钢的应力-应变特性
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Overview
资料来源: 布莱克斯堡弗吉尼亚理工大学土木与环境工程系罗伯特. 里昂
材料对人类发展的重要性, 清楚地被世界历史的早期分类所捕捉到石器时代、铁器时代和青铜时代等时期。引进西门子和麦地那工艺生产钢在 mid-1800s 是一个最重要的发展, 在发动工业革命, 改变了大部分欧洲和美国在下半年的19年.世纪从耕地社会到今天的都市和机械化的社会。钢, 在其几乎无限的变化, 是我们周围, 从我们的厨房用具, 汽车, 到生命线, 如电力传输网络和供水系统。在这个实验中, 我们将研究两种类型的钢的应力-应变行为, 这些钢材与土木工程应用中通常看到的范围有关-从非常温和的热轧钢材到坚硬的冷轧的钢。
Principles
钢的术语通常用来表示主要是铁 (Fe) 的材料, 通常在95% 到98% 的范围内。纯铁是同素异形体, 在室温下以身体为中心的立方 (BCC) 结构, 在912°C 之上变成以面为中心的立方 (FCC) 结构。FCC 结构中的空空间和晶体结构中的缺陷允许其他原子, 如碳 (C) 原子, 通过扩散从间隙 (或空) 空间中添加或移除。这些增加, 以及随后发展的不同的晶体结构, 是由于加热和冷却在不同的速率和温度范围, 一个过程称为热处理。这项技术已有2000年的知名度, 但多年来一直在大马士革钢铁等应用领域保持着秘密 (≈300AD)。
如果我们扩大 FCC 结构中的开放圈, 直到球体开始接触, 然后切割这个原子结构的基本立方体, 结果就是单元单元。在这些新球体开始接触铁原子之前, 可以添加41.4% 的铁离子直径的球体。碳原子是铁的直径的 56%, 因此新的结构会随着碳原子的引入而扭曲。钢的性能可以通过改变这些畸变的大小、频率和分布来操纵。
锻铁是钢铁最有用的前身之一, 其碳含量超过2%。结果表明, 民用钢材的最佳碳含量为0.2% 至0.5%。许多早期的冶金处理过程旨在将碳含量带到这些水平, 这是经济生产的体积。在美国和西门子在英国的过程中的麦地那过程是这些早期技术的两个更成功的例子。目前最常用的工艺是电弧炉和基本氧炉。除碳外, 大多数现代钢还含有锰 (锰)、铬 (铬)、钼 (钼)、铜 (铜)、镍 (镍) 和其他金属, 以提高强度、变形力和韧性。这些合金对工程性能的影响的一个简单例子是所谓的碳当量 (CE):
CE 是确定某一钢的可焊性的有用指标;通常情况下, CE < 0.4% 代表的是一种焊接的钢材。由于金属结构中的许多连接是通过焊接制造的, 所以这是在指定建筑材料时要记住的一个有用的指标。
正如朱庇特视频中提到的“物质常数” , 为了建模目的, 我们需要确定应力和应变之间的关系。stressstrain 曲线 (图 1) 给出了许多材料行为的最佳简单描述。由于在压缩加载时存在屈曲问题, 并且在多个方向上均匀地加载材料时遇到困难, 因此通常运行单轴拉伸试验来确定应力应变曲线。本试验提供了主要工程特性的基本信息, 主要是均质金属材料。
典型的拉力试验是由 ASTM E8 描述的。ASTM E8 定义了要使用的测试标本的类型和大小、要使用的典型设备和用于金属拉伸试验的数据。
图 1: 低碳钢的应力应变曲线。
由于我们需要通过非常大的塑料应变测量, 所以应变测量不能总是在整个变形范围内进行应变计 (最多 40%); 在试样破裂之前, 胶水几乎总是会失效。一个计, 其中包括一个小 C 框架与悬臂式武器检测应变仪和适当校准, 通常使用高达约20%。由于计是一种昂贵而精致的仪器, 因此需要在试样破裂前去除;试验将停止, 并在试样达到其最大应力和从试样上的标记估计的最大变形后不久计。
感兴趣的主要属性是 (图 2):
比例限制:比例极限是应力与应变成线性比例的最大应力, 即胡克定律是严格适用的(朱庇特视频- “物质常数”).这个值通常是通过观察在恒定的十字头速度条件下运行测试时的应力率变化来确定的。在线性弹性范围内, 应力速率与应变速率成正比, 理想情况下是恒定的。当材料开始塑化性能时, 由于应变速率的增加, 应力速率开始下降。当初始应力率开始下降时, 比例极限被视为应力。
屈服点:许多金属呈现出一个尖锐的屈服点或应力, 在这种压力下, 这种菌株的压力会继续迅速增加。这在应力-应变曲线中由水平线或屈服高原来证明。屈服点大致对应于原子晶格中滑移开始发生的载荷。这种滑移是通过达到一些临界剪切力触发的, 并且比从第一原理计算出来的低得多, 因为晶体结构中存在许多缺陷。在一些材料中, 如在试验中测试的低碳钢, 在材料到达屈服高原之前, 应力会有很小但明显的下降, 从而产生上、下屈服点。对于不表现出明确屈服点的材料, 使用当量屈服强度。我们将在朱庇特视频中详细研究这个定义, 关于“铝的应力应变特性”, 它涉及铝的这些性质。
图 2: 低应变变量的定义。
弹性模量:材料的弹性模量被定义为应力应变图直线部分的斜率, 如图2所示。这个属性在朱庇特视频中讨论了关于“物质常数”。E 是一个相对较大的数字:30 x 106 psi (210Gpa) 的钢材;10 x 106 psi (70 GPa) 为铝;1.5 X 106 psi (10.5 GPa) 为橡木;和 0.5 x 106 psi (3.5 GPa) 的有机玻璃。
韧性模量:韧性模量是应力-应变图弹性部分下的面积, 其单位体积单位为能级。弹性模量测量材料吸收能量的能力而不经历永久性变形。
应变硬化模量:由于滑动, 或位错运动, 触发屈服高原开始达到晶界 (或区域的晶格是在不同的角度), 错位开始 “堆积”, 并需要额外的能量, 以传播其移动到其他谷物。这导致了应力-应变行为的刚性, 尽管应变硬化模量通常至少是低于杨氏模量的一个数量级。
极限强度:这是在测试过程中达到的工程应力的最大值, 在试样开始颈部 (或改变区域) 前不久发生 (图 3)。
最大应变:当试样破裂时, 该值被视为应变值。由于计一般已被删除的时间, 我们到达这一点的测试和变形已经本地化 (缩进) 到一个非常短的距离沿标本长度, 这个值是很难测量实验。因此, 当指定材料而不是最大应变值时, 通常使用均匀伸长率和伸长率。
图 3: 大应变的定义。
均匀伸长率:伸长率被定义为试样在颈缩前的伸长率 (长度/原始长度的变化)。
伸长率:通常二个标记, 名义上2在. 除, 在测试之前被做对样品。经过试验, 将两块破碎试样尽可能地放在一起, 最后的变形 remeasured。这是一个粗略的, 但有用的方法, 指定最小伸长的材料在工程环境。
百分比区域:同样的伸长率, 有可能尝试做一个测量的最终面积的骨折标本。通过在断裂前将力除以这个区域, 就有可能获得材料的真正强度的概念。
韧性:韧性被定义为应力应变图下的总面积。它是衡量材料在骨折前经受大的永久性变形的能力的量度。其单位与韧性弹性模量相同。
上面描述的属性可以用来评估给定的材料将如何符合朱庇特视频中讨论的“材料常数”的性能标准。在安全方面, 强度和变形能力特征是关键;这些特征通常被分组在韧性行为的期限之下。韧性行为意味着材料将屈服, 并能够保持其强度在一个大的塑性变形制度。一个大的韧性是可取的, 这在实践上意味着一个结构会给出即将出现的故障的迹象, 例如在灾难性崩溃发生之前非常大的可见变形, 允许其占用时间疏散结构。
相比之下, 表现出脆性行为的材料, 通常会以突然的、灾难性的方式失败。这是 cementatious 和陶瓷材料的例子, 它的拉伸能力较差。混凝土梁在这种情况下会失败, 因为它的张力很弱。为了弥补这个陷阱, 一个地方钢筋在混凝土梁的拉区, 把它们变成钢筋混凝土梁。
重要的是要认识到脆性和韧性行为不是一个内在的物质行为。正如我们将在朱庇特视频中看到的“洛克韦氏硬度测试”, 服从在室温下韧性的碳钢, 在低应变加载速率条件下, 以非常快的应变加载条件 (冲击) 在低温下可能导致脆性行为。此外, 重要的是要认识到, 一些材料, 如铸铁, 可能是非常脆的紧张, 但韧性的压缩。
在这一点上, 需要定义的另外两个重要的材料特性是各向同性和同质性, 因为它们影响我们对材料建模的选择。如果材料的弹性特性在各个方向上都是相同的, 则说它是各向同性的。大多数工程材料是由与整个身体的尺寸相比较小的晶体制成的。这些晶体是随机定向的, 所以统计的材料的行为可以被认为是各向同性的。其他材料, 如木材和其他纤维材料, 可以有类似的弹性性质在两个方向仅 (正交异性) 或在所有三方向 (各向异性)。
另一方面, 如果材料的弹性特性在整个身体中都是相同的, 则说它是均匀的。为了设计目的, 大多数建筑材料被假定为均匀的。这是有效的, 即使材料, 如混凝土有不同的阶段 (砂浆和石块), 因为我们一般都在谈论的特点更大的体积, 可以认为统计上均匀。
Procedure
Results
From the measurements (Fig. 5 and Table 1.), a mild steel may have elongations in the 25%-40% range, while the harder steel may be one-half of that. It is important to note that almost all the deformation is localized in a small volume and thus the %elongation is only an average; locally the strain could be much higher. Note also that the %reduction of area is also a very difficult measurement to make as the surfaces are uneven; thus this value will range considerably.
| Specimen | A36 | C1018 | in. |
| % Elongation | 33.3 | 17.3 | % |
| % Area Reduction | 54.3 | 50.1 | % |
| Tensile Yield Stress | 58.6 | 73.0 | ksi |
| Tensile Strength | 86.6 | 99.9 | ksi |
| Stress at Fracture | 58.6 | 86.7 | ksi |
| Modulus of Elasticity | 29393 | 29362 | ksi |
Table 1. Steel test summary.
Figure 4: Typical ductile (left image) and brittle (right image) failure surface.
In general, these will vary from a ductile shear (cup-cone) fracture, such as would be expected from a failure such as that shown in Fig. 4, to a brittle cleavage fracture. Typical graphical results for the complete stress-strain curves are shown in Fig. 5. Note the very large differences in the stress-strain characteristic, range from a very mild but ductile A36 steel to a very strong but non-ductile C1018. Note that both are conventionally called steel, but their performance is markedly different.
Figure 5: Final stress-strain curve.
Applications and Summary
This experiment described how to obtain a stress-strain curve for typical steel. Differences in the stress-strain curves can be traced to either difference in the processing (e.g., cold working vs. hot rolling) and chemical composition (e.g., percent of carbon and other alloys). The tests showed that low-carbon steel is a very ductile material when loaded in uniaxial tension.
It is always relevant to compare experimental results to published values. The latter generally represent a minimum value from the specification based on 95% confidence limit, so it is likely that any strength value tabulated will be exceeded in the test, usually by a 5%-15% margin. However, much higher values are possible, as materials tend to be classified downwards if they do not meet some specification requirement. The strain values are generally going to be close to those published. The modulus of elasticity, on the other hand, should not vary significantly. If the value of E is not close to the published one, a through reexamination of error sources should be carried out. For example, the error may be due to slipping of the extensometer, improper calibration of the load cell or extensometer, wrong input voltages into the sensors, wrong parameters being input into the software, to name but a few.
Steel is a widely used material in the construction industry. Its applications include:
- Rolled steel I-shaped structural sections commonly used in conventional multi-story buildings because it is easy to prefabricate and connect the components, saving time in the construction process.
- Welded deep plate I-girders used in bridges, where the sections are built-up by welding deep, thin stiffened webs and thick flanges. This puts most of the material in its most useful position (the flanges), optimizing the design for strength and stiffness and reducing the overall cost of the project.
- Bolts and fasteners used in connections, where generally high strength and moderate ductility are required. These fasteners are used in myriads of products ranging from cars to household appliances.
The most important application of the tension test described herein is in the quality control process during the manufacturing of steel, aluminum and similar metals used in the construction industry. ASTM standards require that such test be run on representative samples of each heat of steel, and such results must be traceable to established benchmarks. The safety of the public is intimately tied to making sure that this type of quality control procedure is standardized and followed. Poor quality in construction materials, and lack of ductility at the material and structural level, are the most common cause of collapses during and after earthquakes and similar natural disasters. Lack of strength in critical components led to the failure of the I-35W bridge in Minneapolis in 2007 and use of substandard materials are at the root of many of the collapses that occur in developing countries, such the one that took over a thousand lives in 2013 when the Savar building collapsed in Dhaka (Bangladash).
On an everyday basis, one can cite the example of the automobile industry, which greatly benefits from knowing stress-strain behavior of steel and other materials when designing cars to perform safely and effectively in a crash situation. By designing cars that have strength in certain parts, while allowing for strain and ductility in other parts, manufacturers can create better crash management, but only if they can accurately surmise the stress-strain characteristics of each part.
Transcript
Steel is a general term for iron alloyed with carbon and other elements like chromium, manganese, and nickel.
Variations in the composition and processing methods can tailor its properties for construction of cars, bridges, and skyscrapers, to name only a few of the nearly infinite possible uses.
Understanding steel’s response to load is important when designing safe buildings and structures. One fundamental tool for modeling material characteristics is the stress-strain curve.
We will use the uniaxial tensile test to study the elastic and inelastic behavior of a mild hot-rolled steel and a hard cold-rolled steel, which represent low and high limits respectively of tensile strengths in civil engineering applications.
Stress is defined as the force divided by the area over which it is applied. Strain is the change in length divided by the initial length. Stress-strain curves describe the elastic and inelastic properties of materials by showing how a material like steel responds to applied force.
The uniaxial tensile test is typically used for studying stress and strain. In this test, a machine slowly pulls the ends of a sample with greater and greater force and measures the resulting elongation. The metal tension test is described by ASTM E8, which defines the type and size of the specimen, the type of equipment, and the data to be reported.
The stress-strain curve reveals many properties of the material under test. Among them, elastic modulus (the slope of the initial linear region, where deformation is proportional to load), modulus of resilience (the area beneath the linear region, which measures a material’s capacity to absorb energy without permanent deformation), proportional limit (the stress at the point the curve deviates from linearity), yield points (where stress versus strain suddenly decreases or changes), and yield plateau (where deformation increases rapidly without increasing stress).
Steel is a ductile material. Ductility is defined as the change in length at failure divided by the initial length. Toughness is the ability of a material to absorb energy before it fractures.
Now that we understand some of the basic characteristics of materials, let’s look at a method to measure stress and strain in the laboratory and investigate the relationship between these two quantities.
Obtain cylindrical test specimens for two types of steel, one mild and hot-rolled, such as A36, and one hard and cold-rolled, such as C1018.
Use a caliper to measure the diameter at several locations near the middle of the specimen. Make these measurements to the nearest 2000th of an inch.
Next, hold the specimen firmly. Scribe a gauge length of approximately two inches. Make the mark clear but very shallow to avoid creating a stress concentration that can lead to fracture. Measure the actual marked gauge length to the nearest 2000th of an inch.
Finally, install a strain gauge. The specimen is now ready for testing.
We will be using a universal testing machine, or UTM, to measure the tensile properties of the specimens. Turn on the testing machine and initialize the software. Set up appropriate graphing and data acquisition parameters, then select a test procedure that is compatible with the ASTM E8 protocol.
Set strain rates for the low strains zero to 5% and for high strain ranges greater than 5% respectively. These should be close to 0.05 inches per minute for the initial loading and 0.5 inches per minute after 5% strain. Then set any additional actions in the software, such as stopping the machine at 5% strain in the extensometer to remove it before specimen failure.
Manually raise the crosshead so the full length of the specimen fits easily between the top and bottom grips. Carefully insert the specimen into the top grip to about 80% of the grip depth. Align the specimen inside the top grip and tighten slightly to prevent the specimen from falling. Slowly lower the top crosshead. Once the specimen is within about 80% of the bottom grip depth, start specimen alignment within the bottom grips. The specimen should float in the center of the fully opened bottom grip. Apply lateral pressure to the specimen through the grips to ensure that no slipping occurs during testing. Note the tightening process introduces a small axial force on the specimen.
Use the software to impose a preload to compensate for this force and record its value. Attach the electronic extensometers securely to the specimen according to the manufacturer’s instruction. The blades of the extensometer should be approximately centered on the specimen. If a strain gauge is being used, connect it.
Begin the test by applying tensile load to the specimen. Observe the live reading of applied load on the computer display. To confirm the specimen is not slipping through the grips, make sure the measured load is increasing linearly. Sometime before sample failure, the software will automatically pause the test. Leave the sample in the test machine and remove the extensometer. Resume applying tensile load until failure. Upon reaching the maximum load, the measured loads begin to decrease. At this point, the specimen starts to neck. Final fracture should occur in this necked region through ductile tearing.
After the test has ended, raise the crosshead, loosen the top grip, and remove the broken piece of specimen from it. Loosen the bottom grip and remove the other half of the specimen. Record the value at the maximum tensile load. Save the recorded data and the stress-strain curve.
Carefully fit the ends of the fractured specimen together and measure the distance between the gauge marks to the nearest 2000th of an inch. Record the final gauge length. Finally, measure the diameter of the specimen at the smallest cross section to the nearest 2000th of an inch.
To determine material properties, first take a look at the data for the A36 mild hot-rolled steel and the data for C1018 hard cold-rolled steel, respectively.
Now calculate the percent elongation for each specimen, knowing the final gauge and the initial gauge length. Calculate the reduction of area for each specimen, using the final diameter and the initial diameter of the specimen. Record these values in a results table.
Next, calculate other material parameters using the experimental stress-strain curves. A quick comparison of these curves for the two specimens shows their very different elastic and inelastic behaviors. From the much greater strain at lower levels of stress, the A36 steel is softer and far more ductile than the C1018 steel.
For the A36 steel, the stress at failure is about 58.6 kilopounds per square inch, substantially above the nominal value of 36.0 kilopounds per square inch. Maximum stress is about 86.6 kilopounds per square inch at a strain of about 20%.
This magnified plot shows an upward yield point at about 58.6 kilopounds per square inch and a lower yield point at about 56.8 kilopounds per square inch. The beginning of the yield plateau is also visible here. Strain gauge data reveals a linear elastic region for the A36 steel with a slope defined as Young’s Modulus of about 29,393 kilopounds per square inch. This result is very close to the nominal value of 29,000 kilopounds per square inch.
At the point where the data deviates from linearity, we can determine the proportional limit is about 55.58 kilopounds per square inch. For comparison, due to the nonlinearity of its stress-strain curve, the C1018 steel has a very low proportional limit.
Results from the extensometer covers strain up to 5%. Data for the A36 steel shows the plastic plateau and the beginning of strain hardening where the curve rises again at a strain of about 2.7%. In contrast, the C1018 has no clear yield plateau.
Finish the data analysis by summarizing the test results for the two steel samples in the following table.
The elongation of a mild hot-rolled steel is in the range of 25 to 40%. In contrast, the elongation of a hard cold-rolled steel is only half this amount. The percent elongation is an average value for the length of material between the gauge marks, but almost all the deformation is localized to a small region around the fracture point. Consequently, the local strain could be much greater than the average.
Physical examination of the two specimens show large differences in the way they fail, corresponding to differences in their stress-strain curves.
The A36 steel has a failure surface with material drawn out at the rim during gradual final deformation and greater elongation at lower stresses, indicating a very mild but ductile metal.
In contrast, the C1018 steel has a flat failure surface, corresponding to sudden fracture and much less elongation at much higher stresses, characteristics of high strength but low ductility.
Let’s look at some common applications of steel from the perspective of the relationship between stress and strain.
Civil engineers analyze structural collapses in bridges and buildings in order to improve future structural designs. This process has led to steel components like rolled I-beams for multi-story buildings, welded deep-plate I-girders for bridges, and high-strength bolts and fasteners. Each requires different types of steel with specified strengths and ductilities, often first understood through examination of their stress-strain curves.
Engineers use the stress-strain characteristics of materials to make safer automobiles. Knowing the strength and ductility of the frame and how it deforms in response to impact forces, engineers can design an automobile’s body to absorb energy during collision and increase the chance of surviving a crash.
You’ve just watched JoVE’s Introduction to Stress-Strain Characteristics of Steel.
You should now know how to perform a uniaxial tensile test to determine the tensile properties of metallic materials and how to analyze stress-strain curves for typical steels.
Thanks for watching!