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下文为西门子公司网站上的小白科普文，为关于疲劳分析的的基础知识。文章写得简明易懂，在可读性上要优于专业书籍中的文字。 摘要如下：
What is a SN-Curve?https://community.sw./s/article/what-is-a-sn-curve What is a SN-Curve? 什么是S-N曲线？ A SN-Curve (sometimes written S-N Curve) is a plot of the magnitude of an alternating stress versus the number of cycles to failure for a given material. Typically both the stress and number of cycles are displayed on logarithmic scales. 一个SN曲线（有时也写作S-N曲线）是一个，给定材质的，交变应力相对于发生失效的循环次数的图表。典型做法是，应力与循环数都是以对数尺度的方式呈现。 Given a load time history and a SN-Curve, one can use Miner's Rule to determine the accumulated damage or fatigue life of a mechanical part. 有了一个载荷时间历程，有了SN曲线，人就能使用迈纳法则来确定一个机械零件的累积损伤和疲劳寿命。 History SN-Curves were developed by the German scientist August Wöhler (Figure 1) during the resulting investigation of an 1842 train crash in Versailles, France. In this crash, the axle of the train locomotive failed under the repeated “low level” cyclic stress of everyday usage on the railroad. SN曲线是由德国科学家August Wohler，在对1842年发生在法国凡尔赛的一次火车撞击进行调查时发展出来的。此次撞击中，机车的轮轴，每天在铁道上经受持续的“低水平”循环应力作用下，发生失效。
Figure 1: August Wöhler (1819 to 1914) developed SN-Curves to understand railcar axle failures While investigating, Wöhler discovered that cracks formed and slowly grew on an axle surface. The cracks, after reaching a critical size, would suddenly propagate and the axle would fail. The level of these loads was less than the ultimate strength and/or yield strength of the material used to manufacture the axle. 在调查过程中，Wohler发现，在轮轴表面形成有缓慢生长的裂纹。裂纹，在达到一定大小后，会突然扩展，轮轴就失效了。这些载荷的水平低于轮轴制造所用材质的最终强度和/或屈服强度。
Wöhler developed an apparatus to apply repeated loads to railroad axles and chart the relationship between load level and number of repeated cycles to failure. “Wöhler Curves” plot the relationship of alternating/cyclic stress levels against the number of cycles to failure. Wohler开发一套装置，用来在机轴上重复施加载荷，并用图表绘制出载荷水平与发生失效的重复次数的关系。“Wohler曲线”绘出了交变/周期应力水平与达到失效的循环次数的关系。
Designing an axle to withstand the initial static loads associated with holding up a locomotive was well understood. It was fairly obvious if an axle could carry the weight of a train if it did not collapse immediately. The concept of low level cyclic stresses, repeated over a long time, was relatively new and not well understood. For many observers at the time, it seemed unpredictable when an axle might suddenly fail. It was not until Wöhler developed his SN-Curves that cyclic stress became better understood, and fatigue life could be predicted in a more consistent manner. 设计一个轮轴，来承载机车相关的初始静载，是容易理解。一个轮轴，如果没有马上断掉的话，其是否能够载列车重量，是非常明显的。长期反复出现的低水平周期应力，这个概念，在那里还相当新，难以理解。对那时许多观察者来说，一个轮轴突然失效这事是不可预知的。直到Wohler开发出SN曲线，周期应力才得到较好的理解，疲劳寿命才能以一个更统一的方式实现预测。 How is a SN-Curve created for a given material? 如何为给定材质生成SN曲线？ Today, these curves are often developed by using a metal coupon testing machine (Figure 2). A small metal coupon is placed into the machine and subjected to a cyclic (or alternating) stress time history until a crack or failure occurs in the metal coupon. 现在，这些曲线，经常是使用金属试样在试验机，开发出来的。一个小的试样，放置在试验装置中，试样随周期性的应力时间历程，直到金属试样上有开裂，或发生失效。
Figure 2: Coupon testing is used to create SN-Curves for materials 试样试验，用于创制材质的SN曲线。 Several coupons must be tested at different stress levels to develop a SN-Curve. Figure 3 illustrates a typical SN-Curve derived from testing metal coupons. 多个试样在不同的应力水平下进行试验，来开发SN曲线。图3呈现的是典型的SN曲线，来源自试验金属试板。
A SN-Curve functions as a “lookup table” between alternating stress level and the number of cycles to failure (Figure 4). Most SN-Curves generally slope downward from the upper left to the lower right. This indicates that high level amplitude cycles have fewer number of cycles to failure compared to lower level amplitude cycles. SN曲线，用起来可视作交变应力和失效循环次数之间的查询表格。大部分SN曲线一般是自左上角到右下角。这意味着幅值较高的循环，发生失效的循环次数较幅值较小时更低。
In a fatigue test like this, the frequency at which the cycles are applied is not considered to be a factor in the number of cycles to failure. It is strictly the number of cycles, and not the rate at which the cycles are applied, that affect the SN-Curve results. 在类似这种疲劳试验中，周期施加的频率对于发生失效的循环次数并不是考虑的因素。这严格来说，影响SN曲线结果的是循环次数，并不是循环施加的频率。 In real life, the frequency of the cycles can be a factor, especially if the loading frequency coincides with a natural frequency or resonance of the object which amplifies the magnitude of the cycles. 在真实世界，循环的频率会是一个因素的，特别是载荷施加频率与固有频率一致，或与物体谐振，放大循环的幅度。， Plastic, Elastic and Infinite Regions 塑性，弹性和无限区 A SN-Curve can contain several different areas: a plastic region, an elastic region and an infinite life region as shown in Figure 5. SN曲线能包括多个不同区域：塑性区，弹性区及无限区，如图5所示。
There are three key values that separate the plastic, elastic and infinite life regions (Figure 5): 三个关键值来区分塑性，弹性和无限寿命区（图5）：
Several of the values on the SN-Curve can be found by doing a static stress-strain test on a material coupon (see Figure 6). SN曲线上多个值可通过通过对材质进行静态应力-应变试验
For example, the Ultimate Strength stress is the value that causes a failure for one cycle. The Yield Strength stress level divides the plastic and elastic region. 例如，极限强度应力是单个周期就引起失效的值。屈服强度分隔了塑性及弹性区。 Infinite Life 无限寿命 Some materials, like steel, exhibit an infinite life region (Figure 7). In this region, if the stress levels are below a certain level, an infinite number of cycles can be applied without causing a failure (of course, no test has been performed for an infinite number of cycles in real life, but a million+ cycles is typical). 某些材质，如钢材，呈现出无限寿命区（图7）。在这个区间，如果应力水平低于一定水平，循环次数可以无限次而不造成失效（当然，真实世界不可能做无限循环次数，但百万次以上是典型做法）。
Critical components (ie, engine crankshafts and rods) are usually designed for infinite life because cycles are speed dependent and accumulate quickly. All the cyclic stress levels that the part is subjected to must be below the endurance limit to have infinite life. 关键组件（ie, 引擎曲轴，及杆）经常设计为无限寿命，因为循环次数与寿命相关，且快速累积。所有的循环应力水平，必须是低于耐久极限，才有无限寿命。 Infinite life is not in effect under certain conditions: 无限寿命在以下状况下并不有效：
Different metals have different endurance limits. Some typical endurance limits are show in Table 1. 不同的金属有不同的耐久极限。表1中一些典型的耐久极限值。
Table 1: Typical Endurance limits of specific metals Many non-ferrous metals and alloys, such as aluminum, magnesium, and copper alloys, do not exhibit well-defined endurance limits (Figure 8). 许多非铁金属和合金，例如铝，锰，和铜合金，并没有并没有表现出清晰可见的耐久极限。
Where steel has a definite change in slope at the endurance limit, aluminum and other metals do not always have a distinct change. To determine if a part or object is operating in the infinite life region, the Goodman-Haigh diagram is often used. In addition to the cycle amplitude, mean stress is also accounted for in the Goodman-Haigh approach. 要确定一个零件或物体是否运行在无限寿命区，经常使用Goodman-Haigh图。
Elastic Region In the elastic region (Figure 9), the relationship between stress and strain remains linear. When a cycle is applied and removed, the material returns to its original shape and/or length. This region is also referred to as the “High Cycle Fatigue” region, because a high number of stress cycles, at a low amplitude, can cause the part to fail. 在弹性区，应力与应变的关系仍旧是线性的。当一个周期施加施后，然后移除，材质会恢复至原有形状及/或长度。此区也可称这“高周疲劳”区，在较低应力幅值下，应力周期数很高时会造成零件疲劳。
Typical factors that influence the performance of a material in the elastic region are residual stresses and geometric considerations. For example, a severe geometry change in the material may be more likely to have a crack initiate than a smooth geometry change. 在弹性区，影响材质性能的典型因素，有残余应力和几何结构。例如，突然的结构变化会比光滑的过渡更可能发生开裂。 注：结构突变在塑性区不敏感吗？ Plastic Region 塑性区 In the plastic region (Figure 10), the material experiences high stress levels, causing the shape and/or geometry to change due to the repeated application of stress cycles. This region is also referred to as the “Low Cycle Fatigue” region of the SN-Curve, where a low number of stress cycles, with a high amplitude, result in failure. 在塑性区，材质经受较高的应力水平，由于重复的施加应力引起形状和/ 或结构改变。这个区域同样指SN曲线的“低周疲劳”区，也就是在较高的应力幅值时，较少的应力循环就会造成失效。 注：低周疲劳与高周疲劳的分界点是如何定义的？10^4还是10^5?“低周疲劳”一定是在“塑性区”？
Material plasticity and geometryare big influences on the number of cycles to failure in the plastic region. 材质塑性和几何结构对于塑性区的失效的循环次数影响巨大。 Calculating fatigue life or damage in the plastic region of a material with a SN-Curve is probably best avoided. If cyclic stress levels are in the plastic region, a strain life approach would typically be recommended instead, which includes an E-N (Strain vs Number of cycles) as part of the analysis. Strain life also takes into account the order or sequence in which loads are applied. 使用SN曲线，计算某一材质在塑性区的疲劳寿命或损伤，最要要避开。如果循环应力水平位于塑性区，反而是推荐经常用的应力寿命法，其包含有E-N作为分析的一部分。应变寿命同样考虑载荷施加的次序。 SN-Curve Libraries Tests for materials can be expensive to run. Ideally, the tests should be repeated many times and at many different stress levels. With enough experiments, the SN-Curve would consist of a series of confidence intervals around the main curve as shown in Figure 11. 材质的试验做起来很昂贵。理想做法，试验重复进行很多次，使用不同的应力水平。有了足够的实验次数，绕着主曲线，一系列可信区间组成了SN曲线，如图11所示。 注：什么是confidence interval?
Some materials have well known curves because they are very commonly used. Some materials do not. When a new alloy is developed, the SN-Curve may be completely unknown and testing will be required to determine the curve. Conventionally, five different stress levels with three repeats at each level is considered the minimum to determine a SN-Curve. 一些材质的曲线到处都是，因为他们经常使用。某些材质则不然。当新开发出一种新合金，SN曲线就是完全未知的，需要做试验来确定曲线。常规做法，至少考虑五个不同的应力水平，每个应该水平重复三次，以此确定一个SN曲线。 The book “FKM Analytical Strength Assessment” contains many material SN-curves. It is published by the VDMA (Verband Deutscher Maschinen- und Anlagenbau e.V.), a German engineering association of engineering companies, which includes Siemens. 《FKM 分析强度评价》中包含许多材质的SN曲线。由VDMA，一家由包含西门子等工程公司组成的德国工程协会，出版。 Logarithmic Nature of SN-Curve: Double amplitude vs Double cycles example Consider the following hypothetical time histories to be evaluated for damage: 考虑评估以下假定时间历程造成的损伤：
First consider time history #1 and time history #2 shown in Figure 12. These time histories have: 考虑图12中所示的时间历程1和时间历程2。这些时间历程有：
Figure 12: Time history #1 vs Time history #2 Using Miner's Rule, one sees that the cumulative damage of time history #2 is double compared to time history #1 (see Figure 13). 使用迈纳法则，可见时间历程2的累积损伤是时间历程1的两倍（见图13）。
Next compare the damage potential in load time history #1 vs time history #3 shown in Figure 14. These time histories have: 其次，比较时间历程1 与 时间历程3的潜在损伤。这些时间历程有：
Figure 14: Time history #1 vs Time history #3 Using Miner’s Rule to analyze the load time history with a SN-Curve, one sees that the cumulative damage of time history #3 is 20 times compared to time history #1 (Figure 15), even though the amplitude of the cycles are only double in time history #3 compared to time history #1. 使用迈纳法则来分析，根据SN曲线来分析载荷时间历程，可见时间历程3的积聚损伤，是时间历程1的20倍，即使循环幅值仅是时间历程1的两倍。
Figure 15: Cumulative cycle count and cumulative damage of Time history #1 vs Time history #3 Why does doubling the stress level result in twenty times the damage? This is because the SN-Curve is actually a log vs log graph, which is easy to forget when viewing what appears to be straight lines in the log-log respresentation of the SN-Curve (Figure 16). 为什么应力水平翻倍，造成的操作是20倍呢？这是因为SN曲线实际上是对数 vs 对方图表，看起来时，很容易忘掉对数表现出的直线到底是什么意思。
Figure 16: SN-Curves plotted in Linear vs. Linear and Log vs. Log The relationship between stress level and number of cycles to failure is not linear, which has very important implications for fatigue life. 应力水平与失效的循环次数的关系并不是线性的，这对疲劳寿命的意味非常重要。 注：implication: SN-Curve Slope: K-factor k因子 The slope of the log-log SN-Curve is defined by “k-factor”. This "k-factor" governs the relationship between the stress level and the number of cycles to failure. 对数SN曲线的坡度定义为K因子。这个K因子定义了应力水平与失效循环次数的关系。 The "k-factor" was developed by Wöhler to easily relate the load (ie, stress) to the life (number of cycles to failure). Figure 17 shows how the Wöhler curve relates load to life via the k-factor in the elastic region of a SN-Curve. k因子是由Wohler发明的，很简单地将载荷与寿命关系起来。图17显示了SN曲线弹性区通过k因子载荷与寿命是如何关联的。
Because of this log vs log relationship, it means that a small change in load amplitude can have a very large change in the fatigue life or damage. In Table 2 below, with k-factor of 5, a 15% change in load results in a factor of 2 change in damage/fatigue life. 因为是对数关系，这意味着载荷幅值的小改变，对疲劳寿命或损伤的影响巨大。以下表格2，k因子是5，载荷改变15%，就损伤/疲劳寿命，造成因子变为2。
Table 2: k-factor versus stress level and fatigue life The logarithmic relationship between alternating stress level and the number of cycles to failure is an important consideration in accelerating fatigue testing. As the k-factor gets larger, small increases in load (ie, stress) create larger and larger changes in life. This can be used to accelerate a durability test. By increasing the load a small amount, so that the failure mode is not changed, one can still get large reductions in test time. 交变应力水平与失效循环次数的对数关系加快疲劳试验的一重要考量。k因子越大，载荷较小增加，会造成寿命的较大改变。这可以用来加快耐久试验。载荷增加一小点，失效模式不发生改变，人仍旧可以在试验时间上进行较大的缩减。 注：durability test: As a general rule of thumb, one can associate the following k-factors with the following: 作为一个常用的经验法则，可以将以下的k因子与下面所说关联起来：
SN-Curve adjustments due to Mean Stress 由平均应力而调整SN曲线。 When using SN-Curves, there can be extenuating circumstances where the SN-Curve must be adjusted to reflect certain situations. 当使用SN曲线时，会有些减轻情形，此时SN曲线必须调整来反映这些情况。 Take the stress time history in Figure 18. The average or mean stress of the cycles is zero. 图18中的时间历程。循环的平均应力是零。
Figure 18: Cyclic stress cycles with mean stress of zero Why track the mean stress? In real world loading situations, there could be a mean stress other than zero acting on the part. For example, the suspension system of a car has to carry the static weight (or load) of the car. As the car drives on the road, cyclic stresses/loads are applied by bumps in the road while the car weight is applying a mean stress (which is not zero). 为什么要追踪平均应力？真实世界的载荷情况中，作用在零件上的平均应力并不总是零。例如，轿车的悬空系统必须承载车子的静载荷。当车辆行驶在路上时，循环应力会在路上的颠簸中产生应力/载荷，整个过程中，车重在施加一个平均应力（非零）。 There are two different types of mean stress that a part may encounter: tension and compression. 零件可能碰到的两种不同类型的平均应力：拉伸和压缩。 In the case of tension (Figure 19), there is a positive mean stress. In a metal coupon test, a static tensile mean stress creates a load that tries to pull the coupon apart. 对于拉伸，平均应力是正的。在金属试板试验中，静态拉伸平均应力产生一种要将试件拉断的载荷。
Figure 19: Cyclic stress cycles with positive mean stress greater than zero (tension) This additional tension reduces the number of cycles to failure. The part would fail sooner than the SN-Curve with mean stress of zero would predict. 附加拉伸会降低失效循环次数。零件失效会较平均应力为零的SN曲线所预测的更快。 The static mean stress could also be pushing the part together, creating compression (Figure 20). This compression would extend the life of the part, making it last longer than the zero mean stress SN-Curve would predict. 静态平均应力也会将零件挤到一起，产生压缩。这个压缩会延长零件的寿命，较平均应力为零的SN曲线所预测的寿命更长。
Figure 20: Cyclic stress cycles with negative mean stress greater than zero (compression) Mean stress effectively shifts the SN-Curve up or down (Figure 21). A tensile mean stress in effect shifts the SN-Curve downward so it takes fewer number of cycles to fail. A compressive mean stress shifts the SN-Curve upward so the number of cycles to failure is higher. 平均应力会有效地让SN曲线上下偏移。拉伸平均应力会让SN曲线下移，失效的循环数更少。压缩平均应力让SN曲线上移，失效的循环次数更高。
Figure 21: SN-Curve adjustments due to mean stress Typically, SN-Curves are developed for a specific “Stress Ratio” as shown in Figure 22. The “stress ratio” called R is the lower value of the stress divided by upper value of the stress in cyclic stress time history. It is a convenient way to designate the conditions for a SN-Curve test. For example, in the aerospace industry, many components are tested with a stress ratio of 0.1, which ensures a net tension on the component. 典型情况是，SN曲线是就一具体的“应力比”发展出的，如图22所示。应力比R是循环应力时间历程中的低应力值/高应力值。这是一种指定SN曲线试验情况的简便方式。例如，在航空行业，许多组件试验的应力比是0.1，这保证组件是处于纯拉伸状态。
Figure 22: Diagram of stress ratios For fully-reversed loading conditions with mean stress of 0, R is equal to -1. For static loading, R is equal to 1. For a case where the mean stress is tensile and equal to the stress amplitude, R is equal to 0. 对于载荷全反转的载荷工况，平均应力为零，R为-1的情况。对于静态载荷，R为1。当平均应力是拉伸状态，且等于应力幅，R等于零。 For more information, read the article on Mean Stress and Stress Ratios. SN-Curve Adjustments due to Loading How the load is applied to the structure makes a difference in the number of cycles to failure. The load can be applied in several ways: torsional, bending, axially, etc as shown in Figure 23. 载荷在结构上施加的方式也会让失效的循环次数产生不同。载荷施加的方式会有许多种：扭转，弯曲，轴向，如图23所示。
Figure 23: Different types of loads/stresses The load scaling correction factors (Cf) are different and depend on the material. The correction factors are used to scale the stress up or down based on the type of load being applied. In the case of Bending vs Torsion for the material in Figure 23, the adjustment is 40%. 载荷比例修改因子（cf）是不同的，据材质而变。修正因子，基于载荷施加的方式，用于放大可缩小应力。按图23中的材质的弯曲vs扭转，调整值是40%。 Other SN-Curve Adjustments There are many other reasons why a SN-Curve may need to be adjusted. Other SN-Curve adjustments include part size, surface finishes, notches in the geometry, etc. 为什么SN曲线需要调整，是有许多原因的。其它的SN曲线调整包括零件大小，表面光洁度，几何结构的缺口，等等。 END |
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来自： sangdavinc > 《待分类》
