Tham khảo tài liệu 'introduction to elasticity part 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | INTRODUCTION TO ELASTICITY David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge MA 02139 January 21 2000 Introduction This module outlines the basic mechanics of elastic response a physical phenomenon that materials often but do not always exhibit. An elastic material is one that deforms immediately upon loading maintains a constant deformation as long as the load is held constant and returns immediately to its original undeformed shape when the load is removed. This module will also introduce two essential concepts in Mechanics of Materials stress and strain. Tensile strength and tensile stress Perhaps the most natural test of a material s mechanical properties is the tension test in which a strip or cylinder of the material having length L and cross-sectional area A is anchored at one end and subjected to an axial load P - a load acting along the specimen s long axis - at the other. See Fig. 1 . As the load is increased gradually the axial deflection s of the loaded end will increase also. Eventually the test specimen breaks or does something else catastrophic often fracturing suddenly into two or more pieces. Materials can fail mechanically in many different ways for instance recall how blackboard chalk a piece of fresh wood and Silly Putty break. As engineers we naturally want to understand such matters as how s is related to P and what ultimate fracture load we might expect in a specimen of different size than the original one. As materials technologists we wish to understand how these relationships are influenced by the constitution and microstructure of the material. Figure 1 The tension test. One of the pivotal historical developments in our understanding of material mechanical properties was the realization that the strength of a uniaxially loaded specimen is related to the 1 magnitude of its cross-sectional area. This notion is reasonable when one considers the strength to arise from the number of
