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1、Lesson 2 Tensile stress-strain behavior The relationship between stress and strain in a particular material is determined by means of a tensile test.A specimen of the material,usually in the form of a round bar,is placed in a testing machine and subjected to tension.The force on the bar and the elon
2、gation of the bar are measured as the load is increased.The stress in the bar is found by dividing the force by the cross-sectional area,and the strain is found by dividing the elongation by the length along which the elongation occurs.In this manner a complete stress-strain diagram can be obtained
3、for the material.The typical shape of the stress-strain diagram for structural steel is shown in Fig.1,where the axial strains are plotted on the horizontal axis and the corresponding stresses are given by the ordinates to the cure OABCED.Form O to A the stress and strain are directly proportional t
4、o one another and the diagram is linear.Beyond point A the linear relationship between stress and strain no longer exists,hence the stress at A is called the proportional limit.With an increase in loading,the strain increases more rapidly than the stress,until at point B a considerable elongation be
5、gins to occur with no appreciable increase in the tensile force.This phenomenon is known as yielding of the material,and the stress at point B is called the yield point or yield stress.In the region BC the material is said to have become plastic,and the bar may actually elongate plastically by an am
6、ount which is 10 to 15 times the elongation which occurs up to the proportional limit.At point C the material begins to strain harden and to offer additional resistance to increase in load.Thus,with further elongation the stress increases,and it reaches its maximum vale,or ultimate stress,at point D
7、.Beyond this point further stretching of the bar is accompanied by a reduction in the load,and fracture of the specimen finally occurs at point E on the diagram.During elongation of the bar a lateral contraction occurs,resulting in a decrease in the cross-sectional area of the bar.This phenomenon ha
8、s no effect on the stress-strain diagram up to about point C,but beyond that point the decease in area will have a noticeable effect upon the calculated value of stress.A pronounced necking of the bar occurs(see Fig.2),and if the actual cross=sectional area at the narrow part of the neck is used in
9、calculating ,it will be found that the true stress-strain curve follows the dashed line CE.Whereas the total load the bar can carry does indeed diminish after the ultimate stress is reached(line DE),this reduction is due to the decrease in are and not to a loss in strength of the material itself.The
10、 material actually withstands an increase in stress up to the point of failure.For most practical purpose,however,the conventional stress-strain cure OABCDE,based upon the original cross-sectional area of the specimen,provides satisfactory information for design purposes.The diagram in Fig.1 has bee
11、n drawn to show the general characteristics of the stress-strain cure.There is an initial region on the stress-strain curve in which the material behaves both elastically and linearly.The region from O to A on the stress-strain diagram for steel is an example.The presence of a pronounced yield point
12、 followed by large plastic strains is somewhat unique to steel,which is the most common structural metal in use today.Aluminium alloys exhibit a more gradual transition from the linear to the nonlinear region.Both steel and many aluminium alloys will undergo large strains before failure and are therefore classified as ductile.On the other hand,material that are brittle fait at relatively low values of strain.Examples include ceramics,cast iron,concrete,certain metallic alloys,and glass.