, tests. Since the crack is initiated from an arbitrarydefect in a test piece, the experimental data of fatiguelife may be somewhat scattered. Therefore, for thetime-consuming task of obtaining an average value forfatigue life a large number of samples is necessary. Test methods in determining the fatigue life can be categorized as follows: periodic loading between fixed stress (or strain) limits in tension or compression, reversed shear stresses obtained by torsional deformation, and reversed bending stresses in one dimension (flexing of a sheet) or two dimensions (rotary deflectionof a cylinder). One of the disadvantages with these conventional methods is the difficulty in controlling the bending strain, because it depends on the modulus of the rubbery material. Furthermore, the fatigue life of rubber products is very sensitive to both the magnitude and type of applied strain and, therefore, may only rarely be correlated with field performance of the product subjected to more complicated strain patterns 3. The scientific basis for the optimization of fatigue life is to determine the rate of fatigue crack growth overa broad range of tearing energies. In practice, rubber products usually meet with progressive weakening of mechanical properties, and finally reach failure due to mechanical fatigue, i.e. continual crack growth undersinusoidal excitation with an extended period of time. The crack growth characteristics of rubbery materials must be, therefore, an important factor determining their strength and durability 4. The fatigue crack growth is affected by not only material variables such as rubber type, but also test conditions such as test frequency, temperature, strain amplitude, and so on 5,6. The crack growth is delayed somehow by strain-induced crystallization at the crack tip in crystallizable elastomers such as NR. On the other hand, non-crystallizable elastomers like SBR will follow time-dependent crack growth behavior. In this study, using a newly designed test machine, an advanced test method is introduced in order tocharacterize the crack growth behavior of rubbery materials. The effects of temperature and frequency on the fatigue crack growth are investigated as well.2. Experimental2.1. Mechanical arrangement for measuring the rate of fatigue crack growth A schematic diagram is shown in Fig. 1 of a new test machine for investigating the fatigue crack growth of rubbery materials. The clamps hold the rubber specimen located in a temperature-controlled chamber, withthe upper clamp connected to the load cell fixed to a crosshead, and the bottom clamp connected to a disktype drum cam driven by an electrical servo-motor (or if necessary driven by hydraulic servo-power). The temperature can be regulated electrically from room temperature up to 200 8C. The position of the crossheadwith load cell is fixed using a fixing ring at a predetermined value of displacement or force and, if required, a stressstrain curve is obtained by a single revolution of the cam. The rubber specimen is periodically subjected to rectilinear updown motion ranging from 1 to 10 Hz, a cycle which is controlled by the rotation speed of the motor. The amplitude of displacement is adjusted up to 200% in extension by the magnitude of off-center of the shaft joined to the cam. The non-relaxing condition, defined as the ratio of minimum to maximum deformation in the case of a strain-controlled test, can be controlled by adjusting a prestrain device positioned above the upper clamp. The crack growth of the rubber specimen was monitored through an image process system with a high speed CCD color camera. Measurements were made to track the tip of the crack, and the length of crack growth was automatically recorded as a function of the strain cycles, providing the rate of fatigue crack growth.2.2. Determination of tearing energy (G)and fatigue crack propagation The energy criterion for crack growth, originallyproposed by Griffith 7, is applied to mechanical fatigue of rubbery materials. As shown in Fig. 2, aninitial crack c in a specimen of thickness t and at constant length l (no work applied) will propagate if the decrease in the total elastic energy E of the specimen per unit increase in the crack is greater or equal to the tearing energy G required to grow the crack. The postulation is mathematically expressed as follows:Ke1=tTevE=vcTRG (1) For experimental purposes, the tearing energy G can be simply calculated from the easily measurable applied force on well-defined test geometries, one of which is the pure shear test piece 8 as shown in Fig. 2. The following equation is applied to determine the tearing energy in this case: GZUho (2) where U is the strain energy density, and ho is the unstrained height of the test piece. Because the tearing energy G does not depend on the crack length, as indicated in Eq. (2), the pure shear geometry is regarded as stable. The value of U can be simply determined here from the area under the stressstrain curve for the test piece at a given displacement. The fatigue crack growth behavior under the applied dynamic stress is usually expressed as the length of crack growth per each repeating cycle (dc/dn) as a function of the tearing energy (G), where the value of dc/dn is the rate of fatigue crack growth 1. There must be an effect of ozone in the atmosphere on crack growth in the range of low tearing energy over an extended period of time. However, it is negligibly small compared to that of the mechanical factor. On the assumption that the crack growth is mainly caused by the mechanical factor, most rubbery materials obey a power law dependency between the crack growth rate and the tearing energy as followsdc=dnZAGa : (3) where A and a are constants. Since the crack growth behavior of rubbers under dynamically repeating load is independent of the geometry of the test piece, the behavior provides the true properties of rubber strength or fatigue.2.3. Preparation of rubber specimen and operationflow of fatigue crack growth measurements Natural rubber (SMR-CV60) and styrenebutadienerubber (SBR 1500S, bound styrene 23.5%, Kumho Petrochemical Co., Ltd, Korea) were used for this study. Identical amounts (50 phr) of carbon black N351 were added to both rubber compounds. The formulation of rubber compounds used in this study is given in Table 1. Mixing was carried out according to ASTM D3191-00 for SBR and ASTM D3192-00 for NR compounds, respectively. The rubber compounds were vulcanized to provide the pure shear test piece of 2 mm thicknessshown in Fig. 2. The length and height of the specimen were designed to be 200 and 20 mm, respectively. An initial cut, about 30 mmlong, was made in one end of the specimen, and the tip was sharpened using a lubricated razor blade. The specimen was then placed in the newly designed tester in this work as described in Section 2.1.a Part per hundred parts of rubber, by weight. b SMR-CV60. c SBR1500S (Kumho Petrochemical Co., Ltd, Korea). d Stearic acid. e N-tert-butyl-2-benzothiazoic sulfenamide. f N-(1,3-dimethylbutyl),N0-phenyl-p-phenylenediamine. A dynamic strain up to 100% was applied at various loading frequencies ranging from 1 to 10 Hz. All the experiments were performed under the fully relaxing condition, i.e. the minimum strain was zero. The length of the crack propagated, c, was monitored in situ using a high-speed CCD color camera. Photographs obtained from the experiments for NR compound are shown in Fig. 3. Image control and calibration in advance are essential to ensure precise measurements of the length of crack growth. The measurements were taken at a splitsecond interval. The rate of crack propagation, dc/dn, was then obtained from the slope of the plot between the crack length and the number of cycles, n. The observed rate of crack was analyzed in terms of the fracture energy, G. The strain energy density, U, was calculated from the observed relation between the tensile load and displacement using the uncut specimen at each strain level subjected to the crack growth test. The operational procedures described above are summarized as a flow chart shown in Fig. 4.3. Results As can be seen in Fig. 5, the experimental results on the crack length versus loading cycles for C/B reinforced SBR compound yields a linear plot, the slope of which indicates the crack growth rate of the rubber compound. The experimental values of strain energy density (U) for NR and SBR rubber compounds are shown in Fig. 6, in which the s3 curve inserted shows how to determine the strain energy density. Fig. 5. Determination of the crack growth rate (dc/dn) from the plot ofcrack growth (c) versus loading cycle (n) for C/B filled SBRcompound at strain 35%, frequency 1 Hz, and temperature 40 8C The U values were nearly identical at a temperature of 40 8C for NR and SBR rubber compounds, however, the values deviated from each other as the temperature increased up to 100 8C. The U value of SBR rubber increased beyond than that of NR rubber at high temperatures, which may be due to relatively high flexibility in NR molecules at higher temperatures. The crack growth rate (dc/dn) of NR and SBR rubber compounds, respectively, are plotted as a function of the fracture energy (G) using a loglog scale. The experimental results are shown in Fig. 7. Over the range of fracture energies employed, generally from about 300 to 60,000 J/m2, the rates of crack propagation increased linearly with the tearing energy. These experimental results obey the power law dependency as indicated in Eq. (3).Fig. 6. Strain energy density (U) for C/B filled NR and SBR compounds at different temperature (U determined from the area. The exponent a values of the equation are listed in Table 2, which are shown to be inreasonably good agreement with results from other studies 2,5. The exponent a values are dependent mainly on rubber type used and compounding ingredients to a lesser extent. The a values for the NR compound ranged from 2.08 to 2.13, and for the SBR compound from 3.78 to 4.21, depending on test temperature and frequency.Fig. 7. Crack growth rates (dc/dn) are plotted as a function of tearing energy (G) for C/B filled NR and SBR compounds at different temperaturesand repeating frequencies. The lower value of the exponent for the NR compound denotes more resistance to crack growth at a given tearing energy. This outstanding characteristic is considered to originate from the strain-induced crystallization at the crack tip of the NR rubber. The effect of loading frequency up to 10 Hz on the crack growth behavior was not significant. On the other hand, the effect of temperature was seen to be very substantial: as temperature increased from 40 to 100 8C, the rate of crack growth increased to about 10 times the rate at a given tearing energy for the NR rubber compound, while the increase was to about 100 times the rate for the SBR rubber compound. The different behavior on temperature dependence of the crack propagation seems to be mainly attributed to the different degrees of mechanical hysteresis in these rubber compounds. For engineering design of a rubber component comparison of the crack growth rate in terms of tearing energy will offer a good indication to select the best rubber and allow for a decision to be made in the development of blends of various rubbers to optimize 4. Conclusion The experimental results obtained are summarizedas follows. An advanced test methodology using anewly designed test machine was successfully appliedto determine fatigue crack growth characteristics. The test method makes it possible to measure in situ the length of the crack growth by tracking the crack tip through a high speed CCD color camera during dynamic loading. Some measurements were made of fatigue crack growth for NR and SBR rubber compounds. The power law relation between crack growth rate and tearing energy was confirmed by the new test methodology. The a values for the NR compound ranged from 2.08 to 2.13, and for the SBR compound, from 3.78 to 4.21, depending on test temperature and frequency. The lower values of the NR compound indicate that the NR compound is more resistant to fatigue crack growth than the SBR compound.橡胶材料的疲劳特性的一种检测方法摘要橡胶材料的疲劳特性是影响材料的强度和韧性的重要因素。因此，设计一种方法来检测橡胶的疲劳特性是必要的，在这篇文章中介绍了一种新设计的检测机。这种方法是为了检测在重复载荷下的疲劳特性，如：每次循环的疲劳增长，用一种纯几何剪切学在定义了一系列张紧力的情况下，用断裂能量方程。检测也可以观察检测温度和载荷频率的影响，一个高倍CCD摄象机用来跟踪疲劳破坏的路径。一种新的测量方法遵循疲劳增长率和断裂能量增长的规律。对NR,SBR的混合物组成的橡胶和大量的典型的NR橡胶做了比较发现，一般情况下，NR混合物组成的橡胶比SBR混合物组成的橡胶数值低，这表明NR橡胶比SBR橡胶更耐疲劳。1. 介绍一些橡胶制品比如轮胎，是汽车的重要组成部分不仅支撑它的载荷而且确保它们的刹车和牵引，在使用中受制于动力弯曲，由于疲劳的出现和里程的增加而失灵。这种现象被称为疲劳，是在循环载荷伴随着微小裂纹在橡胶矩阵中自然发生的裂纹引起的失灵。最近，Ellul对橡胶的机械疲劳做了一个详细的评论。疲劳寿命通常定义为在可控的特殊压力或者可控的张力作用下将一个试验件变成两个所经过循环的次数.由于裂纹从试件的任意缺陷开始出现，疲劳寿命的实验数据可能有些分散。因此，为了完成获得疲劳寿命的平均价值这样耗时的任务，大量的样本是必要的。确定疲劳寿命的试验方法可以分类如下：压缩或松弛中固定压力（或张力）的定期载荷界限，通过扭转变形得到的扭转剪切应力，扭转弯曲应力单一层（一面的弯曲）或两个层面（圆柱的扭曲变形）。这些常规方法的一个缺点就是抗弯应变很难控制，因为它取决于橡胶材料的弹性模数。此外，橡胶产品的疲劳寿命对应用应变的规模和类型是非常敏感的，因而，或许与产品的性能只有很少的关联，而更多的是受复杂的应变模式的影响。疲劳寿命优化的科学基础是确定疲劳扩展速率超出外力断裂能量的局限范围。在实践中，橡胶制品常常会遇见逐步削弱的力学性能，最终由于机械疲劳导致失败，即正弦激励下持续了一段时间的不断的裂纹扩展。因此，橡胶材料的裂纹扩展特性一定是决定其强度和耐久性的重要因素之一。疲劳裂纹扩展不仅受物质的变数，例如橡胶的类型决定，还受如测试频率，温度，应变振幅等的测试条件决定。可结晶的弹性材料，如天然橡胶弹性体，在裂纹尖端的应变诱导结晶可以以某种方式延缓裂纹扩展。一方面，非结晶热塑性弹性体，像丁苯橡胶，将遵循不稳定的时间依赖性裂纹扩展行为。在这项研究中，采用新设计的试验机，先进测试方法的采用取代了橡胶材料裂纹扩展行为的特征化。温度和频率对疲劳裂纹扩展的影响也进行了研究。2，实验2。1 疲劳裂纹扩展率的机械安排图1是一个新的调查橡胶材料疲劳裂纹扩展的检测机的原理示意图。用夹子夹住橡胶标本，置于一个温度控制室，上部钳与测压元件连接，固定在横梁上。底部钳连接到电动伺服电机驱动（或者有必要的话用液压伺服的功率驱动）的盘式凸轮轴上。温度可以从室温电动调节到200 8C 。测压元件的十字接头位置用固定板固定在位移或压力的预定值处，如果需要的话，可以通过凸轮螺旋转动得到一个应力应变曲线。橡胶试样定期受到从1到10赫兹的直线上下运动，这是一个由发动机的转速控制的循环轮转。通过与凸轮相连接的轴的偏离中心幅度可以将位移振幅横向伸展调高至200%。“非松弛情况”，就应变控制的测试而言，被定义最小应变和最大应变的比率，它可以通过调整位于上盘制动螺旋上的预应变装置来控制。橡胶标本的裂纹扩展用高速CCD彩色摄像机通过一种图像处理系统进行监测。这些测量被用来跟踪裂缝的顶端，裂纹扩展的长度被自动记录为一个应变周期函数，提供疲劳裂纹扩展的速率。2。2测定断裂能量（G）和疲劳裂纹扩展性能裂纹扩展的能量判据最初是由Griffith提出的，被应用于橡胶材料的机械疲劳中。如图2所示，这个假设可以用数学公式表述如下：Ke1=tTevE=vcTRG (1)实验的目的是撕裂能源G可以从明确的试验几何中的简易可测量作用力中简单地计算出，其中之一是纯剪切试验中的试件，如图。 2所示。以下公式是用于测定撕裂能量的，其条件是：GZUho （ 2 ）中U是应变能量密度，ho是试件的无应变高度。由于撕裂能量G并不取决于裂纹长度，正如Eq中显示的，纯剪切几何被视为固定值。在这里，U的值可以从试件在给定的位移下应力应变曲线面积中简单的测定出来。
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