Elastic And Plastic Behaviour Of Materials Pdf

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Elastic-Plastic Behavior of Compacted Loess under Direct and Cyclic Tension

Tensile strain is one of the main variables that affect fracturing in soil. This paper focuses on an experimental investigation of the deformation characteristics of remolded loess in direct and cyclic tension tests. The material behavior was approximated as elastic-plastic by ignoring the effect of time.

In direct tests, the results showed that the change in slope of the stress-strain curve depended on the water content. The plastic constitutive relation was described by two methods. In cyclic loading and unloading tests, the remolded loess exhibited hysteresis a phase lag , which led to dissipation of the mechanical energy. And no compaction limit phenomenon was found.

A simple mathematical model was proposed to predict the plastic cyclic characteristics, and it was validated by the new test data. In many areas of geotechnical engineering, soil is subjected to tensile stress. Tensile cracks often form in tensile stress regions [ 1 , 2 ].

Cracks are caused by several factors, such as extrusion, uneven settlement, and dehydration [ 3 — 5 ]. These tensile regions can have negative impacts on infrastructures, such as embankment cracks, slope collapse, and earth-retaining wall instability and so on [ 6 — 9 ].

The wide occurrence of tensile phenomena requires a better understanding of their mechanical properties. Considerable attention has been focused on the tensile fracturing of soils in recent years, mainly including experimental strength tests [ 10 — 14 ] and strength prediction models [ 15 — 18 ]. As is known, strength and ultimate deformation are two important parameters affecting soil fracture.

In previous studies, strength and stress were the main research contents. However, deformation characteristics in tension have been ignored. The usual investigation was just to obtain a full stress-strain curve. Obviously, it is not enough for the study of deformation mechanism.

The tensile deformation increases gradually in the tension region; in addition to the monotonous increasing load, there is also the effect of cyclic load. For example, the temporary earthwork stack around an excavation may accelerate crack expansion in the stretched zone.

Therefore, it is imperative to conduct investigations of the deformation of soils under direct and cyclic loading. There are extensive loess areas in western China. Loess are typically a kind of clayey silt, and the silt content 0. Intact loess features a random particle arrangement, high porosity, and significant number of macropores [ 19 , 20 ]. Land instability hazards here are common and varied, in which ground fissures and surface subsidence are closely related to tensile characteristics [ 21 ].

Taking loess as the research object, this paper focuses on an experimental investigation of tensile deformation especially plastic strain as it is thought that the plastic deformation would play a more disadvantageous role than elastic deformation.

A series of tests was performed on samples with different dry densities and water contents. First, in direct tests, the modulus of elasticity, yield limit, and hardening conditions were obtained and analyzed. Then, the hysteresis loops, dynamic strength, and cyclic plastic strain were discussed in the loading-unloading tests.

Eventually, an elastic-plastic phenomenological model was presented to describe the plastic cyclic behaviour of soils. This paper may open up a new realm for soil tension research. The results supplemented the shortcomings of tension deformation. It will provide the reference for fracture-resistant designs, also the evaluation for the safety stability of geotechnical construction.

The laboratory tests were carried out with a uniaxial direct tension test apparatus, as illustrated in Figure 1. The apparatus consisted of three systems: load application system, displacement measurement system, and platen regulating system. The rectangular specimen was placed on a platform with uniformly distributed roller bearings on the bottom. The tensile mold comprised two rectangular grooves with sides that were free to open. This design prevented the ends of the specimens from being extruded using clamps.

One mold was affixed to the apparatus, and the other was connected to the loading system and could move horizontally. The displacement data were collected by economical and practical dial gauges. Fifteen grams of epoxy structural adhesive were applied to connect the mold to the specimen before the experiment. There was nearly no stress concentration on the specimen ends to ensure force uniformity over the entire length of the sample.

A detailed description of the tensile equipment was given in our previous paper [ 22 ]. The compaction device for the remolded sample is shown in Figure 2. The apparatus contained three components: a hollow box groove, removable templates, and telescopic bolt shanks.

The latter two moved together to form a tightly connected sample space. The template could be removed; therefore, the intact specimen was easy to remove from the device. The properties of the prepared soil samples are shown in Table 1 , and their particle-size distribution curves are shown in Figure 3. The soils can be considered well-graded soils. Subsequently, the soils were compacted layer by layer a total of three equal layers to the required dry density in a homemade mold.

Vaseline was applied to the inner wall to ensure that the sample could be completely removed. Each sample was installed in the tensile apparatus and covered with a thin layer of Vaseline to prevent evaporation. To evaluate the mechanical behavior of the material, two kinds of tests were performed: i direct tensile tests at different water contents and ii loading-unloading cyclic tests while maintaining or increasing the maximum load per cycle.

All of the unloading levels were higher than the yield limit. The effective length L 0 is calculated as the sample length minus the length between the two clamps. Direct tensile tests were performed on three identical samples. The mean mechanical parameters i.

The measurement of the elastic modulus and yield limit presents experimental problems depending on soil type, state, constitutive relations, and test precision. In this study, the elastic modulus was obtained using the following method.

The stress-strain curve was initially approximately a straight line regarded as the elastic phase and gradually showed nonlinearity with increasing axial load. The stress-strain data and fitting curves of one sample are shown in Figure 4.

The elastic modulus can be calculated:. Plastic deformation will occur when the stress exceeds the yield strength. Both the yield limit and elastic modulus decreased with increasing water content. The tensile strength also decreased with increasing water content over a certain range [ 11 , 18 , 24 , 25 ]. The yield limit and elastic modulus in the tests were strongly correlated with the tensile strength Figure 5.

Figure 4 shows that the strain continued to increase with tensile stress until fracturing occurred. What we are interested in is how the plastic strain changes when the stress exceeds the yield limit, that is, plastic constitutive relation under direct tension. Stress can be assumed as a function of total plastic work W p from the standpoint of energy mechanism [ 26 ].

In a limited deformation process, W p is defined as the work consumed by plastic deformation per unit volume i. Based on the assumption, the plastic constitutive relation of this material can be written as.

In Figure 6 , it could be intuitively seen that the plastic work was zero at low stress level. When the stress exceeded the yield limit, the growth rate of plastic specific work was getting faster and faster. In addition, under the same stress condition, the plastic work consumed by the sample with high moisture content was obviously higher than that of the sample with low moisture content.

It was illustrated that water content was a key factor affecting plastic deformation, and the higher the moisture content was, the more significant the plastic deformation would be.

Plastic constitutive equation could also be described by another way. The results are shown in Figure 7. Obviously, the plasticity development was consistent with Figure 6.

In order to further study the elastoplastic characteristics, particularly the plastic deformation, loading-unloading cyclic tests were carried out at room temperature. The dry density was 1. The loading histories are shown in Table 3. The stress-strain curves for loading patterns I and II are shown only the data of cyclic loading and unloading are presented in Figures 8 and 9 , respectively.

Hysteresis loops were produced under each loading and unloading cycle, which led to dissipation of mechanical energy. Similar trends were reported in [ 27 ]. Each loading curve was fitted by linear function, and the results are shown in Table 4. It could be seen that the fitted slopes of the loading curves decreased gradually, which quantitatively indicated that the elastic modulus decreased with the cyclic loading.

After a cycle of loading and unloading, the distance between the soil particles may increase, so the original dry density of the sample would decrease with it. Thus, the connecting force and adhesion may be weakened, which may reduce the ability of the soil to resist deformation i. The deformation after a loading-unloading cycle increased due to the stress history. Point A is on the initial loading curve, and point B is on the reloading curve. However, there are no restrictions to deformation in direction of axial tension, so no strain limit was observed.

The cyclic stress-plastic strain curves are shown in Figures 11 and Similarly, the plastic deformation exhibited hysteresis a phase lag , which showed that the plastic deformation recovered slightly. During unloading, in theory, plastic strain should have been constant, and the total deformation elastic and plastic deformation recovered due to the recovery of elastic strain. In this test, the decrease of plastic deformation may be caused by the inertia of the elastic recovery.

Plastic strain would decrease slightly with the elastic recovery. In addition, the tensile strengths of the samples decreased compared with the direct tests by varying degrees Figure The stiffness of the specimen decreased after the cyclic loading, which may also have led to weakening of the interparticle connection and cohesion force.

Plasticity (physics)

Objects deform when pushed, pulled, and twisted. Elasticity is the measure of the amount that the object can return to its original shape after these external forces and pressures stop. The opposite of elasticity is plasticity ; when something is stretched, and it stays stretched, the material is said to be plastic. When energy goes into changing the shape of some material and it stays changed, that is said to be plastic deformation. When the material goes back to its original form, that's elastic deformation. Manufacturing goods from raw materials involves a great deal of plastic deformation.

Behavior of Materials. • Elastic. • Viscous. • Plastic. Hooke's Law: σ = Ee σ = stress. E = Young's modulus e = extension (one-dimensional strain). E = σ/e = stress/.

Elasticity vs plasticity

Theory of Metal Forming Plasticity pp Cite as. A property of various metals that describes their ability to undergo permanent stains is called plasticity. The uniaxial tension test is a convenient method to indicate plastic behaviours of a material.

In physics and materials science , plasticity , also known as plastic deformation , is the ability of a solid material to undergo permanent deformation , a non-reversible change of shape in response to applied forces. In engineering, the transition from elastic behavior to plastic behavior is known as yielding. Plastic deformation is observed in most materials, particularly metals , soils , rocks , concrete , and foams.

Contributors and Attributions

 Могу я для вас что-нибудь сделать. Клушар задумался, польщенный оказанным вниманием. - Если честно… - Он вытянул шею и подвигал головой влево и вправо.  - Мне не помешала бы еще одна подушка, если вас это не затруднит. - Нисколько.

Это было дыхание дьявола, ищущее выхода и вырывающееся из закрытой пещеры. Стратмор так и остался стоять на коленях, парализованный ужасающим, неуклонно приближающимся звуком. Самый дорогой компьютер в мире на его глазах превращался в восьмиэтажный ад. Стратмор медленно повернулся к Сьюзан. Тоже неподвижная, она стояла у дверей шифровалки.

Это очень важная часть! - заявил лейтенант.  - Это не ребро или палец, как в церквях Галиции. Вам и в самом деле стоило бы задержаться и посмотреть. - Может быть, я так и сделаю. - Mala suerte, - вздохнул лейтенант.

Поскольку для одновременного подрыва устройств была необходима точнейшая координация действий, все эти изделия были связаны между собой телефонными линиями через Интернет. Двое суток встроенные часы устройств обменивались бесконечными потоками зашифрованной синхронизирующейся информации. АНБ, перехватывая эти информационные импульсы, игнорировало их, считая аномалией сети, безобидной тарабарщиной.

Беккер задумался: Я бы хотел, чтобы ты как следует вымыл голову, научился говорить по-человечески и нашел себе работу. Но решил, что хочет от этого парня слишком многого. - Мне нужна кое-какая информация, - сказал. - Проваливал бы ты отсюда. - Я ищу одного человека.

 - Включилось питание от автономных генераторов. Это аварийное электропитание в шифровалке было устроено таким образом, чтобы системы охлаждения ТРАНСТЕКСТА имели приоритет перед всеми другими системами, в том числе освещением и электронными дверными замками. При этом внезапное отключение электроснабжения не прерывало работу ТРАНСТЕКСТА и его фреоновой системы охлаждения. Если бы этого не было, температура от трех миллионов работающих процессоров поднялась бы до недопустимого уровня - скорее всего силиконовые чипы воспламенились бы и расплавились.


  1. Matilda C. 25.05.2021 at 15:30

    Tensile strain is one of the main variables that affect fracturing in soil.

  2. Yamal M. 27.05.2021 at 05:03

    metal deformed to an extent that it cannot fully recover its original dimensions ⇒ plastic deformation (shape of the material changes, atoms are permanently.

  3. Arnou L. 28.05.2021 at 10:40

    We referred to the proportionality constant between stress and strain as the elastic modulus.

  4. Daniel S. 01.06.2021 at 21:36

    Introduction to Engineering Materials pp Cite as.