8. Match English words with their Ukrainian equivalents:

1. friction a) текучість металу

2. application b) пошкодження

3. yield c) повзучість металу

4. creep d) взаємозв’язок

5. resistance e) застосування

6. failure f) опір

7. correlation g) тертя

9. Make a plan of the text. Lesson 8

1. Find in the text English equivalents for the following Ukrainian words and word combinations:

критерій, теорія опору, добре відомий інженер, інженерна механіка,

припущення, видатний, переконливий, вимір, пружність, текучість,

порівняння, вираз, напрямок, тиск, стиснутий, різноманітний, межа,

поломка, зразок, розмір, погодження, розрив, застосування, поверхня,

простір, надійний, випуклість, попередня умова, перевага, простота.

2. Read and translate the text: Mohr's Strength Theories

Mohr used the stress circle method in developing his theory of strength in 1900. Otto Mohr was a very young professor. At the age of thirty-two years old, he was already a well-known engineer and was invited by the Stuttgart Polytechnicum Institute to become the professor of engineering mechanics. His lectures aroused great interest in his students, some of whom were themselves outstanding, such as Bach and Foppl. Foppl stated that all the students agreed that Mohr was their finest teacher. Mohr always tried to bring something fresh and interesting to the students' attention. The reason for his students' interest in his lectures stemmed from the fact that he not only knew the subject thoroughly, but also had himself done much in the creation of the science which he presented. Mohr made a more complete study of the strength of materials. He considered failure in broad senses; that is, it can be yielding of the material or fracture. Mohr's criterion may be considered as a generalized version of the Tresca criterion. Both criteria were based on the assumption that the maximum shear stress is the only decisive measure of impending failure. Flow ever, while the Tresca criterion assumed that the critical value of the shear stress is a constant, Mohr's failure criterion considered the limiting shear stress in a plane to be a function of the normal stress in the same section at an element point.

Mohr considered only the largest stress circle. He called it the principal circle and suggested that such circles should be constructed when experimenting for each stress condition in which failure occurs. The strength of materials under a complex stress state can be determined by the corresponding limiting principal circle.

At that time, most engineers working in stress analysis followed Saint-Venant and used the maximum strain theory as their criterion of failure. A number of tests were made with combined stresses with a view to checking Mohr's theory. All these tests were made with brittle materials and the results obtained were not in agreement with Mohr's theory. Voigt came to the conclusion that the question of strength is too complicated, and that it is impossible to devise a single theory for successful application to all kinds of structural materials.

This criterion is now referred to as the Mohr-Coulomb strength theory. In the special case of metallic materials with the same strength in tension and in compression, the Mohr-Coulomb strength theory is reduced to the maximum-shear stress criterion of Tresca.

At that time, Mohr followed Saint-Venant's notion and used the maximum strain theory in deriving formulas for calculating safe dimensions of structures. But at the same time he was interested in the various other strength theories, and to clarify the question of which should be used, he conducted some interesting experiments. By using a thick walled cylinder of high-grade steel, he succeeded in making compressive tests of various materials under great hydrostatic pressures. He found that an isotropic material could withstand very high pressure in that condition. He designed and constructed a special device for producing compression of a cubic specimen in two perpendicular directions and made a series of tests of this kind with cement specimens. It is the earliest high-pressure test.

Haigh and Westgaard introduced the limit surface in a 3D principal stress space. The advantage of such space lies in its simplicity and visual presentation. It is called the Haigh-Wesagaard space or stress space. Photographs of geometric models of such surfaces corresponding to various yield criteria before 1944 can be found in the papers by Burzynski and Meldahi. The yield surface in the stress space can be transformed into the strain space. A comparison of various strength theories applied in machine design before the 1930s was given by Marin.

A lot of strength theories and expressions were presented after Mohr. The proposed criteria and material models in the20th century are too many, and it is difficult to classify them. Fortunately, a fundamental postulate concerning the yield surfaces was introduced by Drucker and Bishop with the convexity of yield surface determined.

After that the convexity of yield surface was generalized to the strain space by Ilyushin in 1961. Since then the study of strength theory has been developing on a more reliable theoretical basis.