Обучение чтению литературы на английском языке по специальности «Прикладная механика» (120

Ultimate strength. If the load on the bar increases, the unit stress and unit strain increase until the maximum unit stress is reached, which is called the ultimate strength. A brittle material breaks when stressed to the ultimate strength whereas a ductile material continues to stretch. The ultimate strength of material is defined as the maximum unit stress that can be developed in the material, as determined from the original cross section of the bar or specimen; the cross section of a bar of ductile material decreases somewhat as the bar is stressed above yield point.

After the ultimate strength of a ductile material is developed, the bar begins to “neck down” rapidly reducing the cross section area, the area being called neck down section. And the load required to cause the bar to continue stretching decreases. The load on the bar at the instant of rupture is called the breaking load. The breaking load divided by the area of the neck-down section is the value of the unit stress in the bar when rupture occurs, and this value is considerably greater than the ultimate strength.

Elastic Limit. It has been found by careful measurement that, if a bar is subjected to a gradually increasing stress, the unit stress is proportional to the corresponding unit deformation until a certain limiting value of the unit stress is reached. This limiting value of the unit stress is known as the proportional elastic limit of the material or, more briefly, the proportional limit. The proportional limit may be defined as the maximum unit stress up to which the ratio of unit stress to unit strain is constant. The statement that stress is proportional to strain is known as Hooke’s law, and a material which obeys Hooke’s law does so only within a limited range of stress, i.e., up to the proportional limit.

The deformations resulting from stressing a bar disappear when the stress is removed, provided the stress does not exceed a certain limit. If this limit is exceeded, the resulting strain does not entirely disappear when the stress is removed; that part of the strain which remains is called the permanent set. The unit stress at this limit is called the elastic limit and corresponds approximately to the proportional limit. The elastic limit may be defined as the maximum unit stress that may be applied without producing a permanent set. To obtain an accurate value of the elastic limit according to this definition it is necessary to detect the slightest amount of permanent stress. The value obtained will

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depend on the precision of the measuring instruments, the increments of load, whether large or small, the rapidity of loading, and the duration of loading. Ordinarily, no permanent set is noticed until after the proportional limit is reached.

In order to determine experimentally the value of the elastic limit for a material, a bar is subjected to a relatively small axial load and the load is released. If the extensometer shows that the bar has acquired no permanent deformation, a larger load is applied and then released, etc. Thus the stress in the bar is increased in small increments until a unit stress is found which, on release of the stress, leaves a very small set in the bar, for the minimum unit stress at which set first occurs is the elastic limit.

2. Match the Russian equivalents to the English ones with the words factor, limit, strain.

А. Friction factor, safety factor, numerical factor, power factor, quality factor.

В. Коэффициент трения, запас прочности, числовой коэффициент, коэффициент мощности, добротность, гибкий, прочный, оправданный, маневренный, ценный, рабочий, видимый,

А. Endurance limit, fatigue limit, apparent elastic limit, probability limit, rupture limit, yield limit.

В. Предел выносливости, предел усталости, предельный срок службы, условный предел упругости, предел прочности на разрыв, вероятностный предел, предел текучести.

А. Residual strain, repeated strain, shear strain, buckling strain, volume strain, extension strain, homogeneous strain, internal strain, longitudinal strain, mean strain.

В. Разрушающая деформация, деформация продольного изгиба, однородная деформация, относительное удлинение, внутренняя деформация, продольная деформация, остаточная деформация.

3. Look through Text 2B and answer the following questions.

1. What is the modulus of elasticity? 2. How is the modulus of elasticity expressed? 3. When may the deformation be calculated? 4. Why is the modulus of elasticity rendered a measure of stiffness of the material? 5. What is Poisson’ ratio? 6. What is denoted by symbol

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M? 7. When may the deformation from the application of known stress be calculated?

Text 2B. Modulus of Elasticity

For many materials the ratio of unit stress to unit strain is constant up to the proportional limit. This constant ratio is called the modulus of elasticity. Since unit strains are dimensionless, the modulus of elasticity has the same dimensions as unit stress and is usually expressed in pounds per square inch. For many engineering materials the value of the modulus is sometimes called Young’s modulus and represented by E. Thus E = = S/ε. When the value of the modulus of elasticity is known, the deformation resulting from the application of the known stress may be calculated or the stress causing the known deformation may be found.

Since the stiffness of a material is the rate with the respect to elastic strain, at which unit stress in the material increase as load is applied, it follows that the modulus of elasticity of a material is a measure of the stiffness of the material. Thus, if one material has the modulus of elasticity twice as large as another material, the elastic unit strain in one material for a given unit stress is one half as large as that in the other material, and hence the one material is twice as stiff as the other one. It should be noted that the modulus of elasticity is expressed in the same units as is unit stress since E is a ratio of length to length and is therefore merely a number. If a bar is subjected to an axial tensile load, the bar is elongated in the direction of the load, that is, in the longitudinal direction, and at the same time the lateral dimension of the bar decreases. The ratio of the lateral unit stress to the longitudinal unit strain is called Poisson’s ratio, it will be denoted by M.

4. Translate the following sentences paying attention to the underlined words.

A. 1. In order to determine the magnitude of these stresses it is necessary to know the bending moment and shearing force. 2. For usual rail road track this constant has a value of the order of K=1,500 lb/sq. in.

3.The results are not true because the testing machine is out of order.

4.This numerical algorithm is capable of calculating second-order differential equations.

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B. 1.We consider undesired shocks to originate from a variety of sources. 2. The work presented was originally carried out using a modified System 81. 3.The original version of the model has already been used in the safety analysis. 4. By reviewing the photographs taken of the dam during construction the engineer understood the origin of the open crack.

C.1. The stress strain relations depend on whether the material is in loading or unloading conditions. 2. In all these calculations the principal stress is checked individually whether a positive value has been reached.3. It is difficult to say whether these experiments will result in valuable information.

D.1. Fatigue failure may result from resonant vibration. 3. Some limitations of this method may result in considerable statistic uncertainties (неопределенности). 4. The resulting curve can be seen in this diagram. 5. The reduction in shock severity results from the release of the shock energy. 6. This error is systematic and comes in addition to other errors, such as those resulting from calibration inaccuracy.

5.Translate the sentences paying attention to the infinitive in different functions.

A.1. The temperature distribution in the plate is assumed to be uniform in the transverse direction. 2. Problems of this nature are expected to frequently occur in practice. 3. Euler’s paper is considered to be the first work on structural stability. 4. Two different kinds of unbalance are supposed to occur in practice.

B.1. The subject of wheel-rail contact stresses seems to be of increased importance nowadays. 2. The method proved to be ideally suited to the technique of calibration used. 3. A stationary process is sure to have an additional property. 4. The event in question is certain to happen. 5. The influence of compressive stress on both fracture strain and the rate of negative work hardening (деформационное разупрочнение) in steel appears to depend on the number of microcracks.

C.1. Another factor to be considered is the environment. 2. The approach to be discussed is useful. 3. One of the most powerful method to be used is the frequency analysis technique. 4. The value to be employed for x must depend on a number of physical factors.

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D. 1. To eliminate all undesired vibrations is possible in a very few cases. 2. To investigate the phenomenon it was decided to rerun the analysis with higher concrete strength.

6. Translate the following text in written form using a dictionary.

Text 2C. Material Behavior Model

The model implemented employs three basic features to describe material behavior, namely (1) a nonlinear stress-strain relation including strain softening to allow for the weakening of the material in compression; (2) failure envelopes that define cracking in tension and crushing in compression and (3) a strategy to model the post-cracking and crushing behavior of the material.

While calculating, the material is to be subjected to cyclic loading conditions, since the numerical solution allows for unloading and reloading including tensile failures. However, as it becomes apparent, the cyclic loading conditions are only modeled realistically in the situation of essentially proportional loading.

In the following, the material model is described for infinitesimal displacement conditions using the engineering stresses and engineering strains. In order to analyze problems with large rotation conditions the total Lagrangian stress and strain variables must be substituted for the engineering variables and then the model proves to be applicable.

The general multi-axial stress strain relations are derived from a uni-axial stress strain relations δ versus e . In the paper the authors describe the multi-axial and uni-axial stress strain relations employed in the model and concentrate on the behavior prior to tensile cracking or compression crushing. In the discussion all uni-axial parameters are identified by a tilde (~).

7. Translate the text from Russian into English.

Text 2D. New Method Development

Разработан метод смещения (displacement) матрицы. Данный метод применим к упруго-пластичным задачам и дает возмож-

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ность сделать статистический и динамический анализ произвольных (arbitrary), сложных двух-, трех-размерных конструкций, которые могут состоять из однородных или неоднородных, изотропных или неизотропных материалов. Теория основана на пошаговой нагрузке или развитии деформации и учитывает критерий текучести. Метод проверен на треугольном элементе с линейным распределением деформации. Этот метод несколько лет назад считался невозможным. Данная статья дает оценку трем сложным подходам этого метода и указывает теоретические критерии по их применению, что подтверждается численным анализом. Нужно подчеркнуть, что этот метод и техника его применения могут быть успешными только при использовании большого современного компьютера и наличия полного программного обеспечения.

UNIT 3

New Words and Word Combinations

Conform to the established standards — соответствовать установленным стандартам

Depend on toughness — зависеть от ударной вязкости (прочности, крепости)

Discover new information concerning — получить новую информацию

Form a neck — образовать шейку

Fasten the ends of the bar — прикрепить концы бруса Hardness — твердость

Hold for the given range of stress — справедливо для данного уровня нагрузки

Malleability — ковкость

Plot values graphically — нанести значения на график Occur — иметь место, происходить

Obtain information — получить информацию

Result in the breaking of specimen — привести к разрушению образца

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Stiffness — жесткость

Stretch the bar — увеличить, удлинить брус

1. Read and translate the text.

Text 3A. Stress Strain Diagram and Related Properties

The usefulness of various materials is resisting the action of forces depends on such mechanical properties as elasticity, strength, toughness, brittleness, ductility, malleability, hardness and stiffness. These properties are measured by means of laboratory tests, the purpose of which may be either to discover new information concerning the properties of the material or to determine of the properties of a given material conform t5o already established standards. The American Society of Testing Materials (A.S.T.M.) has, as the result of research and study over period of many years, evolved standards test and test procedures.

The tension test is one of the simplest and most commonly made tests and from it a considerable amount of important information may be obtained. The specimen to be used in a tension test may be either round or rectangular. The ends of the bar are fastened in the testing machine which applies to the bar a slowly but uniformly increasing pull which eventually results in the breaking of the specimen. Testing machines are equipped with devices for indicating the total pull at all times. Changes in length of a specified portion of the bar known as the gage length are measured by means of an instrument known as an extensometer. Simultaneous readings of total stress and total strain are made and recorded at regular and frequent intervals throughout the test.

The results of the tension test are shown graphically in the form of a curve obtained by plotting values of unit stress as ordinates and corresponding values of unit strain as abscissas. This curve is called the stress-strain diagram. The first portion of the diagrams is a straight line showing that the unit stress is proportional to unit strain. In other words, Hooke’s law holds for this range of stress. The modulus of elasticity being the ratio of unit stress to unit strain is the slope of this line.

If the unit stress is increased beyond the proportional limit at which deformation continues without increase in stress the curve becomes

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horizontal. The unit stress at this point is known as the yield point. For some materials the yielding point is accompanied by a temporary decrease in unit stress.

Further stretching of the bar after the yield point is reached is accompanied by increase in unit stress, and the curve rises until it reaches its maximum height. The unit stress at this point is called the ultimate strength. If continued stretching of the bar takes place, the deformation becomes localized somewhere along the length thus forming a neck. Owing to the decreased area of cross section of the necked portion rupture finally occurs, the unit stress at this point is called the rupture strength.

Some materials do not have a well-defined yield point. For these materials a stress called the yield strength is often used instead. The yield strength may be defined as the unit stress at which a specified permanent set will result. A permanent set of 0,2 per cent of the gage length is common.

2. Match the Russian equivalents to the English word combinations with the word “strength”, “motion”.

A.Alternating motion, continuous motion, damped motion, discontinuous motion, forced motion, lateral motion, longitudinal motion, operating motion, oscillatory motion, proper motion, random motion, rigid motion, swinging motion, variable motion.

B.Жесткое перемещение, рабочий ход, продольное движение, поперечное движение, вынужденные колебания, прерывистое движение, непрерывное движение, возвратно-поступательное движение, колебательное движение, собственное движение, беспорядочное движение, переменное движение.

А. Breaking strength, creep strength, endurance strength, ultimate strength, rupture strength, yield strength, strength of materials, compression strength, fatigue strength, fracture strength, impact strength, tensile strength.

В. Сопротивление разрыву, предел текучести, прочность на разрыв, предел прочности, предел усталости, прочность на сжатие, сопротивление материалов, предел прочности на растяжение, сопротивление удару, предел выносливости, сопротивление разрушению, предел ползучести.

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3.Translate the sentences paying attention to the translation of the attributes.

1.Compact tension specimens were utilized in determining the steel fatigue crack growth properties. 2. The thermal buckling (прочность на продольный изгиб) stress problems are solved for a simply supported rectangular thick plate in a state of uniform compressive or tensile initial stress plus initial bending stress. 3. The objective of the paper is to present the 3D concrete material model considering the tri-axial nonlinear stress-strain behavior tensile cracking and compressive crushing material failure conditions. 4. There are a number of factors to prevent a wider acceptability of non-linear finite element analysis procedures in the concrete structure analysis.

4.Look through Text 3B and answer the following questions.

1.How does materials frequently behave when the action of stresses are not maintained? 2. When does fluctuation usually occur?

3.What is the result of fluctuation? 4. What is endurance limit? 5. What is usable strength? 6. What is factor of safety? 7. Why should the working factor of safety be less than the design factor? 8. What properties of the material should be considered while choosing the usable strength?

Text 3B. Effect of Repeated Stresses. Fatigue.

Materials used in structures and machines are frequently required to resist the action of stresses which are not maintained at a constant value but fluctuate as a result of repeated application and removal of the load. The fluctuation may consist of a complete reversal of stress or of a variation between a higher value and a lower value of the same stress. If a material is subjected to a very large number of stress repetitions or reversals, failure may occur at the value of the unit stress much less than that which would cause failure when stress is maintained constant. Failure resulting from a large number of reversals or repetitions of stress is sometimes called fatigue failure.

The measure of the strength of a material under the action of repeated stress is the endurance limit which is defined as the maximum value of the unit stress that may be repeated an indefinite number of times without causing failure.

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The term factor of safety, as denoted in design, is the ratio of the usable strength of a material to the allowable unit stress. When applied to a member already in service, the factor of safety denoted the ratio of the usable strength to the actual working unit stress. To distinguish between the two applications of the term it is customary to refer to the ratio of usable strength to allowable stress as a design and to the ratio strength to working stress as a working factor of safety. It will be evident that when a member is loaded to the capacity for which it was designed the working factor of safety is less that the design factor.

Since the usable strength of a material may be any one of several properties including ultimate strength, yield point, endurance limit, creep limit, etc. it follows that the significance of a factor of safety is not complete unless it is understood which property of the material is being considered as the usable strength. In the absence of any statement to the contrary, it is ordinarily understood that the factor of safety is based upon the ultimate strength, i.e., rupture under static loading conditions.

5.Translate the sentences paying attention to the modal verbs and its equivalents.

1.The structure is to be analyzed prior to testing. 2. It should be noted that strain softening post-cracking models are to be used with the caution. 3. After consulting the photographs the engineer was able to determine the origin of the open crack 4. From Fig. 2 one can conclude that a small crack will tend to grow since its critical value is exceeded.

5.Such a situation might be achieved in practice by heating the die and cooling the material. 6. It is to be said that every of a structure beyond the elastic limit and establish its ultimate strength under dead load member, every support, every part has a definite function to perform.

7.To investigate the behavior we have to use for the model the same material as for the actual structure. 8. In the structure every bar has to carry a definite force.

6.Translate the following sentences paying attention to the underlined words.

1.Random vibrations are met rather frequently. 2. That was the

effect of temperature “shock” or rather temperature changes. 3. The problem of testing large specimens is solved by the use of multiple

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