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1、原文：Stress-Strain Relationships and Behavior5.1 INRODUCTION5.2 MODELS FOR DEFORMATION BEHAVIOR5.3 ELASTIC DEFORMATION5.4 ANISOTROPIC MATERIALS5.5 SUMMARYOBJECTIVESl Become familiar with the elastic, plastic, steady creep, and transient creep types of strain, as well as simple rheological models for r
2、epresenting the stress-strain-time behavior for each.l Explore three-dimensional stress-strain relationships for linear-elastic deformation in isotropic materials, analyzing the interdependence of stresses or strains imposed in more than one direction.l Extend the knowledge of elastic behavior to ba
3、sic cases of anisotropy, including sheets of matrix-and fiber composite material.5.1 INRODUCTIONThe three major types of deformation that occur in engineering materials are elastic, plastic, and creep deformation. These have already been discussed in Chapter 2 from the viewpoint of physical mechanis
4、ms and general trends in behavior for metals, polymers, and ceramics. Recall that elastic deformation is associated with the stretching, but not breaking, of chemical bonds. In contrast, the two types of inelastic deformation involve processes where atoms change their relative positions, such as sli
5、p of crystal planes or sliding if chain molecules. If the inelastic deformation is time dependent, it is classed as creep, as distinguished from plastic deformation, which is not time dependent.In engineering design and analysis, equations describing stress-strain behavior, called stress-strain rela
6、tionships, or constitutive equations, are frequently needed. For example, in elementary mechanics of materials, elastic behavior with a linear stress-strain relationship is assumed and used in calculating stresses and deflections in simple components such as beams and shafts. More complex situations
7、 of geometry and loading can be analyzed by employing the same basic assumptions in the form of theory of elasticity. This is now often accomplished by using the numerical technique called finite element analysis with a digital computer.Stress-strain relationships need to consider behavior in three
8、dimensions. In addition to elastic strains, the equations may also need to include plastic strains and creep strains. Treatment of creep strain requires the introduction of time as an additional variable. Regardless of the method used, analysis to determine stresses and deflections always requires a
9、ppropriate stress-strain relationships for the particular material involved.For calculations involving stress and strain, we express strain as a dimensionless quantity, as derived from length change, =L/L. Hence, strains given as percentages need to be converted to the dimensionless form, =%/100, as
10、 do strains given as microstrain, =/106.In the chapter, we will first consider one-dimensional stress-strain behavior and some corresponding simple physical models for elastic, plastic, and creep deformation. The discussion of elastic deformation will then be extended to three dimensions, starting w
11、ith isotropic behavior, where the elastic properties are the same in all directions. We will also consider simple cases of anisotropy, where the elastic properties vary with direction, as in composite materials. However, discussion of three-dimensional plastic and creep deformation behavior will be
12、postponed to Chapters 12 and 15, respectively.5.2 MODELS FOR DEFORMATION BEHAVIORSimple mechanical devices, such as linear springs, frictional sliders, and viscous dashpots, can be used as an aid to understanding the various types of deformation. Four such models and their responses to an applied fo
13、rce are illustrated in Fig.5.1. Such devices and combinations of them are called rheological models.Elastic deformation, Fig.5.1(a), is similar to the behavior of a simple linear spring characterized by its constant k. The deformation is always proportional to force, x=P/k, and it is recovered insta
14、ntly upon unloading. Plastic deformation, Fig.5.1(b), is similar to the movement of a block of mass m on a horizontal plane. The static and kinetic coefficients of friction are assumed to be equal, so that there is a critical force for motion P0=mg, where g is the acceleration of gravity. If a const
15、ant applied force P is less than the critical value, PP0, the block moves with an acceleration a =(P-P0)/m (5.1)When the force is removed at time t, the block has moved a distance a=at2/2, and it remains at this new location. Hence, the model behavior produces a permanent deformation, xp.Creep defor
16、mation can be subdivided into two types. Steady-state creep, Fig.5.1(c), proceeds at a constant rate under constant force. Such behavior occurs in a linear dashpot, which is an element where the velocity, , is proportional to the force. The constant of proportionality is the dashpot constant c, so that a constant value of force P gives a constant velocity, , re
